%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP158^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 08:56:01 AM UTC 2026
% Result : Theorem 283.65s 41.71s
% Output : Refutation 283.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP158^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n016.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:28:36 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : ITP158^2 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.46 % Domain : Interactive Theorem Proving
% 0.28/0.46 % Problem : Sledgehammer Prover problem prob_480__3258466_1
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Des21]
% 0.28/0.46 % Names : Prover/prob_480__3258466_1 [Des21]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.67 v8.1.0, 0.75 v7.5.0
% 0.28/0.46 % Syntax : Number of formulae : 329 ( 136 unt; 62 typ; 0 def)
% 0.28/0.46 % Number of atoms : 659 ( 401 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 7 ( 2 avg)
% 0.28/0.46 % Number of connectives : 6098 ( 145 ~; 26 |; 82 &;5557 @)
% 0.28/0.46 % ( 0 <=>; 288 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 28 ( 9 avg)
% 0.28/0.46 % Number of types : 4 ( 3 usr)
% 0.28/0.46 % Number of type conns : 259 ( 259 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 62 ( 59 usr; 6 con; 0-5 aty)
% 0.28/0.46 % Number of variables : 1312 ( 14 ^;1171 !; 77 ?;1312 :)
% 0.28/0.46 % ( 50 !>; 0 ?*; 0 @-; 0 @+)
% 0.28/0.46 % SPC : TH1_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:20:06.928
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % Could-be-implicit typings (6)
% 0.28/0.46 thf(ty_t_Prover__Mirabelle__xkffrtyxot_Oform,type,
% 0.28/0.46 prover2006609834e_form: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_t_Prover__Mirabelle__xkffrtyxot_OU,type,
% 0.28/0.46 prover_Mirabelle_U: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.28/0.46 product_prod: $tType > $tType > $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_t_List_Olist,type,
% 0.28/0.46 list: $tType > $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_t_Set_Oset,type,
% 0.28/0.46 set: $tType > $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_t_Nat_Onat,type,
% 0.28/0.46 nat: $tType ).
% 0.28/0.46
% 0.28/0.46 % Explicit typings (56)
% 0.28/0.46 thf(sy_cl_HOL_Otype,type,
% 0.28/0.46 type:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.28/0.46 ord:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.28/0.46 linorder:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.28/0.46 zero_zero:
% 0.28/0.46 !>[A: $tType] : A ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_If,type,
% 0.28/0.46 if:
% 0.28/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oappend,type,
% 0.28/0.46 append:
% 0.28/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Obind,type,
% 0.28/0.46 bind:
% 0.28/0.46 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Obutlast,type,
% 0.28/0.46 butlast:
% 0.28/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Ocan__select,type,
% 0.28/0.46 can_select:
% 0.28/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oconcat,type,
% 0.28/0.46 concat:
% 0.28/0.46 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Ocount__list,type,
% 0.28/0.46 count_list:
% 0.28/0.46 !>[A: $tType] : ( ( list @ A ) > A > nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Ogen__length,type,
% 0.28/0.46 gen_length:
% 0.28/0.46 !>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oinsert,type,
% 0.28/0.46 insert:
% 0.28/0.46 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olast,type,
% 0.28/0.46 last:
% 0.28/0.46 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olenlex,type,
% 0.28/0.46 lenlex:
% 0.28/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olex,type,
% 0.28/0.46 lex:
% 0.28/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olexord,type,
% 0.28/0.46 lexord:
% 0.28/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_OCons,type,
% 0.28/0.46 cons:
% 0.28/0.46 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_ONil,type,
% 0.28/0.46 nil:
% 0.28/0.46 !>[A: $tType] : ( list @ A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist_Oset,type,
% 0.28/0.46 set2:
% 0.28/0.46 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist__ex1,type,
% 0.28/0.46 list_ex1:
% 0.28/0.46 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olist__update,type,
% 0.28/0.46 list_update:
% 0.28/0.46 !>[A: $tType] : ( ( list @ A ) > nat > A > ( list @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olistrel,type,
% 0.28/0.46 listrel:
% 0.28/0.46 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Olistrel1,type,
% 0.28/0.46 listrel1:
% 0.28/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Omaps,type,
% 0.28/0.46 maps:
% 0.28/0.46 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Omeasures,type,
% 0.28/0.46 measures:
% 0.28/0.46 !>[A: $tType] : ( ( list @ ( A > nat ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_On__lists,type,
% 0.28/0.46 n_lists:
% 0.28/0.46 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Onth,type,
% 0.28/0.46 nth:
% 0.28/0.46 !>[A: $tType] : ( ( list @ A ) > nat > A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Oproduct__lists,type,
% 0.28/0.46 product_lists:
% 0.28/0.46 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Orotate1,type,
% 0.28/0.46 rotate1:
% 0.28/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Osubseqs,type,
% 0.28/0.46 subseqs:
% 0.28/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_List_Otake,type,
% 0.28/0.46 take:
% 0.28/0.46 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.28/0.46 size_size:
% 0.28/0.46 !>[A: $tType] : ( A > nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.28/0.46 ord_less:
% 0.28/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.28/0.46 product_Pair:
% 0.28/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.28/0.46 produc2004651681e_prod:
% 0.28/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.28/0.46 product_rec_prod:
% 0.28/0.46 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Prover__Mirabelle__xkffrtyxot_OSEval,type,
% 0.28/0.46 prover1899965912_SEval: ( product_prod @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ) ) > ( nat > prover_Mirabelle_U ) > ( list @ prover2006609834e_form ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Prover__Mirabelle__xkffrtyxot_OSvalid,type,
% 0.28/0.46 prover1090191840Svalid: ( list @ prover2006609834e_form ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Ofinst,type,
% 0.28/0.46 prover48307765_finst: prover2006609834e_form > nat > prover2006609834e_form ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Oflatten,type,
% 0.28/0.46 prover12291693latten:
% 0.28/0.46 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Oform_OFAll,type,
% 0.28/0.46 prover946642470e_FAll: prover2006609834e_form > prover2006609834e_form ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Ofv,type,
% 0.28/0.46 prover_Mirabelle_fv: prover2006609834e_form > ( list @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Ois__env,type,
% 0.28/0.46 prover1043414700is_env: ( product_prod @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ) ) > ( nat > prover_Mirabelle_U ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Omaxvar,type,
% 0.28/0.46 prover572158330maxvar: ( list @ nat ) > nat ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Prover__Mirabelle__xkffrtyxot_OpreSuc,type,
% 0.28/0.46 prover1646808149preSuc: ( list @ nat ) > ( list @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Osfv,type,
% 0.28/0.46 prover_Mirabelle_sfv: ( list @ prover2006609834e_form ) > ( list @ nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Relation_Oirrefl,type,
% 0.28/0.46 irrefl:
% 0.28/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Set_OCollect,type,
% 0.28/0.46 collect:
% 0.28/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Set_Othe__elem,type,
% 0.28/0.46 the_elem:
% 0.28/0.46 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_member,type,
% 0.28/0.46 member:
% 0.28/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_a,type,
% 0.28/0.46 a: set @ prover_Mirabelle_U ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_b,type,
% 0.28/0.46 b: nat > ( list @ prover_Mirabelle_U ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_f,type,
% 0.28/0.46 f: prover2006609834e_form ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_s,type,
% 0.28/0.46 s: list @ prover2006609834e_form ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_u,type,
% 0.28/0.46 u: nat ).
% 0.28/0.46
% 0.28/0.46 % Relevant facts (255)
% 0.28/0.46 thf(fact_0_form_Oinject_I5_J,axiom,
% 0.28/0.46 ! [X5: prover2006609834e_form,Y5: prover2006609834e_form] :
% 0.28/0.46 ( ( ( prover946642470e_FAll @ X5 )
% 0.28/0.46 = ( prover946642470e_FAll @ Y5 ) )
% 0.28/0.46 = ( X5 = Y5 ) ) ).
% 0.28/0.46
% 0.28/0.46 % form.inject(5)
% 0.28/0.46 thf(fact_1_SEval_Osimps_I1_J,axiom,
% 0.28/0.46 ! [M: product_prod @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ),E: nat > prover_Mirabelle_U] :
% 0.28/0.46 ~ ( prover1899965912_SEval @ M @ E @ ( nil @ prover2006609834e_form ) ) ).
% 0.28/0.46
% 0.28/0.46 % SEval.simps(1)
% 0.28/0.46 thf(fact_2_SEval__cong,axiom,
% 0.28/0.46 ! [S: list @ prover2006609834e_form,E1: nat > prover_Mirabelle_U,E2: nat > prover_Mirabelle_U,M: product_prod @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o )] :
% 0.28/0.46 ( ! [X: nat] :
% 0.28/0.46 ( ( member @ nat @ X @ ( set2 @ nat @ ( prover_Mirabelle_sfv @ S ) ) )
% 0.28/0.46 => ( ( E1 @ X )
% 0.28/0.46 = ( E2 @ X ) ) )
% 0.28/0.46 => ( ( prover1899965912_SEval @ M @ E1 @ S )
% 0.28/0.46 = ( prover1899965912_SEval @ M @ E2 @ S ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % SEval_cong
% 0.28/0.46 thf(fact_3_SEval__append,axiom,
% 0.28/0.46 ! [M: product_prod @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ),E: nat > prover_Mirabelle_U,Xs: list @ prover2006609834e_form,Ys: list @ prover2006609834e_form] :
% 0.28/0.46 ( ( prover1899965912_SEval @ M @ E @ ( append @ prover2006609834e_form @ Xs @ Ys ) )
% 0.28/0.46 = ( ( prover1899965912_SEval @ M @ E @ Xs )
% 0.28/0.46 | ( prover1899965912_SEval @ M @ E @ Ys ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % SEval_append
% 0.28/0.46 thf(fact_4_sound__FAll,axiom,
% 0.28/0.46 ! [U: nat,F: prover2006609834e_form,S: list @ prover2006609834e_form] :
% 0.28/0.46 ( ~ ( member @ nat @ U @ ( set2 @ nat @ ( prover_Mirabelle_sfv @ ( cons @ prover2006609834e_form @ ( prover946642470e_FAll @ F ) @ S ) ) ) )
% 0.28/0.46 => ( ( prover1090191840Svalid @ ( append @ prover2006609834e_form @ S @ ( cons @ prover2006609834e_form @ ( prover48307765_finst @ F @ U ) @ ( nil @ prover2006609834e_form ) ) ) )
% 0.28/0.46 => ( prover1090191840Svalid @ ( cons @ prover2006609834e_form @ ( prover946642470e_FAll @ F ) @ S ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sound_FAll
% 0.28/0.46 thf(fact_5_append1__eq__conv,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A,X2: A,Ys: list @ A,Y: A] :
% 0.28/0.46 ( ( ( append @ A @ Xs @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.28/0.46 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.28/0.46 = ( ( Xs = Ys )
% 0.28/0.46 & ( X2 = Y ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append1_eq_conv
% 0.28/0.46 thf(fact_6_append__Nil2,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A] :
% 0.28/0.46 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.28/0.46 = Xs ) ).
% 0.28/0.46
% 0.28/0.46 % append_Nil2
% 0.28/0.46 thf(fact_7_append__self__conv,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.28/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.28/0.46 = Xs )
% 0.28/0.46 = ( Ys
% 0.28/0.46 = ( nil @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_self_conv
% 0.28/0.46 thf(fact_8_self__append__conv,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.28/0.46 ( ( Xs
% 0.28/0.46 = ( append @ A @ Xs @ Ys ) )
% 0.28/0.46 = ( Ys
% 0.28/0.46 = ( nil @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % self_append_conv
% 0.28/0.46 thf(fact_9_append__self__conv2,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.28/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.28/0.46 = Ys )
% 0.28/0.46 = ( Xs
% 0.28/0.46 = ( nil @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_self_conv2
% 0.28/0.46 thf(fact_10_self__append__conv2,axiom,
% 0.28/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.28/0.46 ( ( Ys
% 0.28/0.46 = ( append @ A @ Xs @ Ys ) )
% 0.28/0.46 = ( Xs
% 0.28/0.46 = ( nil @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % self_append_conv2
% 0.28/0.46 thf(fact_11_Nil__is__append__conv,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.28/0.46 ( ( ( nil @ A )
% 0.28/0.46 = ( append @ A @ Xs @ Ys ) )
% 0.28/0.46 = ( ( Xs
% 0.28/0.46 = ( nil @ A ) )
% 0.28/0.46 & ( Ys
% 0.28/0.46 = ( nil @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Nil_is_append_conv
% 0.28/0.46 thf(fact_12_append__is__Nil__conv,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.28/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.28/0.46 = ( nil @ A ) )
% 0.28/0.46 = ( ( Xs
% 0.28/0.46 = ( nil @ A ) )
% 0.28/0.46 & ( Ys
% 0.28/0.46 = ( nil @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_is_Nil_conv
% 0.28/0.46 thf(fact_13_append_Oright__neutral,axiom,
% 0.28/0.46 ! [A: $tType,A2: list @ A] :
% 0.28/0.46 ( ( append @ A @ A2 @ ( nil @ A ) )
% 0.28/0.46 = A2 ) ).
% 0.28/0.46
% 0.28/0.46 % append.right_neutral
% 0.28/0.46 thf(fact_14_Svalid__def,axiom,
% 0.28/0.46 ( prover1090191840Svalid
% 0.28/0.46 = ( ^ [S2: list @ prover2006609834e_form] :
% 0.28/0.46 ! [MI: product_prod @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ),E3: nat > prover_Mirabelle_U] :
% 0.28/0.46 ( ( prover1043414700is_env @ MI @ E3 )
% 0.28/0.46 => ( prover1899965912_SEval @ MI @ E3 @ S2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Svalid_def
% 0.28/0.46 thf(fact_15_split__list,axiom,
% 0.28/0.46 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.46 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.46 => ? [Ys2: list @ A,Zs: list @ A] :
% 0.28/0.46 ( Xs
% 0.28/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % split_list
% 0.28/0.46 thf(fact_16_list_Oinject,axiom,
% 0.28/0.46 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.28/0.46 ( ( ( cons @ A @ X21 @ X22 )
% 0.28/0.46 = ( cons @ A @ Y21 @ Y22 ) )
% 0.28/0.46 = ( ( X21 = Y21 )
% 0.28/0.46 & ( X22 = Y22 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.inject
% 0.28/0.46 thf(fact_17_same__append__eq,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.28/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.28/0.46 = ( append @ A @ Xs @ Zs2 ) )
% 0.28/0.46 = ( Ys = Zs2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % same_append_eq
% 0.28/0.46 thf(fact_18_append__same__eq,axiom,
% 0.28/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.28/0.46 ( ( ( append @ A @ Ys @ Xs )
% 0.28/0.46 = ( append @ A @ Zs2 @ Xs ) )
% 0.28/0.46 = ( Ys = Zs2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_same_eq
% 0.28/0.46 thf(fact_19_append__assoc,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.28/0.46 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs2 )
% 0.28/0.46 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_assoc
% 0.28/0.46 thf(fact_20_append_Oassoc,axiom,
% 0.28/0.46 ! [A: $tType,A2: list @ A,B2: list @ A,C2: list @ A] :
% 0.28/0.46 ( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C2 )
% 0.28/0.46 = ( append @ A @ A2 @ ( append @ A @ B2 @ C2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append.assoc
% 0.28/0.46 thf(fact_21_not__Cons__self2,axiom,
% 0.28/0.46 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.46 ( ( cons @ A @ X2 @ Xs )
% 0.28/0.46 != Xs ) ).
% 0.28/0.46
% 0.28/0.46 % not_Cons_self2
% 0.28/0.46 thf(fact_22_sfv__nil,axiom,
% 0.28/0.46 ( ( prover_Mirabelle_sfv @ ( nil @ prover2006609834e_form ) )
% 0.28/0.46 = ( nil @ nat ) ) ).
% 0.28/0.46
% 0.28/0.46 % sfv_nil
% 0.28/0.46 thf(fact_23_append__eq__append__conv2,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A,Ts: list @ A] :
% 0.28/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.28/0.46 = ( append @ A @ Zs2 @ Ts ) )
% 0.28/0.46 = ( ? [Us: list @ A] :
% 0.28/0.46 ( ( ( Xs
% 0.28/0.46 = ( append @ A @ Zs2 @ Us ) )
% 0.28/0.46 & ( ( append @ A @ Us @ Ys )
% 0.28/0.46 = Ts ) )
% 0.28/0.46 | ( ( ( append @ A @ Xs @ Us )
% 0.28/0.46 = Zs2 )
% 0.28/0.46 & ( Ys
% 0.28/0.46 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_eq_append_conv2
% 0.28/0.46 thf(fact_24_append__eq__appendI,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys: list @ A,Us2: list @ A] :
% 0.28/0.46 ( ( ( append @ A @ Xs @ Xs1 )
% 0.28/0.46 = Zs2 )
% 0.28/0.46 => ( ( Ys
% 0.28/0.46 = ( append @ A @ Xs1 @ Us2 ) )
% 0.28/0.46 => ( ( append @ A @ Xs @ Ys )
% 0.28/0.46 = ( append @ A @ Zs2 @ Us2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % append_eq_appendI
% 0.28/0.46 thf(fact_25_strict__sorted_Oinduct,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.28/0.46 ( ( P @ ( nil @ A ) )
% 0.28/0.46 => ( ! [X: A,Ys2: list @ A] :
% 0.28/0.46 ( ( P @ Ys2 )
% 0.28/0.46 => ( P @ ( cons @ A @ X @ Ys2 ) ) )
% 0.28/0.46 => ( P @ A0 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % strict_sorted.induct
% 0.28/0.46 thf(fact_26_strict__sorted_Ocases,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linorder @ A )
% 0.28/0.46 => ! [X2: list @ A] :
% 0.28/0.46 ( ( X2
% 0.28/0.46 != ( nil @ A ) )
% 0.28/0.46 => ~ ! [X: A,Ys2: list @ A] :
% 0.28/0.46 ( X2
% 0.28/0.46 != ( cons @ A @ X @ Ys2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % strict_sorted.cases
% 0.28/0.46 thf(fact_27_map__tailrec__rev_Oinduct,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.28/0.46 ( ! [F2: A > B,X_1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_1 )
% 0.28/0.46 => ( ! [F2: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 0.28/0.46 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A3 ) @ Bs ) )
% 0.28/0.46 => ( P @ F2 @ ( cons @ A @ A3 @ As ) @ Bs ) )
% 0.28/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % map_tailrec_rev.induct
% 0.28/0.46 thf(fact_28_list__nonempty__induct,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.28/0.46 ( ( Xs
% 0.28/0.46 != ( nil @ A ) )
% 0.28/0.46 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.28/0.46 => ( ! [X: A,Xs2: list @ A] :
% 0.28/0.46 ( ( Xs2
% 0.28/0.46 != ( nil @ A ) )
% 0.28/0.46 => ( ( P @ Xs2 )
% 0.28/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) ) ) )
% 0.28/0.46 => ( P @ Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list_nonempty_induct
% 0.28/0.46 thf(fact_29_successively_Oinduct,axiom,
% 0.28/0.46 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.28/0.46 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.28/0.46 => ( ! [P2: A > A > $o,X: A] : ( P @ P2 @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.28/0.46 => ( ! [P2: A > A > $o,X: A,Y2: A,Xs2: list @ A] :
% 0.28/0.46 ( ( P @ P2 @ ( cons @ A @ Y2 @ Xs2 ) )
% 0.28/0.46 => ( P @ P2 @ ( cons @ A @ X @ ( cons @ A @ Y2 @ Xs2 ) ) ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % successively.induct
% 0.28/0.46 thf(fact_30_arg__min__list_Oinduct,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType] :
% 0.28/0.46 ( ( linorder @ B )
% 0.28/0.46 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.28/0.46 ( ! [F2: A > B,X: A] : ( P @ F2 @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.28/0.46 => ( ! [F2: A > B,X: A,Y2: A,Zs: list @ A] :
% 0.28/0.46 ( ( P @ F2 @ ( cons @ A @ Y2 @ Zs ) )
% 0.28/0.46 => ( P @ F2 @ ( cons @ A @ X @ ( cons @ A @ Y2 @ Zs ) ) ) )
% 0.28/0.46 => ( ! [A3: A > B] : ( P @ A3 @ ( nil @ A ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % arg_min_list.induct
% 0.28/0.46 thf(fact_31_remdups__adj_Oinduct,axiom,
% 0.28/0.46 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.28/0.46 ( ( P @ ( nil @ A ) )
% 0.28/0.46 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.28/0.46 => ( ! [X: A,Y2: A,Xs2: list @ A] :
% 0.28/0.46 ( ( ( X = Y2 )
% 0.28/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 0.28/0.46 => ( ( ( X != Y2 )
% 0.28/0.46 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 0.28/0.46 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 0.28/0.46 => ( P @ A0 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % remdups_adj.induct
% 0.28/0.46 thf(fact_32_sorted__wrt_Oinduct,axiom,
% 0.28/0.46 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.28/0.46 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.28/0.46 => ( ! [P2: A > A > $o,X: A,Ys2: list @ A] :
% 0.28/0.46 ( ( P @ P2 @ Ys2 )
% 0.28/0.46 => ( P @ P2 @ ( cons @ A @ X @ Ys2 ) ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sorted_wrt.induct
% 0.28/0.46 thf(fact_33_remdups__adj_Ocases,axiom,
% 0.28/0.46 ! [A: $tType,X2: list @ A] :
% 0.28/0.46 ( ( X2
% 0.28/0.46 != ( nil @ A ) )
% 0.28/0.46 => ( ! [X: A] :
% 0.28/0.46 ( X2
% 0.28/0.46 != ( cons @ A @ X @ ( nil @ A ) ) )
% 0.28/0.46 => ~ ! [X: A,Y2: A,Xs2: list @ A] :
% 0.28/0.46 ( X2
% 0.28/0.46 != ( cons @ A @ X @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % remdups_adj.cases
% 0.28/0.46 thf(fact_34_transpose_Ocases,axiom,
% 0.28/0.46 ! [A: $tType,X2: list @ ( list @ A )] :
% 0.28/0.46 ( ( X2
% 0.28/0.46 != ( nil @ ( list @ A ) ) )
% 0.28/0.46 => ( ! [Xss: list @ ( list @ A )] :
% 0.28/0.46 ( X2
% 0.28/0.46 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.28/0.46 => ~ ! [X: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.28/0.46 ( X2
% 0.28/0.46 != ( cons @ ( list @ A ) @ ( cons @ A @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % transpose.cases
% 0.28/0.46 thf(fact_35_shuffles_Oinduct,axiom,
% 0.28/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.28/0.46 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.28/0.46 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 0.28/0.46 => ( ! [X: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.28/0.46 ( ( P @ Xs2 @ ( cons @ A @ Y2 @ Ys2 ) )
% 0.28/0.46 => ( ( P @ ( cons @ A @ X @ Xs2 ) @ Ys2 )
% 0.28/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % shuffles.induct
% 0.28/0.46 thf(fact_36_min__list_Oinduct,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ord @ A )
% 0.28/0.46 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.28/0.46 ( ! [X: A,Xs2: list @ A] :
% 0.28/0.46 ( ! [X212: A,X222: list @ A] :
% 0.28/0.46 ( ( Xs2
% 0.28/0.46 = ( cons @ A @ X212 @ X222 ) )
% 0.28/0.46 => ( P @ Xs2 ) )
% 0.28/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 0.28/0.46 => ( ( P @ ( nil @ A ) )
% 0.28/0.46 => ( P @ A0 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % min_list.induct
% 0.28/0.46 thf(fact_37_min__list_Ocases,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ord @ A )
% 0.28/0.46 => ! [X2: list @ A] :
% 0.28/0.46 ( ! [X: A,Xs2: list @ A] :
% 0.28/0.46 ( X2
% 0.28/0.46 != ( cons @ A @ X @ Xs2 ) )
% 0.28/0.46 => ( X2
% 0.28/0.46 = ( nil @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % min_list.cases
% 0.28/0.46 thf(fact_38_induct__list012,axiom,
% 0.28/0.46 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.28/0.46 ( ( P @ ( nil @ A ) )
% 0.28/0.46 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.28/0.46 => ( ! [X: A,Y2: A,Zs: list @ A] :
% 0.28/0.46 ( ( P @ Zs )
% 0.28/0.46 => ( ( P @ ( cons @ A @ Y2 @ Zs ) )
% 0.28/0.46 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y2 @ Zs ) ) ) ) )
% 0.28/0.46 => ( P @ Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % induct_list012
% 0.28/0.46 thf(fact_39_splice_Oinduct,axiom,
% 0.28/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.28/0.46 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.28/0.46 => ( ! [X: A,Xs2: list @ A,Ys2: list @ A] :
% 0.28/0.46 ( ( P @ Ys2 @ Xs2 )
% 0.28/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) @ Ys2 ) )
% 0.28/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % splice.induct
% 0.28/0.46 thf(fact_40_list__induct2_H,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.28/0.46 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.28/0.46 => ( ! [X: A,Xs2: list @ A] : ( P @ ( cons @ A @ X @ Xs2 ) @ ( nil @ B ) )
% 0.28/0.46 => ( ! [Y2: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y2 @ Ys2 ) )
% 0.28/0.46 => ( ! [X: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 0.28/0.46 ( ( P @ Xs2 @ Ys2 )
% 0.28/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) )
% 0.28/0.46 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list_induct2'
% 0.28/0.46 thf(fact_41_neq__Nil__conv,axiom,
% 0.28/0.46 ! [A: $tType,Xs: list @ A] :
% 0.28/0.46 ( ( Xs
% 0.28/0.46 != ( nil @ A ) )
% 0.28/0.46 = ( ? [Y3: A,Ys3: list @ A] :
% 0.28/0.46 ( Xs
% 0.28/0.46 = ( cons @ A @ Y3 @ Ys3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % neq_Nil_conv
% 0.28/0.46 thf(fact_42_list_Oinducts,axiom,
% 0.28/0.46 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.28/0.46 ( ( P @ ( nil @ A ) )
% 0.28/0.46 => ( ! [X1: A,X23: list @ A] :
% 0.28/0.46 ( ( P @ X23 )
% 0.28/0.46 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 0.28/0.46 => ( P @ List ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.inducts
% 0.28/0.46 thf(fact_43_list_Oexhaust,axiom,
% 0.28/0.46 ! [A: $tType,Y: list @ A] :
% 0.28/0.46 ( ( Y
% 0.28/0.46 != ( nil @ A ) )
% 0.28/0.46 => ~ ! [X213: A,X223: list @ A] :
% 0.28/0.46 ( Y
% 0.28/0.46 != ( cons @ A @ X213 @ X223 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.exhaust
% 0.28/0.46 thf(fact_44_mem__Collect__eq,axiom,
% 0.28/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.28/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.28/0.46 = ( P @ A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % mem_Collect_eq
% 0.28/0.46 thf(fact_45_Collect__mem__eq,axiom,
% 0.28/0.46 ! [A: $tType,A4: set @ A] :
% 0.28/0.46 ( ( collect @ A
% 0.28/0.46 @ ^ [X3: A] : ( member @ A @ X3 @ A4 ) )
% 0.28/0.46 = A4 ) ).
% 0.28/0.46
% 0.28/0.46 % Collect_mem_eq
% 0.28/0.46 thf(fact_46_Collect__cong,axiom,
% 0.28/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.28/0.46 ( ! [X: A] :
% 0.28/0.46 ( ( P @ X )
% 0.28/0.46 = ( Q @ X ) )
% 0.28/0.46 => ( ( collect @ A @ P )
% 0.28/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Collect_cong
% 0.28/0.46 thf(fact_47_ext,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.28/0.46 ( ! [X: A] :
% 0.28/0.46 ( ( F @ X )
% 0.28/0.46 = ( G @ X ) )
% 0.28/0.46 => ( F = G ) ) ).
% 0.28/0.46
% 0.28/0.46 % ext
% 0.28/0.46 thf(fact_48_list_OdiscI,axiom,
% 0.28/0.46 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.28/0.46 ( ( List
% 0.28/0.46 = ( cons @ A @ X21 @ X22 ) )
% 0.28/0.46 => ( List
% 0.28/0.46 != ( nil @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.discI
% 0.28/0.46 thf(fact_49_list_Odistinct_I1_J,axiom,
% 0.28/0.46 ! [A: $tType,X21: A,X22: list @ A] :
% 0.28/0.46 ( ( nil @ A )
% 0.28/0.46 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.distinct(1)
% 0.28/0.46 thf(fact_50_list_Oset__cases,axiom,
% 0.28/0.46 ! [A: $tType,E: A,A2: list @ A] :
% 0.28/0.46 ( ( member @ A @ E @ ( set2 @ A @ A2 ) )
% 0.28/0.46 => ( ! [Z2: list @ A] :
% 0.28/0.46 ( A2
% 0.28/0.46 != ( cons @ A @ E @ Z2 ) )
% 0.28/0.46 => ~ ! [Z1: A,Z2: list @ A] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( cons @ A @ Z1 @ Z2 ) )
% 0.28/0.46 => ~ ( member @ A @ E @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.set_cases
% 0.28/0.46 thf(fact_51_set__ConsD,axiom,
% 0.28/0.46 ! [A: $tType,Y: A,X2: A,Xs: list @ A] :
% 0.28/0.46 ( ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X2 @ Xs ) ) )
% 0.28/0.46 => ( ( Y = X2 )
% 0.28/0.46 | ( member @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % set_ConsD
% 0.28/0.46 thf(fact_52_list_Oset__intros_I1_J,axiom,
% 0.28/0.46 ! [A: $tType,X21: A,X22: list @ A] : ( member @ A @ X21 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list.set_intros(1)
% 0.28/0.47 thf(fact_53_list_Oset__intros_I2_J,axiom,
% 0.28/0.47 ! [A: $tType,Y: A,X22: list @ A,X21: A] :
% 0.28/0.47 ( ( member @ A @ Y @ ( set2 @ A @ X22 ) )
% 0.28/0.47 => ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list.set_intros(2)
% 0.28/0.47 thf(fact_54_append__Cons,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A,Ys: list @ A] :
% 0.28/0.47 ( ( append @ A @ ( cons @ A @ X2 @ Xs ) @ Ys )
% 0.28/0.47 = ( cons @ A @ X2 @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % append_Cons
% 0.28/0.47 thf(fact_55_Cons__eq__appendI,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.28/0.47 ( ( ( cons @ A @ X2 @ Xs1 )
% 0.28/0.47 = Ys )
% 0.28/0.47 => ( ( Xs
% 0.28/0.47 = ( append @ A @ Xs1 @ Zs2 ) )
% 0.28/0.47 => ( ( cons @ A @ X2 @ Xs )
% 0.28/0.47 = ( append @ A @ Ys @ Zs2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Cons_eq_appendI
% 0.28/0.47 thf(fact_56_append_Oleft__neutral,axiom,
% 0.28/0.47 ! [A: $tType,A2: list @ A] :
% 0.28/0.47 ( ( append @ A @ ( nil @ A ) @ A2 )
% 0.28/0.47 = A2 ) ).
% 0.28/0.47
% 0.28/0.47 % append.left_neutral
% 0.28/0.47 thf(fact_57_append__Nil,axiom,
% 0.28/0.47 ! [A: $tType,Ys: list @ A] :
% 0.28/0.47 ( ( append @ A @ ( nil @ A ) @ Ys )
% 0.28/0.47 = Ys ) ).
% 0.28/0.47
% 0.28/0.47 % append_Nil
% 0.28/0.47 thf(fact_58_eq__Nil__appendI,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.28/0.47 ( ( Xs = Ys )
% 0.28/0.47 => ( Xs
% 0.28/0.47 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_Nil_appendI
% 0.28/0.47 thf(fact_59_rev__nonempty__induct,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 != ( nil @ A ) )
% 0.28/0.47 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.28/0.47 => ( ! [X: A,Xs2: list @ A] :
% 0.28/0.47 ( ( Xs2
% 0.28/0.47 != ( nil @ A ) )
% 0.28/0.47 => ( ( P @ Xs2 )
% 0.28/0.47 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ) )
% 0.28/0.47 => ( P @ Xs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_nonempty_induct
% 0.28/0.47 thf(fact_60_append__eq__Cons__conv,axiom,
% 0.28/0.47 ! [A: $tType,Ys: list @ A,Zs2: list @ A,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ( ( append @ A @ Ys @ Zs2 )
% 0.28/0.47 = ( cons @ A @ X2 @ Xs ) )
% 0.28/0.47 = ( ( ( Ys
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 & ( Zs2
% 0.28/0.47 = ( cons @ A @ X2 @ Xs ) ) )
% 0.28/0.47 | ? [Ys4: list @ A] :
% 0.28/0.47 ( ( Ys
% 0.28/0.47 = ( cons @ A @ X2 @ Ys4 ) )
% 0.28/0.47 & ( ( append @ A @ Ys4 @ Zs2 )
% 0.28/0.47 = Xs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % append_eq_Cons_conv
% 0.28/0.47 thf(fact_61_Cons__eq__append__conv,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.28/0.47 ( ( ( cons @ A @ X2 @ Xs )
% 0.28/0.47 = ( append @ A @ Ys @ Zs2 ) )
% 0.28/0.47 = ( ( ( Ys
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 & ( ( cons @ A @ X2 @ Xs )
% 0.28/0.47 = Zs2 ) )
% 0.28/0.47 | ? [Ys4: list @ A] :
% 0.28/0.47 ( ( ( cons @ A @ X2 @ Ys4 )
% 0.28/0.47 = Ys )
% 0.28/0.47 & ( Xs
% 0.28/0.47 = ( append @ A @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Cons_eq_append_conv
% 0.28/0.47 thf(fact_62_rev__exhaust,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 != ( nil @ A ) )
% 0.28/0.47 => ~ ! [Ys2: list @ A,Y2: A] :
% 0.28/0.47 ( Xs
% 0.28/0.47 != ( append @ A @ Ys2 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_exhaust
% 0.28/0.47 thf(fact_63_rev__induct,axiom,
% 0.28/0.47 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.28/0.47 ( ( P @ ( nil @ A ) )
% 0.28/0.47 => ( ! [X: A,Xs2: list @ A] :
% 0.28/0.47 ( ( P @ Xs2 )
% 0.28/0.47 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) )
% 0.28/0.47 => ( P @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_induct
% 0.28/0.47 thf(fact_64_split__list__first__prop__iff,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.28/0.47 ( ( ? [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 & ( P @ X3 ) ) )
% 0.28/0.47 = ( ? [Ys3: list @ A,X3: A] :
% 0.28/0.47 ( ? [Zs3: list @ A] :
% 0.28/0.47 ( Xs
% 0.28/0.47 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.28/0.47 & ( P @ X3 )
% 0.28/0.47 & ! [Y3: A] :
% 0.28/0.47 ( ( member @ A @ Y3 @ ( set2 @ A @ Ys3 ) )
% 0.28/0.47 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_list_first_prop_iff
% 0.28/0.47 thf(fact_65_split__list__last__prop__iff,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.28/0.47 ( ( ? [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 & ( P @ X3 ) ) )
% 0.28/0.47 = ( ? [Ys3: list @ A,X3: A,Zs3: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.28/0.47 & ( P @ X3 )
% 0.28/0.47 & ! [Y3: A] :
% 0.28/0.47 ( ( member @ A @ Y3 @ ( set2 @ A @ Zs3 ) )
% 0.28/0.47 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_list_last_prop_iff
% 0.28/0.47 thf(fact_66_in__set__conv__decomp__first,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 0.28/0.47 & ~ ( member @ A @ X2 @ ( set2 @ A @ Ys3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_set_conv_decomp_first
% 0.28/0.47 thf(fact_67_in__set__conv__decomp__last,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 0.28/0.47 & ~ ( member @ A @ X2 @ ( set2 @ A @ Zs3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_set_conv_decomp_last
% 0.28/0.47 thf(fact_68_split__list__first__propE,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.28/0.47 ( ? [X4: A] :
% 0.28/0.47 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 & ( P @ X4 ) )
% 0.28/0.47 => ~ ! [Ys2: list @ A,X: A] :
% 0.28/0.47 ( ? [Zs: list @ A] :
% 0.28/0.47 ( Xs
% 0.28/0.47 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.28/0.47 => ( ( P @ X )
% 0.28/0.47 => ~ ! [Xa: A] :
% 0.28/0.47 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 0.28/0.47 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_list_first_propE
% 0.28/0.47 thf(fact_69_split__list__last__propE,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.28/0.47 ( ? [X4: A] :
% 0.28/0.47 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 & ( P @ X4 ) )
% 0.28/0.47 => ~ ! [Ys2: list @ A,X: A,Zs: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.28/0.47 => ( ( P @ X )
% 0.28/0.47 => ~ ! [Xa: A] :
% 0.28/0.47 ( ( member @ A @ Xa @ ( set2 @ A @ Zs ) )
% 0.28/0.47 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_list_last_propE
% 0.28/0.47 thf(fact_70_split__list__first__prop,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.28/0.47 ( ? [X4: A] :
% 0.28/0.47 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 & ( P @ X4 ) )
% 0.28/0.47 => ? [Ys2: list @ A,X: A] :
% 0.28/0.47 ( ? [Zs: list @ A] :
% 0.28/0.47 ( Xs
% 0.28/0.47 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.28/0.47 & ( P @ X )
% 0.28/0.47 & ! [Xa: A] :
% 0.28/0.47 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 0.28/0.47 => ~ ( P @ Xa ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_list_first_prop
% 0.28/0.47 thf(fact_71_split__list__last__prop,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.28/0.47 ( ? [X4: A] :
% 0.28/0.47 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 & ( P @ X4 ) )
% 0.28/0.47 => ? [Ys2: list @ A,X: A,Zs: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.28/0.47 & ( P @ X )
% 0.28/0.47 & ! [Xa: A] :
% 0.28/0.47 ( ( member @ A @ Xa @ ( set2 @ A @ Zs ) )
% 0.28/0.47 => ~ ( P @ Xa ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_list_last_prop
% 0.28/0.47 thf(fact_72_in__set__conv__decomp,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 0.28/0.47 ( Xs
% 0.28/0.47 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_set_conv_decomp
% 0.28/0.47 thf(fact_73_append__Cons__eq__iff,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A,Ys: list @ A,Xs3: list @ A,Ys5: list @ A] :
% 0.28/0.47 ( ~ ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ( ~ ( member @ A @ X2 @ ( set2 @ A @ Ys ) )
% 0.28/0.47 => ( ( ( append @ A @ Xs @ ( cons @ A @ X2 @ Ys ) )
% 0.28/0.47 = ( append @ A @ Xs3 @ ( cons @ A @ X2 @ Ys5 ) ) )
% 0.28/0.47 = ( ( Xs = Xs3 )
% 0.28/0.47 & ( Ys = Ys5 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % append_Cons_eq_iff
% 0.28/0.47 thf(fact_74_split__list__propE,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.28/0.47 ( ? [X4: A] :
% 0.28/0.47 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 & ( P @ X4 ) )
% 0.28/0.47 => ~ ! [Ys2: list @ A,X: A] :
% 0.28/0.47 ( ? [Zs: list @ A] :
% 0.28/0.47 ( Xs
% 0.28/0.47 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.28/0.47 => ~ ( P @ X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_list_propE
% 0.28/0.47 thf(fact_75_split__list__first,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ? [Ys2: list @ A,Zs: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 0.28/0.47 & ~ ( member @ A @ X2 @ ( set2 @ A @ Ys2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_list_first
% 0.28/0.47 thf(fact_76_split__list__prop,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.28/0.47 ( ? [X4: A] :
% 0.28/0.47 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 & ( P @ X4 ) )
% 0.28/0.47 => ? [Ys2: list @ A,X: A] :
% 0.28/0.47 ( ? [Zs: list @ A] :
% 0.28/0.47 ( Xs
% 0.28/0.47 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.28/0.47 & ( P @ X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_list_prop
% 0.28/0.47 thf(fact_77_split__list__last,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ? [Ys2: list @ A,Zs: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 0.28/0.47 & ~ ( member @ A @ X2 @ ( set2 @ A @ Zs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_list_last
% 0.28/0.47 thf(fact_78_old_Oprod_Oinject,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
% 0.28/0.47 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.28/0.47 = ( product_Pair @ A @ B @ A5 @ B3 ) )
% 0.28/0.47 = ( ( A2 = A5 )
% 0.28/0.47 & ( B2 = B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.inject
% 0.28/0.47 thf(fact_79_prod_Oinject,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,X12: A,X24: B,Y1: A,Y23: B] :
% 0.28/0.47 ( ( ( product_Pair @ A @ B @ X12 @ X24 )
% 0.28/0.47 = ( product_Pair @ A @ B @ Y1 @ Y23 ) )
% 0.28/0.47 = ( ( X12 = Y1 )
% 0.28/0.47 & ( X24 = Y23 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod.inject
% 0.28/0.47 thf(fact_80_the__elem__set,axiom,
% 0.28/0.47 ! [A: $tType,X2: A] :
% 0.28/0.47 ( ( the_elem @ A @ ( set2 @ A @ ( cons @ A @ X2 @ ( nil @ A ) ) ) )
% 0.28/0.47 = X2 ) ).
% 0.28/0.47
% 0.28/0.47 % the_elem_set
% 0.28/0.47 thf(fact_81_bind__simps_I2_J,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,X2: B,Xs: list @ B,F: B > ( list @ A )] :
% 0.28/0.47 ( ( bind @ B @ A @ ( cons @ B @ X2 @ Xs ) @ F )
% 0.28/0.47 = ( append @ A @ ( F @ X2 ) @ ( bind @ B @ A @ Xs @ F ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bind_simps(2)
% 0.28/0.47 thf(fact_82_maps__simps_I1_J,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,F: B > ( list @ A ),X2: B,Xs: list @ B] :
% 0.28/0.47 ( ( maps @ B @ A @ F @ ( cons @ B @ X2 @ Xs ) )
% 0.28/0.47 = ( append @ A @ ( F @ X2 ) @ ( maps @ B @ A @ F @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % maps_simps(1)
% 0.28/0.47 thf(fact_83_not__in__set__insert,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ~ ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ( ( insert @ A @ X2 @ Xs )
% 0.28/0.47 = ( cons @ A @ X2 @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_in_set_insert
% 0.28/0.47 thf(fact_84_insert__Nil,axiom,
% 0.28/0.47 ! [A: $tType,X2: A] :
% 0.28/0.47 ( ( insert @ A @ X2 @ ( nil @ A ) )
% 0.28/0.47 = ( cons @ A @ X2 @ ( nil @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_Nil
% 0.28/0.47 thf(fact_85_sfv__cons,axiom,
% 0.28/0.47 ! [A2: prover2006609834e_form,List: list @ prover2006609834e_form] :
% 0.28/0.47 ( ( prover_Mirabelle_sfv @ ( cons @ prover2006609834e_form @ A2 @ List ) )
% 0.28/0.47 = ( append @ nat @ ( prover_Mirabelle_fv @ A2 ) @ ( prover_Mirabelle_sfv @ List ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sfv_cons
% 0.28/0.47 thf(fact_86_rotate1_Osimps_I2_J,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ( rotate1 @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.28/0.47 = ( append @ A @ Xs @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rotate1.simps(2)
% 0.28/0.47 thf(fact_87_butlast__snoc,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,X2: A] :
% 0.28/0.47 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X2 @ ( nil @ A ) ) ) )
% 0.28/0.47 = Xs ) ).
% 0.28/0.47
% 0.28/0.47 % butlast_snoc
% 0.28/0.47 thf(fact_88_rotate1__is__Nil__conv,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A] :
% 0.28/0.47 ( ( ( rotate1 @ A @ Xs )
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 = ( Xs
% 0.28/0.47 = ( nil @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rotate1_is_Nil_conv
% 0.28/0.47 thf(fact_89_set__rotate1,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A] :
% 0.28/0.47 ( ( set2 @ A @ ( rotate1 @ A @ Xs ) )
% 0.28/0.47 = ( set2 @ A @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_rotate1
% 0.28/0.47 thf(fact_90_in__set__insert,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ( ( insert @ A @ X2 @ Xs )
% 0.28/0.47 = Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_set_insert
% 0.28/0.47 thf(fact_91_bind__simps_I1_J,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.28/0.47 ( ( bind @ B @ A @ ( nil @ B ) @ F )
% 0.28/0.47 = ( nil @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % bind_simps(1)
% 0.28/0.47 thf(fact_92_map__tailrec__rev_Ocases,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,X2: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 0.28/0.47 ( ! [F2: A > B,Bs: list @ B] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 0.28/0.47 => ~ ! [F2: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A3 @ As ) @ Bs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % map_tailrec_rev.cases
% 0.28/0.47 thf(fact_93_butlast_Osimps_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( butlast @ A @ ( nil @ A ) )
% 0.28/0.47 = ( nil @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % butlast.simps(1)
% 0.28/0.47 thf(fact_94_in__set__butlastD,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ( member @ A @ X2 @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 0.28/0.47 => ( member @ A @ X2 @ ( set2 @ A @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_set_butlastD
% 0.28/0.47 thf(fact_95_rotate1_Osimps_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( rotate1 @ A @ ( nil @ A ) )
% 0.28/0.47 = ( nil @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % rotate1.simps(1)
% 0.28/0.47 thf(fact_96_arg__min__list_Ocases,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType] :
% 0.28/0.47 ( ( linorder @ B )
% 0.28/0.47 => ! [X2: product_prod @ ( A > B ) @ ( list @ A )] :
% 0.28/0.47 ( ! [F2: A > B,X: A] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.28/0.47 => ( ! [F2: A > B,X: A,Y2: A,Zs: list @ A] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X @ ( cons @ A @ Y2 @ Zs ) ) ) )
% 0.28/0.47 => ~ ! [A3: A > B] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ A3 @ ( nil @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % arg_min_list.cases
% 0.28/0.47 thf(fact_97_sorted__wrt_Ocases,axiom,
% 0.28/0.47 ! [A: $tType,X2: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.28/0.47 ( ! [P2: A > A > $o] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P2 @ ( nil @ A ) ) )
% 0.28/0.47 => ~ ! [P2: A > A > $o,X: A,Ys2: list @ A] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P2 @ ( cons @ A @ X @ Ys2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sorted_wrt.cases
% 0.28/0.47 thf(fact_98_successively_Ocases,axiom,
% 0.28/0.47 ! [A: $tType,X2: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.28/0.47 ( ! [P2: A > A > $o] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P2 @ ( nil @ A ) ) )
% 0.28/0.47 => ( ! [P2: A > A > $o,X: A] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P2 @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.28/0.47 => ~ ! [P2: A > A > $o,X: A,Y2: A,Xs2: list @ A] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P2 @ ( cons @ A @ X @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % successively.cases
% 0.28/0.47 thf(fact_99_splice_Ocases,axiom,
% 0.28/0.47 ! [A: $tType,X2: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.28/0.47 ( ! [Ys2: list @ A] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys2 ) )
% 0.28/0.47 => ~ ! [X: A,Xs2: list @ A,Ys2: list @ A] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs2 ) @ Ys2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % splice.cases
% 0.28/0.47 thf(fact_100_shuffles_Ocases,axiom,
% 0.28/0.47 ! [A: $tType,X2: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.28/0.47 ( ! [Ys2: list @ A] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys2 ) )
% 0.28/0.47 => ( ! [Xs2: list @ A] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( nil @ A ) ) )
% 0.28/0.47 => ~ ! [X: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % shuffles.cases
% 0.28/0.47 thf(fact_101_list__bind__cong,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,Xs: list @ A,Ys: list @ A,F: A > ( list @ B ),G: A > ( list @ B )] :
% 0.28/0.47 ( ( Xs = Ys )
% 0.28/0.47 => ( ! [X: A] :
% 0.28/0.47 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ( ( F @ X )
% 0.28/0.47 = ( G @ X ) ) )
% 0.28/0.47 => ( ( bind @ A @ B @ Xs @ F )
% 0.28/0.47 = ( bind @ A @ B @ Ys @ G ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_bind_cong
% 0.28/0.47 thf(fact_102_butlast_Osimps_I2_J,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,X2: A] :
% 0.28/0.47 ( ( ( Xs
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 => ( ( butlast @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.28/0.47 = ( nil @ A ) ) )
% 0.28/0.47 & ( ( Xs
% 0.28/0.47 != ( nil @ A ) )
% 0.28/0.47 => ( ( butlast @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.28/0.47 = ( cons @ A @ X2 @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % butlast.simps(2)
% 0.28/0.47 thf(fact_103_butlast__append,axiom,
% 0.28/0.47 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.28/0.47 ( ( ( Ys
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.28/0.47 = ( butlast @ A @ Xs ) ) )
% 0.28/0.47 & ( ( Ys
% 0.28/0.47 != ( nil @ A ) )
% 0.28/0.47 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.28/0.47 = ( append @ A @ Xs @ ( butlast @ A @ Ys ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % butlast_append
% 0.28/0.47 thf(fact_104_in__set__butlast__appendI,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A,Ys: list @ A] :
% 0.28/0.47 ( ( ( member @ A @ X2 @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 0.28/0.47 | ( member @ A @ X2 @ ( set2 @ A @ ( butlast @ A @ Ys ) ) ) )
% 0.28/0.47 => ( member @ A @ X2 @ ( set2 @ A @ ( butlast @ A @ ( append @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_set_butlast_appendI
% 0.28/0.47 thf(fact_105_maps__simps_I2_J,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.28/0.47 ( ( maps @ B @ A @ F @ ( nil @ B ) )
% 0.28/0.47 = ( nil @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % maps_simps(2)
% 0.28/0.47 thf(fact_106_surj__pair,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 0.28/0.47 ? [X: A,Y2: B] :
% 0.28/0.47 ( P3
% 0.28/0.47 = ( product_Pair @ A @ B @ X @ Y2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % surj_pair
% 0.28/0.47 thf(fact_107_prod__cases,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 0.28/0.47 ( ! [A3: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A3 @ B4 ) )
% 0.28/0.47 => ( P @ P3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases
% 0.28/0.47 thf(fact_108_Pair__inject,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
% 0.28/0.47 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.28/0.47 = ( product_Pair @ A @ B @ A5 @ B3 ) )
% 0.28/0.47 => ~ ( ( A2 = A5 )
% 0.28/0.47 => ( B2 != B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Pair_inject
% 0.28/0.47 thf(fact_109_prod__cases3,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.28/0.47 ~ ! [A3: A,B4: B,C3: C] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases3
% 0.28/0.47 thf(fact_110_prod__cases4,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.28/0.47 ~ ! [A3: A,B4: B,C3: C,D2: D] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases4
% 0.28/0.47 thf(fact_111_prod__cases5,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) )] :
% 0.28/0.47 ~ ! [A3: A,B4: B,C3: C,D2: D,E5: E4] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E4 ) @ C3 @ ( product_Pair @ D @ E4 @ D2 @ E5 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases5
% 0.28/0.47 thf(fact_112_prod__cases6,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E4: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) )] :
% 0.28/0.47 ~ ! [A3: A,B4: B,C3: C,D2: D,E5: E4,F2: F3] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E4 @ F3 ) @ D2 @ ( product_Pair @ E4 @ F3 @ E5 @ F2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases6
% 0.28/0.47 thf(fact_113_prod__cases7,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,E4: $tType,F3: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) )] :
% 0.28/0.47 ~ ! [A3: A,B4: B,C3: C,D2: D,E5: E4,F2: F3,G3: G2] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) @ D2 @ ( product_Pair @ E4 @ ( product_prod @ F3 @ G2 ) @ E5 @ ( product_Pair @ F3 @ G2 @ F2 @ G3 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases7
% 0.28/0.47 thf(fact_114_prod__induct3,axiom,
% 0.28/0.47 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.28/0.47 ( ! [A3: A,B4: B,C3: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) )
% 0.28/0.47 => ( P @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_induct3
% 0.28/0.47 thf(fact_115_prod__induct4,axiom,
% 0.28/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.28/0.47 ( ! [A3: A,B4: B,C3: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) )
% 0.28/0.47 => ( P @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_induct4
% 0.28/0.47 thf(fact_116_prod__induct5,axiom,
% 0.28/0.47 ! [E4: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) )] :
% 0.28/0.47 ( ! [A3: A,B4: B,C3: C,D2: D,E5: E4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E4 ) @ C3 @ ( product_Pair @ D @ E4 @ D2 @ E5 ) ) ) ) )
% 0.28/0.47 => ( P @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_induct5
% 0.28/0.47 thf(fact_117_prod__induct6,axiom,
% 0.28/0.47 ! [F3: $tType,E4: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) )] :
% 0.28/0.47 ( ! [A3: A,B4: B,C3: C,D2: D,E5: E4,F2: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E4 @ F3 ) @ D2 @ ( product_Pair @ E4 @ F3 @ E5 @ F2 ) ) ) ) ) )
% 0.28/0.47 => ( P @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_induct6
% 0.28/0.47 thf(fact_118_prod__induct7,axiom,
% 0.28/0.47 ! [G2: $tType,F3: $tType,E4: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) )] :
% 0.28/0.47 ( ! [A3: A,B4: B,C3: C,D2: D,E5: E4,F2: F3,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) @ D2 @ ( product_Pair @ E4 @ ( product_prod @ F3 @ G2 ) @ E5 @ ( product_Pair @ F3 @ G2 @ F2 @ G3 ) ) ) ) ) ) )
% 0.28/0.47 => ( P @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_induct7
% 0.28/0.47 thf(fact_119_old_Oprod_Oexhaust,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.28/0.47 ~ ! [A3: A,B4: B] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( product_Pair @ A @ B @ A3 @ B4 ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.exhaust
% 0.28/0.47 thf(fact_120_old_Oprod_Oinducts,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.28/0.47 ( ! [A3: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A3 @ B4 ) )
% 0.28/0.47 => ( P @ Prod ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.inducts
% 0.28/0.47 thf(fact_121_List_Oinsert__def,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( insert @ A )
% 0.28/0.47 = ( ^ [X3: A,Xs4: list @ A] : ( if @ ( list @ A ) @ ( member @ A @ X3 @ ( set2 @ A @ Xs4 ) ) @ Xs4 @ ( cons @ A @ X3 @ Xs4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % List.insert_def
% 0.28/0.47 thf(fact_122_old_Oprod_Orec,axiom,
% 0.28/0.47 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.28/0.47 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.28/0.47 = ( F1 @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.rec
% 0.28/0.47 thf(fact_123_flatten_Osimps_I2_J,axiom,
% 0.28/0.47 ! [A: $tType,A2: list @ A,List: list @ ( list @ A )] :
% 0.28/0.47 ( ( prover12291693latten @ A @ ( cons @ ( list @ A ) @ A2 @ List ) )
% 0.28/0.47 = ( append @ A @ A2 @ ( prover12291693latten @ A @ List ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % flatten.simps(2)
% 0.28/0.47 thf(fact_124_flatten_Osimps_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( prover12291693latten @ A @ ( nil @ ( list @ A ) ) )
% 0.28/0.47 = ( nil @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % flatten.simps(1)
% 0.28/0.47 thf(fact_125_product__lists_Osimps_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.28/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % product_lists.simps(1)
% 0.28/0.47 thf(fact_126_append__butlast__last__id,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 != ( nil @ A ) )
% 0.28/0.47 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 0.28/0.47 = Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % append_butlast_last_id
% 0.28/0.47 thf(fact_127_fv_Osimps_I5_J,axiom,
% 0.28/0.47 ! [F: prover2006609834e_form] :
% 0.28/0.47 ( ( prover_Mirabelle_fv @ ( prover946642470e_FAll @ F ) )
% 0.28/0.47 = ( prover1646808149preSuc @ ( prover_Mirabelle_fv @ F ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % fv.simps(5)
% 0.28/0.47 thf(fact_128_last__appendR,axiom,
% 0.28/0.47 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.28/0.47 ( ( Ys
% 0.28/0.47 != ( nil @ A ) )
% 0.28/0.47 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.28/0.47 = ( last @ A @ Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % last_appendR
% 0.28/0.47 thf(fact_129_last__appendL,axiom,
% 0.28/0.47 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.28/0.47 ( ( Ys
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.28/0.47 = ( last @ A @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % last_appendL
% 0.28/0.47 thf(fact_130_last__snoc,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,X2: A] :
% 0.28/0.47 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X2 @ ( nil @ A ) ) ) )
% 0.28/0.47 = X2 ) ).
% 0.28/0.47
% 0.28/0.47 % last_snoc
% 0.28/0.47 thf(fact_131_last__ConsR,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,X2: A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 != ( nil @ A ) )
% 0.28/0.47 => ( ( last @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.28/0.47 = ( last @ A @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % last_ConsR
% 0.28/0.47 thf(fact_132_last__ConsL,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,X2: A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 => ( ( last @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.28/0.47 = X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % last_ConsL
% 0.28/0.47 thf(fact_133_last_Osimps,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,X2: A] :
% 0.28/0.47 ( ( ( Xs
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 => ( ( last @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.28/0.47 = X2 ) )
% 0.28/0.47 & ( ( Xs
% 0.28/0.47 != ( nil @ A ) )
% 0.28/0.47 => ( ( last @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.28/0.47 = ( last @ A @ Xs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % last.simps
% 0.28/0.47 thf(fact_134_last__in__set,axiom,
% 0.28/0.47 ! [A: $tType,As2: list @ A] :
% 0.28/0.47 ( ( As2
% 0.28/0.47 != ( nil @ A ) )
% 0.28/0.47 => ( member @ A @ ( last @ A @ As2 ) @ ( set2 @ A @ As2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % last_in_set
% 0.28/0.47 thf(fact_135_longest__common__suffix,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.28/0.47 ? [Ss: list @ A,Xs5: list @ A,Ys6: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( append @ A @ Xs5 @ Ss ) )
% 0.28/0.47 & ( Ys
% 0.28/0.47 = ( append @ A @ Ys6 @ Ss ) )
% 0.28/0.47 & ( ( Xs5
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 | ( Ys6
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 | ( ( last @ A @ Xs5 )
% 0.28/0.47 != ( last @ A @ Ys6 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % longest_common_suffix
% 0.28/0.47 thf(fact_136_last__append,axiom,
% 0.28/0.47 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.28/0.47 ( ( ( Ys
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.28/0.47 = ( last @ A @ Xs ) ) )
% 0.28/0.47 & ( ( Ys
% 0.28/0.47 != ( nil @ A ) )
% 0.28/0.47 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.28/0.47 = ( last @ A @ Ys ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % last_append
% 0.28/0.47 thf(fact_137_preSuc_Osimps_I1_J,axiom,
% 0.28/0.47 ( ( prover1646808149preSuc @ ( nil @ nat ) )
% 0.28/0.47 = ( nil @ nat ) ) ).
% 0.28/0.47
% 0.28/0.47 % preSuc.simps(1)
% 0.28/0.47 thf(fact_138_snoc__eq__iff__butlast,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,X2: A,Ys: list @ A] :
% 0.28/0.47 ( ( ( append @ A @ Xs @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.28/0.47 = Ys )
% 0.28/0.47 = ( ( Ys
% 0.28/0.47 != ( nil @ A ) )
% 0.28/0.47 & ( ( butlast @ A @ Ys )
% 0.28/0.47 = Xs )
% 0.28/0.47 & ( ( last @ A @ Ys )
% 0.28/0.47 = X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % snoc_eq_iff_butlast
% 0.28/0.47 thf(fact_139_snoc__listrel1__snoc__iff,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,X2: A,Ys: list @ A,Y: A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) @ ( listrel1 @ A @ R ) )
% 0.28/0.47 = ( ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.28/0.47 & ( X2 = Y ) )
% 0.28/0.47 | ( ( Xs = Ys )
% 0.28/0.47 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ R ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % snoc_listrel1_snoc_iff
% 0.28/0.47 thf(fact_140_subseqs_Osimps_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( subseqs @ A @ ( nil @ A ) )
% 0.28/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subseqs.simps(1)
% 0.28/0.47 thf(fact_141_concat__eq__append__conv,axiom,
% 0.28/0.47 ! [A: $tType,Xss2: list @ ( list @ A ),Ys: list @ A,Zs2: list @ A] :
% 0.28/0.47 ( ( ( concat @ A @ Xss2 )
% 0.28/0.47 = ( append @ A @ Ys @ Zs2 ) )
% 0.28/0.47 = ( ( ( Xss2
% 0.28/0.47 = ( nil @ ( list @ A ) ) )
% 0.28/0.47 => ( ( Ys
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 & ( Zs2
% 0.28/0.47 = ( nil @ A ) ) ) )
% 0.28/0.47 & ( ( Xss2
% 0.28/0.47 != ( nil @ ( list @ A ) ) )
% 0.28/0.47 => ? [Xss1: list @ ( list @ A ),Xs4: list @ A,Xs6: list @ A,Xss22: list @ ( list @ A )] :
% 0.28/0.47 ( ( Xss2
% 0.28/0.47 = ( append @ ( list @ A ) @ Xss1 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs4 @ Xs6 ) @ Xss22 ) ) )
% 0.28/0.47 & ( Ys
% 0.28/0.47 = ( append @ A @ ( concat @ A @ Xss1 ) @ Xs4 ) )
% 0.28/0.47 & ( Zs2
% 0.28/0.47 = ( append @ A @ Xs6 @ ( concat @ A @ Xss22 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % concat_eq_append_conv
% 0.28/0.47 thf(fact_142_lexord__same__pref__iff,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs2 ) ) @ ( lexord @ A @ R ) )
% 0.28/0.47 = ( ? [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ X3 ) @ R ) )
% 0.28/0.47 | ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys @ Zs2 ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_same_pref_iff
% 0.28/0.47 thf(fact_143_concat__eq__Nil__conv,axiom,
% 0.28/0.47 ! [A: $tType,Xss2: list @ ( list @ A )] :
% 0.28/0.47 ( ( ( concat @ A @ Xss2 )
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 = ( ! [X3: list @ A] :
% 0.28/0.47 ( ( member @ ( list @ A ) @ X3 @ ( set2 @ ( list @ A ) @ Xss2 ) )
% 0.28/0.47 => ( X3
% 0.28/0.47 = ( nil @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % concat_eq_Nil_conv
% 0.28/0.47 thf(fact_144_Nil__eq__concat__conv,axiom,
% 0.28/0.47 ! [A: $tType,Xss2: list @ ( list @ A )] :
% 0.28/0.47 ( ( ( nil @ A )
% 0.28/0.47 = ( concat @ A @ Xss2 ) )
% 0.28/0.47 = ( ! [X3: list @ A] :
% 0.28/0.47 ( ( member @ ( list @ A ) @ X3 @ ( set2 @ ( list @ A ) @ Xss2 ) )
% 0.28/0.47 => ( X3
% 0.28/0.47 = ( nil @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil_eq_concat_conv
% 0.28/0.47 thf(fact_145_concat__append,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ ( list @ A ),Ys: list @ ( list @ A )] :
% 0.28/0.47 ( ( concat @ A @ ( append @ ( list @ A ) @ Xs @ Ys ) )
% 0.28/0.47 = ( append @ A @ ( concat @ A @ Xs ) @ ( concat @ A @ Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % concat_append
% 0.28/0.47 thf(fact_146_Cons__listrel1__Cons,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A,Y: A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 @ Xs ) @ ( cons @ A @ Y @ Ys ) ) @ ( listrel1 @ A @ R ) )
% 0.28/0.47 = ( ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ R )
% 0.28/0.47 & ( Xs = Ys ) )
% 0.28/0.47 | ( ( X2 = Y )
% 0.28/0.47 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Cons_listrel1_Cons
% 0.28/0.47 thf(fact_147_lexord__cons__cons,axiom,
% 0.28/0.47 ! [A: $tType,A2: A,X2: list @ A,B2: A,Y: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ A2 @ X2 ) @ ( cons @ A @ B2 @ Y ) ) @ ( lexord @ A @ R ) )
% 0.28/0.47 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.28/0.47 | ( ( A2 = B2 )
% 0.28/0.47 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ Y ) @ ( lexord @ A @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_cons_cons
% 0.28/0.47 thf(fact_148_lexord__Nil__left,axiom,
% 0.28/0.47 ! [A: $tType,Y: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Y ) @ ( lexord @ A @ R ) )
% 0.28/0.47 = ( ? [A6: A,X3: list @ A] :
% 0.28/0.47 ( Y
% 0.28/0.47 = ( cons @ A @ A6 @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_Nil_left
% 0.28/0.47 thf(fact_149_subseqs__refl,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A] : ( member @ ( list @ A ) @ Xs @ ( set2 @ ( list @ A ) @ ( subseqs @ A @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subseqs_refl
% 0.28/0.47 thf(fact_150_Cons__in__subseqsD,axiom,
% 0.28/0.47 ! [A: $tType,Y: A,Ys: list @ A,Xs: list @ A] :
% 0.28/0.47 ( ( member @ ( list @ A ) @ ( cons @ A @ Y @ Ys ) @ ( set2 @ ( list @ A ) @ ( subseqs @ A @ Xs ) ) )
% 0.28/0.47 => ( member @ ( list @ A ) @ Ys @ ( set2 @ ( list @ A ) @ ( subseqs @ A @ Xs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Cons_in_subseqsD
% 0.28/0.47 thf(fact_151_listrel1I2,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A ),X2: A] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 @ Xs ) @ ( cons @ A @ X2 @ Ys ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel1I2
% 0.28/0.47 thf(fact_152_not__listrel1__Nil,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( nil @ A ) ) @ ( listrel1 @ A @ R ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_listrel1_Nil
% 0.28/0.47 thf(fact_153_not__Nil__listrel1,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Xs ) @ ( listrel1 @ A @ R ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_Nil_listrel1
% 0.28/0.47 thf(fact_154_append__listrel1I,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A ),Us2: list @ A,Vs: list @ A] :
% 0.28/0.47 ( ( ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.28/0.47 & ( Us2 = Vs ) )
% 0.28/0.47 | ( ( Xs = Ys )
% 0.28/0.47 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Us2 @ Vs ) @ ( listrel1 @ A @ R ) ) ) )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Ys @ Vs ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % append_listrel1I
% 0.28/0.47 thf(fact_155_concat_Osimps_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( concat @ A @ ( nil @ ( list @ A ) ) )
% 0.28/0.47 = ( nil @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % concat.simps(1)
% 0.28/0.47 thf(fact_156_lexord__linear,axiom,
% 0.28/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X2: list @ A,Y: list @ A] :
% 0.28/0.47 ( ! [A3: A,B4: A] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B4 ) @ R )
% 0.28/0.47 | ( A3 = B4 )
% 0.28/0.47 | ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ A3 ) @ R ) )
% 0.28/0.47 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ Y ) @ ( lexord @ A @ R ) )
% 0.28/0.47 | ( X2 = Y )
% 0.28/0.47 | ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Y @ X2 ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_linear
% 0.28/0.47 thf(fact_157_lexord__irreflexive,axiom,
% 0.28/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A] :
% 0.28/0.47 ( ! [X: A] :
% 0.28/0.47 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ X ) @ R )
% 0.28/0.47 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Xs ) @ ( lexord @ A @ R ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_irreflexive
% 0.28/0.47 thf(fact_158_concat_Osimps_I2_J,axiom,
% 0.28/0.47 ! [A: $tType,X2: list @ A,Xs: list @ ( list @ A )] :
% 0.28/0.47 ( ( concat @ A @ ( cons @ ( list @ A ) @ X2 @ Xs ) )
% 0.28/0.47 = ( append @ A @ X2 @ ( concat @ A @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % concat.simps(2)
% 0.28/0.47 thf(fact_159_lexord__Nil__right,axiom,
% 0.28/0.47 ! [A: $tType,X2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ ( nil @ A ) ) @ ( lexord @ A @ R ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_Nil_right
% 0.28/0.47 thf(fact_160_lexord__append__leftI,axiom,
% 0.28/0.47 ! [A: $tType,U: list @ A,V: list @ A,R: set @ ( product_prod @ A @ A ),X2: list @ A] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ U @ V ) @ ( lexord @ A @ R ) )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ X2 @ U ) @ ( append @ A @ X2 @ V ) ) @ ( lexord @ A @ R ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_append_leftI
% 0.28/0.47 thf(fact_161_listrel1I1,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Y: A,R: set @ ( product_prod @ A @ A ),Xs: list @ A] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ R )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 @ Xs ) @ ( cons @ A @ Y @ Xs ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel1I1
% 0.28/0.47 thf(fact_162_Cons__listrel1E1,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 @ Xs ) @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.28/0.47 => ( ! [Y2: A] :
% 0.28/0.47 ( ( Ys
% 0.28/0.47 = ( cons @ A @ Y2 @ Xs ) )
% 0.28/0.47 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y2 ) @ R ) )
% 0.28/0.47 => ~ ! [Zs: list @ A] :
% 0.28/0.47 ( ( Ys
% 0.28/0.47 = ( cons @ A @ X2 @ Zs ) )
% 0.28/0.47 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Zs ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Cons_listrel1E1
% 0.28/0.47 thf(fact_163_Cons__listrel1E2,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Y: A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( cons @ A @ Y @ Ys ) ) @ ( listrel1 @ A @ R ) )
% 0.28/0.47 => ( ! [X: A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( cons @ A @ X @ Ys ) )
% 0.28/0.47 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R ) )
% 0.28/0.47 => ~ ! [Zs: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( cons @ A @ Y @ Zs ) )
% 0.28/0.47 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Zs @ Ys ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Cons_listrel1E2
% 0.28/0.47 thf(fact_164_lexord__partial__trans,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A ),Ys: list @ A,Zs2: list @ A] :
% 0.28/0.47 ( ! [X: A,Y2: A,Z: A] :
% 0.28/0.47 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y2 ) @ R )
% 0.28/0.47 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z ) @ R )
% 0.28/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z ) @ R ) ) ) )
% 0.28/0.47 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( lexord @ A @ R ) )
% 0.28/0.47 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys @ Zs2 ) @ ( lexord @ A @ R ) )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Zs2 ) @ ( lexord @ A @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_partial_trans
% 0.28/0.47 thf(fact_165_lexord__append__leftD,axiom,
% 0.28/0.47 ! [A: $tType,X2: list @ A,U: list @ A,V: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ X2 @ U ) @ ( append @ A @ X2 @ V ) ) @ ( lexord @ A @ R ) )
% 0.28/0.47 => ( ! [A3: A] :
% 0.28/0.47 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ A3 ) @ R )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ U @ V ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_append_leftD
% 0.28/0.47 thf(fact_166_lexord__append__rightI,axiom,
% 0.28/0.47 ! [A: $tType,Y: list @ A,X2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ? [B5: A,Z3: list @ A] :
% 0.28/0.47 ( Y
% 0.28/0.47 = ( cons @ A @ B5 @ Z3 ) )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ ( append @ A @ X2 @ Y ) ) @ ( lexord @ A @ R ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_append_rightI
% 0.28/0.47 thf(fact_167_concat__eq__appendD,axiom,
% 0.28/0.47 ! [A: $tType,Xss2: list @ ( list @ A ),Ys: list @ A,Zs2: list @ A] :
% 0.28/0.47 ( ( ( concat @ A @ Xss2 )
% 0.28/0.47 = ( append @ A @ Ys @ Zs2 ) )
% 0.28/0.47 => ( ( Xss2
% 0.28/0.47 != ( nil @ ( list @ A ) ) )
% 0.28/0.47 => ? [Xss12: list @ ( list @ A ),Xs2: list @ A,Xs5: list @ A,Xss23: list @ ( list @ A )] :
% 0.28/0.47 ( ( Xss2
% 0.28/0.47 = ( append @ ( list @ A ) @ Xss12 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.28/0.47 & ( Ys
% 0.28/0.47 = ( append @ A @ ( concat @ A @ Xss12 ) @ Xs2 ) )
% 0.28/0.47 & ( Zs2
% 0.28/0.47 = ( append @ A @ Xs5 @ ( concat @ A @ Xss23 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % concat_eq_appendD
% 0.28/0.47 thf(fact_168_listrel1E,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.28/0.47 => ~ ! [X: A,Y2: A] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y2 ) @ R )
% 0.28/0.47 => ! [Us3: list @ A,Vs2: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( append @ A @ Us3 @ ( cons @ A @ X @ Vs2 ) ) )
% 0.28/0.47 => ( Ys
% 0.28/0.47 != ( append @ A @ Us3 @ ( cons @ A @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel1E
% 0.28/0.47 thf(fact_169_listrel1I,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Y: A,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Us2: list @ A,Vs: list @ A,Ys: list @ A] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ R )
% 0.28/0.47 => ( ( Xs
% 0.28/0.47 = ( append @ A @ Us2 @ ( cons @ A @ X2 @ Vs ) ) )
% 0.28/0.47 => ( ( Ys
% 0.28/0.47 = ( append @ A @ Us2 @ ( cons @ A @ Y @ Vs ) ) )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel1I
% 0.28/0.47 thf(fact_170_lexord__append__left__rightI,axiom,
% 0.28/0.47 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),U: list @ A,X2: list @ A,Y: list @ A] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ U @ ( cons @ A @ A2 @ X2 ) ) @ ( append @ A @ U @ ( cons @ A @ B2 @ Y ) ) ) @ ( lexord @ A @ R ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_append_left_rightI
% 0.28/0.47 thf(fact_171_lexord__same__pref__if__irrefl,axiom,
% 0.28/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.28/0.47 ( ( irrefl @ A @ R )
% 0.28/0.47 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs2 ) ) @ ( lexord @ A @ R ) )
% 0.28/0.47 = ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys @ Zs2 ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_same_pref_if_irrefl
% 0.28/0.47 thf(fact_172_listrel_Ocases,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,A1: list @ A,A22: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ A1 @ A22 ) @ ( listrel @ A @ B @ R ) )
% 0.28/0.47 => ( ( ( A1
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 => ( A22
% 0.28/0.47 != ( nil @ B ) ) )
% 0.28/0.47 => ~ ! [X: A,Y2: B,Xs2: list @ A] :
% 0.28/0.47 ( ( A1
% 0.28/0.47 = ( cons @ A @ X @ Xs2 ) )
% 0.28/0.47 => ! [Ys2: list @ B] :
% 0.28/0.47 ( ( A22
% 0.28/0.47 = ( cons @ B @ Y2 @ Ys2 ) )
% 0.28/0.47 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y2 ) @ R )
% 0.28/0.47 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys2 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel.cases
% 0.28/0.47 thf(fact_173_listrel_Osimps,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,A1: list @ A,A22: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ A1 @ A22 ) @ ( listrel @ A @ B @ R ) )
% 0.28/0.47 = ( ( ( A1
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 & ( A22
% 0.28/0.47 = ( nil @ B ) ) )
% 0.28/0.47 | ? [X3: A,Y3: B,Xs4: list @ A,Ys3: list @ B] :
% 0.28/0.47 ( ( A1
% 0.28/0.47 = ( cons @ A @ X3 @ Xs4 ) )
% 0.28/0.47 & ( A22
% 0.28/0.47 = ( cons @ B @ Y3 @ Ys3 ) )
% 0.28/0.47 & ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R )
% 0.28/0.47 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs4 @ Ys3 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel.simps
% 0.28/0.47 thf(fact_174_listrel_Oinducts,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,X12: list @ A,X24: list @ B,R: set @ ( product_prod @ A @ B ),P: ( list @ A ) > ( list @ B ) > $o] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ X12 @ X24 ) @ ( listrel @ A @ B @ R ) )
% 0.28/0.47 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.28/0.47 => ( ! [X: A,Y2: B,Xs2: list @ A,Ys2: list @ B] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y2 ) @ R )
% 0.28/0.47 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys2 ) @ ( listrel @ A @ B @ R ) )
% 0.28/0.47 => ( ( P @ Xs2 @ Ys2 )
% 0.28/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) ) ) )
% 0.28/0.47 => ( P @ X12 @ X24 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel.inducts
% 0.28/0.47 thf(fact_175_lexord__irrefl,axiom,
% 0.28/0.47 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( irrefl @ A @ R2 )
% 0.28/0.47 => ( irrefl @ ( list @ A ) @ ( lexord @ A @ R2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_irrefl
% 0.28/0.47 thf(fact_176_listrel_ONil,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B )] : ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ ( nil @ B ) ) @ ( listrel @ A @ B @ R ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel.Nil
% 0.28/0.47 thf(fact_177_listrel__Nil1,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,Xs: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Xs ) @ ( listrel @ A @ B @ R ) )
% 0.28/0.47 => ( Xs
% 0.28/0.47 = ( nil @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel_Nil1
% 0.28/0.47 thf(fact_178_listrel__Nil2,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ B )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ ( nil @ B ) ) @ ( listrel @ A @ B @ R ) )
% 0.28/0.47 => ( Xs
% 0.28/0.47 = ( nil @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel_Nil2
% 0.28/0.47 thf(fact_179_listrel__Cons2,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,Xs: list @ A,Y: B,Ys: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ ( cons @ B @ Y @ Ys ) ) @ ( listrel @ A @ B @ R ) )
% 0.28/0.47 => ~ ! [X: A,Xs2: list @ A] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( cons @ A @ X @ Xs2 ) )
% 0.28/0.47 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R )
% 0.28/0.47 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel_Cons2
% 0.28/0.47 thf(fact_180_listrel__Cons1,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,Y: A,Ys: list @ A,Xs: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ Y @ Ys ) @ Xs ) @ ( listrel @ A @ B @ R ) )
% 0.28/0.47 => ~ ! [Y2: B,Ys2: list @ B] :
% 0.28/0.47 ( ( Xs
% 0.28/0.47 = ( cons @ B @ Y2 @ Ys2 ) )
% 0.28/0.47 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Y @ Y2 ) @ R )
% 0.28/0.47 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Ys @ Ys2 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel_Cons1
% 0.28/0.47 thf(fact_181_listrel_OCons,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,X2: A,Y: B,R: set @ ( product_prod @ A @ B ),Xs: list @ A,Ys: list @ B] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y ) @ R )
% 0.28/0.47 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ Ys ) @ ( listrel @ A @ B @ R ) )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ X2 @ Xs ) @ ( cons @ B @ Y @ Ys ) ) @ ( listrel @ A @ B @ R ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel.Cons
% 0.28/0.47 thf(fact_182_irrefl__def,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( irrefl @ A )
% 0.28/0.47 = ( ^ [R3: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ! [A6: A] :
% 0.28/0.47 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A6 @ A6 ) @ R3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % irrefl_def
% 0.28/0.47 thf(fact_183_irreflI,axiom,
% 0.28/0.47 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ! [A3: A] :
% 0.28/0.47 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ A3 ) @ R2 )
% 0.28/0.47 => ( irrefl @ A @ R2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % irreflI
% 0.28/0.47 thf(fact_184_lenlex__append2,axiom,
% 0.28/0.47 ! [A: $tType,R2: set @ ( product_prod @ A @ A ),Us2: list @ A,Xs: list @ A,Ys: list @ A] :
% 0.28/0.47 ( ( irrefl @ A @ R2 )
% 0.28/0.47 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Us2 @ Xs ) @ ( append @ A @ Us2 @ Ys ) ) @ ( lenlex @ A @ R2 ) )
% 0.28/0.47 = ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( lenlex @ A @ R2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lenlex_append2
% 0.28/0.47 thf(fact_185_Nil__lenlex__iff1,axiom,
% 0.28/0.47 ! [A: $tType,Ns: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ns ) @ ( lenlex @ A @ R ) )
% 0.28/0.47 = ( Ns
% 0.28/0.47 != ( nil @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil_lenlex_iff1
% 0.28/0.47 thf(fact_186_lenlex__irreflexive,axiom,
% 0.28/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A] :
% 0.28/0.47 ( ! [X: A] :
% 0.28/0.47 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ X ) @ R )
% 0.28/0.47 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Xs ) @ ( lenlex @ A @ R ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lenlex_irreflexive
% 0.28/0.47 thf(fact_187_Nil__lenlex__iff2,axiom,
% 0.28/0.47 ! [A: $tType,Ns: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ns @ ( nil @ A ) ) @ ( lenlex @ A @ R ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil_lenlex_iff2
% 0.28/0.47 thf(fact_188_irrefl__lex,axiom,
% 0.28/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( irrefl @ A @ R )
% 0.28/0.47 => ( irrefl @ ( list @ A ) @ ( lex @ A @ R ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % irrefl_lex
% 0.28/0.47 thf(fact_189_internal__case__prod__conv,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 0.28/0.47 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.28/0.47 = ( C2 @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % internal_case_prod_conv
% 0.28/0.47 thf(fact_190_list__ex1__simps_I1_J,axiom,
% 0.28/0.47 ! [A: $tType,P: A > $o] :
% 0.28/0.47 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_ex1_simps(1)
% 0.28/0.47 thf(fact_191_list__ex1__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( list_ex1 @ A )
% 0.28/0.47 = ( ^ [P4: A > $o,Xs4: list @ A] :
% 0.28/0.47 ? [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ ( set2 @ A @ Xs4 ) )
% 0.28/0.47 & ( P4 @ X3 )
% 0.28/0.47 & ! [Y3: A] :
% 0.28/0.47 ( ( ( member @ A @ Y3 @ ( set2 @ A @ Xs4 ) )
% 0.28/0.47 & ( P4 @ Y3 ) )
% 0.28/0.47 => ( Y3 = X3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_ex1_iff
% 0.28/0.47 thf(fact_192_Nil__notin__lex,axiom,
% 0.28/0.47 ! [A: $tType,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys ) @ ( lex @ A @ R ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil_notin_lex
% 0.28/0.47 thf(fact_193_Nil2__notin__lex,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( nil @ A ) ) @ ( lex @ A @ R ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nil2_notin_lex
% 0.28/0.47 thf(fact_194_lex__append__leftI,axiom,
% 0.28/0.47 ! [A: $tType,Ys: list @ A,Zs2: list @ A,R: set @ ( product_prod @ A @ A ),Xs: list @ A] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys @ Zs2 ) @ ( lex @ A @ R ) )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs2 ) ) @ ( lex @ A @ R ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lex_append_leftI
% 0.28/0.47 thf(fact_195_lexl__not__refl,axiom,
% 0.28/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X2: list @ A] :
% 0.28/0.47 ( ( irrefl @ A @ R )
% 0.28/0.47 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ X2 ) @ ( lex @ A @ R ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexl_not_refl
% 0.28/0.47 thf(fact_196_lex__append__left__iff,axiom,
% 0.28/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.28/0.47 ( ! [X: A] :
% 0.28/0.47 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ X ) @ R )
% 0.28/0.47 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs2 ) ) @ ( lex @ A @ R ) )
% 0.28/0.47 = ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys @ Zs2 ) @ ( lex @ A @ R ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lex_append_left_iff
% 0.28/0.47 thf(fact_197_lex__append__leftD,axiom,
% 0.28/0.47 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.28/0.47 ( ! [X: A] :
% 0.28/0.47 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ X ) @ R )
% 0.28/0.47 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs2 ) ) @ ( lex @ A @ R ) )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys @ Zs2 ) @ ( lex @ A @ R ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lex_append_leftD
% 0.28/0.47 thf(fact_198_can__select__set__list__ex1,axiom,
% 0.28/0.47 ! [A: $tType,P: A > $o,A4: list @ A] :
% 0.28/0.47 ( ( can_select @ A @ P @ ( set2 @ A @ A4 ) )
% 0.28/0.47 = ( list_ex1 @ A @ P @ A4 ) ) ).
% 0.28/0.47
% 0.28/0.47 % can_select_set_list_ex1
% 0.28/0.47 thf(fact_199_Cons__in__lex,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A,Y: A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 @ Xs ) @ ( cons @ A @ Y @ Ys ) ) @ ( lex @ A @ R ) )
% 0.28/0.47 = ( ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ R )
% 0.28/0.47 & ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Ys ) ) )
% 0.28/0.47 | ( ( X2 = Y )
% 0.28/0.47 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( lex @ A @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Cons_in_lex
% 0.28/0.47 thf(fact_200_append__eq__append__conv,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,Us2: list @ A,Vs: list @ A] :
% 0.28/0.47 ( ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.28/0.47 | ( ( size_size @ ( list @ A ) @ Us2 )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Vs ) ) )
% 0.28/0.47 => ( ( ( append @ A @ Xs @ Us2 )
% 0.28/0.47 = ( append @ A @ Ys @ Vs ) )
% 0.28/0.47 = ( ( Xs = Ys )
% 0.28/0.47 & ( Us2 = Vs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % append_eq_append_conv
% 0.28/0.47 thf(fact_201_length__rotate1,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A] :
% 0.28/0.47 ( ( size_size @ ( list @ A ) @ ( rotate1 @ A @ Xs ) )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % length_rotate1
% 0.28/0.47 thf(fact_202_listrel1__eq__len,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.28/0.47 => ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel1_eq_len
% 0.28/0.47 thf(fact_203_in__set__product__lists__length,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Xss2: list @ ( list @ A )] :
% 0.28/0.47 ( ( member @ ( list @ A ) @ Xs @ ( set2 @ ( list @ A ) @ ( product_lists @ A @ Xss2 ) ) )
% 0.28/0.47 => ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 = ( size_size @ ( list @ ( list @ A ) ) @ Xss2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_set_product_lists_length
% 0.28/0.47 thf(fact_204_can__select__def,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( can_select @ A )
% 0.28/0.47 = ( ^ [P4: A > $o,A7: set @ A] :
% 0.28/0.47 ? [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ A7 )
% 0.28/0.47 & ( P4 @ X3 )
% 0.28/0.47 & ! [Y3: A] :
% 0.28/0.47 ( ( ( member @ A @ Y3 @ A7 )
% 0.28/0.47 & ( P4 @ Y3 ) )
% 0.28/0.47 => ( Y3 = X3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % can_select_def
% 0.28/0.47 thf(fact_205_Ex__list__of__length,axiom,
% 0.28/0.47 ! [A: $tType,N: nat] :
% 0.28/0.47 ? [Xs2: list @ A] :
% 0.28/0.47 ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.28/0.47 = N ) ).
% 0.28/0.47
% 0.28/0.47 % Ex_list_of_length
% 0.28/0.47 thf(fact_206_neq__if__length__neq,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.28/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 != ( size_size @ ( list @ A ) @ Ys ) )
% 0.28/0.47 => ( Xs != Ys ) ) ).
% 0.28/0.47
% 0.28/0.47 % neq_if_length_neq
% 0.28/0.47 thf(fact_207_list__induct3,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,C: $tType,Xs: list @ A,Ys: list @ B,Zs2: list @ C,P: ( list @ A ) > ( list @ B ) > ( list @ C ) > $o] :
% 0.28/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 = ( size_size @ ( list @ B ) @ Ys ) )
% 0.28/0.47 => ( ( ( size_size @ ( list @ B ) @ Ys )
% 0.28/0.47 = ( size_size @ ( list @ C ) @ Zs2 ) )
% 0.28/0.47 => ( ( P @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) )
% 0.28/0.47 => ( ! [X: A,Xs2: list @ A,Y2: B,Ys2: list @ B,Z: C,Zs: list @ C] :
% 0.28/0.47 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.28/0.47 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 0.28/0.47 => ( ( ( size_size @ ( list @ B ) @ Ys2 )
% 0.28/0.47 = ( size_size @ ( list @ C ) @ Zs ) )
% 0.28/0.47 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.28/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) @ ( cons @ C @ Z @ Zs ) ) ) ) )
% 0.28/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_induct3
% 0.28/0.47 thf(fact_208_list__induct2,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 0.28/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 = ( size_size @ ( list @ B ) @ Ys ) )
% 0.28/0.47 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.28/0.47 => ( ! [X: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 0.28/0.47 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.28/0.47 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 0.28/0.47 => ( ( P @ Xs2 @ Ys2 )
% 0.28/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) ) )
% 0.28/0.47 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_induct2
% 0.28/0.47 thf(fact_209_listrel__eq__len,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ Ys ) @ ( listrel @ A @ B @ R ) )
% 0.28/0.47 => ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 = ( size_size @ ( list @ B ) @ Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel_eq_len
% 0.28/0.47 thf(fact_210_same__length__different,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.28/0.47 ( ( Xs != Ys )
% 0.28/0.47 => ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.28/0.47 => ? [Pre: list @ A,X: A,Xs5: list @ A,Y2: A,Ys6: list @ A] :
% 0.28/0.47 ( ( X != Y2 )
% 0.28/0.47 & ( Xs
% 0.28/0.47 = ( append @ A @ Pre @ ( append @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ Xs5 ) ) )
% 0.28/0.47 & ( Ys
% 0.28/0.47 = ( append @ A @ Pre @ ( append @ A @ ( cons @ A @ Y2 @ ( nil @ A ) ) @ Ys6 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % same_length_different
% 0.28/0.47 thf(fact_211_lexord__sufE,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Zs2: list @ A,Ys: list @ A,Qs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Zs2 ) @ ( append @ A @ Ys @ Qs ) ) @ ( lexord @ A @ R ) )
% 0.28/0.47 => ( ( Xs != Ys )
% 0.28/0.47 => ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.28/0.47 => ( ( ( size_size @ ( list @ A ) @ Zs2 )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Qs ) )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( lexord @ A @ R ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_sufE
% 0.28/0.47 thf(fact_212_lex__append__rightI,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A ),Vs: list @ A,Us2: list @ A] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( lex @ A @ R ) )
% 0.28/0.47 => ( ( ( size_size @ ( list @ A ) @ Vs )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Us2 ) )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Ys @ Vs ) ) @ ( lex @ A @ R ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lex_append_rightI
% 0.28/0.47 thf(fact_213_lenlex__append1,axiom,
% 0.28/0.47 ! [A: $tType,Us2: list @ A,Xs: list @ A,R2: set @ ( product_prod @ A @ A ),Vs: list @ A,Ys: list @ A] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Us2 @ Xs ) @ ( lenlex @ A @ R2 ) )
% 0.28/0.47 => ( ( ( size_size @ ( list @ A ) @ Vs )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.28/0.47 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Us2 @ Vs ) @ ( append @ A @ Xs @ Ys ) ) @ ( lenlex @ A @ R2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lenlex_append1
% 0.28/0.47 thf(fact_214_lexord__lex,axiom,
% 0.28/0.47 ! [A: $tType,X2: list @ A,Y: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ Y ) @ ( lex @ A @ R ) )
% 0.28/0.47 = ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ Y ) @ ( lexord @ A @ R ) )
% 0.28/0.47 & ( ( size_size @ ( list @ A ) @ X2 )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lexord_lex
% 0.28/0.47 thf(fact_215_Cons__lenlex__iff,axiom,
% 0.28/0.47 ! [A: $tType,M: A,Ms: list @ A,N: A,Ns: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ M @ Ms ) @ ( cons @ A @ N @ Ns ) ) @ ( lenlex @ A @ R ) )
% 0.28/0.47 = ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ms ) @ ( size_size @ ( list @ A ) @ Ns ) )
% 0.28/0.47 | ( ( ( size_size @ ( list @ A ) @ Ms )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Ns ) )
% 0.28/0.47 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ M @ N ) @ R ) )
% 0.28/0.47 | ( ( M = N )
% 0.28/0.47 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ms @ Ns ) @ ( lenlex @ A @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Cons_lenlex_iff
% 0.28/0.47 thf(fact_216_length__n__lists__elem,axiom,
% 0.28/0.47 ! [A: $tType,Ys: list @ A,N: nat,Xs: list @ A] :
% 0.28/0.47 ( ( member @ ( list @ A ) @ Ys @ ( set2 @ ( list @ A ) @ ( n_lists @ A @ N @ Xs ) ) )
% 0.28/0.47 => ( ( size_size @ ( list @ A ) @ Ys )
% 0.28/0.47 = N ) ) ).
% 0.28/0.47
% 0.28/0.47 % length_n_lists_elem
% 0.28/0.47 thf(fact_217_length__induct,axiom,
% 0.28/0.47 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.28/0.47 ( ! [Xs2: list @ A] :
% 0.28/0.47 ( ! [Ys7: list @ A] :
% 0.28/0.47 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys7 ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 0.28/0.47 => ( P @ Ys7 ) )
% 0.28/0.47 => ( P @ Xs2 ) )
% 0.28/0.47 => ( P @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % length_induct
% 0.28/0.47 thf(fact_218_n__lists__Nil,axiom,
% 0.28/0.47 ! [A: $tType,N: nat] :
% 0.28/0.47 ( ( ( N
% 0.28/0.47 = ( zero_zero @ nat ) )
% 0.28/0.47 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 0.28/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 0.28/0.47 & ( ( N
% 0.28/0.47 != ( zero_zero @ nat ) )
% 0.28/0.47 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 0.28/0.47 = ( nil @ ( list @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % n_lists_Nil
% 0.28/0.47 thf(fact_219_in__measures_I2_J,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Y: A,F: A > nat,Fs: list @ ( A > nat )] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ ( measures @ A @ ( cons @ ( A > nat ) @ F @ Fs ) ) )
% 0.28/0.47 = ( ( ord_less @ nat @ ( F @ X2 ) @ ( F @ Y ) )
% 0.28/0.47 | ( ( ( F @ X2 )
% 0.28/0.47 = ( F @ Y ) )
% 0.28/0.47 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ ( measures @ A @ Fs ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_measures(2)
% 0.28/0.47 thf(fact_220_in__measures_I1_J,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Y: A] :
% 0.28/0.47 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ ( measures @ A @ ( nil @ ( A > nat ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_measures(1)
% 0.28/0.47 thf(fact_221_length__0__conv,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A] :
% 0.28/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 = ( zero_zero @ nat ) )
% 0.28/0.47 = ( Xs
% 0.28/0.47 = ( nil @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % length_0_conv
% 0.28/0.47 thf(fact_222_length__greater__0__conv,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A] :
% 0.28/0.47 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.28/0.47 = ( Xs
% 0.28/0.47 != ( nil @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % length_greater_0_conv
% 0.28/0.47 thf(fact_223_list_Osize_I3_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( size_size @ ( list @ A ) @ ( nil @ A ) )
% 0.28/0.47 = ( zero_zero @ nat ) ) ).
% 0.28/0.47
% 0.28/0.47 % list.size(3)
% 0.28/0.47 thf(fact_224_length__pos__if__in__set,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % length_pos_if_in_set
% 0.28/0.47 thf(fact_225_measures__less,axiom,
% 0.28/0.47 ! [A: $tType,F: A > nat,X2: A,Y: A,Fs: list @ ( A > nat )] :
% 0.28/0.47 ( ( ord_less @ nat @ ( F @ X2 ) @ ( F @ Y ) )
% 0.28/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ ( measures @ A @ ( cons @ ( A > nat ) @ F @ Fs ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % measures_less
% 0.28/0.47 thf(fact_226_n__lists_Osimps_I1_J,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A] :
% 0.28/0.47 ( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs )
% 0.28/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % n_lists.simps(1)
% 0.28/0.47 thf(fact_227_maxvar_Osimps_I1_J,axiom,
% 0.28/0.47 ( ( prover572158330maxvar @ ( nil @ nat ) )
% 0.28/0.47 = ( zero_zero @ nat ) ) ).
% 0.28/0.47
% 0.28/0.47 % maxvar.simps(1)
% 0.28/0.47 thf(fact_228_count__notin,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ~ ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ( ( count_list @ A @ Xs @ X2 )
% 0.28/0.47 = ( zero_zero @ nat ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % count_notin
% 0.28/0.47 thf(fact_229_count__list_Osimps_I1_J,axiom,
% 0.28/0.47 ! [A: $tType,Y: A] :
% 0.28/0.47 ( ( count_list @ A @ ( nil @ A ) @ Y )
% 0.28/0.47 = ( zero_zero @ nat ) ) ).
% 0.28/0.47
% 0.28/0.47 % count_list.simps(1)
% 0.28/0.47 thf(fact_230_length__code,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( size_size @ ( list @ A ) )
% 0.28/0.47 = ( gen_length @ A @ ( zero_zero @ nat ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % length_code
% 0.28/0.47 thf(fact_231_listrel__iff__nth,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ Ys ) @ ( listrel @ A @ B @ R ) )
% 0.28/0.47 = ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 = ( size_size @ ( list @ B ) @ Ys ) )
% 0.28/0.47 & ! [N2: nat] :
% 0.28/0.47 ( ( ord_less @ nat @ N2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.28/0.47 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ ( nth @ A @ Xs @ N2 ) @ ( nth @ B @ Ys @ N2 ) ) @ R ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel_iff_nth
% 0.28/0.47 thf(fact_232_nth__Cons__0,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ( nth @ A @ ( cons @ A @ X2 @ Xs ) @ ( zero_zero @ nat ) )
% 0.28/0.47 = X2 ) ).
% 0.28/0.47
% 0.28/0.47 % nth_Cons_0
% 0.28/0.47 thf(fact_233_nth__append__length,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,X2: A,Ys: list @ A] :
% 0.28/0.47 ( ( nth @ A @ ( append @ A @ Xs @ ( cons @ A @ X2 @ Ys ) ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.28/0.47 = X2 ) ).
% 0.28/0.47
% 0.28/0.47 % nth_append_length
% 0.28/0.47 thf(fact_234_all__set__conv__all__nth,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.28/0.47 ( ( ! [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ( P @ X3 ) ) )
% 0.28/0.47 = ( ! [I: nat] :
% 0.28/0.47 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.28/0.47 => ( P @ ( nth @ A @ Xs @ I ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % all_set_conv_all_nth
% 0.28/0.47 thf(fact_235_all__nth__imp__all__set,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,P: A > $o,X2: A] :
% 0.28/0.47 ( ! [I2: nat] :
% 0.28/0.47 ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.28/0.47 => ( P @ ( nth @ A @ Xs @ I2 ) ) )
% 0.28/0.47 => ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ( P @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % all_nth_imp_all_set
% 0.28/0.47 thf(fact_236_in__set__conv__nth,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.28/0.47 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 = ( ? [I: nat] :
% 0.28/0.47 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.28/0.47 & ( ( nth @ A @ Xs @ I )
% 0.28/0.47 = X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_set_conv_nth
% 0.28/0.47 thf(fact_237_list__ball__nth,axiom,
% 0.28/0.47 ! [A: $tType,N: nat,Xs: list @ A,P: A > $o] :
% 0.28/0.47 ( ( ord_less @ nat @ N @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.28/0.47 => ( ! [X: A] :
% 0.28/0.47 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ( P @ X ) )
% 0.28/0.47 => ( P @ ( nth @ A @ Xs @ N ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_ball_nth
% 0.28/0.47 thf(fact_238_nth__mem,axiom,
% 0.28/0.47 ! [A: $tType,N: nat,Xs: list @ A] :
% 0.28/0.47 ( ( ord_less @ nat @ N @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.28/0.47 => ( member @ A @ ( nth @ A @ Xs @ N ) @ ( set2 @ A @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nth_mem
% 0.28/0.47 thf(fact_239_gen__length__code_I1_J,axiom,
% 0.28/0.47 ! [A: $tType,N: nat] :
% 0.28/0.47 ( ( gen_length @ A @ N @ ( nil @ A ) )
% 0.28/0.47 = N ) ).
% 0.28/0.47
% 0.28/0.47 % gen_length_code(1)
% 0.28/0.47 thf(fact_240_nth__equalityI,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.28/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.28/0.47 => ( ! [I2: nat] :
% 0.28/0.47 ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.28/0.47 => ( ( nth @ A @ Xs @ I2 )
% 0.28/0.47 = ( nth @ A @ Ys @ I2 ) ) )
% 0.28/0.47 => ( Xs = Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nth_equalityI
% 0.28/0.47 thf(fact_241_Skolem__list__nth,axiom,
% 0.28/0.47 ! [A: $tType,K: nat,P: nat > A > $o] :
% 0.28/0.47 ( ( ! [I: nat] :
% 0.28/0.47 ( ( ord_less @ nat @ I @ K )
% 0.28/0.47 => ? [X6: A] : ( P @ I @ X6 ) ) )
% 0.28/0.47 = ( ? [Xs4: list @ A] :
% 0.28/0.47 ( ( ( size_size @ ( list @ A ) @ Xs4 )
% 0.28/0.47 = K )
% 0.28/0.47 & ! [I: nat] :
% 0.28/0.47 ( ( ord_less @ nat @ I @ K )
% 0.28/0.47 => ( P @ I @ ( nth @ A @ Xs4 @ I ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Skolem_list_nth
% 0.28/0.47 thf(fact_242_list__eq__iff__nth__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ^ [Y4: list @ A,Z4: list @ A] : ( Y4 = Z4 ) )
% 0.28/0.47 = ( ^ [Xs4: list @ A,Ys3: list @ A] :
% 0.28/0.47 ( ( ( size_size @ ( list @ A ) @ Xs4 )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Ys3 ) )
% 0.28/0.47 & ! [I: nat] :
% 0.28/0.47 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ A ) @ Xs4 ) )
% 0.28/0.47 => ( ( nth @ A @ Xs4 @ I )
% 0.28/0.47 = ( nth @ A @ Ys3 @ I ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_eq_iff_nth_eq
% 0.28/0.47 thf(fact_243_nth__butlast,axiom,
% 0.28/0.47 ! [A: $tType,N: nat,Xs: list @ A] :
% 0.28/0.47 ( ( ord_less @ nat @ N @ ( size_size @ ( list @ A ) @ ( butlast @ A @ Xs ) ) )
% 0.28/0.47 => ( ( nth @ A @ ( butlast @ A @ Xs ) @ N )
% 0.28/0.47 = ( nth @ A @ Xs @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nth_butlast
% 0.28/0.47 thf(fact_244_listrel1__iff__update,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.28/0.47 = ( ? [Y3: A,N2: nat] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( nth @ A @ Xs @ N2 ) @ Y3 ) @ R )
% 0.28/0.47 & ( ord_less @ nat @ N2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.28/0.47 & ( Ys
% 0.28/0.47 = ( list_update @ A @ Xs @ N2 @ Y3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % listrel1_iff_update
% 0.28/0.47 thf(fact_245_lex__take__index,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( lex @ A @ R ) )
% 0.28/0.47 => ~ ! [I2: nat] :
% 0.28/0.47 ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.28/0.47 => ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Ys ) )
% 0.28/0.47 => ( ( ( take @ A @ I2 @ Xs )
% 0.28/0.47 = ( take @ A @ I2 @ Ys ) )
% 0.28/0.47 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( nth @ A @ Xs @ I2 ) @ ( nth @ A @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lex_take_index
% 0.28/0.47 thf(fact_246_list__update__overwrite,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,I3: nat,X2: A,Y: A] :
% 0.28/0.47 ( ( list_update @ A @ ( list_update @ A @ Xs @ I3 @ X2 ) @ I3 @ Y )
% 0.28/0.47 = ( list_update @ A @ Xs @ I3 @ Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_update_overwrite
% 0.28/0.47 thf(fact_247_list__update__nonempty,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,K: nat,X2: A] :
% 0.28/0.47 ( ( ( list_update @ A @ Xs @ K @ X2 )
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 = ( Xs
% 0.28/0.47 = ( nil @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_update_nonempty
% 0.28/0.47 thf(fact_248_length__list__update,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,I3: nat,X2: A] :
% 0.28/0.47 ( ( size_size @ ( list @ A ) @ ( list_update @ A @ Xs @ I3 @ X2 ) )
% 0.28/0.47 = ( size_size @ ( list @ A ) @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % length_list_update
% 0.28/0.47 thf(fact_249_list__update__id,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,I3: nat] :
% 0.28/0.47 ( ( list_update @ A @ Xs @ I3 @ ( nth @ A @ Xs @ I3 ) )
% 0.28/0.47 = Xs ) ).
% 0.28/0.47
% 0.28/0.47 % list_update_id
% 0.28/0.47 thf(fact_250_nth__list__update__neq,axiom,
% 0.28/0.47 ! [A: $tType,I3: nat,J: nat,Xs: list @ A,X2: A] :
% 0.28/0.47 ( ( I3 != J )
% 0.28/0.47 => ( ( nth @ A @ ( list_update @ A @ Xs @ I3 @ X2 ) @ J )
% 0.28/0.47 = ( nth @ A @ Xs @ J ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nth_list_update_neq
% 0.28/0.47 thf(fact_251_take__eq__Nil,axiom,
% 0.28/0.47 ! [A: $tType,N: nat,Xs: list @ A] :
% 0.28/0.47 ( ( ( take @ A @ N @ Xs )
% 0.28/0.47 = ( nil @ A ) )
% 0.28/0.47 = ( ( N
% 0.28/0.47 = ( zero_zero @ nat ) )
% 0.28/0.47 | ( Xs
% 0.28/0.47 = ( nil @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % take_eq_Nil
% 0.28/0.47 thf(fact_252_take0,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( take @ A @ ( zero_zero @ nat ) )
% 0.28/0.47 = ( ^ [Xs4: list @ A] : ( nil @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % take0
% 0.28/0.47 thf(fact_253_nth__take,axiom,
% 0.28/0.47 ! [A: $tType,I3: nat,N: nat,Xs: list @ A] :
% 0.28/0.47 ( ( ord_less @ nat @ I3 @ N )
% 0.28/0.47 => ( ( nth @ A @ ( take @ A @ N @ Xs ) @ I3 )
% 0.28/0.47 = ( nth @ A @ Xs @ I3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nth_take
% 0.28/0.47 thf(fact_254_list__update__length,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,X2: A,Ys: list @ A,Y: A] :
% 0.28/0.47 ( ( list_update @ A @ ( append @ A @ Xs @ ( cons @ A @ X2 @ Ys ) ) @ ( size_size @ ( list @ A ) @ Xs ) @ Y )
% 0.28/0.47 = ( append @ A @ Xs @ ( cons @ A @ Y @ Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_update_length
% 0.28/0.47
% 0.28/0.47 % Type constructors (6)
% 0.28/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ord @ A9 )
% 0.28/0.47 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.28/0.47 linorder @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Orderings_Oord_1,axiom,
% 0.28/0.47 ord @ nat ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 0.28/0.47 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_3,axiom,
% 0.28/0.47 linorder @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 0.28/0.47 ord @ $o ).
% 0.28/0.47
% 0.28/0.47 % Helper facts (3)
% 0.28/0.47 thf(help_If_3_1_T,axiom,
% 0.28/0.47 ! [P: $o] :
% 0.28/0.47 ( ( P = $true )
% 0.28/0.47 | ( P = $false ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_If_2_1_T,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Y: A] :
% 0.28/0.47 ( ( if @ A @ $false @ X2 @ Y )
% 0.28/0.47 = Y ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_If_1_1_T,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,Y: A] :
% 0.28/0.47 ( ( if @ A @ $true @ X2 @ Y )
% 0.28/0.47 = X2 ) ).
% 0.28/0.47
% 0.28/0.47 % Conjectures (3)
% 0.28/0.47 thf(conj_0,hypothesis,
% 0.28/0.47 ~ ( member @ nat @ u @ ( set2 @ nat @ ( prover_Mirabelle_sfv @ ( cons @ prover2006609834e_form @ ( prover946642470e_FAll @ f ) @ s ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(conj_1,hypothesis,
% 0.28/0.47 ! [A10: set @ prover_Mirabelle_U,B5: nat > ( list @ prover_Mirabelle_U ) > $o,E6: nat > prover_Mirabelle_U] :
% 0.28/0.47 ( ( prover1043414700is_env @ ( product_Pair @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ) @ A10 @ B5 ) @ E6 )
% 0.28/0.47 => ( prover1899965912_SEval @ ( product_Pair @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ) @ A10 @ B5 ) @ E6 @ ( append @ prover2006609834e_form @ s @ ( cons @ prover2006609834e_form @ ( prover48307765_finst @ f @ u ) @ ( nil @ prover2006609834e_form ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(conj_2,conjecture,
% 0.28/0.47 ! [E5: nat > prover_Mirabelle_U] :
% 0.28/0.47 ( ~ ( prover1043414700is_env @ ( product_Pair @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ) @ a @ b ) @ E5 )
% 0.28/0.47 | ( prover1899965912_SEval @ ( product_Pair @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ) @ a @ b ) @ E5 @ ( cons @ prover2006609834e_form @ ( prover946642470e_FAll @ f ) @ s ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 0.31/1.61 ---- Embedded in THF ---
% 0.31/1.61 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.61 %%% Generated on Tue Feb 24 08:28:37 EST 2026
% 0.31/1.61 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.61 %%% Logic specification used:
% 0.31/1.61 %%% thf(spec, logic, $$dhol).
% 0.31/1.61
% 0.31/1.61 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6AU5jlErjD/DTF2DTF12850.p
% 0.31/1.61 thf(ty_t_Prover__Mirabelle__xkffrtyxot_Oform, type, prover2006609834e_form: $tType).
% 0.31/1.61 thf(ty_t_Prover__Mirabelle__xkffrtyxot_OU, type, prover_Mirabelle_U: $tType).
% 0.31/1.61 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 0.31/1.61 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 0.31/1.61 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.31/1.61 thf(ty_t_Nat_Onat, type, nat: $tType).
% 0.31/1.61 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 0.31/1.61 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 0.31/1.61 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 0.31/1.61 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 0.31/1.61 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 0.31/1.61 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 0.31/1.61 thf(sy_c_List_Obind, type, bind: (!> [A:$tType,B:$tType]: (((list @ A) > ((A > (list @ B)) > (list @ B)))))).
% 0.31/1.61 thf(sy_c_List_Obutlast, type, butlast: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 0.31/1.61 thf(sy_c_List_Ocan__select, type, can_select: (!> [A:$tType]: (((A > $o) > ((set @ A) > $o))))).
% 0.31/1.61 thf(sy_c_List_Oconcat, type, concat: (!> [A:$tType]: (((list @ (list @ A)) > (list @ A))))).
% 0.31/1.61 thf(sy_c_List_Ocount__list, type, count_list: (!> [A:$tType]: (((list @ A) > (A > nat))))).
% 0.31/1.61 thf(sy_c_List_Ogen__length, type, gen_length: (!> [A:$tType]: ((nat > ((list @ A) > nat))))).
% 0.31/1.61 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 0.31/1.61 thf(sy_c_List_Olast, type, last: (!> [A:$tType]: (((list @ A) > A)))).
% 0.31/1.61 thf(sy_c_List_Olenlex, type, lenlex: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (list @ A)) @ (list @ A))))))).
% 0.31/1.61 thf(sy_c_List_Olex, type, lex: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (list @ A)) @ (list @ A))))))).
% 0.31/1.61 thf(sy_c_List_Olexord, type, lexord: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (list @ A)) @ (list @ A))))))).
% 0.31/1.61 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 0.31/1.61 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 0.31/1.61 thf(sy_c_List_Olist_Oset, type, set2: (!> [A:$tType]: (((list @ A) > (set @ A))))).
% 0.31/1.61 thf(sy_c_List_Olist__ex1, type, list_ex1: (!> [A:$tType]: (((A > $o) > ((list @ A) > $o))))).
% 0.31/1.61 thf(sy_c_List_Olist__update, type, list_update: (!> [A:$tType]: (((list @ A) > (nat > (A > (list @ A))))))).
% 0.31/1.61 thf(sy_c_List_Olistrel, type, listrel: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ B)) > (set @ ((product_prod @ (list @ A)) @ (list @ B))))))).
% 0.31/1.61 thf(sy_c_List_Olistrel1, type, listrel1: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (list @ A)) @ (list @ A))))))).
% 0.31/1.61 thf(sy_c_List_Omaps, type, maps: (!> [A:$tType,B:$tType]: (((A > (list @ B)) > ((list @ A) > (list @ B)))))).
% 0.31/1.61 thf(sy_c_List_Omeasures, type, measures: (!> [A:$tType]: (((list @ (A > nat)) > (set @ ((product_prod @ A) @ A)))))).
% 0.31/1.61 thf(sy_c_List_On__lists, type, n_lists: (!> [A:$tType]: ((nat > ((list @ A) > (list @ (list @ A))))))).
% 0.31/1.61 thf(sy_c_List_Onth, type, nth: (!> [A:$tType]: (((list @ A) > (nat > A))))).
% 0.31/1.61 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 0.31/1.61 thf(sy_c_List_Orotate1, type, rotate1: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 0.31/1.61 thf(sy_c_List_Osubseqs, type, subseqs: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 0.31/1.61 thf(sy_c_List_Otake, type, take: (!> [A:$tType]: ((nat > ((list @ A) > (list @ A)))))).
% 0.31/1.61 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 0.31/1.61 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 0.31/1.61 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 0.31/1.61 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 0.31/1.61 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 0.31/1.61 thf(sy_c_Prover__Mirabelle__xkffrtyxot_OSEval, type, prover1899965912_SEval: (((product_prod @ (set @ prover_Mirabelle_U)) @ (nat > ((list @ prover_Mirabelle_U) > $o))) > ((nat > prover_Mirabelle_U) > ((list @ prover2006609834e_form) > $o)))).
% 0.31/1.61 thf(sy_c_Prover__Mirabelle__xkffrtyxot_OSvalid, type, prover1090191840Svalid: ((list @ prover2006609834e_form) > $o)).
% 0.31/1.61 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Ofinst, type, prover48307765_finst: (prover2006609834e_form > (nat > prover2006609834e_form))).
% 0.31/1.61 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Oflatten, type, prover12291693latten: (!> [A:$tType]: (((list @ (list @ A)) > (list @ A))))).
% 0.31/1.61 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Oform_OFAll, type, prover946642470e_FAll: (prover2006609834e_form > prover2006609834e_form)).
% 0.31/1.61 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Ofv, type, prover_Mirabelle_fv: (prover2006609834e_form > (list @ nat))).
% 0.31/1.61 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Ois__env, type, prover1043414700is_env: (((product_prod @ (set @ prover_Mirabelle_U)) @ (nat > ((list @ prover_Mirabelle_U) > $o))) > ((nat > prover_Mirabelle_U) > $o))).
% 0.31/1.61 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Omaxvar, type, prover572158330maxvar: ((list @ nat) > nat)).
% 0.31/1.61 thf(sy_c_Prover__Mirabelle__xkffrtyxot_OpreSuc, type, prover1646808149preSuc: ((list @ nat) > (list @ nat))).
% 0.31/1.61 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Osfv, type, prover_Mirabelle_sfv: ((list @ prover2006609834e_form) > (list @ nat))).
% 0.31/1.61 thf(sy_c_Relation_Oirrefl, type, irrefl: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 0.31/1.61 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.31/1.61 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 0.31/1.61 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.31/1.61 thf(sy_v_a, type, a: (set @ prover_Mirabelle_U)).
% 0.31/1.61 thf(sy_v_b, type, b: (nat > ((list @ prover_Mirabelle_U) > $o))).
% 0.31/1.61 thf(sy_v_f, type, f: prover2006609834e_form).
% 0.31/1.61 thf(sy_v_s, type, s: (list @ prover2006609834e_form)).
% 0.31/1.61 thf(sy_v_u, type, u: nat).
% 0.31/1.61 thf(fact_0_form_Oinject_I5_J, axiom, (! [X5:prover2006609834e_form,Y5:prover2006609834e_form]: ((((prover946642470e_FAll @ X5) = (prover946642470e_FAll @ Y5)) = (X5 = Y5))))).
% 0.31/1.61 thf(fact_1_SEval_Osimps_I1_J, axiom, (! [M:((product_prod @ (set @ prover_Mirabelle_U)) @ (nat > ((list @ prover_Mirabelle_U) > $o))),E:(nat > prover_Mirabelle_U)]: ((~ ((((prover1899965912_SEval @ M) @ E) @ (nil @ prover2006609834e_form))))))).
% 0.31/1.61 thf(fact_2_SEval__cong, axiom, (! [S:(list @ prover2006609834e_form),E1:(nat > prover_Mirabelle_U),E2:(nat > prover_Mirabelle_U),M:((product_prod @ (set @ prover_Mirabelle_U)) @ (nat > ((list @ prover_Mirabelle_U) > $o)))]: (((! [X:nat]: (((((member @ nat) @ X) @ ((set2 @ nat) @ (prover_Mirabelle_sfv @ S))) => ((E1 @ X) = (E2 @ X))))) => ((((prover1899965912_SEval @ M) @ E1) @ S) = (((prover1899965912_SEval @ M) @ E2) @ S)))))).
% 0.31/1.61 thf(fact_3_SEval__append, axiom, (! [M:((product_prod @ (set @ prover_Mirabelle_U)) @ (nat > ((list @ prover_Mirabelle_U) > $o))),E:(nat > prover_Mirabelle_U),Xs:(list @ prover2006609834e_form),Ys:(list @ prover2006609834e_form)]: (((((prover1899965912_SEval @ M) @ E) @ (((append @ prover2006609834e_form) @ Xs) @ Ys)) = ((((prover1899965912_SEval @ M) @ E) @ Xs) | (((prover1899965912_SEval @ M) @ E) @ Ys)))))).
% 0.31/1.61 thf(fact_4_sound__FAll, axiom, (! [U:nat,F:prover2006609834e_form,S:(list @ prover2006609834e_form)]: (((~ ((((member @ nat) @ U) @ ((set2 @ nat) @ (prover_Mirabelle_sfv @ (((cons @ prover2006609834e_form) @ (prover946642470e_FAll @ F)) @ S)))))) => ((prover1090191840Svalid @ (((append @ prover2006609834e_form) @ S) @ (((cons @ prover2006609834e_form) @ ((prover48307765_finst @ F) @ U)) @ (nil @ prover2006609834e_form)))) => (prover1090191840Svalid @ (((cons @ prover2006609834e_form) @ (prover946642470e_FAll @ F)) @ S))))))).
% 0.31/1.61 thf(fact_5_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X2:A,Ys:(list @ A),Y:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X2) @ (nil @ A))) = (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = Ys) & (X2 = Y)))))).
% 0.31/1.61 thf(fact_6_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 0.31/1.61 thf(fact_7_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Xs) = (Ys = (nil @ A)))))).
% 0.31/1.61 thf(fact_8_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys)) = (Ys = (nil @ A)))))).
% 0.31/1.61 thf(fact_9_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Ys) = (Xs = (nil @ A)))))).
% 0.31/1.61 thf(fact_10_self__append__conv2, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Xs) @ Ys)) = (Xs = (nil @ A)))))).
% 0.31/1.61 thf(fact_11_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 0.31/1.61 thf(fact_12_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 0.31/1.61 thf(fact_13_append_Oright__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ A2) @ (nil @ A)) = A2)))).
% 0.31/1.61 thf(fact_14_Svalid__def, axiom, (prover1090191840Svalid = (^ [S2:(list @ prover2006609834e_form)]: ((! [MI:((product_prod @ (set @ prover_Mirabelle_U)) @ (nat > ((list @ prover_Mirabelle_U) > $o))),E3:(nat > prover_Mirabelle_U)]: ((((prover1043414700is_env @ MI) @ E3) => (((prover1899965912_SEval @ MI) @ E3) @ S2)))))))).
% 0.31/1.61 thf(fact_15_split__list, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X2) @ Zs))))))))).
% 0.31/1.61 thf(fact_16_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 0.31/1.61 thf(fact_17_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Xs) @ Zs2)) = (Ys = Zs2))))).
% 0.31/1.61 thf(fact_18_append__same__eq, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Ys) @ Xs) = (((append @ A) @ Zs2) @ Xs)) = (Ys = Zs2))))).
% 0.31/1.61 thf(fact_19_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys)) @ Zs2) = (((append @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs2)))))).
% 0.31/1.61 thf(fact_20_append_Oassoc, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A),C2:(list @ A)]: (((((append @ A) @ (((append @ A) @ A2) @ B2)) @ C2) = (((append @ A) @ A2) @ (((append @ A) @ B2) @ C2)))))).
% 0.31/1.61 thf(fact_21_not__Cons__self2, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((cons @ A) @ X2) @ Xs) != Xs)))).
% 0.31/1.61 thf(fact_22_sfv__nil, axiom, ((prover_Mirabelle_sfv @ (nil @ prover2006609834e_form)) = (nil @ nat))).
% 0.31/1.61 thf(fact_23_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs2) @ Ts)) = (? [Us:(list @ A)]: ((((Xs = (((append @ A) @ Zs2) @ Us)) & ((((append @ A) @ Us) @ Ys) = Ts)) | (((((append @ A) @ Xs) @ Us) = Zs2) & (Ys = (((append @ A) @ Us) @ Ts)))))))))).
% 0.31/1.61 thf(fact_24_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs2:(list @ A),Ys:(list @ A),Us2:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs2) => ((Ys = (((append @ A) @ Xs1) @ Us2)) => ((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs2) @ Us2))))))).
% 0.31/1.61 thf(fact_25_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A,Ys2:(list @ A)]: (((P @ Ys2) => (P @ (((cons @ A) @ X) @ Ys2))))) => (P @ A0))))))))).
% 0.31/1.61 thf(fact_26_strict__sorted_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:(list @ A)]: (((X2 != (nil @ A)) => (~ ((! [X:A,Ys2:(list @ A)]: ((X2 != (((cons @ A) @ X) @ Ys2))))))))))))).
% 0.31/1.61 thf(fact_27_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > B),X_1:(list @ B)]: ((((P @ F2) @ (nil @ A)) @ X_1))) => ((! [F2:(A > B),A3:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F2) @ As) @ (((cons @ B) @ (F2 @ A3)) @ Bs)) => (((P @ F2) @ (((cons @ A) @ A3) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 0.31/1.61 thf(fact_28_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X) @ Xs2)))))) => (P @ Xs))))))).
% 0.31/1.61 thf(fact_29_successively_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P2:(A > (A > $o))]: (((P @ P2) @ (nil @ A)))) => ((! [P2:(A > (A > $o)),X:A]: (((P @ P2) @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [P2:(A > (A > $o)),X:A,Y2:A,Xs2:(list @ A)]: ((((P @ P2) @ (((cons @ A) @ Y2) @ Xs2)) => ((P @ P2) @ (((cons @ A) @ X) @ (((cons @ A) @ Y2) @ Xs2)))))) => ((P @ A0) @ A1))))))).
% 0.31/1.61 thf(fact_30_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F2:(A > B),X:A]: (((P @ F2) @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [F2:(A > B),X:A,Y2:A,Zs:(list @ A)]: ((((P @ F2) @ (((cons @ A) @ Y2) @ Zs)) => ((P @ F2) @ (((cons @ A) @ X) @ (((cons @ A) @ Y2) @ Zs)))))) => ((! [A3:(A > B)]: (((P @ A3) @ (nil @ A)))) => ((P @ A0) @ A1)))))))))).
% 0.31/1.61 thf(fact_31_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Y2:A,Xs2:(list @ A)]: ((((X = Y2) => (P @ (((cons @ A) @ X) @ Xs2))) => (((X != Y2) => (P @ (((cons @ A) @ Y2) @ Xs2))) => (P @ (((cons @ A) @ X) @ (((cons @ A) @ Y2) @ Xs2))))))) => (P @ A0))))))).
% 0.31/1.61 thf(fact_32_sorted__wrt_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P2:(A > (A > $o))]: (((P @ P2) @ (nil @ A)))) => ((! [P2:(A > (A > $o)),X:A,Ys2:(list @ A)]: ((((P @ P2) @ Ys2) => ((P @ P2) @ (((cons @ A) @ X) @ Ys2))))) => ((P @ A0) @ A1)))))).
% 0.31/1.61 thf(fact_33_remdups__adj_Ocases, axiom, (! [A:$tType,X2:(list @ A)]: (((X2 != (nil @ A)) => ((! [X:A]: ((X2 != (((cons @ A) @ X) @ (nil @ A))))) => (~ ((! [X:A,Y2:A,Xs2:(list @ A)]: ((X2 != (((cons @ A) @ X) @ (((cons @ A) @ Y2) @ Xs2)))))))))))).
% 0.31/1.61 thf(fact_34_transpose_Ocases, axiom, (! [A:$tType,X2:(list @ (list @ A))]: (((X2 != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X2 != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X2 != (((cons @ (list @ A)) @ (((cons @ A) @ X) @ Xs2)) @ Xss))))))))))).
% 0.31/1.61 thf(fact_35_shuffles_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ A)))) => ((! [X:A,Xs2:(list @ A),Y2:A,Ys2:(list @ A)]: ((((P @ Xs2) @ (((cons @ A) @ Y2) @ Ys2)) => (((P @ (((cons @ A) @ X) @ Xs2)) @ Ys2) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2)))))) => ((P @ A0) @ A1))))))).
% 0.31/1.61 thf(fact_36_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((! [X:A,Xs2:(list @ A)]: (((! [X212:A,X222:(list @ A)]: (((Xs2 = (((cons @ A) @ X212) @ X222)) => (P @ Xs2)))) => (P @ (((cons @ A) @ X) @ Xs2))))) => ((P @ (nil @ A)) => (P @ A0))))))))).
% 0.31/1.61 thf(fact_37_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X2:(list @ A)]: (((! [X:A,Xs2:(list @ A)]: ((X2 != (((cons @ A) @ X) @ Xs2)))) => (X2 = (nil @ A))))))))).
% 0.31/1.61 thf(fact_38_induct__list012, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Y2:A,Zs:(list @ A)]: (((P @ Zs) => ((P @ (((cons @ A) @ Y2) @ Zs)) => (P @ (((cons @ A) @ X) @ (((cons @ A) @ Y2) @ Zs))))))) => (P @ Xs))))))).
% 0.31/1.61 thf(fact_39_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X:A,Xs2:(list @ A),Ys2:(list @ A)]: ((((P @ Ys2) @ Xs2) => ((P @ (((cons @ A) @ X) @ Xs2)) @ Ys2)))) => ((P @ A0) @ A1)))))).
% 0.31/1.61 thf(fact_40_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X) @ Xs2)) @ (nil @ B)))) => ((! [Y2:B,Ys2:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y2) @ Ys2)))) => ((! [X:A,Xs2:(list @ A),Y2:B,Ys2:(list @ B)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys2))))) => ((P @ Xs) @ Ys)))))))).
% 0.31/1.61 thf(fact_41_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y3:A,Ys3:(list @ A)]: ((Xs = (((cons @ A) @ Y3) @ Ys3)))))))).
% 0.31/1.61 thf(fact_42_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X1:A,X23:(list @ A)]: (((P @ X23) => (P @ (((cons @ A) @ X1) @ X23))))) => (P @ List)))))).
% 0.31/1.61 thf(fact_43_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X213:A,X223:(list @ A)]: ((Y != (((cons @ A) @ X213) @ X223)))))))))).
% 0.31/1.61 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 0.31/1.61 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A4)))) = A4)))).
% 0.31/1.61 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X:A]: (((P @ X) = (Q @ X)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.31/1.61 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X:A]: (((F @ X) = (G @ X)))) => (F = G))))).
% 0.31/1.61 thf(fact_48_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 0.31/1.61 thf(fact_49_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 0.31/1.61 thf(fact_50_list_Oset__cases, axiom, (! [A:$tType,E:A,A2:(list @ A)]: (((((member @ A) @ E) @ ((set2 @ A) @ A2)) => ((! [Z2:(list @ A)]: ((A2 != (((cons @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(list @ A)]: (((A2 = (((cons @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ ((set2 @ A) @ Z2)))))))))))))).
% 0.31/1.61 thf(fact_51_set__ConsD, axiom, (! [A:$tType,Y:A,X2:A,Xs:(list @ A)]: (((((member @ A) @ Y) @ ((set2 @ A) @ (((cons @ A) @ X2) @ Xs))) => ((Y = X2) | (((member @ A) @ Y) @ ((set2 @ A) @ Xs))))))).
% 0.31/1.61 thf(fact_52_list_Oset__intros_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((member @ A) @ X21) @ ((set2 @ A) @ (((cons @ A) @ X21) @ X22)))))).
% 0.31/1.61 thf(fact_53_list_Oset__intros_I2_J, axiom, (! [A:$tType,Y:A,X22:(list @ A),X21:A]: (((((member @ A) @ Y) @ ((set2 @ A) @ X22)) => (((member @ A) @ Y) @ ((set2 @ A) @ (((cons @ A) @ X21) @ X22))))))).
% 0.31/1.61 thf(fact_54_append__Cons, axiom, (! [A:$tType,X2:A,Xs:(list @ A),Ys:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X2) @ Xs)) @ Ys) = (((cons @ A) @ X2) @ (((append @ A) @ Xs) @ Ys)))))).
% 0.31/1.61 thf(fact_55_Cons__eq__appendI, axiom, (! [A:$tType,X2:A,Xs1:(list @ A),Ys:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X2) @ Xs1) = Ys) => ((Xs = (((append @ A) @ Xs1) @ Zs2)) => ((((cons @ A) @ X2) @ Xs) = (((append @ A) @ Ys) @ Zs2))))))).
% 0.31/1.61 thf(fact_56_append_Oleft__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ A2) = A2)))).
% 0.31/1.61 thf(fact_57_append__Nil, axiom, (! [A:$tType,Ys:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys) = Ys)))).
% 0.31/1.61 thf(fact_58_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = Ys) => (Xs = (((append @ A) @ (nil @ A)) @ Ys)))))).
% 0.31/1.61 thf(fact_59_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X) @ (nil @ A)))))))) => (P @ Xs))))))).
% 0.31/1.61 thf(fact_60_append__eq__Cons__conv, axiom, (! [A:$tType,Ys:(list @ A),Zs2:(list @ A),X2:A,Xs:(list @ A)]: ((((((append @ A) @ Ys) @ Zs2) = (((cons @ A) @ X2) @ Xs)) = (((Ys = (nil @ A)) & (Zs2 = (((cons @ A) @ X2) @ Xs))) | (? [Ys4:(list @ A)]: (((Ys = (((cons @ A) @ X2) @ Ys4)) & ((((append @ A) @ Ys4) @ Zs2) = Xs))))))))).
% 0.31/1.61 thf(fact_61_Cons__eq__append__conv, axiom, (! [A:$tType,X2:A,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X2) @ Xs) = (((append @ A) @ Ys) @ Zs2)) = (((Ys = (nil @ A)) & ((((cons @ A) @ X2) @ Xs) = Zs2)) | (? [Ys4:(list @ A)]: ((((((cons @ A) @ X2) @ Ys4) = Ys) & (Xs = (((append @ A) @ Ys4) @ Zs2)))))))))).
% 0.31/1.61 thf(fact_62_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys2:(list @ A),Y2:A]: ((Xs != (((append @ A) @ Ys2) @ (((cons @ A) @ Y2) @ (nil @ A)))))))))))).
% 0.31/1.61 thf(fact_63_rev__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X) @ (nil @ A))))))) => (P @ Xs)))))).
% 0.31/1.61 thf(fact_64_split__list__first__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) & (P @ X3)))) = (? [Ys3:(list @ A),X3:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X3) @ Zs3))))) & ((P @ X3) & (! [Y3:A]: (((((member @ A) @ Y3) @ ((set2 @ A) @ Ys3)) => (~ ((P @ Y3)))))))))))))).
% 0.31/1.61 thf(fact_65_split__list__last__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) & (P @ X3)))) = (? [Ys3:(list @ A),X3:A,Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X3) @ Zs3))) & ((P @ X3) & (! [Y3:A]: (((((member @ A) @ Y3) @ ((set2 @ A) @ Zs3)) => (~ ((P @ Y3)))))))))))))).
% 0.31/1.61 thf(fact_66_in__set__conv__decomp__first, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs3))) & (~ ((((member @ A) @ X2) @ ((set2 @ A) @ Ys3))))))))))).
% 0.31/1.61 thf(fact_67_in__set__conv__decomp__last, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs3))) & (~ ((((member @ A) @ X2) @ ((set2 @ A) @ Zs3))))))))))).
% 0.31/1.61 thf(fact_68_split__list__first__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (~ ((! [Ys2:(list @ A),X:A]: (((? [Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))))) => ((P @ X) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys2)) => (~ ((P @ Xa)))))))))))))))))).
% 0.31/1.61 thf(fact_69_split__list__last__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (~ ((! [Ys2:(list @ A),X:A,Zs:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))) => ((P @ X) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs)) => (~ ((P @ Xa)))))))))))))))))).
% 0.31/1.61 thf(fact_70_split__list__first__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (? [Ys2:(list @ A),X:A]: (((? [Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))))) & ((P @ X) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys2)) => (~ ((P @ Xa)))))))))))))).
% 0.31/1.61 thf(fact_71_split__list__last__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (? [Ys2:(list @ A),X:A,Zs:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))) & ((P @ X) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs)) => (~ ((P @ Xa)))))))))))))).
% 0.31/1.61 thf(fact_72_in__set__conv__decomp, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs3))))))))).
% 0.31/1.61 thf(fact_73_append__Cons__eq__iff, axiom, (! [A:$tType,X2:A,Xs:(list @ A),Ys:(list @ A),Xs3:(list @ A),Ys5:(list @ A)]: (((~ ((((member @ A) @ X2) @ ((set2 @ A) @ Xs)))) => ((~ ((((member @ A) @ X2) @ ((set2 @ A) @ Ys)))) => (((((append @ A) @ Xs) @ (((cons @ A) @ X2) @ Ys)) = (((append @ A) @ Xs3) @ (((cons @ A) @ X2) @ Ys5))) = ((Xs = Xs3) & (Ys = Ys5)))))))).
% 0.31/1.61 thf(fact_74_split__list__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (~ ((! [Ys2:(list @ A),X:A]: (((? [Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))))) => (~ ((P @ X)))))))))))).
% 0.31/1.61 thf(fact_75_split__list__first, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X2) @ Zs))) & (~ ((((member @ A) @ X2) @ ((set2 @ A) @ Ys2))))))))))).
% 0.31/1.61 thf(fact_76_split__list__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (? [Ys2:(list @ A),X:A]: (((? [Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))))) & (P @ X)))))))).
% 0.31/1.61 thf(fact_77_split__list__last, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X2) @ Zs))) & (~ ((((member @ A) @ X2) @ ((set2 @ A) @ Zs))))))))))).
% 0.31/1.61 thf(fact_78_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A5:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A5) @ B3)) = ((A2 = A5) & (B2 = B3)))))).
% 0.31/1.61 thf(fact_79_prod_Oinject, axiom, (! [A:$tType,B:$tType,X12:A,X24:B,Y1:A,Y23:B]: (((((((product_Pair @ A) @ B) @ X12) @ X24) = ((((product_Pair @ A) @ B) @ Y1) @ Y23)) = ((X12 = Y1) & (X24 = Y23)))))).
% 0.31/1.61 thf(fact_80_the__elem__set, axiom, (! [A:$tType,X2:A]: ((((the_elem @ A) @ ((set2 @ A) @ (((cons @ A) @ X2) @ (nil @ A)))) = X2)))).
% 0.31/1.61 thf(fact_81_bind__simps_I2_J, axiom, (! [A:$tType,B:$tType,X2:B,Xs:(list @ B),F:(B > (list @ A))]: ((((((bind @ B) @ A) @ (((cons @ B) @ X2) @ Xs)) @ F) = (((append @ A) @ (F @ X2)) @ ((((bind @ B) @ A) @ Xs) @ F)))))).
% 0.31/1.61 thf(fact_82_maps__simps_I1_J, axiom, (! [A:$tType,B:$tType,F:(B > (list @ A)),X2:B,Xs:(list @ B)]: ((((((maps @ B) @ A) @ F) @ (((cons @ B) @ X2) @ Xs)) = (((append @ A) @ (F @ X2)) @ ((((maps @ B) @ A) @ F) @ Xs)))))).
% 0.31/1.61 thf(fact_83_not__in__set__insert, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((~ ((((member @ A) @ X2) @ ((set2 @ A) @ Xs)))) => ((((insert @ A) @ X2) @ Xs) = (((cons @ A) @ X2) @ Xs)))))).
% 0.31/1.61 thf(fact_84_insert__Nil, axiom, (! [A:$tType,X2:A]: (((((insert @ A) @ X2) @ (nil @ A)) = (((cons @ A) @ X2) @ (nil @ A)))))).
% 0.31/1.61 thf(fact_85_sfv__cons, axiom, (! [A2:prover2006609834e_form,List:(list @ prover2006609834e_form)]: (((prover_Mirabelle_sfv @ (((cons @ prover2006609834e_form) @ A2) @ List)) = (((append @ nat) @ (prover_Mirabelle_fv @ A2)) @ (prover_Mirabelle_sfv @ List)))))).
% 0.31/1.61 thf(fact_86_rotate1_Osimps_I2_J, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: ((((rotate1 @ A) @ (((cons @ A) @ X2) @ Xs)) = (((append @ A) @ Xs) @ (((cons @ A) @ X2) @ (nil @ A))))))).
% 0.31/1.61 thf(fact_87_butlast__snoc, axiom, (! [A:$tType,Xs:(list @ A),X2:A]: ((((butlast @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X2) @ (nil @ A)))) = Xs)))).
% 0.31/1.61 thf(fact_88_rotate1__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rotate1 @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 0.31/1.61 thf(fact_89_set__rotate1, axiom, (! [A:$tType,Xs:(list @ A)]: ((((set2 @ A) @ ((rotate1 @ A) @ Xs)) = ((set2 @ A) @ Xs))))).
% 0.31/1.61 thf(fact_90_in__set__insert, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) => ((((insert @ A) @ X2) @ Xs) = Xs))))).
% 0.31/1.61 thf(fact_91_bind__simps_I1_J, axiom, (! [B:$tType,A:$tType,F:(B > (list @ A))]: ((((((bind @ B) @ A) @ (nil @ B)) @ F) = (nil @ A))))).
% 0.31/1.61 thf(fact_92_map__tailrec__rev_Ocases, axiom, (! [A:$tType,B:$tType,X2:((product_prod @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B)))]: (((! [F2:(A > B),Bs:(list @ B)]: ((X2 != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F2) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ Bs))))) => (~ ((! [F2:(A > B),A3:A,As:(list @ A),Bs:(list @ B)]: ((X2 != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F2) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ A3) @ As)) @ Bs))))))))))).
% 0.31/1.61 thf(fact_93_butlast_Osimps_I1_J, axiom, (! [A:$tType]: ((((butlast @ A) @ (nil @ A)) = (nil @ A))))).
% 0.31/1.61 thf(fact_94_in__set__butlastD, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((member @ A) @ X2) @ ((set2 @ A) @ ((butlast @ A) @ Xs))) => (((member @ A) @ X2) @ ((set2 @ A) @ Xs)))))).
% 0.31/1.61 thf(fact_95_rotate1_Osimps_I1_J, axiom, (! [A:$tType]: ((((rotate1 @ A) @ (nil @ A)) = (nil @ A))))).
% 0.31/1.61 thf(fact_96_arg__min__list_Ocases, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [X2:((product_prod @ (A > B)) @ (list @ A))]: (((! [F2:(A > B),X:A]: ((X2 != ((((product_Pair @ (A > B)) @ (list @ A)) @ F2) @ (((cons @ A) @ X) @ (nil @ A)))))) => ((! [F2:(A > B),X:A,Y2:A,Zs:(list @ A)]: ((X2 != ((((product_Pair @ (A > B)) @ (list @ A)) @ F2) @ (((cons @ A) @ X) @ (((cons @ A) @ Y2) @ Zs)))))) => (~ ((! [A3:(A > B)]: ((X2 != ((((product_Pair @ (A > B)) @ (list @ A)) @ A3) @ (nil @ A))))))))))))))).
% 0.31/1.61 thf(fact_97_sorted__wrt_Ocases, axiom, (! [A:$tType,X2:((product_prod @ (A > (A > $o))) @ (list @ A))]: (((! [P2:(A > (A > $o))]: ((X2 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P2) @ (nil @ A))))) => (~ ((! [P2:(A > (A > $o)),X:A,Ys2:(list @ A)]: ((X2 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P2) @ (((cons @ A) @ X) @ Ys2))))))))))).
% 0.31/1.61 thf(fact_98_successively_Ocases, axiom, (! [A:$tType,X2:((product_prod @ (A > (A > $o))) @ (list @ A))]: (((! [P2:(A > (A > $o))]: ((X2 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P2) @ (nil @ A))))) => ((! [P2:(A > (A > $o)),X:A]: ((X2 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P2) @ (((cons @ A) @ X) @ (nil @ A)))))) => (~ ((! [P2:(A > (A > $o)),X:A,Y2:A,Xs2:(list @ A)]: ((X2 != ((((product_Pair @ (A > (A > $o))) @ (list @ A)) @ P2) @ (((cons @ A) @ X) @ (((cons @ A) @ Y2) @ Xs2))))))))))))).
% 0.31/1.61 thf(fact_99_splice_Ocases, axiom, (! [A:$tType,X2:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys2:(list @ A)]: ((X2 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys2)))) => (~ ((! [X:A,Xs2:(list @ A),Ys2:(list @ A)]: ((X2 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X) @ Xs2)) @ Ys2)))))))))).
% 0.31/1.61 thf(fact_100_shuffles_Ocases, axiom, (! [A:$tType,X2:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys2:(list @ A)]: ((X2 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys2)))) => ((! [Xs2:(list @ A)]: ((X2 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs2) @ (nil @ A))))) => (~ ((! [X:A,Xs2:(list @ A),Y2:A,Ys2:(list @ A)]: ((X2 != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2)))))))))))).
% 0.31/1.61 thf(fact_101_list__bind__cong, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),Ys:(list @ A),F:(A > (list @ B)),G:(A > (list @ B))]: (((Xs = Ys) => ((! [X:A]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => ((F @ X) = (G @ X))))) => (((((bind @ A) @ B) @ Xs) @ F) = ((((bind @ A) @ B) @ Ys) @ G))))))).
% 0.31/1.61 thf(fact_102_butlast_Osimps_I2_J, axiom, (! [A:$tType,Xs:(list @ A),X2:A]: ((((Xs = (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X2) @ Xs)) = (nil @ A))) & ((Xs != (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X2) @ Xs)) = (((cons @ A) @ X2) @ ((butlast @ A) @ Xs)))))))).
% 0.31/1.61 thf(fact_103_butlast__append, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: ((((Ys = (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys)) = ((butlast @ A) @ Xs))) & ((Ys != (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ Xs) @ ((butlast @ A) @ Ys)))))))).
% 0.31/1.61 thf(fact_104_in__set__butlast__appendI, axiom, (! [A:$tType,X2:A,Xs:(list @ A),Ys:(list @ A)]: ((((((member @ A) @ X2) @ ((set2 @ A) @ ((butlast @ A) @ Xs))) | (((member @ A) @ X2) @ ((set2 @ A) @ ((butlast @ A) @ Ys)))) => (((member @ A) @ X2) @ ((set2 @ A) @ ((butlast @ A) @ (((append @ A) @ Xs) @ Ys)))))))).
% 0.31/1.61 thf(fact_105_maps__simps_I2_J, axiom, (! [B:$tType,A:$tType,F:(B > (list @ A))]: ((((((maps @ B) @ A) @ F) @ (nil @ B)) = (nil @ A))))).
% 0.31/1.61 thf(fact_106_surj__pair, axiom, (! [A:$tType,B:$tType,P3:((product_prod @ A) @ B)]: ((? [X:A,Y2:B]: ((P3 = ((((product_Pair @ A) @ B) @ X) @ Y2))))))).
% 0.31/1.61 thf(fact_107_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P3:((product_prod @ A) @ B)]: (((! [A3:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A3) @ B4)))) => (P @ P3))))).
% 0.31/1.61 thf(fact_108_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A5:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A5) @ B3)) => (~ (((A2 = A5) => (B2 != B3)))))))).
% 0.31/1.61 thf(fact_109_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A3:A,B4:B,C3:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A3) @ ((((product_Pair @ B) @ C) @ B4) @ C3)))))))))).
% 0.31/1.61 thf(fact_110_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A3:A,B4:B,C3:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C3) @ D2))))))))))).
% 0.31/1.61 thf(fact_111_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E4:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E4))))]: ((~ ((! [A3:A,B4:B,C3:C,D2:D,E5:E4]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E4)))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E4))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E4)) @ C3) @ ((((product_Pair @ D) @ E4) @ D2) @ E5)))))))))))).
% 0.31/1.61 thf(fact_112_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E4:$tType,F3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ F3)))))]: ((~ ((! [A3:A,B4:B,C3:C,D2:D,E5:E4,F2:F3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ F3))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ F3)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ F3))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E4) @ F3)) @ D2) @ ((((product_Pair @ E4) @ F3) @ E5) @ F2))))))))))))).
% 0.31/1.61 thf(fact_113_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E4:$tType,F3:$tType,G2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ ((product_prod @ F3) @ G2))))))]: ((~ ((! [A3:A,B4:B,C3:C,D2:D,E5:E4,F2:F3,G3:G2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ ((product_prod @ F3) @ G2)))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ ((product_prod @ F3) @ G2))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ ((product_prod @ F3) @ G2)))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E4) @ ((product_prod @ F3) @ G2))) @ D2) @ ((((product_Pair @ E4) @ ((product_prod @ F3) @ G2)) @ E5) @ ((((product_Pair @ F3) @ G2) @ F2) @ G3)))))))))))))).
% 0.31/1.61 thf(fact_114_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A3:A,B4:B,C3:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A3) @ ((((product_Pair @ B) @ C) @ B4) @ C3))))) => (P @ X2))))).
% 0.31/1.61 thf(fact_115_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A3:A,B4:B,C3:C,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C3) @ D2)))))) => (P @ X2))))).
% 0.31/1.61 thf(fact_116_prod__induct5, axiom, (! [E4:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E4)))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E4))))]: (((! [A3:A,B4:B,C3:C,D2:D,E5:E4]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E4)))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E4))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E4)) @ C3) @ ((((product_Pair @ D) @ E4) @ D2) @ E5))))))) => (P @ X2))))).
% 0.31/1.61 thf(fact_117_prod__induct6, axiom, (! [F3:$tType,E4:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ F3))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ F3)))))]: (((! [A3:A,B4:B,C3:C,D2:D,E5:E4,F2:F3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ F3))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ F3)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ F3))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E4) @ F3)) @ D2) @ ((((product_Pair @ E4) @ F3) @ E5) @ F2)))))))) => (P @ X2))))).
% 0.31/1.61 thf(fact_118_prod__induct7, axiom, (! [G2:$tType,F3:$tType,E4:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ ((product_prod @ F3) @ G2)))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ ((product_prod @ F3) @ G2))))))]: (((! [A3:A,B4:B,C3:C,D2:D,E5:E4,F2:F3,G3:G2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ ((product_prod @ F3) @ G2)))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ ((product_prod @ F3) @ G2))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E4) @ ((product_prod @ F3) @ G2)))) @ C3) @ ((((product_Pair @ D) @ ((product_prod @ E4) @ ((product_prod @ F3) @ G2))) @ D2) @ ((((product_Pair @ E4) @ ((product_prod @ F3) @ G2)) @ E5) @ ((((product_Pair @ F3) @ G2) @ F2) @ G3))))))))) => (P @ X2))))).
% 0.31/1.61 thf(fact_119_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A3:A,B4:B]: ((Y != ((((product_Pair @ A) @ B) @ A3) @ B4))))))))).
% 0.31/1.61 thf(fact_120_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A3:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A3) @ B4)))) => (P @ Prod))))).
% 0.31/1.61 thf(fact_121_List_Oinsert__def, axiom, (! [A:$tType]: (((insert @ A) = (^ [X3:A,Xs4:(list @ A)]: (((((if @ (list @ A)) @ (((member @ A) @ X3) @ ((set2 @ A) @ Xs4))) @ Xs4) @ (((cons @ A) @ X3) @ Xs4)))))))).
% 0.31/1.61 thf(fact_122_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 0.31/1.61 thf(fact_123_flatten_Osimps_I2_J, axiom, (! [A:$tType,A2:(list @ A),List:(list @ (list @ A))]: ((((prover12291693latten @ A) @ (((cons @ (list @ A)) @ A2) @ List)) = (((append @ A) @ A2) @ ((prover12291693latten @ A) @ List)))))).
% 0.31/1.61 thf(fact_124_flatten_Osimps_I1_J, axiom, (! [A:$tType]: ((((prover12291693latten @ A) @ (nil @ (list @ A))) = (nil @ A))))).
% 0.31/1.61 thf(fact_125_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 0.31/1.61 thf(fact_126_append__butlast__last__id, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((append @ A) @ ((butlast @ A) @ Xs)) @ (((cons @ A) @ ((last @ A) @ Xs)) @ (nil @ A))) = Xs))))).
% 0.31/1.61 thf(fact_127_fv_Osimps_I5_J, axiom, (! [F:prover2006609834e_form]: (((prover_Mirabelle_fv @ (prover946642470e_FAll @ F)) = (prover1646808149preSuc @ (prover_Mirabelle_fv @ F)))))).
% 0.31/1.61 thf(fact_128_last__appendR, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Ys)))))).
% 0.31/1.61 thf(fact_129_last__appendL, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Xs)))))).
% 0.31/1.61 thf(fact_130_last__snoc, axiom, (! [A:$tType,Xs:(list @ A),X2:A]: ((((last @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X2) @ (nil @ A)))) = X2)))).
% 0.31/1.61 thf(fact_131_last__ConsR, axiom, (! [A:$tType,Xs:(list @ A),X2:A]: (((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X2) @ Xs)) = ((last @ A) @ Xs)))))).
% 0.31/1.61 thf(fact_132_last__ConsL, axiom, (! [A:$tType,Xs:(list @ A),X2:A]: (((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X2) @ Xs)) = X2))))).
% 0.31/1.61 thf(fact_133_last_Osimps, axiom, (! [A:$tType,Xs:(list @ A),X2:A]: ((((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X2) @ Xs)) = X2)) & ((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X2) @ Xs)) = ((last @ A) @ Xs))))))).
% 0.31/1.61 thf(fact_134_last__in__set, axiom, (! [A:$tType,As2:(list @ A)]: (((As2 != (nil @ A)) => (((member @ A) @ ((last @ A) @ As2)) @ ((set2 @ A) @ As2)))))).
% 0.31/1.61 thf(fact_135_longest__common__suffix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((? [Ss:(list @ A),Xs5:(list @ A),Ys6:(list @ A)]: (((Xs = (((append @ A) @ Xs5) @ Ss)) & ((Ys = (((append @ A) @ Ys6) @ Ss)) & ((Xs5 = (nil @ A)) | ((Ys6 = (nil @ A)) | (((last @ A) @ Xs5) != ((last @ A) @ Ys6))))))))))).
% 0.31/1.61 thf(fact_136_last__append, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: ((((Ys = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Xs))) & ((Ys != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Ys))))))).
% 0.31/1.61 thf(fact_137_preSuc_Osimps_I1_J, axiom, ((prover1646808149preSuc @ (nil @ nat)) = (nil @ nat))).
% 0.31/1.61 thf(fact_138_snoc__eq__iff__butlast, axiom, (! [A:$tType,Xs:(list @ A),X2:A,Ys:(list @ A)]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X2) @ (nil @ A))) = Ys) = ((Ys != (nil @ A)) & ((((butlast @ A) @ Ys) = Xs) & (((last @ A) @ Ys) = X2))))))).
% 0.31/1.61 thf(fact_139_snoc__listrel1__snoc__iff, axiom, (! [A:$tType,Xs:(list @ A),X2:A,Ys:(list @ A),Y:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ (((cons @ A) @ X2) @ (nil @ A)))) @ (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A))))) @ ((listrel1 @ A) @ R)) = (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((listrel1 @ A) @ R)) & (X2 = Y)) | ((Xs = Ys) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X2) @ Y)) @ R))))))).
% 0.31/1.61 thf(fact_140_subseqs_Osimps_I1_J, axiom, (! [A:$tType]: ((((subseqs @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 0.31/1.61 thf(fact_141_concat__eq__append__conv, axiom, (! [A:$tType,Xss2:(list @ (list @ A)),Ys:(list @ A),Zs2:(list @ A)]: (((((concat @ A) @ Xss2) = (((append @ A) @ Ys) @ Zs2)) = (((Xss2 = (nil @ (list @ A))) => ((Ys = (nil @ A)) & (Zs2 = (nil @ A)))) & ((Xss2 != (nil @ (list @ A))) => (? [Xss1:(list @ (list @ A)),Xs4:(list @ A),Xs6:(list @ A),Xss22:(list @ (list @ A))]: (((Xss2 = (((append @ (list @ A)) @ Xss1) @ (((cons @ (list @ A)) @ (((append @ A) @ Xs4) @ Xs6)) @ Xss22))) & ((Ys = (((append @ A) @ ((concat @ A) @ Xss1)) @ Xs4)) & (Zs2 = (((append @ A) @ Xs6) @ ((concat @ A) @ Xss22))))))))))))).
% 0.31/1.61 thf(fact_142_lexord__same__pref__iff, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ Ys)) @ (((append @ A) @ Xs) @ Zs2))) @ ((lexord @ A) @ R)) = ((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ X3)) @ R)))) | (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys) @ Zs2)) @ ((lexord @ A) @ R))))))).
% 0.31/1.61 thf(fact_143_concat__eq__Nil__conv, axiom, (! [A:$tType,Xss2:(list @ (list @ A))]: (((((concat @ A) @ Xss2) = (nil @ A)) = (! [X3:(list @ A)]: (((((member @ (list @ A)) @ X3) @ ((set2 @ (list @ A)) @ Xss2)) => (X3 = (nil @ A))))))))).
% 0.31/1.61 thf(fact_144_Nil__eq__concat__conv, axiom, (! [A:$tType,Xss2:(list @ (list @ A))]: ((((nil @ A) = ((concat @ A) @ Xss2)) = (! [X3:(list @ A)]: (((((member @ (list @ A)) @ X3) @ ((set2 @ (list @ A)) @ Xss2)) => (X3 = (nil @ A))))))))).
% 0.31/1.61 thf(fact_145_concat__append, axiom, (! [A:$tType,Xs:(list @ (list @ A)),Ys:(list @ (list @ A))]: ((((concat @ A) @ (((append @ (list @ A)) @ Xs) @ Ys)) = (((append @ A) @ ((concat @ A) @ Xs)) @ ((concat @ A) @ Ys)))))).
% 0.31/1.61 thf(fact_146_Cons__listrel1__Cons, axiom, (! [A:$tType,X2:A,Xs:(list @ A),Y:A,Ys:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X2) @ Xs)) @ (((cons @ A) @ Y) @ Ys))) @ ((listrel1 @ A) @ R)) = (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X2) @ Y)) @ R) & (Xs = Ys)) | ((X2 = Y) & (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((listrel1 @ A) @ R)))))))).
% 0.31/1.61 thf(fact_147_lexord__cons__cons, axiom, (! [A:$tType,A2:A,X2:(list @ A),B2:A,Y:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ A2) @ X2)) @ (((cons @ A) @ B2) @ Y))) @ ((lexord @ A) @ R)) = ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R) | ((A2 = B2) & (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X2) @ Y)) @ ((lexord @ A) @ R)))))))).
% 0.31/1.61 thf(fact_148_lexord__Nil__left, axiom, (! [A:$tType,Y:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Y)) @ ((lexord @ A) @ R)) = (? [A6:A,X3:(list @ A)]: ((Y = (((cons @ A) @ A6) @ X3)))))))).
% 0.31/1.61 thf(fact_149_subseqs__refl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((member @ (list @ A)) @ Xs) @ ((set2 @ (list @ A)) @ ((subseqs @ A) @ Xs)))))).
% 0.31/1.61 thf(fact_150_Cons__in__subseqsD, axiom, (! [A:$tType,Y:A,Ys:(list @ A),Xs:(list @ A)]: (((((member @ (list @ A)) @ (((cons @ A) @ Y) @ Ys)) @ ((set2 @ (list @ A)) @ ((subseqs @ A) @ Xs))) => (((member @ (list @ A)) @ Ys) @ ((set2 @ (list @ A)) @ ((subseqs @ A) @ Xs))))))).
% 0.31/1.61 thf(fact_151_listrel1I2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),R:(set @ ((product_prod @ A) @ A)),X2:A]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((listrel1 @ A) @ R)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X2) @ Xs)) @ (((cons @ A) @ X2) @ Ys))) @ ((listrel1 @ A) @ R)))))).
% 0.31/1.61 thf(fact_152_not__listrel1__Nil, axiom, (! [A:$tType,Xs:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ (nil @ A))) @ ((listrel1 @ A) @ R))))))).
% 0.31/1.61 thf(fact_153_not__Nil__listrel1, axiom, (! [A:$tType,Xs:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Xs)) @ ((listrel1 @ A) @ R))))))).
% 0.31/1.61 thf(fact_154_append__listrel1I, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),R:(set @ ((product_prod @ A) @ A)),Us2:(list @ A),Vs:(list @ A)]: (((((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((listrel1 @ A) @ R)) & (Us2 = Vs)) | ((Xs = Ys) & (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Us2) @ Vs)) @ ((listrel1 @ A) @ R)))) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ Us2)) @ (((append @ A) @ Ys) @ Vs))) @ ((listrel1 @ A) @ R)))))).
% 0.31/1.61 thf(fact_155_concat_Osimps_I1_J, axiom, (! [A:$tType]: ((((concat @ A) @ (nil @ (list @ A))) = (nil @ A))))).
% 0.31/1.61 thf(fact_156_lexord__linear, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),X2:(list @ A),Y:(list @ A)]: (((! [A3:A,B4:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A3) @ B4)) @ R) | ((A3 = B4) | (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ B4) @ A3)) @ R))))) => ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X2) @ Y)) @ ((lexord @ A) @ R)) | ((X2 = Y) | (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Y) @ X2)) @ ((lexord @ A) @ R)))))))).
% 0.31/1.61 thf(fact_157_lexord__irreflexive, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A)]: (((! [X:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ X)) @ R))))) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Xs)) @ ((lexord @ A) @ R)))))))).
% 0.31/1.61 thf(fact_158_concat_Osimps_I2_J, axiom, (! [A:$tType,X2:(list @ A),Xs:(list @ (list @ A))]: ((((concat @ A) @ (((cons @ (list @ A)) @ X2) @ Xs)) = (((append @ A) @ X2) @ ((concat @ A) @ Xs)))))).
% 0.31/1.61 thf(fact_159_lexord__Nil__right, axiom, (! [A:$tType,X2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X2) @ (nil @ A))) @ ((lexord @ A) @ R))))))).
% 0.31/1.61 thf(fact_160_lexord__append__leftI, axiom, (! [A:$tType,U:(list @ A),V:(list @ A),R:(set @ ((product_prod @ A) @ A)),X2:(list @ A)]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ U) @ V)) @ ((lexord @ A) @ R)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ X2) @ U)) @ (((append @ A) @ X2) @ V))) @ ((lexord @ A) @ R)))))).
% 0.31/1.61 thf(fact_161_listrel1I1, axiom, (! [A:$tType,X2:A,Y:A,R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X2) @ Y)) @ R) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X2) @ Xs)) @ (((cons @ A) @ Y) @ Xs))) @ ((listrel1 @ A) @ R)))))).
% 0.31/1.61 thf(fact_162_Cons__listrel1E1, axiom, (! [A:$tType,X2:A,Xs:(list @ A),Ys:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X2) @ Xs)) @ Ys)) @ ((listrel1 @ A) @ R)) => ((! [Y2:A]: (((Ys = (((cons @ A) @ Y2) @ Xs)) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X2) @ Y2)) @ R)))))) => (~ ((! [Zs:(list @ A)]: (((Ys = (((cons @ A) @ X2) @ Zs)) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Zs)) @ ((listrel1 @ A) @ R)))))))))))))).
% 0.31/1.61 thf(fact_163_Cons__listrel1E2, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ (((cons @ A) @ Y) @ Ys))) @ ((listrel1 @ A) @ R)) => ((! [X:A]: (((Xs = (((cons @ A) @ X) @ Ys)) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R)))))) => (~ ((! [Zs:(list @ A)]: (((Xs = (((cons @ A) @ Y) @ Zs)) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Zs) @ Ys)) @ ((listrel1 @ A) @ R)))))))))))))).
% 0.31/1.61 thf(fact_164_lexord__partial__trans, axiom, (! [A:$tType,Xs:(list @ A),R:(set @ ((product_prod @ A) @ A)),Ys:(list @ A),Zs2:(list @ A)]: (((! [X:A,Y2:A,Z:A]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y2)) @ R) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y2) @ Z)) @ R) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Z)) @ R)))))) => ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((lexord @ A) @ R)) => ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys) @ Zs2)) @ ((lexord @ A) @ R)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Zs2)) @ ((lexord @ A) @ R)))))))).
% 0.31/1.61 thf(fact_165_lexord__append__leftD, axiom, (! [A:$tType,X2:(list @ A),U:(list @ A),V:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ X2) @ U)) @ (((append @ A) @ X2) @ V))) @ ((lexord @ A) @ R)) => ((! [A3:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A3) @ A3)) @ R))))) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ U) @ V)) @ ((lexord @ A) @ R))))))).
% 0.31/1.61 thf(fact_166_lexord__append__rightI, axiom, (! [A:$tType,Y:(list @ A),X2:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((? [B5:A,Z3:(list @ A)]: ((Y = (((cons @ A) @ B5) @ Z3)))) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X2) @ (((append @ A) @ X2) @ Y))) @ ((lexord @ A) @ R)))))).
% 0.31/1.61 thf(fact_167_concat__eq__appendD, axiom, (! [A:$tType,Xss2:(list @ (list @ A)),Ys:(list @ A),Zs2:(list @ A)]: (((((concat @ A) @ Xss2) = (((append @ A) @ Ys) @ Zs2)) => ((Xss2 != (nil @ (list @ A))) => (? [Xss12:(list @ (list @ A)),Xs2:(list @ A),Xs5:(list @ A),Xss23:(list @ (list @ A))]: (((Xss2 = (((append @ (list @ A)) @ Xss12) @ (((cons @ (list @ A)) @ (((append @ A) @ Xs2) @ Xs5)) @ Xss23))) & ((Ys = (((append @ A) @ ((concat @ A) @ Xss12)) @ Xs2)) & (Zs2 = (((append @ A) @ Xs5) @ ((concat @ A) @ Xss23)))))))))))).
% 0.31/1.61 thf(fact_168_listrel1E, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((listrel1 @ A) @ R)) => (~ ((! [X:A,Y2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y2)) @ R) => (! [Us3:(list @ A),Vs2:(list @ A)]: (((Xs = (((append @ A) @ Us3) @ (((cons @ A) @ X) @ Vs2))) => (Ys != (((append @ A) @ Us3) @ (((cons @ A) @ Y2) @ Vs2))))))))))))))).
% 0.31/1.61 thf(fact_169_listrel1I, axiom, (! [A:$tType,X2:A,Y:A,R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A),Us2:(list @ A),Vs:(list @ A),Ys:(list @ A)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X2) @ Y)) @ R) => ((Xs = (((append @ A) @ Us2) @ (((cons @ A) @ X2) @ Vs))) => ((Ys = (((append @ A) @ Us2) @ (((cons @ A) @ Y) @ Vs))) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((listrel1 @ A) @ R)))))))).
% 0.31/1.61 thf(fact_170_lexord__append__left__rightI, axiom, (! [A:$tType,A2:A,B2:A,R:(set @ ((product_prod @ A) @ A)),U:(list @ A),X2:(list @ A),Y:(list @ A)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ U) @ (((cons @ A) @ A2) @ X2))) @ (((append @ A) @ U) @ (((cons @ A) @ B2) @ Y)))) @ ((lexord @ A) @ R)))))).
% 0.31/1.61 thf(fact_171_lexord__same__pref__if__irrefl, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: ((((irrefl @ A) @ R) => ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ Ys)) @ (((append @ A) @ Xs) @ Zs2))) @ ((lexord @ A) @ R)) = (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys) @ Zs2)) @ ((lexord @ A) @ R))))))).
% 0.31/1.61 thf(fact_172_listrel_Ocases, axiom, (! [B:$tType,A:$tType,A1:(list @ A),A22:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ A1) @ A22)) @ (((listrel @ A) @ B) @ R)) => (((A1 = (nil @ A)) => (A22 != (nil @ B))) => (~ ((! [X:A,Y2:B,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X) @ Xs2)) => (! [Ys2:(list @ B)]: (((A22 = (((cons @ B) @ Y2) @ Ys2)) => ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y2)) @ R) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs2) @ Ys2)) @ (((listrel @ A) @ B) @ R)))))))))))))))))).
% 0.31/1.61 thf(fact_173_listrel_Osimps, axiom, (! [B:$tType,A:$tType,A1:(list @ A),A22:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ A1) @ A22)) @ (((listrel @ A) @ B) @ R)) = (((A1 = (nil @ A)) & (A22 = (nil @ B))) | (? [X3:A,Y3:B,Xs4:(list @ A),Ys3:(list @ B)]: (((A1 = (((cons @ A) @ X3) @ Xs4)) & ((A22 = (((cons @ B) @ Y3) @ Ys3)) & ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ R) & (((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs4) @ Ys3)) @ (((listrel @ A) @ B) @ R)))))))))))).
% 0.31/1.61 thf(fact_174_listrel_Oinducts, axiom, (! [A:$tType,B:$tType,X12:(list @ A),X24:(list @ B),R:(set @ ((product_prod @ A) @ B)),P:((list @ A) > ((list @ B) > $o))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ X12) @ X24)) @ (((listrel @ A) @ B) @ R)) => (((P @ (nil @ A)) @ (nil @ B)) => ((! [X:A,Y2:B,Xs2:(list @ A),Ys2:(list @ B)]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y2)) @ R) => ((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs2) @ Ys2)) @ (((listrel @ A) @ B) @ R)) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys2))))))) => ((P @ X12) @ X24))))))).
% 0.31/1.61 thf(fact_175_lexord__irrefl, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A))]: ((((irrefl @ A) @ R2) => ((irrefl @ (list @ A)) @ ((lexord @ A) @ R2)))))).
% 0.31/1.61 thf(fact_176_listrel_ONil, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B))]: ((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ (nil @ B))) @ (((listrel @ A) @ B) @ R))))).
% 0.31/1.61 thf(fact_177_listrel__Nil1, axiom, (! [A:$tType,B:$tType,Xs:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ Xs)) @ (((listrel @ A) @ B) @ R)) => (Xs = (nil @ B)))))).
% 0.31/1.61 thf(fact_178_listrel__Nil2, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs) @ (nil @ B))) @ (((listrel @ A) @ B) @ R)) => (Xs = (nil @ A)))))).
% 0.31/1.61 thf(fact_179_listrel__Cons2, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),Y:B,Ys:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs) @ (((cons @ B) @ Y) @ Ys))) @ (((listrel @ A) @ B) @ R)) => (~ ((! [X:A,Xs2:(list @ A)]: (((Xs = (((cons @ A) @ X) @ Xs2)) => ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ R) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs2) @ Ys)) @ (((listrel @ A) @ B) @ R)))))))))))))).
% 0.31/1.61 thf(fact_180_listrel__Cons1, axiom, (! [B:$tType,A:$tType,Y:A,Ys:(list @ A),Xs:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ Y) @ Ys)) @ Xs)) @ (((listrel @ A) @ B) @ R)) => (~ ((! [Y2:B,Ys2:(list @ B)]: (((Xs = (((cons @ B) @ Y2) @ Ys2)) => ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ Y) @ Y2)) @ R) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Ys) @ Ys2)) @ (((listrel @ A) @ B) @ R)))))))))))))).
% 0.31/1.61 thf(fact_181_listrel_OCons, axiom, (! [B:$tType,A:$tType,X2:A,Y:B,R:(set @ ((product_prod @ A) @ B)),Xs:(list @ A),Ys:(list @ B)]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y)) @ R) => ((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs) @ Ys)) @ (((listrel @ A) @ B) @ R)) => (((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ X2) @ Xs)) @ (((cons @ B) @ Y) @ Ys))) @ (((listrel @ A) @ B) @ R))))))).
% 0.31/1.61 thf(fact_182_irrefl__def, axiom, (! [A:$tType]: (((irrefl @ A) = (^ [R3:(set @ ((product_prod @ A) @ A))]: ((! [A6:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A6) @ A6)) @ R3))))))))))).
% 0.31/1.61 thf(fact_183_irreflI, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A))]: (((! [A3:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A3) @ A3)) @ R2))))) => ((irrefl @ A) @ R2))))).
% 0.31/1.61 thf(fact_184_lenlex__append2, axiom, (! [A:$tType,R2:(set @ ((product_prod @ A) @ A)),Us2:(list @ A),Xs:(list @ A),Ys:(list @ A)]: ((((irrefl @ A) @ R2) => ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Us2) @ Xs)) @ (((append @ A) @ Us2) @ Ys))) @ ((lenlex @ A) @ R2)) = (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((lenlex @ A) @ R2))))))).
% 0.31/1.61 thf(fact_185_Nil__lenlex__iff1, axiom, (! [A:$tType,Ns:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ns)) @ ((lenlex @ A) @ R)) = (Ns != (nil @ A)))))).
% 0.31/1.61 thf(fact_186_lenlex__irreflexive, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A)]: (((! [X:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ X)) @ R))))) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Xs)) @ ((lenlex @ A) @ R)))))))).
% 0.31/1.61 thf(fact_187_Nil__lenlex__iff2, axiom, (! [A:$tType,Ns:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ns) @ (nil @ A))) @ ((lenlex @ A) @ R))))))).
% 0.31/1.61 thf(fact_188_irrefl__lex, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A))]: ((((irrefl @ A) @ R) => ((irrefl @ (list @ A)) @ ((lex @ A) @ R)))))).
% 0.31/1.61 thf(fact_189_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C2:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C2) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C2 @ A2) @ B2))))).
% 0.31/1.61 thf(fact_190_list__ex1__simps_I1_J, axiom, (! [A:$tType,P:(A > $o)]: ((~ ((((list_ex1 @ A) @ P) @ (nil @ A))))))).
% 0.31/1.61 thf(fact_191_list__ex1__iff, axiom, (! [A:$tType]: (((list_ex1 @ A) = (^ [P4:(A > $o),Xs4:(list @ A)]: ((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs4)) & ((P4 @ X3) & (! [Y3:A]: ((((((member @ A) @ Y3) @ ((set2 @ A) @ Xs4)) & (P4 @ Y3)) => (Y3 = X3)))))))))))))).
% 0.31/1.61 thf(fact_192_Nil__notin__lex, axiom, (! [A:$tType,Ys:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys)) @ ((lex @ A) @ R))))))).
% 0.31/1.61 thf(fact_193_Nil2__notin__lex, axiom, (! [A:$tType,Xs:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ (nil @ A))) @ ((lex @ A) @ R))))))).
% 0.31/1.61 thf(fact_194_lex__append__leftI, axiom, (! [A:$tType,Ys:(list @ A),Zs2:(list @ A),R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A)]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys) @ Zs2)) @ ((lex @ A) @ R)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ Ys)) @ (((append @ A) @ Xs) @ Zs2))) @ ((lex @ A) @ R)))))).
% 0.31/1.61 thf(fact_195_lexl__not__refl, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),X2:(list @ A)]: ((((irrefl @ A) @ R) => (~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X2) @ X2)) @ ((lex @ A) @ R)))))))).
% 0.31/1.61 thf(fact_196_lex__append__left__iff, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: (((! [X:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ X)) @ R))))) => ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ Ys)) @ (((append @ A) @ Xs) @ Zs2))) @ ((lex @ A) @ R)) = (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys) @ Zs2)) @ ((lex @ A) @ R))))))).
% 0.31/1.61 thf(fact_197_lex__append__leftD, axiom, (! [A:$tType,R:(set @ ((product_prod @ A) @ A)),Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: (((! [X:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ X)) @ R))))) => ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ Ys)) @ (((append @ A) @ Xs) @ Zs2))) @ ((lex @ A) @ R)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ys) @ Zs2)) @ ((lex @ A) @ R))))))).
% 0.31/1.61 thf(fact_198_can__select__set__list__ex1, axiom, (! [A:$tType,P:(A > $o),A4:(list @ A)]: (((((can_select @ A) @ P) @ ((set2 @ A) @ A4)) = (((list_ex1 @ A) @ P) @ A4))))).
% 0.31/1.61 thf(fact_199_Cons__in__lex, axiom, (! [A:$tType,X2:A,Xs:(list @ A),Y:A,Ys:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X2) @ Xs)) @ (((cons @ A) @ Y) @ Ys))) @ ((lex @ A) @ R)) = (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X2) @ Y)) @ R) & (((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ A)) @ Ys))) | ((X2 = Y) & (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((lex @ A) @ R)))))))).
% 0.31/1.61 thf(fact_200_append__eq__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Us2:(list @ A),Vs:(list @ A)]: ((((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ A)) @ Ys)) | (((size_size @ (list @ A)) @ Us2) = ((size_size @ (list @ A)) @ Vs))) => (((((append @ A) @ Xs) @ Us2) = (((append @ A) @ Ys) @ Vs)) = ((Xs = Ys) & (Us2 = Vs))))))).
% 0.31/1.61 thf(fact_201_length__rotate1, axiom, (! [A:$tType,Xs:(list @ A)]: ((((size_size @ (list @ A)) @ ((rotate1 @ A) @ Xs)) = ((size_size @ (list @ A)) @ Xs))))).
% 0.31/1.61 thf(fact_202_listrel1__eq__len, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((listrel1 @ A) @ R)) => (((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ A)) @ Ys)))))).
% 0.31/1.61 thf(fact_203_in__set__product__lists__length, axiom, (! [A:$tType,Xs:(list @ A),Xss2:(list @ (list @ A))]: (((((member @ (list @ A)) @ Xs) @ ((set2 @ (list @ A)) @ ((product_lists @ A) @ Xss2))) => (((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ (list @ A))) @ Xss2)))))).
% 0.31/1.61 thf(fact_204_can__select__def, axiom, (! [A:$tType]: (((can_select @ A) = (^ [P4:(A > $o),A7:(set @ A)]: ((? [X3:A]: (((((member @ A) @ X3) @ A7) & ((P4 @ X3) & (! [Y3:A]: ((((((member @ A) @ Y3) @ A7) & (P4 @ Y3)) => (Y3 = X3)))))))))))))).
% 0.31/1.61 thf(fact_205_Ex__list__of__length, axiom, (! [A:$tType,N:nat]: ((? [Xs2:(list @ A)]: ((((size_size @ (list @ A)) @ Xs2) = N)))))).
% 0.31/1.61 thf(fact_206_neq__if__length__neq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) != ((size_size @ (list @ A)) @ Ys)) => (Xs != Ys))))).
% 0.31/1.61 thf(fact_207_list__induct3, axiom, (! [B:$tType,A:$tType,C:$tType,Xs:(list @ A),Ys:(list @ B),Zs2:(list @ C),P:((list @ A) > ((list @ B) > ((list @ C) > $o)))]: (((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ B)) @ Ys)) => ((((size_size @ (list @ B)) @ Ys) = ((size_size @ (list @ C)) @ Zs2)) => ((((P @ (nil @ A)) @ (nil @ B)) @ (nil @ C)) => ((! [X:A,Xs2:(list @ A),Y2:B,Ys2:(list @ B),Z:C,Zs:(list @ C)]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys2)) => ((((size_size @ (list @ B)) @ Ys2) = ((size_size @ (list @ C)) @ Zs)) => ((((P @ Xs2) @ Ys2) @ Zs) => (((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys2)) @ (((cons @ C) @ Z) @ Zs))))))) => (((P @ Xs) @ Ys) @ Zs2)))))))).
% 0.31/1.61 thf(fact_208_list__induct2, axiom, (! [A:$tType,B:$tType,Xs:(list @ A),Ys:(list @ B),P:((list @ A) > ((list @ B) > $o))]: (((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ B)) @ Ys)) => (((P @ (nil @ A)) @ (nil @ B)) => ((! [X:A,Xs2:(list @ A),Y2:B,Ys2:(list @ B)]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys2)) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys2)))))) => ((P @ Xs) @ Ys))))))).
% 0.31/1.61 thf(fact_209_listrel__eq__len, axiom, (! [A:$tType,B:$tType,Xs:(list @ A),Ys:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs) @ Ys)) @ (((listrel @ A) @ B) @ R)) => (((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ B)) @ Ys)))))).
% 0.31/1.61 thf(fact_210_same__length__different, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs != Ys) => ((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ A)) @ Ys)) => (? [Pre:(list @ A),X:A,Xs5:(list @ A),Y2:A,Ys6:(list @ A)]: (((X != Y2) & ((Xs = (((append @ A) @ Pre) @ (((append @ A) @ (((cons @ A) @ X) @ (nil @ A))) @ Xs5))) & (Ys = (((append @ A) @ Pre) @ (((append @ A) @ (((cons @ A) @ Y2) @ (nil @ A))) @ Ys6)))))))))))).
% 0.31/1.61 thf(fact_211_lexord__sufE, axiom, (! [A:$tType,Xs:(list @ A),Zs2:(list @ A),Ys:(list @ A),Qs:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ Zs2)) @ (((append @ A) @ Ys) @ Qs))) @ ((lexord @ A) @ R)) => ((Xs != Ys) => ((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ A)) @ Ys)) => ((((size_size @ (list @ A)) @ Zs2) = ((size_size @ (list @ A)) @ Qs)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((lexord @ A) @ R))))))))).
% 0.31/1.61 thf(fact_212_lex__append__rightI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),R:(set @ ((product_prod @ A) @ A)),Vs:(list @ A),Us2:(list @ A)]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((lex @ A) @ R)) => ((((size_size @ (list @ A)) @ Vs) = ((size_size @ (list @ A)) @ Us2)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ Us2)) @ (((append @ A) @ Ys) @ Vs))) @ ((lex @ A) @ R))))))).
% 0.31/1.61 thf(fact_213_lenlex__append1, axiom, (! [A:$tType,Us2:(list @ A),Xs:(list @ A),R2:(set @ ((product_prod @ A) @ A)),Vs:(list @ A),Ys:(list @ A)]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Us2) @ Xs)) @ ((lenlex @ A) @ R2)) => ((((size_size @ (list @ A)) @ Vs) = ((size_size @ (list @ A)) @ Ys)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Us2) @ Vs)) @ (((append @ A) @ Xs) @ Ys))) @ ((lenlex @ A) @ R2))))))).
% 0.31/1.61 thf(fact_214_lexord__lex, axiom, (! [A:$tType,X2:(list @ A),Y:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X2) @ Y)) @ ((lex @ A) @ R)) = ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ X2) @ Y)) @ ((lexord @ A) @ R)) & (((size_size @ (list @ A)) @ X2) = ((size_size @ (list @ A)) @ Y))))))).
% 0.31/1.61 thf(fact_215_Cons__lenlex__iff, axiom, (! [A:$tType,M:A,Ms:(list @ A),N:A,Ns:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ M) @ Ms)) @ (((cons @ A) @ N) @ Ns))) @ ((lenlex @ A) @ R)) = ((((ord_less @ nat) @ ((size_size @ (list @ A)) @ Ms)) @ ((size_size @ (list @ A)) @ Ns)) | (((((size_size @ (list @ A)) @ Ms) = ((size_size @ (list @ A)) @ Ns)) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ M) @ N)) @ R)) | ((M = N) & (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Ms) @ Ns)) @ ((lenlex @ A) @ R))))))))).
% 0.31/1.61 thf(fact_216_length__n__lists__elem, axiom, (! [A:$tType,Ys:(list @ A),N:nat,Xs:(list @ A)]: (((((member @ (list @ A)) @ Ys) @ ((set2 @ (list @ A)) @ (((n_lists @ A) @ N) @ Xs))) => (((size_size @ (list @ A)) @ Ys) = N))))).
% 0.31/1.61 thf(fact_217_length__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((! [Xs2:(list @ A)]: (((! [Ys7:(list @ A)]: (((((ord_less @ nat) @ ((size_size @ (list @ A)) @ Ys7)) @ ((size_size @ (list @ A)) @ Xs2)) => (P @ Ys7)))) => (P @ Xs2)))) => (P @ Xs))))).
% 0.31/1.61 thf(fact_218_n__lists__Nil, axiom, (! [A:$tType,N:nat]: ((((N = (zero_zero @ nat)) => ((((n_lists @ A) @ N) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))) & ((N != (zero_zero @ nat)) => ((((n_lists @ A) @ N) @ (nil @ A)) = (nil @ (list @ A)))))))).
% 0.31/1.61 thf(fact_219_in__measures_I2_J, axiom, (! [A:$tType,X2:A,Y:A,F:(A > nat),Fs:(list @ (A > nat))]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X2) @ Y)) @ ((measures @ A) @ (((cons @ (A > nat)) @ F) @ Fs))) = ((((ord_less @ nat) @ (F @ X2)) @ (F @ Y)) | (((F @ X2) = (F @ Y)) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X2) @ Y)) @ ((measures @ A) @ Fs)))))))).
% 0.31/1.61 thf(fact_220_in__measures_I1_J, axiom, (! [A:$tType,X2:A,Y:A]: ((~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X2) @ Y)) @ ((measures @ A) @ (nil @ (A > nat))))))))).
% 0.31/1.61 thf(fact_221_length__0__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) = (zero_zero @ nat)) = (Xs = (nil @ A)))))).
% 0.31/1.61 thf(fact_222_length__greater__0__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((size_size @ (list @ A)) @ Xs)) = (Xs != (nil @ A)))))).
% 0.31/1.61 thf(fact_223_list_Osize_I3_J, axiom, (! [A:$tType]: ((((size_size @ (list @ A)) @ (nil @ A)) = (zero_zero @ nat))))).
% 0.31/1.61 thf(fact_224_length__pos__if__in__set, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ ((size_size @ (list @ A)) @ Xs)))))).
% 0.31/1.61 thf(fact_225_measures__less, axiom, (! [A:$tType,F:(A > nat),X2:A,Y:A,Fs:(list @ (A > nat))]: (((((ord_less @ nat) @ (F @ X2)) @ (F @ Y)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X2) @ Y)) @ ((measures @ A) @ (((cons @ (A > nat)) @ F) @ Fs))))))).
% 0.31/1.61 thf(fact_226_n__lists_Osimps_I1_J, axiom, (! [A:$tType,Xs:(list @ A)]: (((((n_lists @ A) @ (zero_zero @ nat)) @ Xs) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 0.31/1.61 thf(fact_227_maxvar_Osimps_I1_J, axiom, ((prover572158330maxvar @ (nil @ nat)) = (zero_zero @ nat))).
% 0.31/1.61 thf(fact_228_count__notin, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((~ ((((member @ A) @ X2) @ ((set2 @ A) @ Xs)))) => ((((count_list @ A) @ Xs) @ X2) = (zero_zero @ nat)))))).
% 0.31/1.61 thf(fact_229_count__list_Osimps_I1_J, axiom, (! [A:$tType,Y:A]: (((((count_list @ A) @ (nil @ A)) @ Y) = (zero_zero @ nat))))).
% 0.31/1.61 thf(fact_230_length__code, axiom, (! [A:$tType]: (((size_size @ (list @ A)) = ((gen_length @ A) @ (zero_zero @ nat)))))).
% 0.31/1.61 thf(fact_231_listrel__iff__nth, axiom, (! [A:$tType,B:$tType,Xs:(list @ A),Ys:(list @ B),R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ B))) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ Xs) @ Ys)) @ (((listrel @ A) @ B) @ R)) = ((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ B)) @ Ys)) & (! [N2:nat]: (((((ord_less @ nat) @ N2) @ ((size_size @ (list @ A)) @ Xs)) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ (((nth @ A) @ Xs) @ N2)) @ (((nth @ B) @ Ys) @ N2))) @ R))))))))).
% 0.31/1.61 thf(fact_232_nth__Cons__0, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((nth @ A) @ (((cons @ A) @ X2) @ Xs)) @ (zero_zero @ nat)) = X2)))).
% 0.31/1.61 thf(fact_233_nth__append__length, axiom, (! [A:$tType,Xs:(list @ A),X2:A,Ys:(list @ A)]: (((((nth @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X2) @ Ys))) @ ((size_size @ (list @ A)) @ Xs)) = X2)))).
% 0.31/1.61 thf(fact_234_all__set__conv__all__nth, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) => (P @ X3)))) = (! [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ A)) @ Xs)) => (P @ (((nth @ A) @ Xs) @ I))))))))).
% 0.31/1.61 thf(fact_235_all__nth__imp__all__set, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o),X2:A]: (((! [I2:nat]: (((((ord_less @ nat) @ I2) @ ((size_size @ (list @ A)) @ Xs)) => (P @ (((nth @ A) @ Xs) @ I2))))) => ((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) => (P @ X2)))))).
% 0.31/1.61 thf(fact_236_in__set__conv__nth, axiom, (! [A:$tType,X2:A,Xs:(list @ A)]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) = (? [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ A)) @ Xs)) & ((((nth @ A) @ Xs) @ I) = X2)))))))).
% 0.31/1.61 thf(fact_237_list__ball__nth, axiom, (! [A:$tType,N:nat,Xs:(list @ A),P:(A > $o)]: (((((ord_less @ nat) @ N) @ ((size_size @ (list @ A)) @ Xs)) => ((! [X:A]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (P @ X)))) => (P @ (((nth @ A) @ Xs) @ N))))))).
% 0.31/1.61 thf(fact_238_nth__mem, axiom, (! [A:$tType,N:nat,Xs:(list @ A)]: (((((ord_less @ nat) @ N) @ ((size_size @ (list @ A)) @ Xs)) => (((member @ A) @ (((nth @ A) @ Xs) @ N)) @ ((set2 @ A) @ Xs)))))).
% 0.31/1.61 thf(fact_239_gen__length__code_I1_J, axiom, (! [A:$tType,N:nat]: (((((gen_length @ A) @ N) @ (nil @ A)) = N)))).
% 0.31/1.61 thf(fact_240_nth__equalityI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ A)) @ Ys)) => ((! [I2:nat]: (((((ord_less @ nat) @ I2) @ ((size_size @ (list @ A)) @ Xs)) => ((((nth @ A) @ Xs) @ I2) = (((nth @ A) @ Ys) @ I2))))) => (Xs = Ys)))))).
% 0.31/1.61 thf(fact_241_Skolem__list__nth, axiom, (! [A:$tType,K:nat,P:(nat > (A > $o))]: (((! [I:nat]: (((((ord_less @ nat) @ I) @ K) => (? [X6:A]: (((P @ I) @ X6)))))) = (? [Xs4:(list @ A)]: (((((size_size @ (list @ A)) @ Xs4) = K) & (! [I:nat]: (((((ord_less @ nat) @ I) @ K) => ((P @ I) @ (((nth @ A) @ Xs4) @ I)))))))))))).
% 0.31/1.61 thf(fact_242_list__eq__iff__nth__eq, axiom, (! [A:$tType]: (((^ [Y4:(list @ A),Z4:(list @ A)]: ((Y4 = Z4))) = (^ [Xs4:(list @ A),Ys3:(list @ A)]: (((((size_size @ (list @ A)) @ Xs4) = ((size_size @ (list @ A)) @ Ys3)) & (! [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ A)) @ Xs4)) => ((((nth @ A) @ Xs4) @ I) = (((nth @ A) @ Ys3) @ I)))))))))))).
% 0.31/1.61 thf(fact_243_nth__butlast, axiom, (! [A:$tType,N:nat,Xs:(list @ A)]: (((((ord_less @ nat) @ N) @ ((size_size @ (list @ A)) @ ((butlast @ A) @ Xs))) => ((((nth @ A) @ ((butlast @ A) @ Xs)) @ N) = (((nth @ A) @ Xs) @ N)))))).
% 0.31/1.61 thf(fact_244_listrel1__iff__update, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((listrel1 @ A) @ R)) = (? [Y3:A,N2:nat]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ (((nth @ A) @ Xs) @ N2)) @ Y3)) @ R) & ((((ord_less @ nat) @ N2) @ ((size_size @ (list @ A)) @ Xs)) & (Ys = ((((list_update @ A) @ Xs) @ N2) @ Y3)))))))))).
% 0.31/1.61 thf(fact_245_lex__take__index, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((lex @ A) @ R)) => (~ ((! [I2:nat]: (((((ord_less @ nat) @ I2) @ ((size_size @ (list @ A)) @ Xs)) => ((((ord_less @ nat) @ I2) @ ((size_size @ (list @ A)) @ Ys)) => (((((take @ A) @ I2) @ Xs) = (((take @ A) @ I2) @ Ys)) => (~ ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ (((nth @ A) @ Xs) @ I2)) @ (((nth @ A) @ Ys) @ I2))) @ R)))))))))))))).
% 0.31/1.61 thf(fact_246_list__update__overwrite, axiom, (! [A:$tType,Xs:(list @ A),I3:nat,X2:A,Y:A]: ((((((list_update @ A) @ ((((list_update @ A) @ Xs) @ I3) @ X2)) @ I3) @ Y) = ((((list_update @ A) @ Xs) @ I3) @ Y))))).
% 0.31/1.61 thf(fact_247_list__update__nonempty, axiom, (! [A:$tType,Xs:(list @ A),K:nat,X2:A]: (((((((list_update @ A) @ Xs) @ K) @ X2) = (nil @ A)) = (Xs = (nil @ A)))))).
% 0.31/1.61 thf(fact_248_length__list__update, axiom, (! [A:$tType,Xs:(list @ A),I3:nat,X2:A]: ((((size_size @ (list @ A)) @ ((((list_update @ A) @ Xs) @ I3) @ X2)) = ((size_size @ (list @ A)) @ Xs))))).
% 0.31/1.61 thf(fact_249_list__update__id, axiom, (! [A:$tType,Xs:(list @ A),I3:nat]: ((((((list_update @ A) @ Xs) @ I3) @ (((nth @ A) @ Xs) @ I3)) = Xs)))).
% 0.31/1.61 thf(fact_250_nth__list__update__neq, axiom, (! [A:$tType,I3:nat,J:nat,Xs:(list @ A),X2:A]: (((I3 != J) => ((((nth @ A) @ ((((list_update @ A) @ Xs) @ I3) @ X2)) @ J) = (((nth @ A) @ Xs) @ J)))))).
% 0.31/1.61 thf(fact_251_take__eq__Nil, axiom, (! [A:$tType,N:nat,Xs:(list @ A)]: ((((((take @ A) @ N) @ Xs) = (nil @ A)) = ((N = (zero_zero @ nat)) | (Xs = (nil @ A))))))).
% 0.31/1.61 thf(fact_252_take0, axiom, (! [A:$tType]: ((((take @ A) @ (zero_zero @ nat)) = (^ [Xs4:(list @ A)]: ((nil @ A))))))).
% 0.31/1.61 thf(fact_253_nth__take, axiom, (! [A:$tType,I3:nat,N:nat,Xs:(list @ A)]: (((((ord_less @ nat) @ I3) @ N) => ((((nth @ A) @ (((take @ A) @ N) @ Xs)) @ I3) = (((nth @ A) @ Xs) @ I3)))))).
% 0.31/1.61 thf(fact_254_list__update__length, axiom, (! [A:$tType,Xs:(list @ A),X2:A,Ys:(list @ A),Y:A]: ((((((list_update @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X2) @ Ys))) @ ((size_size @ (list @ A)) @ Xs)) @ Y) = (((append @ A) @ Xs) @ (((cons @ A) @ Y) @ Ys)))))).
% 0.31/1.61 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 0.31/1.61 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 0.31/1.61 thf(tcon_Nat_Onat___Orderings_Oord_1, axiom, (ord @ nat)).
% 0.31/1.61 thf(tcon_Set_Oset___Orderings_Oord_2, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 0.31/1.61 thf(tcon_HOL_Obool___Orderings_Olinorder_3, axiom, (linorder @ $o)).
% 0.31/1.61 thf(tcon_HOL_Obool___Orderings_Oord_4, axiom, (ord @ $o)).
% 0.31/1.61 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 0.31/1.61 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $false) @ X2) @ Y) = Y)))).
% 0.31/1.61 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $true) @ X2) @ Y) = X2)))).
% 0.31/1.61 thf(conj_0, hypothesis, (~ ((((member @ nat) @ u) @ ((set2 @ nat) @ (prover_Mirabelle_sfv @ (((cons @ prover2006609834e_form) @ (prover946642470e_FAll @ f)) @ s))))))).
% 0.31/1.61 thf(conj_1, hypothesis, (! [A10:(set @ prover_Mirabelle_U),B5:(nat > ((list @ prover_Mirabelle_U) > $o)),E6:(nat > prover_Mirabelle_U)]: ((((prover1043414700is_env @ ((((product_Pair @ (set @ prover_Mirabelle_U)) @ (nat > ((list @ prover_Mirabelle_U) > $o))) @ A10) @ B5)) @ E6) => (((prover1899965912_SEval @ ((((product_Pair @ (set @ prover_Mirabelle_U)) @ (nat > ((list @ prover_Mirabelle_U) > $o))) @ A10) @ B5)) @ E6) @ (((append @ prover2006609834e_form) @ s) @ (((cons @ prover2006609834e_form) @ ((prover48307765_finst @ f) @ u)) @ (nil @ prover2006609834e_form)))))))).
% 0.31/1.61 thf(conj_2, conjecture, (! [E5:(nat > prover_Mirabelle_U)]: (((~ (((prover1043414700is_env @ ((((product_Pair @ (set @ prover_Mirabelle_U)) @ (nat > ((list @ prover_Mirabelle_U) > $o))) @ a) @ b)) @ E5))) | (((prover1899965912_SEval @ ((((product_Pair @ (set @ prover_Mirabelle_U)) @ (nat > ((list @ prover_Mirabelle_U) > $o))) @ a) @ b)) @ E5) @ (((cons @ prover2006609834e_form) @ (prover946642470e_FAll @ f)) @ s)))))).
% 0.31/1.61 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6AU5jlErjD/DTF2DTF12850.p
% 0.31/1.61 ------------------------
% 0.31/1.65 ---- Cleaned THF ---
% 0.31/1.65 thf(ty_t_Prover__Mirabelle__xkffrtyxot_Oform,type,
% 0.31/1.65 prover2006609834e_form: $tType ).
% 0.31/1.65
% 0.31/1.65 thf(ty_t_Prover__Mirabelle__xkffrtyxot_OU,type,
% 0.31/1.65 prover_Mirabelle_U: $tType ).
% 0.31/1.65
% 0.31/1.65 thf(ty_t_Product__Type_Oprod,type,
% 0.31/1.65 product_prod: $tType > $tType > $tType ).
% 0.31/1.65
% 0.31/1.65 thf(ty_t_List_Olist,type,
% 0.31/1.65 list: $tType > $tType ).
% 0.31/1.65
% 0.31/1.65 thf(ty_t_Set_Oset,type,
% 0.31/1.65 set: $tType > $tType ).
% 0.31/1.65
% 0.31/1.65 thf(ty_t_Nat_Onat,type,
% 0.31/1.65 nat: $tType ).
% 0.31/1.65
% 0.31/1.65 thf(sy_cl_HOL_Otype,type,
% 0.31/1.65 type:
% 0.31/1.65 !>[A: $tType] : $o ).
% 0.31/1.65
% 0.31/1.65 thf(sy_cl_Orderings_Oord,type,
% 0.31/1.65 ord:
% 0.31/1.65 !>[A: $tType] : $o ).
% 0.31/1.65
% 0.31/1.65 thf(sy_cl_Orderings_Olinorder,type,
% 0.31/1.65 linorder:
% 0.31/1.65 !>[A: $tType] : $o ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.31/1.65 zero_zero:
% 0.31/1.65 !>[A: $tType] : A ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_If,type,
% 0.31/1.65 if:
% 0.31/1.65 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Oappend,type,
% 0.31/1.65 append:
% 0.31/1.65 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Obind,type,
% 0.31/1.65 bind:
% 0.31/1.65 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Obutlast,type,
% 0.31/1.65 butlast:
% 0.31/1.65 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Ocan__select,type,
% 0.31/1.65 can_select:
% 0.31/1.65 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) > $o ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Oconcat,type,
% 0.31/1.65 concat:
% 0.31/1.65 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Ocount__list,type,
% 0.31/1.65 count_list:
% 0.31/1.65 !>[A: $tType] : ( ( list @ A ) > A > nat ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Ogen__length,type,
% 0.31/1.65 gen_length:
% 0.31/1.65 !>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Oinsert,type,
% 0.31/1.65 insert:
% 0.31/1.65 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Olast,type,
% 0.31/1.65 last:
% 0.31/1.65 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Olenlex,type,
% 0.31/1.65 lenlex:
% 0.31/1.65 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Olex,type,
% 0.31/1.65 lex:
% 0.31/1.65 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Olexord,type,
% 0.31/1.65 lexord:
% 0.31/1.65 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Olist_OCons,type,
% 0.31/1.65 cons:
% 0.31/1.65 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Olist_ONil,type,
% 0.31/1.65 nil:
% 0.31/1.65 !>[A: $tType] : ( list @ A ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Olist_Oset,type,
% 0.31/1.65 set2:
% 0.31/1.65 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Olist__ex1,type,
% 0.31/1.65 list_ex1:
% 0.31/1.65 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Olist__update,type,
% 0.31/1.65 list_update:
% 0.31/1.65 !>[A: $tType] : ( ( list @ A ) > nat > A > ( list @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Olistrel,type,
% 0.31/1.65 listrel:
% 0.31/1.65 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Olistrel1,type,
% 0.31/1.65 listrel1:
% 0.31/1.65 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Omaps,type,
% 0.31/1.65 maps:
% 0.31/1.65 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Omeasures,type,
% 0.31/1.65 measures:
% 0.31/1.65 !>[A: $tType] : ( ( list @ ( A > nat ) ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_On__lists,type,
% 0.31/1.65 n_lists:
% 0.31/1.65 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Onth,type,
% 0.31/1.65 nth:
% 0.31/1.65 !>[A: $tType] : ( ( list @ A ) > nat > A ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Oproduct__lists,type,
% 0.31/1.65 product_lists:
% 0.31/1.65 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Orotate1,type,
% 0.31/1.65 rotate1:
% 0.31/1.65 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Osubseqs,type,
% 0.31/1.65 subseqs:
% 0.31/1.65 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_List_Otake,type,
% 0.31/1.65 take:
% 0.31/1.65 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.31/1.65 size_size:
% 0.31/1.65 !>[A: $tType] : ( A > nat ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.31/1.65 ord_less:
% 0.31/1.65 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Product__Type_OPair,type,
% 0.31/1.65 product_Pair:
% 0.31/1.65 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.31/1.65 produc2004651681e_prod:
% 0.31/1.65 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.31/1.65 product_rec_prod:
% 0.31/1.65 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Prover__Mirabelle__xkffrtyxot_OSEval,type,
% 0.31/1.65 prover1899965912_SEval: ( product_prod @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ) ) > ( nat > prover_Mirabelle_U ) > ( list @ prover2006609834e_form ) > $o ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Prover__Mirabelle__xkffrtyxot_OSvalid,type,
% 0.31/1.65 prover1090191840Svalid: ( list @ prover2006609834e_form ) > $o ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Ofinst,type,
% 0.31/1.65 prover48307765_finst: prover2006609834e_form > nat > prover2006609834e_form ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Oflatten,type,
% 0.31/1.65 prover12291693latten:
% 0.31/1.65 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Oform_OFAll,type,
% 0.31/1.65 prover946642470e_FAll: prover2006609834e_form > prover2006609834e_form ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Ofv,type,
% 0.31/1.65 prover_Mirabelle_fv: prover2006609834e_form > ( list @ nat ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Ois__env,type,
% 0.31/1.65 prover1043414700is_env: ( product_prod @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ) ) > ( nat > prover_Mirabelle_U ) > $o ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Omaxvar,type,
% 0.31/1.65 prover572158330maxvar: ( list @ nat ) > nat ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Prover__Mirabelle__xkffrtyxot_OpreSuc,type,
% 0.31/1.65 prover1646808149preSuc: ( list @ nat ) > ( list @ nat ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Prover__Mirabelle__xkffrtyxot_Osfv,type,
% 0.31/1.65 prover_Mirabelle_sfv: ( list @ prover2006609834e_form ) > ( list @ nat ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Relation_Oirrefl,type,
% 0.31/1.65 irrefl:
% 0.31/1.65 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Set_OCollect,type,
% 0.31/1.65 collect:
% 0.31/1.65 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_Set_Othe__elem,type,
% 0.31/1.65 the_elem:
% 0.31/1.65 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_c_member,type,
% 0.31/1.65 member:
% 0.31/1.65 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/1.65
% 0.31/1.65 thf(sy_v_a,type,
% 0.31/1.65 a: set @ prover_Mirabelle_U ).
% 0.31/1.65
% 0.31/1.65 thf(sy_v_b,type,
% 0.31/1.65 b: nat > ( list @ prover_Mirabelle_U ) > $o ).
% 0.31/1.65
% 0.31/1.65 thf(sy_v_f,type,
% 0.31/1.65 f: prover2006609834e_form ).
% 0.31/1.65
% 0.31/1.65 thf(sy_v_s,type,
% 0.31/1.65 s: list @ prover2006609834e_form ).
% 0.31/1.65
% 0.31/1.65 thf(sy_v_u,type,
% 0.31/1.65 u: nat ).
% 0.31/1.65
% 0.31/1.65 thf(fact_0_form_Oinject_I5_J,axiom,
% 0.31/1.65 ! [X5: prover2006609834e_form,Y5: prover2006609834e_form] :
% 0.31/1.65 ( ( ( prover946642470e_FAll @ X5 )
% 0.31/1.65 = ( prover946642470e_FAll @ Y5 ) )
% 0.31/1.65 = ( X5 = Y5 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_1_SEval_Osimps_I1_J,axiom,
% 0.31/1.65 ! [M: product_prod @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ),E: nat > prover_Mirabelle_U] :
% 0.31/1.65 ~ ( prover1899965912_SEval @ M @ E @ ( nil @ prover2006609834e_form ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_2_SEval__cong,axiom,
% 0.31/1.65 ! [S: list @ prover2006609834e_form,E1: nat > prover_Mirabelle_U,E2: nat > prover_Mirabelle_U,M: product_prod @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o )] :
% 0.31/1.65 ( ! [X: nat] :
% 0.31/1.65 ( ( member @ nat @ X @ ( set2 @ nat @ ( prover_Mirabelle_sfv @ S ) ) )
% 0.31/1.65 => ( ( E1 @ X )
% 0.31/1.65 = ( E2 @ X ) ) )
% 0.31/1.65 => ( ( prover1899965912_SEval @ M @ E1 @ S )
% 0.31/1.65 = ( prover1899965912_SEval @ M @ E2 @ S ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_3_SEval__append,axiom,
% 0.31/1.65 ! [M: product_prod @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ),E: nat > prover_Mirabelle_U,Xs: list @ prover2006609834e_form,Ys: list @ prover2006609834e_form] :
% 0.31/1.65 ( ( prover1899965912_SEval @ M @ E @ ( append @ prover2006609834e_form @ Xs @ Ys ) )
% 0.31/1.65 = ( ( prover1899965912_SEval @ M @ E @ Xs )
% 0.31/1.65 | ( prover1899965912_SEval @ M @ E @ Ys ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_4_sound__FAll,axiom,
% 0.31/1.65 ! [U: nat,F: prover2006609834e_form,S: list @ prover2006609834e_form] :
% 0.31/1.65 ( ~ ( member @ nat @ U @ ( set2 @ nat @ ( prover_Mirabelle_sfv @ ( cons @ prover2006609834e_form @ ( prover946642470e_FAll @ F ) @ S ) ) ) )
% 0.31/1.65 => ( ( prover1090191840Svalid @ ( append @ prover2006609834e_form @ S @ ( cons @ prover2006609834e_form @ ( prover48307765_finst @ F @ U ) @ ( nil @ prover2006609834e_form ) ) ) )
% 0.31/1.65 => ( prover1090191840Svalid @ ( cons @ prover2006609834e_form @ ( prover946642470e_FAll @ F ) @ S ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_5_append1__eq__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,X2: A,Ys: list @ A,Y: A] :
% 0.31/1.65 ( ( ( append @ A @ Xs @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.31/1.65 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.31/1.65 = ( ( Xs = Ys )
% 0.31/1.65 & ( X2 = Y ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_6_append__Nil2,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A] :
% 0.31/1.65 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.31/1.65 = Xs ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_7_append__self__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( ( append @ A @ Xs @ Ys )
% 0.31/1.65 = Xs )
% 0.31/1.65 = ( Ys
% 0.31/1.65 = ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_8_self__append__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( append @ A @ Xs @ Ys ) )
% 0.31/1.65 = ( Ys
% 0.31/1.65 = ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_9_append__self__conv2,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( ( append @ A @ Xs @ Ys )
% 0.31/1.65 = Ys )
% 0.31/1.65 = ( Xs
% 0.31/1.65 = ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_10_self__append__conv2,axiom,
% 0.31/1.65 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.31/1.65 ( ( Ys
% 0.31/1.65 = ( append @ A @ Xs @ Ys ) )
% 0.31/1.65 = ( Xs
% 0.31/1.65 = ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_11_Nil__is__append__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( ( nil @ A )
% 0.31/1.65 = ( append @ A @ Xs @ Ys ) )
% 0.31/1.65 = ( ( Xs
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 & ( Ys
% 0.31/1.65 = ( nil @ A ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_12_append__is__Nil__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( ( append @ A @ Xs @ Ys )
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 = ( ( Xs
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 & ( Ys
% 0.31/1.65 = ( nil @ A ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_13_append_Oright__neutral,axiom,
% 0.31/1.65 ! [A: $tType,A2: list @ A] :
% 0.31/1.65 ( ( append @ A @ A2 @ ( nil @ A ) )
% 0.31/1.65 = A2 ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_14_Svalid__def,axiom,
% 0.31/1.65 ( prover1090191840Svalid
% 0.31/1.65 = ( ^ [S2: list @ prover2006609834e_form] :
% 0.31/1.65 ! [MI: product_prod @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ),E3: nat > prover_Mirabelle_U] :
% 0.31/1.65 ( ( prover1043414700is_env @ MI @ E3 )
% 0.31/1.65 => ( prover1899965912_SEval @ MI @ E3 @ S2 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_15_split__list,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ? [Ys2: list @ A,Zs: list @ A] :
% 0.31/1.65 ( Xs
% 0.31/1.65 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_16_list_Oinject,axiom,
% 0.31/1.65 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.31/1.65 ( ( ( cons @ A @ X21 @ X22 )
% 0.31/1.65 = ( cons @ A @ Y21 @ Y22 ) )
% 0.31/1.65 = ( ( X21 = Y21 )
% 0.31/1.65 & ( X22 = Y22 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_17_same__append__eq,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.31/1.65 ( ( ( append @ A @ Xs @ Ys )
% 0.31/1.65 = ( append @ A @ Xs @ Zs2 ) )
% 0.31/1.65 = ( Ys = Zs2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_18_append__same__eq,axiom,
% 0.31/1.65 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.31/1.65 ( ( ( append @ A @ Ys @ Xs )
% 0.31/1.65 = ( append @ A @ Zs2 @ Xs ) )
% 0.31/1.65 = ( Ys = Zs2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_19_append__assoc,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.31/1.65 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs2 )
% 0.31/1.65 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs2 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_20_append_Oassoc,axiom,
% 0.31/1.65 ! [A: $tType,A2: list @ A,B2: list @ A,C2: list @ A] :
% 0.31/1.65 ( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C2 )
% 0.31/1.65 = ( append @ A @ A2 @ ( append @ A @ B2 @ C2 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_21_not__Cons__self2,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( cons @ A @ X2 @ Xs )
% 0.31/1.65 != Xs ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_22_sfv__nil,axiom,
% 0.31/1.65 ( ( prover_Mirabelle_sfv @ ( nil @ prover2006609834e_form ) )
% 0.31/1.65 = ( nil @ nat ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_23_append__eq__append__conv2,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A,Ts: list @ A] :
% 0.31/1.65 ( ( ( append @ A @ Xs @ Ys )
% 0.31/1.65 = ( append @ A @ Zs2 @ Ts ) )
% 0.31/1.65 = ( ? [Us: list @ A] :
% 0.31/1.65 ( ( ( Xs
% 0.31/1.65 = ( append @ A @ Zs2 @ Us ) )
% 0.31/1.65 & ( ( append @ A @ Us @ Ys )
% 0.31/1.65 = Ts ) )
% 0.31/1.65 | ( ( ( append @ A @ Xs @ Us )
% 0.31/1.65 = Zs2 )
% 0.31/1.65 & ( Ys
% 0.31/1.65 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_24_append__eq__appendI,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys: list @ A,Us2: list @ A] :
% 0.31/1.65 ( ( ( append @ A @ Xs @ Xs1 )
% 0.31/1.65 = Zs2 )
% 0.31/1.65 => ( ( Ys
% 0.31/1.65 = ( append @ A @ Xs1 @ Us2 ) )
% 0.31/1.65 => ( ( append @ A @ Xs @ Ys )
% 0.31/1.65 = ( append @ A @ Zs2 @ Us2 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_25_strict__sorted_Oinduct,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( linorder @ A )
% 0.31/1.65 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.31/1.65 ( ( P @ ( nil @ A ) )
% 0.31/1.65 => ( ! [X: A,Ys2: list @ A] :
% 0.31/1.65 ( ( P @ Ys2 )
% 0.31/1.65 => ( P @ ( cons @ A @ X @ Ys2 ) ) )
% 0.31/1.65 => ( P @ A0 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_26_strict__sorted_Ocases,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( linorder @ A )
% 0.31/1.65 => ! [X2: list @ A] :
% 0.31/1.65 ( ( X2
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ~ ! [X: A,Ys2: list @ A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( cons @ A @ X @ Ys2 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_27_map__tailrec__rev_Oinduct,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.31/1.65 ( ! [F2: A > B,X_1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_1 )
% 0.31/1.65 => ( ! [F2: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 0.31/1.65 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A3 ) @ Bs ) )
% 0.31/1.65 => ( P @ F2 @ ( cons @ A @ A3 @ As ) @ Bs ) )
% 0.31/1.65 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_28_list__nonempty__induct,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.31/1.65 => ( ! [X: A,Xs2: list @ A] :
% 0.31/1.65 ( ( Xs2
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( ( P @ Xs2 )
% 0.31/1.65 => ( P @ ( cons @ A @ X @ Xs2 ) ) ) )
% 0.31/1.65 => ( P @ Xs ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_29_successively_Oinduct,axiom,
% 0.31/1.65 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.31/1.65 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.31/1.65 => ( ! [P2: A > A > $o,X: A] : ( P @ P2 @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.31/1.65 => ( ! [P2: A > A > $o,X: A,Y2: A,Xs2: list @ A] :
% 0.31/1.65 ( ( P @ P2 @ ( cons @ A @ Y2 @ Xs2 ) )
% 0.31/1.65 => ( P @ P2 @ ( cons @ A @ X @ ( cons @ A @ Y2 @ Xs2 ) ) ) )
% 0.31/1.65 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_30_arg__min__list_Oinduct,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType] :
% 0.31/1.65 ( ( linorder @ B )
% 0.31/1.65 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.31/1.65 ( ! [F2: A > B,X: A] : ( P @ F2 @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.31/1.65 => ( ! [F2: A > B,X: A,Y2: A,Zs: list @ A] :
% 0.31/1.65 ( ( P @ F2 @ ( cons @ A @ Y2 @ Zs ) )
% 0.31/1.65 => ( P @ F2 @ ( cons @ A @ X @ ( cons @ A @ Y2 @ Zs ) ) ) )
% 0.31/1.65 => ( ! [A3: A > B] : ( P @ A3 @ ( nil @ A ) )
% 0.31/1.65 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_31_remdups__adj_Oinduct,axiom,
% 0.31/1.65 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.31/1.65 ( ( P @ ( nil @ A ) )
% 0.31/1.65 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.31/1.65 => ( ! [X: A,Y2: A,Xs2: list @ A] :
% 0.31/1.65 ( ( ( X = Y2 )
% 0.31/1.65 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 0.31/1.65 => ( ( ( X != Y2 )
% 0.31/1.65 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 0.31/1.65 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 0.31/1.65 => ( P @ A0 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_32_sorted__wrt_Oinduct,axiom,
% 0.31/1.65 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.31/1.65 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.31/1.65 => ( ! [P2: A > A > $o,X: A,Ys2: list @ A] :
% 0.31/1.65 ( ( P @ P2 @ Ys2 )
% 0.31/1.65 => ( P @ P2 @ ( cons @ A @ X @ Ys2 ) ) )
% 0.31/1.65 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_33_remdups__adj_Ocases,axiom,
% 0.31/1.65 ! [A: $tType,X2: list @ A] :
% 0.31/1.65 ( ( X2
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( ! [X: A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( cons @ A @ X @ ( nil @ A ) ) )
% 0.31/1.65 => ~ ! [X: A,Y2: A,Xs2: list @ A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( cons @ A @ X @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_34_transpose_Ocases,axiom,
% 0.31/1.65 ! [A: $tType,X2: list @ ( list @ A )] :
% 0.31/1.65 ( ( X2
% 0.31/1.65 != ( nil @ ( list @ A ) ) )
% 0.31/1.65 => ( ! [Xss: list @ ( list @ A )] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.31/1.65 => ~ ! [X: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( cons @ ( list @ A ) @ ( cons @ A @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_35_shuffles_Oinduct,axiom,
% 0.31/1.65 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.31/1.65 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.31/1.65 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 0.31/1.65 => ( ! [X: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.31/1.65 ( ( P @ Xs2 @ ( cons @ A @ Y2 @ Ys2 ) )
% 0.31/1.65 => ( ( P @ ( cons @ A @ X @ Xs2 ) @ Ys2 )
% 0.31/1.65 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) )
% 0.31/1.65 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_36_min__list_Oinduct,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( ord @ A )
% 0.31/1.65 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.31/1.65 ( ! [X: A,Xs2: list @ A] :
% 0.31/1.65 ( ! [X212: A,X222: list @ A] :
% 0.31/1.65 ( ( Xs2
% 0.31/1.65 = ( cons @ A @ X212 @ X222 ) )
% 0.31/1.65 => ( P @ Xs2 ) )
% 0.31/1.65 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 0.31/1.65 => ( ( P @ ( nil @ A ) )
% 0.31/1.65 => ( P @ A0 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_37_min__list_Ocases,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( ord @ A )
% 0.31/1.65 => ! [X2: list @ A] :
% 0.31/1.65 ( ! [X: A,Xs2: list @ A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( cons @ A @ X @ Xs2 ) )
% 0.31/1.65 => ( X2
% 0.31/1.65 = ( nil @ A ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_38_induct__list012,axiom,
% 0.31/1.65 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.31/1.65 ( ( P @ ( nil @ A ) )
% 0.31/1.65 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.31/1.65 => ( ! [X: A,Y2: A,Zs: list @ A] :
% 0.31/1.65 ( ( P @ Zs )
% 0.31/1.65 => ( ( P @ ( cons @ A @ Y2 @ Zs ) )
% 0.31/1.65 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y2 @ Zs ) ) ) ) )
% 0.31/1.65 => ( P @ Xs ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_39_splice_Oinduct,axiom,
% 0.31/1.65 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.31/1.65 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.31/1.65 => ( ! [X: A,Xs2: list @ A,Ys2: list @ A] :
% 0.31/1.65 ( ( P @ Ys2 @ Xs2 )
% 0.31/1.65 => ( P @ ( cons @ A @ X @ Xs2 ) @ Ys2 ) )
% 0.31/1.65 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_40_list__induct2_H,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.31/1.65 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.31/1.65 => ( ! [X: A,Xs2: list @ A] : ( P @ ( cons @ A @ X @ Xs2 ) @ ( nil @ B ) )
% 0.31/1.65 => ( ! [Y2: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y2 @ Ys2 ) )
% 0.31/1.65 => ( ! [X: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 0.31/1.65 ( ( P @ Xs2 @ Ys2 )
% 0.31/1.65 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) )
% 0.31/1.65 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_41_neq__Nil__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 = ( ? [Y3: A,Ys3: list @ A] :
% 0.31/1.65 ( Xs
% 0.31/1.65 = ( cons @ A @ Y3 @ Ys3 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_42_list_Oinducts,axiom,
% 0.31/1.65 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.31/1.65 ( ( P @ ( nil @ A ) )
% 0.31/1.65 => ( ! [X1: A,X23: list @ A] :
% 0.31/1.65 ( ( P @ X23 )
% 0.31/1.65 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 0.31/1.65 => ( P @ List ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_43_list_Oexhaust,axiom,
% 0.31/1.65 ! [A: $tType,Y: list @ A] :
% 0.31/1.65 ( ( Y
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ~ ! [X213: A,X223: list @ A] :
% 0.31/1.65 ( Y
% 0.31/1.65 != ( cons @ A @ X213 @ X223 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_44_mem__Collect__eq,axiom,
% 0.31/1.65 ! [A: $tType,A2: A,P: A > $o] :
% 0.31/1.65 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.31/1.65 = ( P @ A2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_45_Collect__mem__eq,axiom,
% 0.31/1.65 ! [A: $tType,A4: set @ A] :
% 0.31/1.65 ( ( collect @ A
% 0.31/1.65 @ ^ [X3: A] : ( member @ A @ X3 @ A4 ) )
% 0.31/1.65 = A4 ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_46_Collect__cong,axiom,
% 0.31/1.65 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.65 ( ! [X: A] :
% 0.31/1.65 ( ( P @ X )
% 0.31/1.65 = ( Q @ X ) )
% 0.31/1.65 => ( ( collect @ A @ P )
% 0.31/1.65 = ( collect @ A @ Q ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_47_ext,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.31/1.65 ( ! [X: A] :
% 0.31/1.65 ( ( F @ X )
% 0.31/1.65 = ( G @ X ) )
% 0.31/1.65 => ( F = G ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_48_list_OdiscI,axiom,
% 0.31/1.65 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.31/1.65 ( ( List
% 0.31/1.65 = ( cons @ A @ X21 @ X22 ) )
% 0.31/1.65 => ( List
% 0.31/1.65 != ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_49_list_Odistinct_I1_J,axiom,
% 0.31/1.65 ! [A: $tType,X21: A,X22: list @ A] :
% 0.31/1.65 ( ( nil @ A )
% 0.31/1.65 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_50_list_Oset__cases,axiom,
% 0.31/1.65 ! [A: $tType,E: A,A2: list @ A] :
% 0.31/1.65 ( ( member @ A @ E @ ( set2 @ A @ A2 ) )
% 0.31/1.65 => ( ! [Z2: list @ A] :
% 0.31/1.65 ( A2
% 0.31/1.65 != ( cons @ A @ E @ Z2 ) )
% 0.31/1.65 => ~ ! [Z1: A,Z2: list @ A] :
% 0.31/1.65 ( ( A2
% 0.31/1.65 = ( cons @ A @ Z1 @ Z2 ) )
% 0.31/1.65 => ~ ( member @ A @ E @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_51_set__ConsD,axiom,
% 0.31/1.65 ! [A: $tType,Y: A,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X2 @ Xs ) ) )
% 0.31/1.65 => ( ( Y = X2 )
% 0.31/1.65 | ( member @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_52_list_Oset__intros_I1_J,axiom,
% 0.31/1.65 ! [A: $tType,X21: A,X22: list @ A] : ( member @ A @ X21 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_53_list_Oset__intros_I2_J,axiom,
% 0.31/1.65 ! [A: $tType,Y: A,X22: list @ A,X21: A] :
% 0.31/1.65 ( ( member @ A @ Y @ ( set2 @ A @ X22 ) )
% 0.31/1.65 => ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_54_append__Cons,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( append @ A @ ( cons @ A @ X2 @ Xs ) @ Ys )
% 0.31/1.65 = ( cons @ A @ X2 @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_55_Cons__eq__appendI,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.31/1.65 ( ( ( cons @ A @ X2 @ Xs1 )
% 0.31/1.65 = Ys )
% 0.31/1.65 => ( ( Xs
% 0.31/1.65 = ( append @ A @ Xs1 @ Zs2 ) )
% 0.31/1.65 => ( ( cons @ A @ X2 @ Xs )
% 0.31/1.65 = ( append @ A @ Ys @ Zs2 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_56_append_Oleft__neutral,axiom,
% 0.31/1.65 ! [A: $tType,A2: list @ A] :
% 0.31/1.65 ( ( append @ A @ ( nil @ A ) @ A2 )
% 0.31/1.65 = A2 ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_57_append__Nil,axiom,
% 0.31/1.65 ! [A: $tType,Ys: list @ A] :
% 0.31/1.65 ( ( append @ A @ ( nil @ A ) @ Ys )
% 0.31/1.65 = Ys ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_58_eq__Nil__appendI,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( Xs = Ys )
% 0.31/1.65 => ( Xs
% 0.31/1.65 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_59_rev__nonempty__induct,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.31/1.65 => ( ! [X: A,Xs2: list @ A] :
% 0.31/1.65 ( ( Xs2
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( ( P @ Xs2 )
% 0.31/1.65 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ) )
% 0.31/1.65 => ( P @ Xs ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_60_append__eq__Cons__conv,axiom,
% 0.31/1.65 ! [A: $tType,Ys: list @ A,Zs2: list @ A,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( ( append @ A @ Ys @ Zs2 )
% 0.31/1.65 = ( cons @ A @ X2 @ Xs ) )
% 0.31/1.65 = ( ( ( Ys
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 & ( Zs2
% 0.31/1.65 = ( cons @ A @ X2 @ Xs ) ) )
% 0.31/1.65 | ? [Ys4: list @ A] :
% 0.31/1.65 ( ( Ys
% 0.31/1.65 = ( cons @ A @ X2 @ Ys4 ) )
% 0.31/1.65 & ( ( append @ A @ Ys4 @ Zs2 )
% 0.31/1.65 = Xs ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_61_Cons__eq__append__conv,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.31/1.65 ( ( ( cons @ A @ X2 @ Xs )
% 0.31/1.65 = ( append @ A @ Ys @ Zs2 ) )
% 0.31/1.65 = ( ( ( Ys
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 & ( ( cons @ A @ X2 @ Xs )
% 0.31/1.65 = Zs2 ) )
% 0.31/1.65 | ? [Ys4: list @ A] :
% 0.31/1.65 ( ( ( cons @ A @ X2 @ Ys4 )
% 0.31/1.65 = Ys )
% 0.31/1.65 & ( Xs
% 0.31/1.65 = ( append @ A @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_62_rev__exhaust,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ~ ! [Ys2: list @ A,Y2: A] :
% 0.31/1.65 ( Xs
% 0.31/1.65 != ( append @ A @ Ys2 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_63_rev__induct,axiom,
% 0.31/1.65 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.31/1.65 ( ( P @ ( nil @ A ) )
% 0.31/1.65 => ( ! [X: A,Xs2: list @ A] :
% 0.31/1.65 ( ( P @ Xs2 )
% 0.31/1.65 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) )
% 0.31/1.65 => ( P @ Xs ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_64_split__list__first__prop__iff,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.31/1.65 ( ( ? [X3: A] :
% 0.31/1.65 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 & ( P @ X3 ) ) )
% 0.31/1.65 = ( ? [Ys3: list @ A,X3: A] :
% 0.31/1.65 ( ? [Zs3: list @ A] :
% 0.31/1.65 ( Xs
% 0.31/1.65 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.31/1.65 & ( P @ X3 )
% 0.31/1.65 & ! [Y3: A] :
% 0.31/1.65 ( ( member @ A @ Y3 @ ( set2 @ A @ Ys3 ) )
% 0.31/1.65 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_65_split__list__last__prop__iff,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.31/1.65 ( ( ? [X3: A] :
% 0.31/1.65 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 & ( P @ X3 ) ) )
% 0.31/1.65 = ( ? [Ys3: list @ A,X3: A,Zs3: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.31/1.65 & ( P @ X3 )
% 0.31/1.65 & ! [Y3: A] :
% 0.31/1.65 ( ( member @ A @ Y3 @ ( set2 @ A @ Zs3 ) )
% 0.31/1.65 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_66_in__set__conv__decomp__first,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 0.31/1.65 & ~ ( member @ A @ X2 @ ( set2 @ A @ Ys3 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_67_in__set__conv__decomp__last,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 0.31/1.65 & ~ ( member @ A @ X2 @ ( set2 @ A @ Zs3 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_68_split__list__first__propE,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.31/1.65 ( ? [X4: A] :
% 0.31/1.65 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 & ( P @ X4 ) )
% 0.31/1.65 => ~ ! [Ys2: list @ A,X: A] :
% 0.31/1.65 ( ? [Zs: list @ A] :
% 0.31/1.65 ( Xs
% 0.31/1.65 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.31/1.65 => ( ( P @ X )
% 0.31/1.65 => ~ ! [Xa: A] :
% 0.31/1.65 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 0.31/1.65 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_69_split__list__last__propE,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.31/1.65 ( ? [X4: A] :
% 0.31/1.65 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 & ( P @ X4 ) )
% 0.31/1.65 => ~ ! [Ys2: list @ A,X: A,Zs: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.31/1.65 => ( ( P @ X )
% 0.31/1.65 => ~ ! [Xa: A] :
% 0.31/1.65 ( ( member @ A @ Xa @ ( set2 @ A @ Zs ) )
% 0.31/1.65 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_70_split__list__first__prop,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.31/1.65 ( ? [X4: A] :
% 0.31/1.65 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 & ( P @ X4 ) )
% 0.31/1.65 => ? [Ys2: list @ A,X: A] :
% 0.31/1.65 ( ? [Zs: list @ A] :
% 0.31/1.65 ( Xs
% 0.31/1.65 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.31/1.65 & ( P @ X )
% 0.31/1.65 & ! [Xa: A] :
% 0.31/1.65 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 0.31/1.65 => ~ ( P @ Xa ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_71_split__list__last__prop,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.31/1.65 ( ? [X4: A] :
% 0.31/1.65 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 & ( P @ X4 ) )
% 0.31/1.65 => ? [Ys2: list @ A,X: A,Zs: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.31/1.65 & ( P @ X )
% 0.31/1.65 & ! [Xa: A] :
% 0.31/1.65 ( ( member @ A @ Xa @ ( set2 @ A @ Zs ) )
% 0.31/1.65 => ~ ( P @ Xa ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_72_in__set__conv__decomp,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 0.31/1.65 ( Xs
% 0.31/1.65 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_73_append__Cons__eq__iff,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A,Ys: list @ A,Xs3: list @ A,Ys5: list @ A] :
% 0.31/1.65 ( ~ ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ( ~ ( member @ A @ X2 @ ( set2 @ A @ Ys ) )
% 0.31/1.65 => ( ( ( append @ A @ Xs @ ( cons @ A @ X2 @ Ys ) )
% 0.31/1.65 = ( append @ A @ Xs3 @ ( cons @ A @ X2 @ Ys5 ) ) )
% 0.31/1.65 = ( ( Xs = Xs3 )
% 0.31/1.65 & ( Ys = Ys5 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_74_split__list__propE,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.31/1.65 ( ? [X4: A] :
% 0.31/1.65 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 & ( P @ X4 ) )
% 0.31/1.65 => ~ ! [Ys2: list @ A,X: A] :
% 0.31/1.65 ( ? [Zs: list @ A] :
% 0.31/1.65 ( Xs
% 0.31/1.65 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.31/1.65 => ~ ( P @ X ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_75_split__list__first,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ? [Ys2: list @ A,Zs: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 0.31/1.65 & ~ ( member @ A @ X2 @ ( set2 @ A @ Ys2 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_76_split__list__prop,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.31/1.65 ( ? [X4: A] :
% 0.31/1.65 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 & ( P @ X4 ) )
% 0.31/1.65 => ? [Ys2: list @ A,X: A] :
% 0.31/1.65 ( ? [Zs: list @ A] :
% 0.31/1.65 ( Xs
% 0.31/1.65 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.31/1.65 & ( P @ X ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_77_split__list__last,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ? [Ys2: list @ A,Zs: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 0.31/1.65 & ~ ( member @ A @ X2 @ ( set2 @ A @ Zs ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_78_old_Oprod_Oinject,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
% 0.31/1.65 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.31/1.65 = ( product_Pair @ A @ B @ A5 @ B3 ) )
% 0.31/1.65 = ( ( A2 = A5 )
% 0.31/1.65 & ( B2 = B3 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_79_prod_Oinject,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,X12: A,X24: B,Y1: A,Y23: B] :
% 0.31/1.65 ( ( ( product_Pair @ A @ B @ X12 @ X24 )
% 0.31/1.65 = ( product_Pair @ A @ B @ Y1 @ Y23 ) )
% 0.31/1.65 = ( ( X12 = Y1 )
% 0.31/1.65 & ( X24 = Y23 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_80_the__elem__set,axiom,
% 0.31/1.65 ! [A: $tType,X2: A] :
% 0.31/1.65 ( ( the_elem @ A @ ( set2 @ A @ ( cons @ A @ X2 @ ( nil @ A ) ) ) )
% 0.31/1.65 = X2 ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_81_bind__simps_I2_J,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,X2: B,Xs: list @ B,F: B > ( list @ A )] :
% 0.31/1.65 ( ( bind @ B @ A @ ( cons @ B @ X2 @ Xs ) @ F )
% 0.31/1.65 = ( append @ A @ ( F @ X2 ) @ ( bind @ B @ A @ Xs @ F ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_82_maps__simps_I1_J,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,F: B > ( list @ A ),X2: B,Xs: list @ B] :
% 0.31/1.65 ( ( maps @ B @ A @ F @ ( cons @ B @ X2 @ Xs ) )
% 0.31/1.65 = ( append @ A @ ( F @ X2 ) @ ( maps @ B @ A @ F @ Xs ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_83_not__in__set__insert,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ~ ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ( ( insert @ A @ X2 @ Xs )
% 0.31/1.65 = ( cons @ A @ X2 @ Xs ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_84_insert__Nil,axiom,
% 0.31/1.65 ! [A: $tType,X2: A] :
% 0.31/1.65 ( ( insert @ A @ X2 @ ( nil @ A ) )
% 0.31/1.65 = ( cons @ A @ X2 @ ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_85_sfv__cons,axiom,
% 0.31/1.65 ! [A2: prover2006609834e_form,List: list @ prover2006609834e_form] :
% 0.31/1.65 ( ( prover_Mirabelle_sfv @ ( cons @ prover2006609834e_form @ A2 @ List ) )
% 0.31/1.65 = ( append @ nat @ ( prover_Mirabelle_fv @ A2 ) @ ( prover_Mirabelle_sfv @ List ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_86_rotate1_Osimps_I2_J,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( rotate1 @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.31/1.65 = ( append @ A @ Xs @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_87_butlast__snoc,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,X2: A] :
% 0.31/1.65 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X2 @ ( nil @ A ) ) ) )
% 0.31/1.65 = Xs ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_88_rotate1__is__Nil__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A] :
% 0.31/1.65 ( ( ( rotate1 @ A @ Xs )
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 = ( Xs
% 0.31/1.65 = ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_89_set__rotate1,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A] :
% 0.31/1.65 ( ( set2 @ A @ ( rotate1 @ A @ Xs ) )
% 0.31/1.65 = ( set2 @ A @ Xs ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_90_in__set__insert,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ( ( insert @ A @ X2 @ Xs )
% 0.31/1.65 = Xs ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_91_bind__simps_I1_J,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.31/1.65 ( ( bind @ B @ A @ ( nil @ B ) @ F )
% 0.31/1.65 = ( nil @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_92_map__tailrec__rev_Ocases,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,X2: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 0.31/1.65 ( ! [F2: A > B,Bs: list @ B] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 0.31/1.65 => ~ ! [F2: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A3 @ As ) @ Bs ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_93_butlast_Osimps_I1_J,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( butlast @ A @ ( nil @ A ) )
% 0.31/1.65 = ( nil @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_94_in__set__butlastD,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( member @ A @ X2 @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 0.31/1.65 => ( member @ A @ X2 @ ( set2 @ A @ Xs ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_95_rotate1_Osimps_I1_J,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( rotate1 @ A @ ( nil @ A ) )
% 0.31/1.65 = ( nil @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_96_arg__min__list_Ocases,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType] :
% 0.31/1.65 ( ( linorder @ B )
% 0.31/1.65 => ! [X2: product_prod @ ( A > B ) @ ( list @ A )] :
% 0.31/1.65 ( ! [F2: A > B,X: A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.31/1.65 => ( ! [F2: A > B,X: A,Y2: A,Zs: list @ A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ F2 @ ( cons @ A @ X @ ( cons @ A @ Y2 @ Zs ) ) ) )
% 0.31/1.65 => ~ ! [A3: A > B] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( A > B ) @ ( list @ A ) @ A3 @ ( nil @ A ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_97_sorted__wrt_Ocases,axiom,
% 0.31/1.65 ! [A: $tType,X2: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.31/1.65 ( ! [P2: A > A > $o] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P2 @ ( nil @ A ) ) )
% 0.31/1.65 => ~ ! [P2: A > A > $o,X: A,Ys2: list @ A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P2 @ ( cons @ A @ X @ Ys2 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_98_successively_Ocases,axiom,
% 0.31/1.65 ! [A: $tType,X2: product_prod @ ( A > A > $o ) @ ( list @ A )] :
% 0.31/1.65 ( ! [P2: A > A > $o] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P2 @ ( nil @ A ) ) )
% 0.31/1.65 => ( ! [P2: A > A > $o,X: A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P2 @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.31/1.65 => ~ ! [P2: A > A > $o,X: A,Y2: A,Xs2: list @ A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( A > A > $o ) @ ( list @ A ) @ P2 @ ( cons @ A @ X @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_99_splice_Ocases,axiom,
% 0.31/1.65 ! [A: $tType,X2: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.31/1.65 ( ! [Ys2: list @ A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys2 ) )
% 0.31/1.65 => ~ ! [X: A,Xs2: list @ A,Ys2: list @ A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs2 ) @ Ys2 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_100_shuffles_Ocases,axiom,
% 0.31/1.65 ! [A: $tType,X2: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.31/1.65 ( ! [Ys2: list @ A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys2 ) )
% 0.31/1.65 => ( ! [Xs2: list @ A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs2 @ ( nil @ A ) ) )
% 0.31/1.65 => ~ ! [X: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.31/1.65 ( X2
% 0.31/1.65 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_101_list__bind__cong,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,Xs: list @ A,Ys: list @ A,F: A > ( list @ B ),G: A > ( list @ B )] :
% 0.31/1.65 ( ( Xs = Ys )
% 0.31/1.65 => ( ! [X: A] :
% 0.31/1.65 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ( ( F @ X )
% 0.31/1.65 = ( G @ X ) ) )
% 0.31/1.65 => ( ( bind @ A @ B @ Xs @ F )
% 0.31/1.65 = ( bind @ A @ B @ Ys @ G ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_102_butlast_Osimps_I2_J,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,X2: A] :
% 0.31/1.65 ( ( ( Xs
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 => ( ( butlast @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.31/1.65 = ( nil @ A ) ) )
% 0.31/1.65 & ( ( Xs
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( ( butlast @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.31/1.65 = ( cons @ A @ X2 @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_103_butlast__append,axiom,
% 0.31/1.65 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.31/1.65 ( ( ( Ys
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.31/1.65 = ( butlast @ A @ Xs ) ) )
% 0.31/1.65 & ( ( Ys
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.31/1.65 = ( append @ A @ Xs @ ( butlast @ A @ Ys ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_104_in__set__butlast__appendI,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( ( member @ A @ X2 @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 0.31/1.65 | ( member @ A @ X2 @ ( set2 @ A @ ( butlast @ A @ Ys ) ) ) )
% 0.31/1.65 => ( member @ A @ X2 @ ( set2 @ A @ ( butlast @ A @ ( append @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_105_maps__simps_I2_J,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.31/1.65 ( ( maps @ B @ A @ F @ ( nil @ B ) )
% 0.31/1.65 = ( nil @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_106_surj__pair,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 0.31/1.65 ? [X: A,Y2: B] :
% 0.31/1.65 ( P3
% 0.31/1.65 = ( product_Pair @ A @ B @ X @ Y2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_107_prod__cases,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 0.31/1.65 ( ! [A3: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A3 @ B4 ) )
% 0.31/1.65 => ( P @ P3 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_108_Pair__inject,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
% 0.31/1.65 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.31/1.65 = ( product_Pair @ A @ B @ A5 @ B3 ) )
% 0.31/1.65 => ~ ( ( A2 = A5 )
% 0.31/1.65 => ( B2 != B3 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_109_prod__cases3,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.31/1.65 ~ ! [A3: A,B4: B,C3: C] :
% 0.31/1.65 ( Y
% 0.31/1.65 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_110_prod__cases4,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.31/1.65 ~ ! [A3: A,B4: B,C3: C,D2: D] :
% 0.31/1.65 ( Y
% 0.31/1.65 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_111_prod__cases5,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,C: $tType,D: $tType,E4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) )] :
% 0.31/1.65 ~ ! [A3: A,B4: B,C3: C,D2: D,E5: E4] :
% 0.31/1.65 ( Y
% 0.31/1.65 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E4 ) @ C3 @ ( product_Pair @ D @ E4 @ D2 @ E5 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_112_prod__cases6,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,C: $tType,D: $tType,E4: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) )] :
% 0.31/1.65 ~ ! [A3: A,B4: B,C3: C,D2: D,E5: E4,F2: F3] :
% 0.31/1.65 ( Y
% 0.31/1.65 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E4 @ F3 ) @ D2 @ ( product_Pair @ E4 @ F3 @ E5 @ F2 ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_113_prod__cases7,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,C: $tType,D: $tType,E4: $tType,F3: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) )] :
% 0.31/1.65 ~ ! [A3: A,B4: B,C3: C,D2: D,E5: E4,F2: F3,G3: G2] :
% 0.31/1.65 ( Y
% 0.31/1.65 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) @ D2 @ ( product_Pair @ E4 @ ( product_prod @ F3 @ G2 ) @ E5 @ ( product_Pair @ F3 @ G2 @ F2 @ G3 ) ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_114_prod__induct3,axiom,
% 0.31/1.65 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.31/1.65 ( ! [A3: A,B4: B,C3: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B4 @ C3 ) ) )
% 0.31/1.65 => ( P @ X2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_115_prod__induct4,axiom,
% 0.31/1.65 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.31/1.65 ( ! [A3: A,B4: B,C3: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C3 @ D2 ) ) ) )
% 0.31/1.65 => ( P @ X2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_116_prod__induct5,axiom,
% 0.31/1.65 ! [E4: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) )] :
% 0.31/1.65 ( ! [A3: A,B4: B,C3: C,D2: D,E5: E4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E4 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E4 ) @ C3 @ ( product_Pair @ D @ E4 @ D2 @ E5 ) ) ) ) )
% 0.31/1.65 => ( P @ X2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_117_prod__induct6,axiom,
% 0.31/1.65 ! [F3: $tType,E4: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) )] :
% 0.31/1.65 ( ! [A3: A,B4: B,C3: C,D2: D,E5: E4,F2: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E4 @ F3 ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E4 @ F3 ) @ D2 @ ( product_Pair @ E4 @ F3 @ E5 @ F2 ) ) ) ) ) )
% 0.31/1.65 => ( P @ X2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_118_prod__induct7,axiom,
% 0.31/1.65 ! [G2: $tType,F3: $tType,E4: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) )] :
% 0.31/1.65 ( ! [A3: A,B4: B,C3: C,D2: D,E5: E4,F2: F3,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) ) @ C3 @ ( product_Pair @ D @ ( product_prod @ E4 @ ( product_prod @ F3 @ G2 ) ) @ D2 @ ( product_Pair @ E4 @ ( product_prod @ F3 @ G2 ) @ E5 @ ( product_Pair @ F3 @ G2 @ F2 @ G3 ) ) ) ) ) ) )
% 0.31/1.65 => ( P @ X2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_119_old_Oprod_Oexhaust,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.31/1.65 ~ ! [A3: A,B4: B] :
% 0.31/1.65 ( Y
% 0.31/1.65 != ( product_Pair @ A @ B @ A3 @ B4 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_120_old_Oprod_Oinducts,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.31/1.65 ( ! [A3: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A3 @ B4 ) )
% 0.31/1.65 => ( P @ Prod ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_121_List_Oinsert__def,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( insert @ A )
% 0.31/1.65 = ( ^ [X3: A,Xs4: list @ A] : ( if @ ( list @ A ) @ ( member @ A @ X3 @ ( set2 @ A @ Xs4 ) ) @ Xs4 @ ( cons @ A @ X3 @ Xs4 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_122_old_Oprod_Orec,axiom,
% 0.31/1.65 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.31/1.65 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.31/1.65 = ( F1 @ A2 @ B2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_123_flatten_Osimps_I2_J,axiom,
% 0.31/1.65 ! [A: $tType,A2: list @ A,List: list @ ( list @ A )] :
% 0.31/1.65 ( ( prover12291693latten @ A @ ( cons @ ( list @ A ) @ A2 @ List ) )
% 0.31/1.65 = ( append @ A @ A2 @ ( prover12291693latten @ A @ List ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_124_flatten_Osimps_I1_J,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( prover12291693latten @ A @ ( nil @ ( list @ A ) ) )
% 0.31/1.65 = ( nil @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_125_product__lists_Osimps_I1_J,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.31/1.65 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_126_append__butlast__last__id,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 0.31/1.65 = Xs ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_127_fv_Osimps_I5_J,axiom,
% 0.31/1.65 ! [F: prover2006609834e_form] :
% 0.31/1.65 ( ( prover_Mirabelle_fv @ ( prover946642470e_FAll @ F ) )
% 0.31/1.65 = ( prover1646808149preSuc @ ( prover_Mirabelle_fv @ F ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_128_last__appendR,axiom,
% 0.31/1.65 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.31/1.65 ( ( Ys
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.31/1.65 = ( last @ A @ Ys ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_129_last__appendL,axiom,
% 0.31/1.65 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.31/1.65 ( ( Ys
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.31/1.65 = ( last @ A @ Xs ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_130_last__snoc,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,X2: A] :
% 0.31/1.65 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X2 @ ( nil @ A ) ) ) )
% 0.31/1.65 = X2 ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_131_last__ConsR,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,X2: A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( ( last @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.31/1.65 = ( last @ A @ Xs ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_132_last__ConsL,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,X2: A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 => ( ( last @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.31/1.65 = X2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_133_last_Osimps,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,X2: A] :
% 0.31/1.65 ( ( ( Xs
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 => ( ( last @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.31/1.65 = X2 ) )
% 0.31/1.65 & ( ( Xs
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( ( last @ A @ ( cons @ A @ X2 @ Xs ) )
% 0.31/1.65 = ( last @ A @ Xs ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_134_last__in__set,axiom,
% 0.31/1.65 ! [A: $tType,As2: list @ A] :
% 0.31/1.65 ( ( As2
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( member @ A @ ( last @ A @ As2 ) @ ( set2 @ A @ As2 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_135_longest__common__suffix,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ? [Ss: list @ A,Xs5: list @ A,Ys6: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( append @ A @ Xs5 @ Ss ) )
% 0.31/1.65 & ( Ys
% 0.31/1.65 = ( append @ A @ Ys6 @ Ss ) )
% 0.31/1.65 & ( ( Xs5
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 | ( Ys6
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 | ( ( last @ A @ Xs5 )
% 0.31/1.65 != ( last @ A @ Ys6 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_136_last__append,axiom,
% 0.31/1.65 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.31/1.65 ( ( ( Ys
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.31/1.65 = ( last @ A @ Xs ) ) )
% 0.31/1.65 & ( ( Ys
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.31/1.65 = ( last @ A @ Ys ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_137_preSuc_Osimps_I1_J,axiom,
% 0.31/1.65 ( ( prover1646808149preSuc @ ( nil @ nat ) )
% 0.31/1.65 = ( nil @ nat ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_138_snoc__eq__iff__butlast,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,X2: A,Ys: list @ A] :
% 0.31/1.65 ( ( ( append @ A @ Xs @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.31/1.65 = Ys )
% 0.31/1.65 = ( ( Ys
% 0.31/1.65 != ( nil @ A ) )
% 0.31/1.65 & ( ( butlast @ A @ Ys )
% 0.31/1.65 = Xs )
% 0.31/1.65 & ( ( last @ A @ Ys )
% 0.31/1.65 = X2 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_139_snoc__listrel1__snoc__iff,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,X2: A,Ys: list @ A,Y: A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) @ ( listrel1 @ A @ R ) )
% 0.31/1.65 = ( ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.31/1.65 & ( X2 = Y ) )
% 0.31/1.65 | ( ( Xs = Ys )
% 0.31/1.65 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ R ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_140_subseqs_Osimps_I1_J,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( subseqs @ A @ ( nil @ A ) )
% 0.31/1.65 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_141_concat__eq__append__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xss2: list @ ( list @ A ),Ys: list @ A,Zs2: list @ A] :
% 0.31/1.65 ( ( ( concat @ A @ Xss2 )
% 0.31/1.65 = ( append @ A @ Ys @ Zs2 ) )
% 0.31/1.65 = ( ( ( Xss2
% 0.31/1.65 = ( nil @ ( list @ A ) ) )
% 0.31/1.65 => ( ( Ys
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 & ( Zs2
% 0.31/1.65 = ( nil @ A ) ) ) )
% 0.31/1.65 & ( ( Xss2
% 0.31/1.65 != ( nil @ ( list @ A ) ) )
% 0.31/1.65 => ? [Xss1: list @ ( list @ A ),Xs4: list @ A,Xs6: list @ A,Xss22: list @ ( list @ A )] :
% 0.31/1.65 ( ( Xss2
% 0.31/1.65 = ( append @ ( list @ A ) @ Xss1 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs4 @ Xs6 ) @ Xss22 ) ) )
% 0.31/1.65 & ( Ys
% 0.31/1.65 = ( append @ A @ ( concat @ A @ Xss1 ) @ Xs4 ) )
% 0.31/1.65 & ( Zs2
% 0.31/1.65 = ( append @ A @ Xs6 @ ( concat @ A @ Xss22 ) ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_142_lexord__same__pref__iff,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs2 ) ) @ ( lexord @ A @ R ) )
% 0.31/1.65 = ( ? [X3: A] :
% 0.31/1.65 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ X3 ) @ R ) )
% 0.31/1.65 | ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys @ Zs2 ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_143_concat__eq__Nil__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xss2: list @ ( list @ A )] :
% 0.31/1.65 ( ( ( concat @ A @ Xss2 )
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 = ( ! [X3: list @ A] :
% 0.31/1.65 ( ( member @ ( list @ A ) @ X3 @ ( set2 @ ( list @ A ) @ Xss2 ) )
% 0.31/1.65 => ( X3
% 0.31/1.65 = ( nil @ A ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_144_Nil__eq__concat__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xss2: list @ ( list @ A )] :
% 0.31/1.65 ( ( ( nil @ A )
% 0.31/1.65 = ( concat @ A @ Xss2 ) )
% 0.31/1.65 = ( ! [X3: list @ A] :
% 0.31/1.65 ( ( member @ ( list @ A ) @ X3 @ ( set2 @ ( list @ A ) @ Xss2 ) )
% 0.31/1.65 => ( X3
% 0.31/1.65 = ( nil @ A ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_145_concat__append,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ ( list @ A ),Ys: list @ ( list @ A )] :
% 0.31/1.65 ( ( concat @ A @ ( append @ ( list @ A ) @ Xs @ Ys ) )
% 0.31/1.65 = ( append @ A @ ( concat @ A @ Xs ) @ ( concat @ A @ Ys ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_146_Cons__listrel1__Cons,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A,Y: A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 @ Xs ) @ ( cons @ A @ Y @ Ys ) ) @ ( listrel1 @ A @ R ) )
% 0.31/1.65 = ( ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ R )
% 0.31/1.65 & ( Xs = Ys ) )
% 0.31/1.65 | ( ( X2 = Y )
% 0.31/1.65 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_147_lexord__cons__cons,axiom,
% 0.31/1.65 ! [A: $tType,A2: A,X2: list @ A,B2: A,Y: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ A2 @ X2 ) @ ( cons @ A @ B2 @ Y ) ) @ ( lexord @ A @ R ) )
% 0.31/1.65 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.31/1.65 | ( ( A2 = B2 )
% 0.31/1.65 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ Y ) @ ( lexord @ A @ R ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_148_lexord__Nil__left,axiom,
% 0.31/1.65 ! [A: $tType,Y: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Y ) @ ( lexord @ A @ R ) )
% 0.31/1.65 = ( ? [A6: A,X3: list @ A] :
% 0.31/1.65 ( Y
% 0.31/1.65 = ( cons @ A @ A6 @ X3 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_149_subseqs__refl,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A] : ( member @ ( list @ A ) @ Xs @ ( set2 @ ( list @ A ) @ ( subseqs @ A @ Xs ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_150_Cons__in__subseqsD,axiom,
% 0.31/1.65 ! [A: $tType,Y: A,Ys: list @ A,Xs: list @ A] :
% 0.31/1.65 ( ( member @ ( list @ A ) @ ( cons @ A @ Y @ Ys ) @ ( set2 @ ( list @ A ) @ ( subseqs @ A @ Xs ) ) )
% 0.31/1.65 => ( member @ ( list @ A ) @ Ys @ ( set2 @ ( list @ A ) @ ( subseqs @ A @ Xs ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_151_listrel1I2,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A ),X2: A] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 @ Xs ) @ ( cons @ A @ X2 @ Ys ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_152_not__listrel1__Nil,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( nil @ A ) ) @ ( listrel1 @ A @ R ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_153_not__Nil__listrel1,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Xs ) @ ( listrel1 @ A @ R ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_154_append__listrel1I,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A ),Us2: list @ A,Vs: list @ A] :
% 0.31/1.65 ( ( ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.31/1.65 & ( Us2 = Vs ) )
% 0.31/1.65 | ( ( Xs = Ys )
% 0.31/1.65 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Us2 @ Vs ) @ ( listrel1 @ A @ R ) ) ) )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Ys @ Vs ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_155_concat_Osimps_I1_J,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( concat @ A @ ( nil @ ( list @ A ) ) )
% 0.31/1.65 = ( nil @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_156_lexord__linear,axiom,
% 0.31/1.65 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X2: list @ A,Y: list @ A] :
% 0.31/1.65 ( ! [A3: A,B4: A] :
% 0.31/1.65 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ B4 ) @ R )
% 0.31/1.65 | ( A3 = B4 )
% 0.31/1.65 | ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ B4 @ A3 ) @ R ) )
% 0.31/1.65 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ Y ) @ ( lexord @ A @ R ) )
% 0.31/1.65 | ( X2 = Y )
% 0.31/1.65 | ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Y @ X2 ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_157_lexord__irreflexive,axiom,
% 0.31/1.65 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A] :
% 0.31/1.65 ( ! [X: A] :
% 0.31/1.65 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ X ) @ R )
% 0.31/1.65 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Xs ) @ ( lexord @ A @ R ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_158_concat_Osimps_I2_J,axiom,
% 0.31/1.65 ! [A: $tType,X2: list @ A,Xs: list @ ( list @ A )] :
% 0.31/1.65 ( ( concat @ A @ ( cons @ ( list @ A ) @ X2 @ Xs ) )
% 0.31/1.65 = ( append @ A @ X2 @ ( concat @ A @ Xs ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_159_lexord__Nil__right,axiom,
% 0.31/1.65 ! [A: $tType,X2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ ( nil @ A ) ) @ ( lexord @ A @ R ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_160_lexord__append__leftI,axiom,
% 0.31/1.65 ! [A: $tType,U: list @ A,V: list @ A,R: set @ ( product_prod @ A @ A ),X2: list @ A] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ U @ V ) @ ( lexord @ A @ R ) )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ X2 @ U ) @ ( append @ A @ X2 @ V ) ) @ ( lexord @ A @ R ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_161_listrel1I1,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Y: A,R: set @ ( product_prod @ A @ A ),Xs: list @ A] :
% 0.31/1.65 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ R )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 @ Xs ) @ ( cons @ A @ Y @ Xs ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_162_Cons__listrel1E1,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 @ Xs ) @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.31/1.65 => ( ! [Y2: A] :
% 0.31/1.65 ( ( Ys
% 0.31/1.65 = ( cons @ A @ Y2 @ Xs ) )
% 0.31/1.65 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y2 ) @ R ) )
% 0.31/1.65 => ~ ! [Zs: list @ A] :
% 0.31/1.65 ( ( Ys
% 0.31/1.65 = ( cons @ A @ X2 @ Zs ) )
% 0.31/1.65 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Zs ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_163_Cons__listrel1E2,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Y: A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( cons @ A @ Y @ Ys ) ) @ ( listrel1 @ A @ R ) )
% 0.31/1.65 => ( ! [X: A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( cons @ A @ X @ Ys ) )
% 0.31/1.65 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R ) )
% 0.31/1.65 => ~ ! [Zs: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( cons @ A @ Y @ Zs ) )
% 0.31/1.65 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Zs @ Ys ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_164_lexord__partial__trans,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A ),Ys: list @ A,Zs2: list @ A] :
% 0.31/1.65 ( ! [X: A,Y2: A,Z: A] :
% 0.31/1.65 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y2 ) @ R )
% 0.31/1.65 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y2 @ Z ) @ R )
% 0.31/1.65 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Z ) @ R ) ) ) )
% 0.31/1.65 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( lexord @ A @ R ) )
% 0.31/1.65 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys @ Zs2 ) @ ( lexord @ A @ R ) )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Zs2 ) @ ( lexord @ A @ R ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_165_lexord__append__leftD,axiom,
% 0.31/1.65 ! [A: $tType,X2: list @ A,U: list @ A,V: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ X2 @ U ) @ ( append @ A @ X2 @ V ) ) @ ( lexord @ A @ R ) )
% 0.31/1.65 => ( ! [A3: A] :
% 0.31/1.65 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ A3 ) @ R )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ U @ V ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_166_lexord__append__rightI,axiom,
% 0.31/1.65 ! [A: $tType,Y: list @ A,X2: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ? [B5: A,Z3: list @ A] :
% 0.31/1.65 ( Y
% 0.31/1.65 = ( cons @ A @ B5 @ Z3 ) )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ ( append @ A @ X2 @ Y ) ) @ ( lexord @ A @ R ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_167_concat__eq__appendD,axiom,
% 0.31/1.65 ! [A: $tType,Xss2: list @ ( list @ A ),Ys: list @ A,Zs2: list @ A] :
% 0.31/1.65 ( ( ( concat @ A @ Xss2 )
% 0.31/1.65 = ( append @ A @ Ys @ Zs2 ) )
% 0.31/1.65 => ( ( Xss2
% 0.31/1.65 != ( nil @ ( list @ A ) ) )
% 0.31/1.65 => ? [Xss12: list @ ( list @ A ),Xs2: list @ A,Xs5: list @ A,Xss23: list @ ( list @ A )] :
% 0.31/1.65 ( ( Xss2
% 0.31/1.65 = ( append @ ( list @ A ) @ Xss12 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.31/1.65 & ( Ys
% 0.31/1.65 = ( append @ A @ ( concat @ A @ Xss12 ) @ Xs2 ) )
% 0.31/1.65 & ( Zs2
% 0.31/1.65 = ( append @ A @ Xs5 @ ( concat @ A @ Xss23 ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_168_listrel1E,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.31/1.65 => ~ ! [X: A,Y2: A] :
% 0.31/1.65 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y2 ) @ R )
% 0.31/1.65 => ! [Us3: list @ A,Vs2: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( append @ A @ Us3 @ ( cons @ A @ X @ Vs2 ) ) )
% 0.31/1.65 => ( Ys
% 0.31/1.65 != ( append @ A @ Us3 @ ( cons @ A @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_169_listrel1I,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Y: A,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Us2: list @ A,Vs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ R )
% 0.31/1.65 => ( ( Xs
% 0.31/1.65 = ( append @ A @ Us2 @ ( cons @ A @ X2 @ Vs ) ) )
% 0.31/1.65 => ( ( Ys
% 0.31/1.65 = ( append @ A @ Us2 @ ( cons @ A @ Y @ Vs ) ) )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_170_lexord__append__left__rightI,axiom,
% 0.31/1.65 ! [A: $tType,A2: A,B2: A,R: set @ ( product_prod @ A @ A ),U: list @ A,X2: list @ A,Y: list @ A] :
% 0.31/1.65 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ U @ ( cons @ A @ A2 @ X2 ) ) @ ( append @ A @ U @ ( cons @ A @ B2 @ Y ) ) ) @ ( lexord @ A @ R ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_171_lexord__same__pref__if__irrefl,axiom,
% 0.31/1.65 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.31/1.65 ( ( irrefl @ A @ R )
% 0.31/1.65 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs2 ) ) @ ( lexord @ A @ R ) )
% 0.31/1.65 = ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys @ Zs2 ) @ ( lexord @ A @ R ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_172_listrel_Ocases,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,A1: list @ A,A22: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ A1 @ A22 ) @ ( listrel @ A @ B @ R ) )
% 0.31/1.65 => ( ( ( A1
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 => ( A22
% 0.31/1.65 != ( nil @ B ) ) )
% 0.31/1.65 => ~ ! [X: A,Y2: B,Xs2: list @ A] :
% 0.31/1.65 ( ( A1
% 0.31/1.65 = ( cons @ A @ X @ Xs2 ) )
% 0.31/1.65 => ! [Ys2: list @ B] :
% 0.31/1.65 ( ( A22
% 0.31/1.65 = ( cons @ B @ Y2 @ Ys2 ) )
% 0.31/1.65 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y2 ) @ R )
% 0.31/1.65 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys2 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_173_listrel_Osimps,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,A1: list @ A,A22: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ A1 @ A22 ) @ ( listrel @ A @ B @ R ) )
% 0.31/1.65 = ( ( ( A1
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 & ( A22
% 0.31/1.65 = ( nil @ B ) ) )
% 0.31/1.65 | ? [X3: A,Y3: B,Xs4: list @ A,Ys3: list @ B] :
% 0.31/1.65 ( ( A1
% 0.31/1.65 = ( cons @ A @ X3 @ Xs4 ) )
% 0.31/1.65 & ( A22
% 0.31/1.65 = ( cons @ B @ Y3 @ Ys3 ) )
% 0.31/1.65 & ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R )
% 0.31/1.65 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs4 @ Ys3 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_174_listrel_Oinducts,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,X12: list @ A,X24: list @ B,R: set @ ( product_prod @ A @ B ),P: ( list @ A ) > ( list @ B ) > $o] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ X12 @ X24 ) @ ( listrel @ A @ B @ R ) )
% 0.31/1.65 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.31/1.65 => ( ! [X: A,Y2: B,Xs2: list @ A,Ys2: list @ B] :
% 0.31/1.65 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y2 ) @ R )
% 0.31/1.65 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys2 ) @ ( listrel @ A @ B @ R ) )
% 0.31/1.65 => ( ( P @ Xs2 @ Ys2 )
% 0.31/1.65 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) ) ) )
% 0.31/1.65 => ( P @ X12 @ X24 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_175_lexord__irrefl,axiom,
% 0.31/1.65 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( irrefl @ A @ R2 )
% 0.31/1.65 => ( irrefl @ ( list @ A ) @ ( lexord @ A @ R2 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_176_listrel_ONil,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B )] : ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ ( nil @ B ) ) @ ( listrel @ A @ B @ R ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_177_listrel__Nil1,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,Xs: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Xs ) @ ( listrel @ A @ B @ R ) )
% 0.31/1.65 => ( Xs
% 0.31/1.65 = ( nil @ B ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_178_listrel__Nil2,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ B )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ ( nil @ B ) ) @ ( listrel @ A @ B @ R ) )
% 0.31/1.65 => ( Xs
% 0.31/1.65 = ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_179_listrel__Cons2,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,Xs: list @ A,Y: B,Ys: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ ( cons @ B @ Y @ Ys ) ) @ ( listrel @ A @ B @ R ) )
% 0.31/1.65 => ~ ! [X: A,Xs2: list @ A] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( cons @ A @ X @ Xs2 ) )
% 0.31/1.65 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ R )
% 0.31/1.65 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs2 @ Ys ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_180_listrel__Cons1,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,Y: A,Ys: list @ A,Xs: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ Y @ Ys ) @ Xs ) @ ( listrel @ A @ B @ R ) )
% 0.31/1.65 => ~ ! [Y2: B,Ys2: list @ B] :
% 0.31/1.65 ( ( Xs
% 0.31/1.65 = ( cons @ B @ Y2 @ Ys2 ) )
% 0.31/1.65 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ Y @ Y2 ) @ R )
% 0.31/1.65 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Ys @ Ys2 ) @ ( listrel @ A @ B @ R ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_181_listrel_OCons,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,X2: A,Y: B,R: set @ ( product_prod @ A @ B ),Xs: list @ A,Ys: list @ B] :
% 0.31/1.65 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y ) @ R )
% 0.31/1.65 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ Ys ) @ ( listrel @ A @ B @ R ) )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ X2 @ Xs ) @ ( cons @ B @ Y @ Ys ) ) @ ( listrel @ A @ B @ R ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_182_irrefl__def,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( irrefl @ A )
% 0.31/1.65 = ( ^ [R3: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ! [A6: A] :
% 0.31/1.65 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A6 @ A6 ) @ R3 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_183_irreflI,axiom,
% 0.31/1.65 ! [A: $tType,R2: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ! [A3: A] :
% 0.31/1.65 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A3 @ A3 ) @ R2 )
% 0.31/1.65 => ( irrefl @ A @ R2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_184_lenlex__append2,axiom,
% 0.31/1.65 ! [A: $tType,R2: set @ ( product_prod @ A @ A ),Us2: list @ A,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( irrefl @ A @ R2 )
% 0.31/1.65 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Us2 @ Xs ) @ ( append @ A @ Us2 @ Ys ) ) @ ( lenlex @ A @ R2 ) )
% 0.31/1.65 = ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( lenlex @ A @ R2 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_185_Nil__lenlex__iff1,axiom,
% 0.31/1.65 ! [A: $tType,Ns: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ns ) @ ( lenlex @ A @ R ) )
% 0.31/1.65 = ( Ns
% 0.31/1.65 != ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_186_lenlex__irreflexive,axiom,
% 0.31/1.65 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A] :
% 0.31/1.65 ( ! [X: A] :
% 0.31/1.65 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ X ) @ R )
% 0.31/1.65 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Xs ) @ ( lenlex @ A @ R ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_187_Nil__lenlex__iff2,axiom,
% 0.31/1.65 ! [A: $tType,Ns: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ns @ ( nil @ A ) ) @ ( lenlex @ A @ R ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_188_irrefl__lex,axiom,
% 0.31/1.65 ! [A: $tType,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( irrefl @ A @ R )
% 0.31/1.65 => ( irrefl @ ( list @ A ) @ ( lex @ A @ R ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_189_internal__case__prod__conv,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,C: $tType,C2: B > C > A,A2: B,B2: C] :
% 0.31/1.65 ( ( produc2004651681e_prod @ B @ C @ A @ C2 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.31/1.65 = ( C2 @ A2 @ B2 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_190_list__ex1__simps_I1_J,axiom,
% 0.31/1.65 ! [A: $tType,P: A > $o] :
% 0.31/1.65 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_191_list__ex1__iff,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( list_ex1 @ A )
% 0.31/1.65 = ( ^ [P4: A > $o,Xs4: list @ A] :
% 0.31/1.65 ? [X3: A] :
% 0.31/1.65 ( ( member @ A @ X3 @ ( set2 @ A @ Xs4 ) )
% 0.31/1.65 & ( P4 @ X3 )
% 0.31/1.65 & ! [Y3: A] :
% 0.31/1.65 ( ( ( member @ A @ Y3 @ ( set2 @ A @ Xs4 ) )
% 0.31/1.65 & ( P4 @ Y3 ) )
% 0.31/1.65 => ( Y3 = X3 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_192_Nil__notin__lex,axiom,
% 0.31/1.65 ! [A: $tType,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys ) @ ( lex @ A @ R ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_193_Nil2__notin__lex,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( nil @ A ) ) @ ( lex @ A @ R ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_194_lex__append__leftI,axiom,
% 0.31/1.65 ! [A: $tType,Ys: list @ A,Zs2: list @ A,R: set @ ( product_prod @ A @ A ),Xs: list @ A] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys @ Zs2 ) @ ( lex @ A @ R ) )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs2 ) ) @ ( lex @ A @ R ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_195_lexl__not__refl,axiom,
% 0.31/1.65 ! [A: $tType,R: set @ ( product_prod @ A @ A ),X2: list @ A] :
% 0.31/1.65 ( ( irrefl @ A @ R )
% 0.31/1.65 => ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ X2 ) @ ( lex @ A @ R ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_196_lex__append__left__iff,axiom,
% 0.31/1.65 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.31/1.65 ( ! [X: A] :
% 0.31/1.65 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ X ) @ R )
% 0.31/1.65 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs2 ) ) @ ( lex @ A @ R ) )
% 0.31/1.65 = ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys @ Zs2 ) @ ( lex @ A @ R ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_197_lex__append__leftD,axiom,
% 0.31/1.65 ! [A: $tType,R: set @ ( product_prod @ A @ A ),Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.31/1.65 ( ! [X: A] :
% 0.31/1.65 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ X ) @ R )
% 0.31/1.65 => ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs2 ) ) @ ( lex @ A @ R ) )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ys @ Zs2 ) @ ( lex @ A @ R ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_198_can__select__set__list__ex1,axiom,
% 0.31/1.65 ! [A: $tType,P: A > $o,A4: list @ A] :
% 0.31/1.65 ( ( can_select @ A @ P @ ( set2 @ A @ A4 ) )
% 0.31/1.65 = ( list_ex1 @ A @ P @ A4 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_199_Cons__in__lex,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A,Y: A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 @ Xs ) @ ( cons @ A @ Y @ Ys ) ) @ ( lex @ A @ R ) )
% 0.31/1.65 = ( ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ R )
% 0.31/1.65 & ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Ys ) ) )
% 0.31/1.65 | ( ( X2 = Y )
% 0.31/1.65 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( lex @ A @ R ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_200_append__eq__append__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A,Us2: list @ A,Vs: list @ A] :
% 0.31/1.65 ( ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.31/1.65 | ( ( size_size @ ( list @ A ) @ Us2 )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Vs ) ) )
% 0.31/1.65 => ( ( ( append @ A @ Xs @ Us2 )
% 0.31/1.65 = ( append @ A @ Ys @ Vs ) )
% 0.31/1.65 = ( ( Xs = Ys )
% 0.31/1.65 & ( Us2 = Vs ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_201_length__rotate1,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A] :
% 0.31/1.65 ( ( size_size @ ( list @ A ) @ ( rotate1 @ A @ Xs ) )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Xs ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_202_listrel1__eq__len,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.31/1.65 => ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Ys ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_203_in__set__product__lists__length,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Xss2: list @ ( list @ A )] :
% 0.31/1.65 ( ( member @ ( list @ A ) @ Xs @ ( set2 @ ( list @ A ) @ ( product_lists @ A @ Xss2 ) ) )
% 0.31/1.65 => ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 = ( size_size @ ( list @ ( list @ A ) ) @ Xss2 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_204_can__select__def,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( can_select @ A )
% 0.31/1.65 = ( ^ [P4: A > $o,A7: set @ A] :
% 0.31/1.65 ? [X3: A] :
% 0.31/1.65 ( ( member @ A @ X3 @ A7 )
% 0.31/1.65 & ( P4 @ X3 )
% 0.31/1.65 & ! [Y3: A] :
% 0.31/1.65 ( ( ( member @ A @ Y3 @ A7 )
% 0.31/1.65 & ( P4 @ Y3 ) )
% 0.31/1.65 => ( Y3 = X3 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_205_Ex__list__of__length,axiom,
% 0.31/1.65 ! [A: $tType,N: nat] :
% 0.31/1.65 ? [Xs2: list @ A] :
% 0.31/1.65 ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/1.65 = N ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_206_neq__if__length__neq,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 != ( size_size @ ( list @ A ) @ Ys ) )
% 0.31/1.65 => ( Xs != Ys ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_207_list__induct3,axiom,
% 0.31/1.65 ! [B: $tType,A: $tType,C: $tType,Xs: list @ A,Ys: list @ B,Zs2: list @ C,P: ( list @ A ) > ( list @ B ) > ( list @ C ) > $o] :
% 0.31/1.65 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 = ( size_size @ ( list @ B ) @ Ys ) )
% 0.31/1.65 => ( ( ( size_size @ ( list @ B ) @ Ys )
% 0.31/1.65 = ( size_size @ ( list @ C ) @ Zs2 ) )
% 0.31/1.65 => ( ( P @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) )
% 0.31/1.65 => ( ! [X: A,Xs2: list @ A,Y2: B,Ys2: list @ B,Z: C,Zs: list @ C] :
% 0.31/1.65 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/1.65 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 0.31/1.65 => ( ( ( size_size @ ( list @ B ) @ Ys2 )
% 0.31/1.65 = ( size_size @ ( list @ C ) @ Zs ) )
% 0.31/1.65 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.31/1.65 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) @ ( cons @ C @ Z @ Zs ) ) ) ) )
% 0.31/1.65 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_208_list__induct2,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 0.31/1.65 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 = ( size_size @ ( list @ B ) @ Ys ) )
% 0.31/1.65 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.31/1.65 => ( ! [X: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 0.31/1.65 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/1.65 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 0.31/1.65 => ( ( P @ Xs2 @ Ys2 )
% 0.31/1.65 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) ) )
% 0.31/1.65 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_209_listrel__eq__len,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ Ys ) @ ( listrel @ A @ B @ R ) )
% 0.31/1.65 => ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 = ( size_size @ ( list @ B ) @ Ys ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_210_same__length__different,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( Xs != Ys )
% 0.31/1.65 => ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.31/1.65 => ? [Pre: list @ A,X: A,Xs5: list @ A,Y2: A,Ys6: list @ A] :
% 0.31/1.65 ( ( X != Y2 )
% 0.31/1.65 & ( Xs
% 0.31/1.65 = ( append @ A @ Pre @ ( append @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ Xs5 ) ) )
% 0.31/1.65 & ( Ys
% 0.31/1.65 = ( append @ A @ Pre @ ( append @ A @ ( cons @ A @ Y2 @ ( nil @ A ) ) @ Ys6 ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_211_lexord__sufE,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Zs2: list @ A,Ys: list @ A,Qs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Zs2 ) @ ( append @ A @ Ys @ Qs ) ) @ ( lexord @ A @ R ) )
% 0.31/1.65 => ( ( Xs != Ys )
% 0.31/1.65 => ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.31/1.65 => ( ( ( size_size @ ( list @ A ) @ Zs2 )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Qs ) )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( lexord @ A @ R ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_212_lex__append__rightI,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A ),Vs: list @ A,Us2: list @ A] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( lex @ A @ R ) )
% 0.31/1.65 => ( ( ( size_size @ ( list @ A ) @ Vs )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Us2 ) )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Ys @ Vs ) ) @ ( lex @ A @ R ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_213_lenlex__append1,axiom,
% 0.31/1.65 ! [A: $tType,Us2: list @ A,Xs: list @ A,R2: set @ ( product_prod @ A @ A ),Vs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Us2 @ Xs ) @ ( lenlex @ A @ R2 ) )
% 0.31/1.65 => ( ( ( size_size @ ( list @ A ) @ Vs )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.31/1.65 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Us2 @ Vs ) @ ( append @ A @ Xs @ Ys ) ) @ ( lenlex @ A @ R2 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_214_lexord__lex,axiom,
% 0.31/1.65 ! [A: $tType,X2: list @ A,Y: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ Y ) @ ( lex @ A @ R ) )
% 0.31/1.65 = ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ X2 @ Y ) @ ( lexord @ A @ R ) )
% 0.31/1.65 & ( ( size_size @ ( list @ A ) @ X2 )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Y ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_215_Cons__lenlex__iff,axiom,
% 0.31/1.65 ! [A: $tType,M: A,Ms: list @ A,N: A,Ns: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ M @ Ms ) @ ( cons @ A @ N @ Ns ) ) @ ( lenlex @ A @ R ) )
% 0.31/1.65 = ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ms ) @ ( size_size @ ( list @ A ) @ Ns ) )
% 0.31/1.65 | ( ( ( size_size @ ( list @ A ) @ Ms )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Ns ) )
% 0.31/1.65 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ M @ N ) @ R ) )
% 0.31/1.65 | ( ( M = N )
% 0.31/1.65 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Ms @ Ns ) @ ( lenlex @ A @ R ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_216_length__n__lists__elem,axiom,
% 0.31/1.65 ! [A: $tType,Ys: list @ A,N: nat,Xs: list @ A] :
% 0.31/1.65 ( ( member @ ( list @ A ) @ Ys @ ( set2 @ ( list @ A ) @ ( n_lists @ A @ N @ Xs ) ) )
% 0.31/1.65 => ( ( size_size @ ( list @ A ) @ Ys )
% 0.31/1.65 = N ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_217_length__induct,axiom,
% 0.31/1.65 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.31/1.65 ( ! [Xs2: list @ A] :
% 0.31/1.65 ( ! [Ys7: list @ A] :
% 0.31/1.65 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys7 ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 0.31/1.65 => ( P @ Ys7 ) )
% 0.31/1.65 => ( P @ Xs2 ) )
% 0.31/1.65 => ( P @ Xs ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_218_n__lists__Nil,axiom,
% 0.31/1.65 ! [A: $tType,N: nat] :
% 0.31/1.65 ( ( ( N
% 0.31/1.65 = ( zero_zero @ nat ) )
% 0.31/1.65 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 0.31/1.65 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 0.31/1.65 & ( ( N
% 0.31/1.65 != ( zero_zero @ nat ) )
% 0.31/1.65 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 0.31/1.65 = ( nil @ ( list @ A ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_219_in__measures_I2_J,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Y: A,F: A > nat,Fs: list @ ( A > nat )] :
% 0.31/1.65 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ ( measures @ A @ ( cons @ ( A > nat ) @ F @ Fs ) ) )
% 0.31/1.65 = ( ( ord_less @ nat @ ( F @ X2 ) @ ( F @ Y ) )
% 0.31/1.65 | ( ( ( F @ X2 )
% 0.31/1.65 = ( F @ Y ) )
% 0.31/1.65 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ ( measures @ A @ Fs ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_220_in__measures_I1_J,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Y: A] :
% 0.31/1.65 ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ ( measures @ A @ ( nil @ ( A > nat ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_221_length__0__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A] :
% 0.31/1.65 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 = ( zero_zero @ nat ) )
% 0.31/1.65 = ( Xs
% 0.31/1.65 = ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_222_length__greater__0__conv,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A] :
% 0.31/1.65 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.65 = ( Xs
% 0.31/1.65 != ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_223_list_Osize_I3_J,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( size_size @ ( list @ A ) @ ( nil @ A ) )
% 0.31/1.65 = ( zero_zero @ nat ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_224_length__pos__if__in__set,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_225_measures__less,axiom,
% 0.31/1.65 ! [A: $tType,F: A > nat,X2: A,Y: A,Fs: list @ ( A > nat )] :
% 0.31/1.65 ( ( ord_less @ nat @ ( F @ X2 ) @ ( F @ Y ) )
% 0.31/1.65 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X2 @ Y ) @ ( measures @ A @ ( cons @ ( A > nat ) @ F @ Fs ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_226_n__lists_Osimps_I1_J,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A] :
% 0.31/1.65 ( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs )
% 0.31/1.65 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_227_maxvar_Osimps_I1_J,axiom,
% 0.31/1.65 ( ( prover572158330maxvar @ ( nil @ nat ) )
% 0.31/1.65 = ( zero_zero @ nat ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_228_count__notin,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ~ ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ( ( count_list @ A @ Xs @ X2 )
% 0.31/1.65 = ( zero_zero @ nat ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_229_count__list_Osimps_I1_J,axiom,
% 0.31/1.65 ! [A: $tType,Y: A] :
% 0.31/1.65 ( ( count_list @ A @ ( nil @ A ) @ Y )
% 0.31/1.65 = ( zero_zero @ nat ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_230_length__code,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( size_size @ ( list @ A ) )
% 0.31/1.65 = ( gen_length @ A @ ( zero_zero @ nat ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_231_listrel__iff__nth,axiom,
% 0.31/1.65 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,R: set @ ( product_prod @ A @ B )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ Xs @ Ys ) @ ( listrel @ A @ B @ R ) )
% 0.31/1.65 = ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 = ( size_size @ ( list @ B ) @ Ys ) )
% 0.31/1.65 & ! [N2: nat] :
% 0.31/1.65 ( ( ord_less @ nat @ N2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.65 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ ( nth @ A @ Xs @ N2 ) @ ( nth @ B @ Ys @ N2 ) ) @ R ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_232_nth__Cons__0,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( nth @ A @ ( cons @ A @ X2 @ Xs ) @ ( zero_zero @ nat ) )
% 0.31/1.65 = X2 ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_233_nth__append__length,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,X2: A,Ys: list @ A] :
% 0.31/1.65 ( ( nth @ A @ ( append @ A @ Xs @ ( cons @ A @ X2 @ Ys ) ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.65 = X2 ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_234_all__set__conv__all__nth,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.31/1.65 ( ( ! [X3: A] :
% 0.31/1.65 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ( P @ X3 ) ) )
% 0.31/1.65 = ( ! [I: nat] :
% 0.31/1.65 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.65 => ( P @ ( nth @ A @ Xs @ I ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_235_all__nth__imp__all__set,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,P: A > $o,X2: A] :
% 0.31/1.65 ( ! [I2: nat] :
% 0.31/1.65 ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.65 => ( P @ ( nth @ A @ Xs @ I2 ) ) )
% 0.31/1.65 => ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ( P @ X2 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_236_in__set__conv__nth,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Xs: list @ A] :
% 0.31/1.65 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.31/1.65 = ( ? [I: nat] :
% 0.31/1.65 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.65 & ( ( nth @ A @ Xs @ I )
% 0.31/1.65 = X2 ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_237_list__ball__nth,axiom,
% 0.31/1.65 ! [A: $tType,N: nat,Xs: list @ A,P: A > $o] :
% 0.31/1.65 ( ( ord_less @ nat @ N @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.65 => ( ! [X: A] :
% 0.31/1.65 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.31/1.65 => ( P @ X ) )
% 0.31/1.65 => ( P @ ( nth @ A @ Xs @ N ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_238_nth__mem,axiom,
% 0.31/1.65 ! [A: $tType,N: nat,Xs: list @ A] :
% 0.31/1.65 ( ( ord_less @ nat @ N @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.65 => ( member @ A @ ( nth @ A @ Xs @ N ) @ ( set2 @ A @ Xs ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_239_gen__length__code_I1_J,axiom,
% 0.31/1.65 ! [A: $tType,N: nat] :
% 0.31/1.65 ( ( gen_length @ A @ N @ ( nil @ A ) )
% 0.31/1.65 = N ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_240_nth__equalityI,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.31/1.65 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.31/1.65 => ( ! [I2: nat] :
% 0.31/1.65 ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.65 => ( ( nth @ A @ Xs @ I2 )
% 0.31/1.65 = ( nth @ A @ Ys @ I2 ) ) )
% 0.31/1.65 => ( Xs = Ys ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_241_Skolem__list__nth,axiom,
% 0.31/1.65 ! [A: $tType,K: nat,P: nat > A > $o] :
% 0.31/1.65 ( ( ! [I: nat] :
% 0.31/1.65 ( ( ord_less @ nat @ I @ K )
% 0.31/1.65 => ? [X6: A] : ( P @ I @ X6 ) ) )
% 0.31/1.65 = ( ? [Xs4: list @ A] :
% 0.31/1.65 ( ( ( size_size @ ( list @ A ) @ Xs4 )
% 0.31/1.65 = K )
% 0.31/1.65 & ! [I: nat] :
% 0.31/1.65 ( ( ord_less @ nat @ I @ K )
% 0.31/1.65 => ( P @ I @ ( nth @ A @ Xs4 @ I ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_242_list__eq__iff__nth__eq,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( ^ [Y4: list @ A,Z4: list @ A] : ( Y4 = Z4 ) )
% 0.31/1.65 = ( ^ [Xs4: list @ A,Ys3: list @ A] :
% 0.31/1.65 ( ( ( size_size @ ( list @ A ) @ Xs4 )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Ys3 ) )
% 0.31/1.65 & ! [I: nat] :
% 0.31/1.65 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ A ) @ Xs4 ) )
% 0.31/1.65 => ( ( nth @ A @ Xs4 @ I )
% 0.31/1.65 = ( nth @ A @ Ys3 @ I ) ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_243_nth__butlast,axiom,
% 0.31/1.65 ! [A: $tType,N: nat,Xs: list @ A] :
% 0.31/1.65 ( ( ord_less @ nat @ N @ ( size_size @ ( list @ A ) @ ( butlast @ A @ Xs ) ) )
% 0.31/1.65 => ( ( nth @ A @ ( butlast @ A @ Xs ) @ N )
% 0.31/1.65 = ( nth @ A @ Xs @ N ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_244_listrel1__iff__update,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.31/1.65 = ( ? [Y3: A,N2: nat] :
% 0.31/1.65 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( nth @ A @ Xs @ N2 ) @ Y3 ) @ R )
% 0.31/1.65 & ( ord_less @ nat @ N2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.65 & ( Ys
% 0.31/1.65 = ( list_update @ A @ Xs @ N2 @ Y3 ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_245_lex__take__index,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.31/1.65 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( lex @ A @ R ) )
% 0.31/1.65 => ~ ! [I2: nat] :
% 0.31/1.65 ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.65 => ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Ys ) )
% 0.31/1.65 => ( ( ( take @ A @ I2 @ Xs )
% 0.31/1.65 = ( take @ A @ I2 @ Ys ) )
% 0.31/1.65 => ~ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( nth @ A @ Xs @ I2 ) @ ( nth @ A @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_246_list__update__overwrite,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,I3: nat,X2: A,Y: A] :
% 0.31/1.65 ( ( list_update @ A @ ( list_update @ A @ Xs @ I3 @ X2 ) @ I3 @ Y )
% 0.31/1.65 = ( list_update @ A @ Xs @ I3 @ Y ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_247_list__update__nonempty,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,K: nat,X2: A] :
% 0.31/1.65 ( ( ( list_update @ A @ Xs @ K @ X2 )
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 = ( Xs
% 0.31/1.65 = ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_248_length__list__update,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,I3: nat,X2: A] :
% 0.31/1.65 ( ( size_size @ ( list @ A ) @ ( list_update @ A @ Xs @ I3 @ X2 ) )
% 0.31/1.65 = ( size_size @ ( list @ A ) @ Xs ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_249_list__update__id,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,I3: nat] :
% 0.31/1.65 ( ( list_update @ A @ Xs @ I3 @ ( nth @ A @ Xs @ I3 ) )
% 0.31/1.65 = Xs ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_250_nth__list__update__neq,axiom,
% 0.31/1.65 ! [A: $tType,I3: nat,J: nat,Xs: list @ A,X2: A] :
% 0.31/1.65 ( ( I3 != J )
% 0.31/1.65 => ( ( nth @ A @ ( list_update @ A @ Xs @ I3 @ X2 ) @ J )
% 0.31/1.65 = ( nth @ A @ Xs @ J ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_251_take__eq__Nil,axiom,
% 0.31/1.65 ! [A: $tType,N: nat,Xs: list @ A] :
% 0.31/1.65 ( ( ( take @ A @ N @ Xs )
% 0.31/1.65 = ( nil @ A ) )
% 0.31/1.65 = ( ( N
% 0.31/1.65 = ( zero_zero @ nat ) )
% 0.31/1.65 | ( Xs
% 0.31/1.65 = ( nil @ A ) ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_252_take0,axiom,
% 0.31/1.65 ! [A: $tType] :
% 0.31/1.65 ( ( take @ A @ ( zero_zero @ nat ) )
% 0.31/1.65 = ( ^ [Xs4: list @ A] : ( nil @ A ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_253_nth__take,axiom,
% 0.31/1.65 ! [A: $tType,I3: nat,N: nat,Xs: list @ A] :
% 0.31/1.65 ( ( ord_less @ nat @ I3 @ N )
% 0.31/1.65 => ( ( nth @ A @ ( take @ A @ N @ Xs ) @ I3 )
% 0.31/1.65 = ( nth @ A @ Xs @ I3 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(fact_254_list__update__length,axiom,
% 0.31/1.65 ! [A: $tType,Xs: list @ A,X2: A,Ys: list @ A,Y: A] :
% 0.31/1.65 ( ( list_update @ A @ ( append @ A @ Xs @ ( cons @ A @ X2 @ Ys ) ) @ ( size_size @ ( list @ A ) @ Xs ) @ Y )
% 0.31/1.65 = ( append @ A @ Xs @ ( cons @ A @ Y @ Ys ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/1.65 ! [A8: $tType,A9: $tType] :
% 0.31/1.65 ( ( ord @ A9 )
% 0.31/1.65 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.31/1.65 linorder @ nat ).
% 0.31/1.65
% 0.31/1.65 thf(tcon_Nat_Onat___Orderings_Oord_1,axiom,
% 0.31/1.65 ord @ nat ).
% 0.31/1.65
% 0.31/1.65 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 0.31/1.65 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(tcon_HOL_Obool___Orderings_Olinorder_3,axiom,
% 0.31/1.65 linorder @ $o ).
% 0.31/1.65
% 0.31/1.65 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 0.31/1.65 ord @ $o ).
% 0.31/1.65
% 0.31/1.65 thf(help_If_3_1_T,axiom,
% 0.31/1.65 ! [P: $o] :
% 0.31/1.65 ( ( P = $true )
% 0.31/1.65 | ( P = $false ) ) ).
% 0.31/1.65
% 0.31/1.65 thf(help_If_2_1_T,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Y: A] :
% 0.31/1.65 ( ( if @ A @ $false @ X2 @ Y )
% 0.31/1.65 = Y ) ).
% 0.31/1.65
% 0.31/1.65 thf(help_If_1_1_T,axiom,
% 0.31/1.65 ! [A: $tType,X2: A,Y: A] :
% 0.31/1.65 ( ( if @ A @ $true @ X2 @ Y )
% 0.31/1.66 = X2 ) ).
% 0.31/1.66
% 0.31/1.66 thf(conj_0,hypothesis,
% 0.31/1.66 ~ ( member @ nat @ u @ ( set2 @ nat @ ( prover_Mirabelle_sfv @ ( cons @ prover2006609834e_form @ ( prover946642470e_FAll @ f ) @ s ) ) ) ) ).
% 0.31/1.66
% 0.31/1.66 thf(conj_1,hypothesis,
% 0.31/1.66 ! [A10: set @ prover_Mirabelle_U,B5: nat > ( list @ prover_Mirabelle_U ) > $o,E6: nat > prover_Mirabelle_U] :
% 0.31/1.66 ( ( prover1043414700is_env @ ( product_Pair @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ) @ A10 @ B5 ) @ E6 )
% 0.31/1.66 => ( prover1899965912_SEval @ ( product_Pair @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ) @ A10 @ B5 ) @ E6 @ ( append @ prover2006609834e_form @ s @ ( cons @ prover2006609834e_form @ ( prover48307765_finst @ f @ u ) @ ( nil @ prover2006609834e_form ) ) ) ) ) ).
% 0.31/1.66
% 0.31/1.66 thf(conj_2,conjecture,
% 0.31/1.66 ! [E5: nat > prover_Mirabelle_U] :
% 0.31/1.66 ( ~ ( prover1043414700is_env @ ( product_Pair @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ) @ a @ b ) @ E5 )
% 0.31/1.66 | ( prover1899965912_SEval @ ( product_Pair @ ( set @ prover_Mirabelle_U ) @ ( nat > ( list @ prover_Mirabelle_U ) > $o ) @ a @ b ) @ E5 @ ( cons @ prover2006609834e_form @ ( prover946642470e_FAll @ f ) @ s ) ) ) ).
% 0.31/1.66 ------------------------
% 0.31/1.67 % (13122)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/183Mi)
% 0.31/1.68 % (13123)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_12850 for (2999ds/4Mi)
% 0.31/1.68 % (13125)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/2Mi)
% 0.31/1.68 % (13126)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_12850 for (2999ds/2Mi)
% 0.31/1.68 % (13124)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_12850 for (2999ds/27Mi)
% 0.31/1.68 % (13127)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_12850 for (2999ds/275Mi)
% 0.31/1.68 % (13128)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/18Mi)
% 0.31/1.68 % (13126)Instruction limit reached!
% 0.31/1.68 % (13126)------------------------------
% 0.31/1.68 % (13126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.68 % (13126)Termination reason: Unknown
% 0.31/1.68 % (13126)Termination phase: shuffling
% 0.31/1.68
% 0.31/1.68 % (13126)Memory used [KB]: 1407
% 0.31/1.68 % (13126)Time elapsed: 0.003 s
% 0.31/1.68 % (13126)Instructions burned: 2 (million)
% 0.31/1.68 % (13126)------------------------------
% 0.31/1.68 % (13126)------------------------------
% 0.31/1.68 % (13125)Instruction limit reached!
% 0.31/1.68 % (13125)------------------------------
% 0.31/1.68 % (13125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.68 % (13125)Termination reason: Unknown
% 0.31/1.68 % (13125)Termination phase: shuffling
% 0.31/1.68
% 0.31/1.68 % (13125)Memory used [KB]: 1407
% 0.31/1.68 % (13125)Time elapsed: 0.004 s
% 0.31/1.68 % (13125)Instructions burned: 3 (million)
% 0.31/1.68 % (13125)------------------------------
% 0.31/1.68 % (13125)------------------------------
% 0.31/1.68 % (13123)Instruction limit reached!
% 0.31/1.68 % (13123)------------------------------
% 0.31/1.68 % (13123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.68 % (13123)Termination reason: Unknown
% 0.31/1.68 % (13123)Termination phase: shuffling
% 0.31/1.68
% 0.31/1.68 % (13123)Memory used [KB]: 1535
% 0.31/1.68 % (13123)Time elapsed: 0.005 s
% 0.31/1.68 % (13123)Instructions burned: 5 (million)
% 0.31/1.68 % (13123)------------------------------
% 0.31/1.68 % (13123)------------------------------
% 0.31/1.69 % (13128)Instruction limit reached!
% 0.31/1.69 % (13128)------------------------------
% 0.31/1.69 % (13128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.69 % (13128)Termination reason: Unknown
% 0.31/1.69 % (13128)Termination phase: shuffling
% 0.31/1.69
% 0.31/1.69 % (13128)Memory used [KB]: 1791
% 0.31/1.69 % (13128)Time elapsed: 0.014 s
% 0.31/1.69 % (13128)Instructions burned: 19 (million)
% 0.31/1.69 % (13128)------------------------------
% 0.31/1.69 % (13128)------------------------------
% 3.06/1.70 % (13124)Instruction limit reached!
% 3.06/1.70 % (13124)------------------------------
% 3.06/1.70 % (13124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.70 % (13124)Termination reason: Unknown
% 3.06/1.70 % (13124)Termination phase: shuffling
% 3.06/1.70
% 3.06/1.70 % (13124)Memory used [KB]: 1918
% 3.06/1.70 % (13124)Time elapsed: 0.019 s
% 3.06/1.70 % (13124)Instructions burned: 27 (million)
% 3.06/1.70 % (13124)------------------------------
% 3.06/1.70 % (13124)------------------------------
% 3.06/1.70 % (13129)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/3Mi)
% 3.06/1.70 % (13130)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_12850 for (2999ds/37Mi)
% 3.06/1.70 % (13131)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_12850 for (2999ds/15Mi)
% 3.06/1.70 % (13129)Instruction limit reached!
% 3.06/1.70 % (13129)------------------------------
% 3.06/1.70 % (13129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.70 % (13129)Termination reason: Unknown
% 3.06/1.70 % (13129)Termination phase: shuffling
% 3.06/1.70
% 3.06/1.70 % (13129)Memory used [KB]: 1407
% 3.06/1.70 % (13129)Time elapsed: 0.004 s
% 3.06/1.70 % (13129)Instructions burned: 3 (million)
% 3.06/1.70 % (13129)------------------------------
% 3.06/1.70 % (13129)------------------------------
% 3.06/1.71 % (13132)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_12850 for (2999ds/3Mi)
% 3.06/1.71 % (13131)Instruction limit reached!
% 3.06/1.71 % (13131)------------------------------
% 3.06/1.71 % (13131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.71 % (13131)Termination reason: Unknown
% 3.06/1.71 % (13131)Termination phase: shuffling
% 3.06/1.71
% 3.06/1.71 % (13131)Memory used [KB]: 1663
% 3.06/1.71 % (13131)Time elapsed: 0.012 s
% 3.06/1.71 % (13131)Instructions burned: 15 (million)
% 3.06/1.71 % (13131)------------------------------
% 3.06/1.71 % (13131)------------------------------
% 3.06/1.71 % (13132)Instruction limit reached!
% 3.06/1.71 % (13132)------------------------------
% 3.06/1.71 % (13132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.71 % (13132)Termination reason: Unknown
% 3.06/1.71 % (13132)Termination phase: shuffling
% 3.06/1.71
% 3.06/1.71 % (13132)Memory used [KB]: 1407
% 3.06/1.71 % (13132)Time elapsed: 0.004 s
% 3.06/1.71 % (13132)Instructions burned: 3 (million)
% 3.06/1.71 % (13132)------------------------------
% 3.06/1.71 % (13132)------------------------------
% 3.06/1.72 % (13133)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_12850 for (2999ds/1041Mi)
% 3.06/1.72 % (13134)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/7Mi)
% 3.06/1.72 % (13130)Instruction limit reached!
% 3.06/1.72 % (13130)------------------------------
% 3.06/1.72 % (13130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.72 % (13130)Termination reason: Unknown
% 3.06/1.72 % (13130)Termination phase: shuffling
% 3.06/1.72
% 3.06/1.72 % (13130)Memory used [KB]: 2174
% 3.06/1.72 % (13130)Time elapsed: 0.021 s
% 3.06/1.72 % (13130)Instructions burned: 37 (million)
% 3.06/1.72 % (13130)------------------------------
% 3.06/1.72 % (13130)------------------------------
% 3.06/1.72 % (13134)Instruction limit reached!
% 3.06/1.72 % (13134)------------------------------
% 3.06/1.72 % (13134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.72 % (13134)Termination reason: Unknown
% 3.06/1.72 % (13134)Termination phase: shuffling
% 3.06/1.72
% 3.06/1.72 % (13134)Memory used [KB]: 1535
% 3.06/1.72 % (13134)Time elapsed: 0.005 s
% 3.06/1.72 % (13134)Instructions burned: 7 (million)
% 3.06/1.72 % (13134)------------------------------
% 3.06/1.72 % (13134)------------------------------
% 3.06/1.73 % (13135)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/16Mi)
% 3.06/1.73 % (13136)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_12850 for (2999ds/3Mi)
% 3.06/1.73 % (13122)Instruction limit reached!
% 3.06/1.73 % (13122)------------------------------
% 3.06/1.73 % (13122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.73 % (13122)Termination reason: Unknown
% 3.06/1.73 % (13122)Termination phase: Saturation
% 3.06/1.73
% 3.06/1.73 % (13122)Memory used [KB]: 7291
% 3.06/1.73 % (13122)Time elapsed: 0.058 s
% 3.06/1.73 % (13122)Instructions burned: 185 (million)
% 3.06/1.73 % (13122)------------------------------
% 3.06/1.73 % (13122)------------------------------
% 3.06/1.73 % (13138)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/7Mi)
% 3.06/1.73 % (13136)Instruction limit reached!
% 3.06/1.73 % (13136)------------------------------
% 3.06/1.73 % (13136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.73 % (13136)Termination reason: Unknown
% 3.06/1.73 % (13136)Termination phase: shuffling
% 3.06/1.73
% 3.06/1.73 % (13136)Memory used [KB]: 1407
% 3.06/1.73 % (13136)Time elapsed: 0.004 s
% 3.06/1.73 % (13136)Instructions burned: 3 (million)
% 3.06/1.73 % (13136)------------------------------
% 3.06/1.73 % (13136)------------------------------
% 3.06/1.74 % (13138)Instruction limit reached!
% 3.06/1.74 % (13138)------------------------------
% 3.06/1.74 % (13138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.74 % (13138)Termination reason: Unknown
% 3.06/1.74 % (13138)Termination phase: shuffling
% 3.06/1.74
% 3.06/1.74 % (13138)Memory used [KB]: 1535
% 3.06/1.74 % (13138)Time elapsed: 0.004 s
% 3.06/1.74 % (13138)Instructions burned: 7 (million)
% 3.06/1.74 % (13138)------------------------------
% 3.06/1.74 % (13138)------------------------------
% 3.06/1.74 % (13137)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_12850 for (2999ds/3Mi)
% 3.06/1.74 % (13135)Instruction limit reached!
% 3.06/1.74 % (13135)------------------------------
% 3.06/1.74 % (13135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.74 % (13135)Termination reason: Unknown
% 3.06/1.74 % (13135)Termination phase: shuffling
% 3.06/1.74
% 3.06/1.74 % (13135)Memory used [KB]: 1663
% 3.06/1.74 % (13135)Time elapsed: 0.011 s
% 3.06/1.74 % (13135)Instructions burned: 16 (million)
% 3.06/1.74 % (13135)------------------------------
% 3.06/1.74 % (13135)------------------------------
% 3.06/1.74 % (13137)Instruction limit reached!
% 3.06/1.74 % (13137)------------------------------
% 3.06/1.74 % (13137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.74 % (13137)Termination reason: Unknown
% 3.06/1.74 % (13137)Termination phase: shuffling
% 3.06/1.74
% 3.06/1.74 % (13137)Memory used [KB]: 1407
% 3.06/1.74 % (13137)Time elapsed: 0.004 s
% 3.06/1.74 % (13137)Instructions burned: 3 (million)
% 3.06/1.74 % (13137)------------------------------
% 3.06/1.74 % (13137)------------------------------
% 3.06/1.74 % (13139)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/3Mi)
% 3.06/1.74 % (13139)Instruction limit reached!
% 3.06/1.74 % (13139)------------------------------
% 3.06/1.74 % (13139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.74 % (13139)Termination reason: Unknown
% 3.06/1.74 % (13139)Termination phase: shuffling
% 3.06/1.74
% 3.06/1.74 % (13139)Memory used [KB]: 1407
% 3.06/1.74 % (13139)Time elapsed: 0.003 s
% 3.06/1.74 % (13139)Instructions burned: 4 (million)
% 3.06/1.74 % (13139)------------------------------
% 3.06/1.74 % (13139)------------------------------
% 3.06/1.75 % (13141)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/18Mi)
% 3.06/1.75 % (13140)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/4Mi)
% 3.06/1.75 % (13141)Instruction limit reached!
% 3.06/1.75 % (13141)------------------------------
% 3.06/1.75 % (13141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.75 % (13141)Termination reason: Unknown
% 3.06/1.75 % (13141)Termination phase: shuffling
% 3.06/1.75
% 3.06/1.75 % (13141)Memory used [KB]: 1663
% 3.06/1.75 % (13141)Time elapsed: 0.008 s
% 3.06/1.75 % (13141)Instructions burned: 18 (million)
% 3.06/1.75 % (13141)------------------------------
% 3.06/1.75 % (13141)------------------------------
% 3.06/1.75 % (13140)Instruction limit reached!
% 3.06/1.75 % (13140)------------------------------
% 3.06/1.75 % (13140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.75 % (13140)Termination reason: Unknown
% 3.06/1.75 % (13140)Termination phase: shuffling
% 3.06/1.75
% 3.06/1.75 % (13140)Memory used [KB]: 1407
% 3.06/1.75 % (13140)Time elapsed: 0.005 s
% 3.06/1.75 % (13140)Instructions burned: 5 (million)
% 3.06/1.75 % (13140)------------------------------
% 3.06/1.75 % (13140)------------------------------
% 3.06/1.75 % (13144)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_12850 for (2999ds/902Mi)
% 3.06/1.75 % (13142)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/710Mi)
% 3.06/1.76 % (13143)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/6Mi)
% 3.06/1.76 % (13143)Instruction limit reached!
% 3.06/1.76 % (13143)------------------------------
% 3.06/1.76 % (13143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.76 % (13143)Termination reason: Unknown
% 3.06/1.76 % (13143)Termination phase: shuffling
% 3.06/1.76
% 3.06/1.76 % (13143)Memory used [KB]: 1535
% 3.06/1.76 % (13143)Time elapsed: 0.006 s
% 3.06/1.76 % (13143)Instructions burned: 7 (million)
% 3.06/1.76 % (13143)------------------------------
% 3.06/1.76 % (13143)------------------------------
% 3.06/1.76 % (13145)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_12850 for (2999ds/21Mi)
% 3.06/1.76 % (13146)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_12850 for (2999ds/5Mi)
% 3.06/1.77 % (13146)Instruction limit reached!
% 3.06/1.77 % (13146)------------------------------
% 3.06/1.77 % (13146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.77 % (13146)Termination reason: Unknown
% 3.06/1.77 % (13146)Termination phase: shuffling
% 3.06/1.77
% 3.06/1.77 % (13146)Memory used [KB]: 1535
% 3.06/1.77 % (13146)Time elapsed: 0.003 s
% 3.06/1.77 % (13146)Instructions burned: 6 (million)
% 3.06/1.77 % (13146)------------------------------
% 3.06/1.77 % (13146)------------------------------
% 3.06/1.77 % (13145)Instruction limit reached!
% 3.06/1.77 % (13145)------------------------------
% 3.06/1.77 % (13145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.77 % (13145)Termination reason: Unknown
% 3.06/1.77 % (13145)Termination phase: shuffling
% 3.06/1.77
% 3.06/1.77 % (13145)Memory used [KB]: 1791
% 3.06/1.77 % (13145)Time elapsed: 0.010 s
% 3.06/1.77 % (13145)Instructions burned: 23 (million)
% 3.06/1.77 % (13145)------------------------------
% 3.06/1.77 % (13145)------------------------------
% 3.06/1.78 % (13148)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_12850 for (2998ds/377Mi)
% 3.06/1.78 % (13147)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_12850 for (2999ds/6Mi)
% 3.06/1.78 % (13149)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_12850 for (2998ds/779Mi)
% 3.06/1.78 % (13147)Instruction limit reached!
% 3.06/1.78 % (13147)------------------------------
% 3.06/1.78 % (13147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.78 % (13147)Termination reason: Unknown
% 3.06/1.78 % (13147)Termination phase: shuffling
% 3.06/1.78
% 3.06/1.78 % (13147)Memory used [KB]: 1535
% 3.06/1.78 % (13147)Time elapsed: 0.006 s
% 3.06/1.78 % (13147)Instructions burned: 7 (million)
% 3.06/1.78 % (13147)------------------------------
% 3.06/1.78 % (13147)------------------------------
% 3.06/1.80 % (13150)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_12850 for (2998ds/19Mi)
% 3.06/1.81 % (13150)Instruction limit reached!
% 3.06/1.81 % (13150)------------------------------
% 3.06/1.81 % (13150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.81 % (13150)Termination reason: Unknown
% 3.06/1.81 % (13150)Termination phase: shuffling
% 3.06/1.81
% 3.06/1.81 % (13150)Memory used [KB]: 1791
% 3.06/1.81 % (13150)Time elapsed: 0.010 s
% 3.06/1.81 % (13150)Instructions burned: 19 (million)
% 3.06/1.81 % (13150)------------------------------
% 3.06/1.81 % (13150)------------------------------
% 3.06/1.81 % (13127)Instruction limit reached!
% 3.06/1.81 % (13127)------------------------------
% 3.06/1.81 % (13127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.81 % (13127)Termination reason: Unknown
% 3.06/1.81 % (13127)Termination phase: Saturation
% 3.06/1.81
% 3.06/1.81 % (13127)Memory used [KB]: 7547
% 3.06/1.81 % (13127)Time elapsed: 0.133 s
% 3.06/1.81 % (13127)Instructions burned: 276 (million)
% 3.06/1.81 % (13127)------------------------------
% 3.06/1.81 % (13127)------------------------------
% 3.06/1.82 % (13151)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_12850 for (2998ds/879Mi)
% 3.06/1.82 % (13152)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_12850 for (2998ds/17Mi)
% 3.06/1.83 % (13152)Instruction limit reached!
% 3.06/1.83 % (13152)------------------------------
% 3.06/1.83 % (13152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.83 % (13152)Termination reason: Unknown
% 3.06/1.83 % (13152)Termination phase: shuffling
% 3.06/1.83
% 3.06/1.83 % (13152)Memory used [KB]: 1663
% 3.06/1.83 % (13152)Time elapsed: 0.008 s
% 3.06/1.83 % (13152)Instructions burned: 17 (million)
% 3.06/1.83 % (13152)------------------------------
% 3.06/1.83 % (13152)------------------------------
% 3.06/1.84 % (13153)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_12850 for (2998ds/3Mi)
% 3.06/1.84 % (13153)Instruction limit reached!
% 3.06/1.84 % (13153)------------------------------
% 3.06/1.84 % (13153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.84 % (13153)Termination reason: Unknown
% 3.06/1.84 % (13153)Termination phase: shuffling
% 3.06/1.84
% 3.06/1.84 % (13153)Memory used [KB]: 1407
% 3.06/1.84 % (13153)Time elapsed: 0.003 s
% 3.06/1.84 % (13153)Instructions burned: 3 (million)
% 3.06/1.84 % (13153)------------------------------
% 3.06/1.84 % (13153)------------------------------
% 3.06/1.85 % (13154)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_12850 for (2998ds/30Mi)
% 3.06/1.86 % (13154)Instruction limit reached!
% 3.06/1.86 % (13154)------------------------------
% 3.06/1.86 % (13154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.86 % (13154)Termination reason: Unknown
% 3.06/1.86 % (13154)Termination phase: shuffling
% 3.06/1.86
% 3.06/1.86 % (13154)Memory used [KB]: 2046
% 3.06/1.86 % (13154)Time elapsed: 0.013 s
% 3.06/1.86 % (13154)Instructions burned: 31 (million)
% 3.06/1.86 % (13154)------------------------------
% 3.06/1.86 % (13154)------------------------------
% 3.06/1.87 % (13155)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_12850 for (2998ds/127Mi)
% 3.06/1.90 % (13148)Instruction limit reached!
% 3.06/1.90 % (13148)------------------------------
% 3.06/1.90 % (13148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.90 % (13148)Termination reason: Unknown
% 3.06/1.90 % (13148)Termination phase: Saturation
% 3.06/1.90
% 3.06/1.90 % (13148)Memory used [KB]: 8571
% 3.06/1.90 % (13148)Time elapsed: 0.125 s
% 3.06/1.90 % (13148)Instructions burned: 379 (million)
% 3.06/1.90 % (13148)------------------------------
% 3.06/1.90 % (13148)------------------------------
% 3.06/1.91 % (13156)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_12850 for (2997ds/100Mi)
% 3.06/1.91 % (13155)Instruction limit reached!
% 3.06/1.91 % (13155)------------------------------
% 3.06/1.91 % (13155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.91 % (13155)Termination reason: Unknown
% 3.06/1.91 % (13155)Termination phase: Property scanning
% 3.06/1.91
% 3.06/1.91 % (13155)Memory used [KB]: 2558
% 3.06/1.91 % (13155)Time elapsed: 0.042 s
% 3.06/1.91 % (13155)Instructions burned: 128 (million)
% 3.06/1.91 % (13155)------------------------------
% 3.06/1.91 % (13155)------------------------------
% 3.06/1.92 % (13158)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_12850 for (2997ds/3Mi)
% 3.06/1.92 % (13158)Instruction limit reached!
% 3.06/1.92 % (13158)------------------------------
% 3.06/1.92 % (13158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.92 % (13158)Termination reason: Unknown
% 3.06/1.92 % (13158)Termination phase: shuffling
% 3.06/1.92
% 3.06/1.92 % (13158)Memory used [KB]: 1407
% 3.06/1.92 % (13158)Time elapsed: 0.003 s
% 3.06/1.92 % (13158)Instructions burned: 4 (million)
% 3.06/1.92 % (13158)------------------------------
% 3.06/1.92 % (13158)------------------------------
% 3.06/1.93 % (13159)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_12850 for (2997ds/20Mi)
% 3.06/1.94 % (13156)Instruction limit reached!
% 3.06/1.94 % (13156)------------------------------
% 3.06/1.94 % (13156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.94 % (13156)Termination reason: Unknown
% 3.06/1.94 % (13156)Termination phase: Preprocessing 3
% 3.06/1.94
% 3.06/1.94 % (13156)Memory used [KB]: 2686
% 3.06/1.94 % (13156)Time elapsed: 0.032 s
% 3.06/1.94 % (13156)Instructions burned: 102 (million)
% 3.06/1.94 % (13156)------------------------------
% 3.06/1.94 % (13156)------------------------------
% 3.06/1.94 % (13159)Instruction limit reached!
% 3.06/1.94 % (13159)------------------------------
% 3.06/1.94 % (13159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.94 % (13159)Termination reason: Unknown
% 3.06/1.94 % (13159)Termination phase: shuffling
% 3.06/1.94
% 3.06/1.94 % (13159)Memory used [KB]: 1791
% 3.06/1.94 % (13159)Time elapsed: 0.009 s
% 3.06/1.94 % (13159)Instructions burned: 20 (million)
% 3.06/1.94 % (13159)------------------------------
% 3.06/1.94 % (13159)------------------------------
% 3.06/1.95 % (13160)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_12850 for (2997ds/86Mi)
% 3.06/1.95 % (13161)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_12850 for (2997ds/107Mi)
% 3.06/1.98 % (13142)Instruction limit reached!
% 3.06/1.98 % (13142)------------------------------
% 3.06/1.98 % (13142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.98 % (13142)Termination reason: Unknown
% 3.06/1.98 % (13142)Termination phase: Saturation
% 3.06/1.98
% 3.06/1.98 % (13142)Memory used [KB]: 8443
% 3.06/1.98 % (13142)Time elapsed: 0.226 s
% 3.06/1.98 % (13142)Instructions burned: 710 (million)
% 3.06/1.98 % (13142)------------------------------
% 3.06/1.98 % (13142)------------------------------
% 3.06/1.98 % (13160)Instruction limit reached!
% 3.06/1.98 % (13160)------------------------------
% 3.06/1.98 % (13160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.98 % (13160)Termination reason: Unknown
% 3.06/1.98 % (13160)Termination phase: Property scanning
% 3.06/1.98
% 3.06/1.98 % (13160)Memory used [KB]: 2558
% 3.06/1.98 % (13160)Time elapsed: 0.030 s
% 3.06/1.98 % (13160)Instructions burned: 86 (million)
% 3.06/1.98 % (13160)------------------------------
% 3.06/1.98 % (13160)------------------------------
% 3.06/1.99 % (13161)Instruction limit reached!
% 3.06/1.99 % (13161)------------------------------
% 3.06/1.99 % (13161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.99 % (13161)Termination reason: Unknown
% 3.06/1.99 % (13161)Termination phase: Property scanning
% 3.06/1.99
% 3.06/1.99 % (13161)Memory used [KB]: 2430
% 3.06/1.99 % (13161)Time elapsed: 0.036 s
% 3.06/1.99 % (13161)Instructions burned: 108 (million)
% 3.06/1.99 % (13161)------------------------------
% 3.06/1.99 % (13161)------------------------------
% 3.06/1.99 % (13162)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_12850 for (2996ds/39Mi)
% 3.06/1.99 % (13163)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_12850 for (2996ds/448Mi)
% 3.06/2.00 % (13164)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_12850 for (2996ds/46Mi)
% 3.06/2.00 % (13162)Instruction limit reached!
% 3.06/2.00 % (13162)------------------------------
% 3.06/2.00 % (13162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/2.00 % (13162)Termination reason: Unknown
% 3.06/2.00 % (13162)Termination phase: shuffling
% 3.06/2.00
% 3.06/2.00 % (13162)Memory used [KB]: 2174
% 3.06/2.00 % (13162)Time elapsed: 0.016 s
% 3.06/2.00 % (13162)Instructions burned: 40 (million)
% 3.06/2.00 % (13162)------------------------------
% 3.06/2.00 % (13162)------------------------------
% 3.06/2.01 % (13164)Instruction limit reached!
% 3.06/2.01 % (13164)------------------------------
% 3.06/2.01 % (13164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/2.01 % (13164)Termination reason: Unknown
% 3.06/2.01 % (13164)Termination phase: Property scanning
% 3.06/2.01
% 3.06/2.01 % (13164)Memory used [KB]: 1918
% 3.06/2.01 % (13164)Time elapsed: 0.017 s
% 3.06/2.01 % (13164)Instructions burned: 46 (million)
% 3.06/2.01 % (13164)------------------------------
% 3.06/2.01 % (13164)------------------------------
% 5.42/2.02 % (13144)Instruction limit reached!
% 5.42/2.02 % (13144)------------------------------
% 5.42/2.02 % (13144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.02 % (13144)Termination reason: Unknown
% 5.42/2.02 % (13144)Termination phase: Saturation
% 5.42/2.02
% 5.42/2.02 % (13144)Memory used [KB]: 8699
% 5.42/2.02 % (13144)Time elapsed: 0.267 s
% 5.42/2.02 % (13144)Instructions burned: 905 (million)
% 5.42/2.02 % (13144)------------------------------
% 5.42/2.02 % (13144)------------------------------
% 5.42/2.02 % (13166)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_12850 for (2996ds/507Mi)
% 5.42/2.02 % (13165)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_12850 for (2996ds/98Mi)
% 5.42/2.03 % (13167)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_12850 for (2996ds/149Mi)
% 5.42/2.03 % (13149)Instruction limit reached!
% 5.42/2.03 % (13149)------------------------------
% 5.42/2.03 % (13149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.03 % (13149)Termination reason: Unknown
% 5.42/2.03 % (13149)Termination phase: Saturation
% 5.42/2.03
% 5.42/2.03 % (13149)Memory used [KB]: 9083
% 5.42/2.03 % (13149)Time elapsed: 0.253 s
% 5.42/2.03 % (13149)Instructions burned: 779 (million)
% 5.42/2.03 % (13149)------------------------------
% 5.42/2.03 % (13149)------------------------------
% 5.42/2.04 % (13168)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_12850 for (2996ds/39Mi)
% 5.42/2.05 % (13133)Instruction limit reached!
% 5.42/2.05 % (13133)------------------------------
% 5.42/2.05 % (13133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.05 % (13133)Termination reason: Unknown
% 5.42/2.05 % (13133)Termination phase: Saturation
% 5.42/2.05
% 5.42/2.05 % (13133)Memory used [KB]: 10106
% 5.42/2.05 % (13133)Time elapsed: 0.337 s
% 5.42/2.05 % (13133)Instructions burned: 1044 (million)
% 5.42/2.05 % (13133)------------------------------
% 5.42/2.05 % (13133)------------------------------
% 5.42/2.06 % (13168)Instruction limit reached!
% 5.42/2.06 % (13168)------------------------------
% 5.42/2.06 % (13168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.06 % (13168)Termination reason: Unknown
% 5.42/2.06 % (13168)Termination phase: Property scanning
% 5.42/2.06
% 5.42/2.06 % (13168)Memory used [KB]: 1918
% 5.42/2.06 % (13168)Time elapsed: 0.015 s
% 5.42/2.06 % (13168)Instructions burned: 39 (million)
% 5.42/2.06 % (13168)------------------------------
% 5.42/2.06 % (13168)------------------------------
% 5.42/2.06 % (13169)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_12850 for (2996ds/6Mi)
% 5.42/2.06 % (13169)Instruction limit reached!
% 5.42/2.06 % (13169)------------------------------
% 5.42/2.06 % (13169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.06 % (13169)Termination reason: Unknown
% 5.42/2.06 % (13169)Termination phase: shuffling
% 5.42/2.06
% 5.42/2.06 % (13169)Memory used [KB]: 1535
% 5.42/2.06 % (13169)Time elapsed: 0.004 s
% 5.42/2.06 % (13169)Instructions burned: 9 (million)
% 5.42/2.06 % (13169)------------------------------
% 5.42/2.06 % (13169)------------------------------
% 5.42/2.06 % (13170)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_12850 for (2995ds/1087Mi)
% 5.42/2.07 % (13167)Instruction limit reached!
% 5.42/2.07 % (13167)------------------------------
% 5.42/2.07 % (13167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.07 % (13167)Termination reason: Unknown
% 5.42/2.07 % (13167)Termination phase: Saturation
% 5.42/2.07
% 5.42/2.07 % (13167)Memory used [KB]: 7164
% 5.42/2.07 % (13167)Time elapsed: 0.045 s
% 5.42/2.07 % (13167)Instructions burned: 151 (million)
% 5.42/2.07 % (13167)------------------------------
% 5.42/2.07 % (13167)------------------------------
% 5.42/2.07 % (13165)Instruction limit reached!
% 5.42/2.07 % (13165)------------------------------
% 5.42/2.07 % (13165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.07 % (13165)Termination reason: Unknown
% 5.42/2.07 % (13165)Termination phase: Preprocessing 1
% 5.42/2.07
% 5.42/2.07 % (13165)Memory used [KB]: 2686
% 5.42/2.07 % (13165)Time elapsed: 0.053 s
% 5.42/2.07 % (13165)Instructions burned: 98 (million)
% 5.42/2.07 % (13165)------------------------------
% 5.42/2.07 % (13165)------------------------------
% 5.42/2.07 % (13151)Refutation not found, non-redundant clauses discarded% (13151)------------------------------
% 5.42/2.07 % (13151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.07 % (13151)Termination reason: Refutation not found, non-redundant clauses discarded
% 5.42/2.07
% 5.42/2.07 % (13151)Memory used [KB]: 8187
% 5.42/2.07 % (13151)Time elapsed: 0.256 s
% 5.42/2.07 % (13151)Instructions burned: 839 (million)
% 5.42/2.07 % (13151)------------------------------
% 5.42/2.07 % (13151)------------------------------
% 5.42/2.07 % (13171)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_12850 for (2995ds/47Mi)
% 5.42/2.08 % (13172)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_12850 for (2995ds/44Mi)
% 5.42/2.08 % (13174)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_12850 for (2995ds/62Mi)
% 5.42/2.09 % (13173)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_12850 for (2995ds/432Mi)
% 5.42/2.09 % (13171)Instruction limit reached!
% 5.42/2.09 % (13171)------------------------------
% 5.42/2.09 % (13171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.09 % (13171)Termination reason: Unknown
% 5.42/2.09 % (13171)Termination phase: Property scanning
% 5.42/2.09
% 5.42/2.09 % (13171)Memory used [KB]: 1918
% 5.42/2.09 % (13171)Time elapsed: 0.016 s
% 5.42/2.09 % (13171)Instructions burned: 48 (million)
% 5.42/2.09 % (13171)------------------------------
% 5.42/2.09 % (13171)------------------------------
% 5.42/2.09 % (13172)Instruction limit reached!
% 5.42/2.09 % (13172)------------------------------
% 5.42/2.09 % (13172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.09 % (13172)Termination reason: Unknown
% 5.42/2.09 % (13172)Termination phase: shuffling
% 5.42/2.09
% 5.42/2.09 % (13172)Memory used [KB]: 2302
% 5.42/2.09 % (13172)Time elapsed: 0.014 s
% 5.42/2.09 % (13172)Instructions burned: 47 (million)
% 5.42/2.09 % (13172)------------------------------
% 5.42/2.09 % (13172)------------------------------
% 5.42/2.10 % (13175)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_12850 for (2995ds/31Mi)
% 5.42/2.10 % (13174)Instruction limit reached!
% 5.42/2.10 % (13174)------------------------------
% 5.42/2.10 % (13174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.10 % (13174)Termination reason: Unknown
% 5.42/2.10 % (13174)Termination phase: Property scanning
% 5.42/2.10
% 5.42/2.10 % (13174)Memory used [KB]: 2430
% 5.42/2.10 % (13174)Time elapsed: 0.018 s
% 5.42/2.10 % (13174)Instructions burned: 62 (million)
% 5.42/2.10 % (13174)------------------------------
% 5.42/2.10 % (13174)------------------------------
% 5.42/2.10 % (13176)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_12850 for (2995ds/96Mi)
% 5.42/2.11 % (13175)Instruction limit reached!
% 5.42/2.11 % (13175)------------------------------
% 5.42/2.11 % (13175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.11 % (13175)Termination reason: Unknown
% 5.42/2.11 % (13175)Termination phase: shuffling
% 5.42/2.11
% 5.42/2.11 % (13175)Memory used [KB]: 1918
% 5.42/2.11 % (13175)Time elapsed: 0.012 s
% 5.42/2.11 % (13175)Instructions burned: 33 (million)
% 5.42/2.11 % (13175)------------------------------
% 5.42/2.11 % (13175)------------------------------
% 5.42/2.11 % (13177)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_12850 for (2995ds/453Mi)
% 5.95/2.12 % (13178)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_12850 for (2995ds/71Mi)
% 5.95/2.12 % (13163)Instruction limit reached!
% 5.95/2.12 % (13163)------------------------------
% 5.95/2.12 % (13163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.12 % (13163)Termination reason: Unknown
% 5.95/2.12 % (13163)Termination phase: Saturation
% 5.95/2.12
% 5.95/2.12 % (13163)Memory used [KB]: 9083
% 5.95/2.12 % (13163)Time elapsed: 0.136 s
% 5.95/2.12 % (13163)Instructions burned: 448 (million)
% 5.95/2.12 % (13163)------------------------------
% 5.95/2.12 % (13163)------------------------------
% 5.95/2.13 % (13176)Instruction limit reached!
% 5.95/2.13 % (13176)------------------------------
% 5.95/2.13 % (13176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.13 % (13176)Termination reason: Unknown
% 5.95/2.13 % (13176)Termination phase: Property scanning
% 5.95/2.13
% 5.95/2.13 % (13176)Memory used [KB]: 2558
% 5.95/2.13 % (13176)Time elapsed: 0.030 s
% 5.95/2.13 % (13176)Instructions burned: 96 (million)
% 5.95/2.13 % (13176)------------------------------
% 5.95/2.13 % (13176)------------------------------
% 5.95/2.13 % (13179)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_12850 for (2995ds/83Mi)
% 5.95/2.14 % (13178)Instruction limit reached!
% 5.95/2.14 % (13178)------------------------------
% 5.95/2.14 % (13178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.14 % (13178)Termination reason: Unknown
% 5.95/2.14 % (13178)Termination phase: Preprocessing 3
% 5.95/2.14
% 5.95/2.14 % (13178)Memory used [KB]: 2430
% 5.95/2.14 % (13178)Time elapsed: 0.024 s
% 5.95/2.14 % (13178)Instructions burned: 72 (million)
% 5.95/2.14 % (13178)------------------------------
% 5.95/2.14 % (13178)------------------------------
% 5.95/2.14 % (13180)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_12850 for (2995ds/11Mi)
% 5.95/2.15 % (13180)Instruction limit reached!
% 5.95/2.15 % (13180)------------------------------
% 5.95/2.15 % (13180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.15 % (13180)Termination reason: Unknown
% 5.95/2.15 % (13180)Termination phase: shuffling
% 5.95/2.15
% 5.95/2.15 % (13180)Memory used [KB]: 1663
% 5.95/2.15 % (13180)Time elapsed: 0.005 s
% 5.95/2.15 % (13180)Instructions burned: 14 (million)
% 5.95/2.15 % (13180)------------------------------
% 5.95/2.15 % (13180)------------------------------
% 5.95/2.15 % (13181)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_12850 for (2995ds/41Mi)
% 5.95/2.16 % (13182)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12850 for (2995ds/6Mi)
% 5.95/2.16 % (13182)Instruction limit reached!
% 5.95/2.16 % (13182)------------------------------
% 5.95/2.16 % (13182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.16 % (13182)Termination reason: Unknown
% 5.95/2.16 % (13182)Termination phase: shuffling
% 5.95/2.16
% 5.95/2.16 % (13182)Memory used [KB]: 1535
% 5.95/2.16 % (13182)Time elapsed: 0.004 s
% 5.95/2.16 % (13182)Instructions burned: 8 (million)
% 5.95/2.16 % (13182)------------------------------
% 5.95/2.16 % (13182)------------------------------
% 5.95/2.16 % (13179)Instruction limit reached!
% 5.95/2.16 % (13179)------------------------------
% 5.95/2.16 % (13179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.16 % (13179)Termination reason: Unknown
% 5.95/2.16 % (13179)Termination phase: Property scanning
% 5.95/2.16
% 5.95/2.16 % (13179)Memory used [KB]: 2430
% 5.95/2.16 % (13179)Time elapsed: 0.028 s
% 5.95/2.16 % (13179)Instructions burned: 86 (million)
% 5.95/2.16 % (13179)------------------------------
% 5.95/2.16 % (13179)------------------------------
% 5.95/2.16 % (13181)Instruction limit reached!
% 5.95/2.16 % (13181)------------------------------
% 5.95/2.16 % (13181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.16 % (13181)Termination reason: Unknown
% 5.95/2.16 % (13181)Termination phase: shuffling
% 5.95/2.16
% 5.95/2.16 % (13181)Memory used [KB]: 2302
% 5.95/2.16 % (13181)Time elapsed: 0.014 s
% 5.95/2.16 % (13181)Instructions burned: 44 (million)
% 5.95/2.16 % (13181)------------------------------
% 5.95/2.16 % (13181)------------------------------
% 5.95/2.17 % (13183)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_12850 for (2995ds/150Mi)
% 5.95/2.17 % (13184)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_12850 for (2995ds/343Mi)
% 5.95/2.17 % (13185)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_12850 for (2994ds/109Mi)
% 5.95/2.18 % (13166)Instruction limit reached!
% 5.95/2.18 % (13166)------------------------------
% 5.95/2.18 % (13166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.18 % (13166)Termination reason: Unknown
% 5.95/2.18 % (13166)Termination phase: Saturation
% 5.95/2.18
% 5.95/2.18 % (13166)Memory used [KB]: 8571
% 5.95/2.18 % (13166)Time elapsed: 0.162 s
% 5.95/2.18 % (13166)Instructions burned: 507 (million)
% 5.95/2.18 % (13166)------------------------------
% 5.95/2.18 % (13166)------------------------------
% 5.95/2.19 % (13186)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_12850 for (2994ds/253Mi)
% 6.30/2.21 % (13185)Instruction limit reached!
% 6.30/2.21 % (13185)------------------------------
% 6.30/2.21 % (13185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.21 % (13185)Termination reason: Unknown
% 6.30/2.21 % (13185)Termination phase: Equality resolution with deletion
% 6.30/2.21
% 6.30/2.21 % (13185)Memory used [KB]: 2558
% 6.30/2.21 % (13185)Time elapsed: 0.034 s
% 6.30/2.21 % (13185)Instructions burned: 109 (million)
% 6.30/2.21 % (13185)------------------------------
% 6.30/2.21 % (13185)------------------------------
% 6.30/2.21 % (13183)Instruction limit reached!
% 6.30/2.21 % (13183)------------------------------
% 6.30/2.21 % (13183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.21 % (13183)Termination reason: Unknown
% 6.30/2.21 % (13183)Termination phase: Saturation
% 6.30/2.21
% 6.30/2.21 % (13183)Memory used [KB]: 2942
% 6.30/2.21 % (13183)Time elapsed: 0.045 s
% 6.30/2.21 % (13183)Instructions burned: 151 (million)
% 6.30/2.21 % (13183)------------------------------
% 6.30/2.21 % (13183)------------------------------
% 6.30/2.22 % (13187)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_12850 for (2994ds/140Mi)
% 6.30/2.22 % (13188)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_12850 for (2994ds/614Mi)
% 6.30/2.23 % (13173)Instruction limit reached!
% 6.30/2.23 % (13173)------------------------------
% 6.30/2.23 % (13173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.23 % (13173)Termination reason: Unknown
% 6.30/2.23 % (13173)Termination phase: Saturation
% 6.30/2.23
% 6.30/2.23 % (13173)Memory used [KB]: 3965
% 6.30/2.23 % (13173)Time elapsed: 0.143 s
% 6.30/2.23 % (13173)Instructions burned: 434 (million)
% 6.30/2.23 % (13173)------------------------------
% 6.30/2.23 % (13173)------------------------------
% 6.30/2.24 % (13177)Instruction limit reached!
% 6.30/2.24 % (13177)------------------------------
% 6.30/2.24 % (13177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.24 % (13177)Termination reason: Unknown
% 6.30/2.24 % (13177)Termination phase: Saturation
% 6.30/2.24
% 6.30/2.24 % (13177)Memory used [KB]: 8571
% 6.30/2.24 % (13177)Time elapsed: 0.127 s
% 6.30/2.24 % (13177)Instructions burned: 453 (million)
% 6.30/2.24 % (13177)------------------------------
% 6.30/2.24 % (13177)------------------------------
% 6.30/2.24 % (13189)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_12850 for (2994ds/202Mi)
% 6.30/2.25 % (13190)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_12850 for (2994ds/339Mi)
% 6.30/2.26 % (13187)Instruction limit reached!
% 6.30/2.26 % (13187)------------------------------
% 6.30/2.26 % (13187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.26 % (13187)Termination reason: Unknown
% 6.30/2.26 % (13187)Termination phase: Saturation
% 6.30/2.26
% 6.30/2.26 % (13187)Memory used [KB]: 7419
% 6.30/2.26 % (13187)Time elapsed: 0.044 s
% 6.30/2.26 % (13187)Instructions burned: 140 (million)
% 6.30/2.26 % (13187)------------------------------
% 6.30/2.26 % (13187)------------------------------
% 6.30/2.27 % (13191)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_12850 for (2994ds/283Mi)
% 6.30/2.27 % (13186)Instruction limit reached!
% 6.30/2.27 % (13186)------------------------------
% 6.30/2.27 % (13186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.27 % (13186)Termination reason: Unknown
% 6.30/2.27 % (13186)Termination phase: Saturation
% 6.30/2.27
% 6.30/2.27 % (13186)Memory used [KB]: 8315
% 6.30/2.27 % (13186)Time elapsed: 0.079 s
% 6.30/2.27 % (13186)Instructions burned: 255 (million)
% 6.30/2.27 % (13186)------------------------------
% 6.30/2.27 % (13186)------------------------------
% 6.30/2.27 % (13184)Instruction limit reached!
% 6.30/2.27 % (13184)------------------------------
% 6.30/2.27 % (13184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.27 % (13184)Termination reason: Unknown
% 6.30/2.27 % (13184)Termination phase: Saturation
% 6.30/2.27
% 6.30/2.27 % (13184)Memory used [KB]: 8059
% 6.30/2.27 % (13184)Time elapsed: 0.105 s
% 6.30/2.27 % (13184)Instructions burned: 345 (million)
% 6.30/2.27 % (13184)------------------------------
% 6.30/2.27 % (13184)------------------------------
% 6.30/2.28 % (13192)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_12850 for (2993ds/134Mi)
% 6.30/2.28 % (13193)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_12850 for (2993ds/298Mi)
% 6.94/2.30 % (13189)Instruction limit reached!
% 6.94/2.30 % (13189)------------------------------
% 6.94/2.30 % (13189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.30 % (13189)Termination reason: Unknown
% 6.94/2.30 % (13189)Termination phase: Saturation
% 6.94/2.30
% 6.94/2.30 % (13189)Memory used [KB]: 8443
% 6.94/2.30 % (13189)Time elapsed: 0.066 s
% 6.94/2.30 % (13189)Instructions burned: 204 (million)
% 6.94/2.30 % (13189)------------------------------
% 6.94/2.30 % (13189)------------------------------
% 6.94/2.31 % (13194)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_12850 for (2993ds/192Mi)
% 6.94/2.32 % (13192)Instruction limit reached!
% 6.94/2.32 % (13192)------------------------------
% 6.94/2.32 % (13192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.32 % (13192)Termination reason: Unknown
% 6.94/2.32 % (13192)Termination phase: Saturation
% 6.94/2.32
% 6.94/2.32 % (13192)Memory used [KB]: 7164
% 6.94/2.32 % (13192)Time elapsed: 0.041 s
% 6.94/2.32 % (13192)Instructions burned: 136 (million)
% 6.94/2.32 % (13192)------------------------------
% 6.94/2.32 % (13192)------------------------------
% 6.94/2.33 % (13195)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_12850 for (2993ds/258Mi)
% 6.94/2.34 % (13190)Instruction limit reached!
% 6.94/2.34 % (13190)------------------------------
% 6.94/2.34 % (13190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.34 % (13190)Termination reason: Unknown
% 6.94/2.34 % (13190)Termination phase: Saturation
% 6.94/2.34
% 6.94/2.34 % (13190)Memory used [KB]: 7675
% 6.94/2.34 % (13190)Time elapsed: 0.099 s
% 6.94/2.34 % (13190)Instructions burned: 339 (million)
% 6.94/2.34 % (13190)------------------------------
% 6.94/2.34 % (13190)------------------------------
% 6.94/2.35 % (13191)Instruction limit reached!
% 6.94/2.35 % (13191)------------------------------
% 6.94/2.35 % (13191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.35 % (13191)Termination reason: Unknown
% 6.94/2.35 % (13191)Termination phase: Saturation
% 6.94/2.35
% 6.94/2.35 % (13191)Memory used [KB]: 7675
% 6.94/2.35 % (13191)Time elapsed: 0.085 s
% 6.94/2.35 % (13191)Instructions burned: 284 (million)
% 6.94/2.35 % (13191)------------------------------
% 6.94/2.35 % (13191)------------------------------
% 6.94/2.35 % (13196)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_12850 for (2993ds/90Mi)
% 6.94/2.36 % (13197)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_12850 for (2993ds/231Mi)
% 6.94/2.37 % (13193)Instruction limit reached!
% 6.94/2.37 % (13193)------------------------------
% 6.94/2.37 % (13193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.37 % (13193)Termination reason: Unknown
% 6.94/2.37 % (13193)Termination phase: Saturation
% 6.94/2.37
% 6.94/2.37 % (13193)Memory used [KB]: 8443
% 6.94/2.37 % (13193)Time elapsed: 0.085 s
% 6.94/2.37 % (13193)Instructions burned: 300 (million)
% 6.94/2.37 % (13193)------------------------------
% 6.94/2.37 % (13193)------------------------------
% 6.94/2.38 % (13194)Instruction limit reached!
% 6.94/2.38 % (13194)------------------------------
% 6.94/2.38 % (13194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.38 % (13194)Termination reason: Unknown
% 6.94/2.38 % (13194)Termination phase: Saturation
% 6.94/2.38
% 6.94/2.38 % (13194)Memory used [KB]: 3582
% 6.94/2.38 % (13194)Time elapsed: 0.063 s
% 6.94/2.38 % (13194)Instructions burned: 194 (million)
% 6.94/2.38 % (13194)------------------------------
% 6.94/2.38 % (13194)------------------------------
% 6.94/2.38 % (13198)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_12850 for (2992ds/458Mi)
% 6.94/2.38 % (13196)Instruction limit reached!
% 6.94/2.38 % (13196)------------------------------
% 6.94/2.38 % (13196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.38 % (13196)Termination reason: Unknown
% 6.94/2.38 % (13196)Termination phase: Property scanning
% 6.94/2.38
% 6.94/2.38 % (13196)Memory used [KB]: 2558
% 6.94/2.38 % (13196)Time elapsed: 0.029 s
% 6.94/2.38 % (13196)Instructions burned: 92 (million)
% 6.94/2.38 % (13196)------------------------------
% 6.94/2.38 % (13196)------------------------------
% 6.94/2.39 % (13199)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_12850 for (2992ds/31Mi)
% 6.94/2.39 % (13200)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_12850 for (2992ds/297Mi)
% 7.48/2.40 % (13199)Instruction limit reached!
% 7.48/2.40 % (13199)------------------------------
% 7.48/2.40 % (13199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.40 % (13199)Termination reason: Unknown
% 7.48/2.40 % (13199)Termination phase: shuffling
% 7.48/2.40
% 7.48/2.40 % (13199)Memory used [KB]: 1918
% 7.48/2.40 % (13199)Time elapsed: 0.013 s
% 7.48/2.40 % (13199)Instructions burned: 32 (million)
% 7.48/2.40 % (13199)------------------------------
% 7.48/2.40 % (13199)------------------------------
% 7.48/2.40 % (13170)Instruction limit reached!
% 7.48/2.40 % (13170)------------------------------
% 7.48/2.40 % (13170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.40 % (13170)Termination reason: Unknown
% 7.48/2.40 % (13170)Termination phase: Saturation
% 7.48/2.40
% 7.48/2.40 % (13170)Memory used [KB]: 8699
% 7.48/2.40 % (13170)Time elapsed: 0.338 s
% 7.48/2.40 % (13170)Instructions burned: 1087 (million)
% 7.48/2.40 % (13170)------------------------------
% 7.48/2.40 % (13170)------------------------------
% 7.48/2.41 % (13195)Instruction limit reached!
% 7.48/2.41 % (13195)------------------------------
% 7.48/2.41 % (13195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.41 % (13195)Termination reason: Unknown
% 7.48/2.41 % (13195)Termination phase: Saturation
% 7.48/2.41
% 7.48/2.41 % (13195)Memory used [KB]: 7931
% 7.48/2.41 % (13195)Time elapsed: 0.100 s
% 7.48/2.41 % (13195)Instructions burned: 261 (million)
% 7.48/2.41 % (13195)------------------------------
% 7.48/2.41 % (13195)------------------------------
% 7.48/2.41 % (13201)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_12850 for (2992ds/987Mi)
% 7.48/2.41 % (13188)Instruction limit reached!
% 7.48/2.41 % (13188)------------------------------
% 7.48/2.41 % (13188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.41 % (13188)Termination reason: Unknown
% 7.48/2.41 % (13188)Termination phase: Saturation
% 7.48/2.41
% 7.48/2.41 % (13188)Memory used [KB]: 8955
% 7.48/2.41 % (13188)Time elapsed: 0.189 s
% 7.48/2.41 % (13188)Instructions burned: 614 (million)
% 7.48/2.41 % (13188)------------------------------
% 7.48/2.41 % (13188)------------------------------
% 7.48/2.41 % (13202)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_12850 for (2992ds/182Mi)
% 7.48/2.42 % (13203)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_12850 for (2992ds/182Mi)
% 7.48/2.42 % (13204)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_12850 for (2992ds/154Mi)
% 7.48/2.43 % (13197)Instruction limit reached!
% 7.48/2.43 % (13197)------------------------------
% 7.48/2.43 % (13197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.43 % (13197)Termination reason: Unknown
% 7.48/2.43 % (13197)Termination phase: Saturation
% 7.48/2.43
% 7.48/2.43 % (13197)Memory used [KB]: 7419
% 7.48/2.43 % (13197)Time elapsed: 0.066 s
% 7.48/2.43 % (13197)Instructions burned: 233 (million)
% 7.48/2.43 % (13197)------------------------------
% 7.48/2.43 % (13197)------------------------------
% 7.48/2.44 % (13205)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_12850 for (2992ds/79Mi)
% 7.48/2.46 % (13205)Instruction limit reached!
% 7.48/2.46 % (13205)------------------------------
% 7.48/2.46 % (13205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.46 % (13205)Termination reason: Unknown
% 7.48/2.46 % (13205)Termination phase: Property scanning
% 7.48/2.46
% 7.48/2.46 % (13205)Memory used [KB]: 2558
% 7.48/2.46 % (13205)Time elapsed: 0.026 s
% 7.48/2.46 % (13205)Instructions burned: 82 (million)
% 7.48/2.46 % (13205)------------------------------
% 7.48/2.46 % (13205)------------------------------
% 7.48/2.46 % (13204)Instruction limit reached!
% 7.48/2.46 % (13204)------------------------------
% 7.48/2.46 % (13204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.46 % (13204)Termination reason: Unknown
% 7.48/2.46 % (13204)Termination phase: Property scanning
% 7.48/2.46
% 7.48/2.46 % (13204)Memory used [KB]: 2686
% 7.48/2.46 % (13204)Time elapsed: 0.043 s
% 7.48/2.46 % (13204)Instructions burned: 157 (million)
% 7.48/2.46 % (13204)------------------------------
% 7.48/2.46 % (13204)------------------------------
% 7.48/2.46 % (13202)Instruction limit reached!
% 7.48/2.46 % (13202)------------------------------
% 7.48/2.46 % (13202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.46 % (13202)Termination reason: Unknown
% 7.48/2.46 % (13202)Termination phase: Saturation
% 7.48/2.46
% 7.48/2.46 % (13202)Memory used [KB]: 7291
% 7.48/2.46 % (13202)Time elapsed: 0.053 s
% 7.48/2.46 % (13202)Instructions burned: 182 (million)
% 7.48/2.46 % (13202)------------------------------
% 7.48/2.46 % (13202)------------------------------
% 7.48/2.47 % (13203)Instruction limit reached!
% 7.48/2.47 % (13203)------------------------------
% 7.48/2.47 % (13203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.47 % (13203)Termination reason: Unknown
% 7.48/2.47 % (13203)Termination phase: Saturation
% 7.48/2.47
% 7.48/2.47 % (13203)Memory used [KB]: 7419
% 7.48/2.47 % (13203)Time elapsed: 0.055 s
% 7.48/2.47 % (13203)Instructions burned: 184 (million)
% 7.48/2.47 % (13203)------------------------------
% 7.48/2.47 % (13203)------------------------------
% 7.48/2.47 % (13206)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_12850 for (2991ds/216Mi)
% 7.48/2.47 % (13207)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_12850 for (2991ds/114Mi)
% 7.48/2.47 % (13208)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_12850 for (2991ds/922Mi)
% 7.48/2.47 % (13200)Instruction limit reached!
% 7.48/2.47 % (13200)------------------------------
% 7.48/2.47 % (13200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.47 % (13200)Termination reason: Unknown
% 7.48/2.47 % (13200)Termination phase: Saturation
% 7.48/2.47
% 7.48/2.48 % (13200)Memory used [KB]: 7675
% 7.48/2.48 % (13200)Time elapsed: 0.086 s
% 7.48/2.48 % (13200)Instructions burned: 297 (million)
% 7.48/2.48 % (13200)------------------------------
% 7.48/2.48 % (13200)------------------------------
% 7.48/2.48 % (13209)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_12850 for (2991ds/182Mi)
% 7.48/2.48 % (13210)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_12850 for (2991ds/164Mi)
% 8.52/2.50 % (13207)Instruction limit reached!
% 8.52/2.50 % (13207)------------------------------
% 8.52/2.50 % (13207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.50 % (13207)Termination reason: Unknown
% 8.52/2.50 % (13207)Termination phase: Property scanning
% 8.52/2.50
% 8.52/2.50 % (13207)Memory used [KB]: 2558
% 8.52/2.50 % (13207)Time elapsed: 0.035 s
% 8.52/2.50 % (13207)Instructions burned: 114 (million)
% 8.52/2.50 % (13207)------------------------------
% 8.52/2.50 % (13207)------------------------------
% 8.52/2.51 % (13211)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_12850 for (2991ds/50Mi)
% 8.52/2.51 % (13198)Instruction limit reached!
% 8.52/2.51 % (13198)------------------------------
% 8.52/2.51 % (13198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.51 % (13198)Termination reason: Unknown
% 8.52/2.51 % (13198)Termination phase: Saturation
% 8.52/2.51
% 8.52/2.51 % (13198)Memory used [KB]: 8443
% 8.52/2.51 % (13198)Time elapsed: 0.138 s
% 8.52/2.51 % (13198)Instructions burned: 458 (million)
% 8.52/2.51 % (13198)------------------------------
% 8.52/2.51 % (13198)------------------------------
% 8.52/2.52 % (13212)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_12850 for (2991ds/368Mi)
% 8.52/2.53 % (13211)Instruction limit reached!
% 8.52/2.53 % (13211)------------------------------
% 8.52/2.53 % (13211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.53 % (13211)Termination reason: Unknown
% 8.52/2.53 % (13211)Termination phase: shuffling
% 8.52/2.53
% 8.52/2.53 % (13211)Memory used [KB]: 2302
% 8.52/2.53 % (13211)Time elapsed: 0.015 s
% 8.52/2.53 % (13211)Instructions burned: 51 (million)
% 8.52/2.53 % (13211)------------------------------
% 8.52/2.53 % (13211)------------------------------
% 8.52/2.53 % (13209)Instruction limit reached!
% 8.52/2.53 % (13209)------------------------------
% 8.52/2.53 % (13209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.53 % (13209)Termination reason: Unknown
% 8.52/2.53 % (13209)Termination phase: Saturation
% 8.52/2.53
% 8.52/2.53 % (13209)Memory used [KB]: 2686
% 8.52/2.53 % (13209)Time elapsed: 0.050 s
% 8.52/2.53 % (13209)Instructions burned: 184 (million)
% 8.52/2.53 % (13209)------------------------------
% 8.52/2.53 % (13209)------------------------------
% 8.52/2.53 % (13210)Instruction limit reached!
% 8.52/2.53 % (13210)------------------------------
% 8.52/2.53 % (13210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.53 % (13210)Termination reason: Unknown
% 8.52/2.53 % (13210)Termination phase: Saturation
% 8.52/2.53
% 8.52/2.53 % (13210)Memory used [KB]: 2686
% 8.52/2.53 % (13210)Time elapsed: 0.046 s
% 8.52/2.53 % (13210)Instructions burned: 164 (million)
% 8.52/2.53 % (13210)------------------------------
% 8.52/2.53 % (13210)------------------------------
% 8.52/2.53 % (13206)Instruction limit reached!
% 8.52/2.53 % (13206)------------------------------
% 8.52/2.53 % (13206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.53 % (13206)Termination reason: Unknown
% 8.52/2.53 % (13206)Termination phase: Saturation
% 8.52/2.53
% 8.52/2.53 % (13206)Memory used [KB]: 7419
% 8.52/2.53 % (13206)Time elapsed: 0.061 s
% 8.52/2.53 % (13206)Instructions burned: 217 (million)
% 8.52/2.53 % (13206)------------------------------
% 8.52/2.53 % (13206)------------------------------
% 8.52/2.54 % (13213)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_12850 for (2991ds/1021Mi)
% 8.52/2.54 % (13214)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_12850 for (2991ds/267Mi)
% 8.52/2.54 % (13215)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_12850 for (2991ds/204Mi)
% 8.52/2.54 % (13216)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_12850 for (2991ds/26Mi)
% 8.52/2.55 % (13216)Instruction limit reached!
% 8.52/2.55 % (13216)------------------------------
% 8.52/2.55 % (13216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.55 % (13216)Termination reason: Unknown
% 8.52/2.55 % (13216)Termination phase: shuffling
% 8.52/2.55
% 8.52/2.55 % (13216)Memory used [KB]: 2046
% 8.52/2.55 % (13216)Time elapsed: 0.009 s
% 8.52/2.55 % (13216)Instructions burned: 29 (million)
% 8.52/2.55 % (13216)------------------------------
% 8.52/2.55 % (13216)------------------------------
% 8.52/2.56 % (13217)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_12850 for (2991ds/53Mi)
% 8.52/2.57 % (13217)Instruction limit reached!
% 8.52/2.57 % (13217)------------------------------
% 8.52/2.57 % (13217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.57 % (13217)Termination reason: Unknown
% 8.52/2.57 % (13217)Termination phase: shuffling
% 8.52/2.57
% 8.52/2.57 % (13217)Memory used [KB]: 2430
% 8.52/2.57 % (13217)Time elapsed: 0.016 s
% 8.52/2.57 % (13217)Instructions burned: 54 (million)
% 8.52/2.57 % (13217)------------------------------
% 8.52/2.57 % (13217)------------------------------
% 8.52/2.58 % (13218)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_12850 for (2990ds/4436Mi)
% 8.95/2.60 % (13215)Instruction limit reached!
% 8.95/2.60 % (13215)------------------------------
% 8.95/2.60 % (13215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.60 % (13215)Termination reason: Unknown
% 8.95/2.60 % (13215)Termination phase: Saturation
% 8.95/2.60
% 8.95/2.60 % (13215)Memory used [KB]: 7291
% 8.95/2.60 % (13215)Time elapsed: 0.060 s
% 8.95/2.60 % (13215)Instructions burned: 206 (million)
% 8.95/2.60 % (13215)------------------------------
% 8.95/2.60 % (13215)------------------------------
% 8.95/2.61 % (13219)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_12850 for (2990ds/1539Mi)
% 8.95/2.61 % (13214)Instruction limit reached!
% 8.95/2.61 % (13214)------------------------------
% 8.95/2.61 % (13214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.61 % (13214)Termination reason: Unknown
% 8.95/2.61 % (13214)Termination phase: Saturation
% 8.95/2.61
% 8.95/2.61 % (13214)Memory used [KB]: 7547
% 8.95/2.61 % (13214)Time elapsed: 0.077 s
% 8.95/2.61 % (13214)Instructions burned: 267 (million)
% 8.95/2.61 % (13214)------------------------------
% 8.95/2.61 % (13214)------------------------------
% 8.95/2.62 % (13220)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_12850 for (2990ds/408Mi)
% 8.95/2.63 % (13212)Instruction limit reached!
% 8.95/2.63 % (13212)------------------------------
% 8.95/2.63 % (13212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.63 % (13212)Termination reason: Unknown
% 8.95/2.63 % (13212)Termination phase: Saturation
% 8.95/2.63
% 8.95/2.63 % (13212)Memory used [KB]: 8059
% 8.95/2.63 % (13212)Time elapsed: 0.111 s
% 8.95/2.63 % (13212)Instructions burned: 369 (million)
% 8.95/2.63 % (13212)------------------------------
% 8.95/2.63 % (13212)------------------------------
% 8.95/2.64 % (13221)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_12850 for (2990ds/5205Mi)
% 9.23/2.71 % (13201)Instruction limit reached!
% 9.23/2.71 % (13201)------------------------------
% 9.23/2.71 % (13201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.23/2.71 % (13201)Termination reason: Unknown
% 9.23/2.71 % (13201)Termination phase: Saturation
% 9.23/2.71
% 9.23/2.71 % (13201)Memory used [KB]: 8955
% 9.23/2.71 % (13201)Time elapsed: 0.303 s
% 9.23/2.71 % (13201)Instructions burned: 988 (million)
% 9.23/2.71 % (13201)------------------------------
% 9.23/2.71 % (13201)------------------------------
% 9.23/2.72 % (13222)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_12850 for (2989ds/1913Mi)
% 9.23/2.75 % (13220)Instruction limit reached!
% 9.23/2.75 % (13220)------------------------------
% 9.23/2.75 % (13220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.23/2.75 % (13220)Termination reason: Unknown
% 9.23/2.75 % (13220)Termination phase: Saturation
% 9.23/2.75
% 9.23/2.75 % (13220)Memory used [KB]: 8955
% 9.23/2.75 % (13220)Time elapsed: 0.128 s
% 9.23/2.75 % (13220)Instructions burned: 408 (million)
% 9.23/2.75 % (13220)------------------------------
% 9.23/2.75 % (13220)------------------------------
% 9.23/2.76 % (13223)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_12850 for (2989ds/4350Mi)
% 9.23/2.77 % (13208)Instruction limit reached!
% 9.23/2.77 % (13208)------------------------------
% 9.23/2.77 % (13208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.23/2.77 % (13208)Termination reason: Unknown
% 9.23/2.77 % (13208)Termination phase: Saturation
% 9.23/2.77
% 9.23/2.77 % (13208)Memory used [KB]: 8699
% 9.23/2.77 % (13208)Time elapsed: 0.300 s
% 9.23/2.77 % (13208)Instructions burned: 924 (million)
% 9.23/2.77 % (13208)------------------------------
% 9.23/2.77 % (13208)------------------------------
% 9.23/2.78 % (13224)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_12850 for (2988ds/68Mi)
% 9.98/2.80 % (13224)Instruction limit reached!
% 9.98/2.80 % (13224)------------------------------
% 9.98/2.80 % (13224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.80 % (13224)Termination reason: Unknown
% 9.98/2.80 % (13224)Termination phase: Preprocessing 3
% 9.98/2.80
% 9.98/2.80 % (13224)Memory used [KB]: 2174
% 9.98/2.80 % (13224)Time elapsed: 0.022 s
% 9.98/2.80 % (13224)Instructions burned: 68 (million)
% 9.98/2.80 % (13224)------------------------------
% 9.98/2.80 % (13224)------------------------------
% 9.98/2.81 % (13225)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_12850 for (2988ds/358Mi)
% 9.98/2.86 % (13213)Instruction limit reached!
% 9.98/2.86 % (13213)------------------------------
% 9.98/2.86 % (13213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.86 % (13213)Termination reason: Unknown
% 9.98/2.86 % (13213)Termination phase: Saturation
% 9.98/2.86
% 9.98/2.86 % (13213)Memory used [KB]: 9722
% 9.98/2.86 % (13213)Time elapsed: 0.326 s
% 9.98/2.86 % (13213)Instructions burned: 1024 (million)
% 9.98/2.86 % (13213)------------------------------
% 9.98/2.86 % (13213)------------------------------
% 9.98/2.87 % (13226)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_12850 for (2988ds/31Mi)
% 9.98/2.88 % (13226)Instruction limit reached!
% 9.98/2.88 % (13226)------------------------------
% 9.98/2.88 % (13226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.88 % (13226)Termination reason: Unknown
% 9.98/2.88 % (13226)Termination phase: Property scanning
% 9.98/2.88
% 9.98/2.88 % (13226)Memory used [KB]: 1918
% 9.98/2.88 % (13226)Time elapsed: 0.012 s
% 9.98/2.88 % (13226)Instructions burned: 33 (million)
% 9.98/2.88 % (13226)------------------------------
% 9.98/2.88 % (13226)------------------------------
% 9.98/2.89 % (13227)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_12850 for (2987ds/279Mi)
% 10.38/2.92 % (13225)Instruction limit reached!
% 10.38/2.92 % (13225)------------------------------
% 10.38/2.92 % (13225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.38/2.92 % (13225)Termination reason: Unknown
% 10.38/2.92 % (13225)Termination phase: Saturation
% 10.38/2.92
% 10.38/2.92 % (13225)Memory used [KB]: 7675
% 10.38/2.92 % (13225)Time elapsed: 0.112 s
% 10.38/2.92 % (13225)Instructions burned: 360 (million)
% 10.38/2.92 % (13225)------------------------------
% 10.38/2.92 % (13225)------------------------------
% 10.38/2.93 % (13228)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_12850 for (2987ds/258Mi)
% 10.38/2.94 % (13227)Refutation not found, incomplete strategy
% 10.38/2.94 % (13227)------------------------------
% 10.38/2.94 % (13227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.38/2.94 % (13227)Termination reason: Refutation not found, incomplete strategy
% 10.38/2.94
% 10.38/2.94
% 10.38/2.94 % (13227)Memory used [KB]: 7419
% 10.38/2.94 % (13227)Time elapsed: 0.051 s
% 10.38/2.94 % (13227)Instructions burned: 179 (million)
% 10.38/2.94 % (13227)------------------------------
% 10.38/2.94 % (13227)------------------------------
% 10.38/2.95 % (13229)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_12850 for (2987ds/26Mi)
% 10.38/2.96 % (13229)Instruction limit reached!
% 10.38/2.96 % (13229)------------------------------
% 10.38/2.96 % (13229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.38/2.96 % (13229)Termination reason: Unknown
% 10.38/2.96 % (13229)Termination phase: shuffling
% 10.38/2.96
% 10.38/2.96 % (13229)Memory used [KB]: 2046
% 10.38/2.96 % (13229)Time elapsed: 0.009 s
% 10.38/2.96 % (13229)Instructions burned: 29 (million)
% 10.38/2.96 % (13229)------------------------------
% 10.38/2.96 % (13229)------------------------------
% 10.38/2.97 % (13230)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_12850 for (2987ds/995Mi)
% 10.38/3.01 % (13228)Instruction limit reached!
% 10.38/3.01 % (13228)------------------------------
% 10.38/3.01 % (13228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.38/3.01 % (13228)Termination reason: Unknown
% 10.38/3.01 % (13228)Termination phase: Saturation
% 10.38/3.01
% 10.38/3.01 % (13228)Memory used [KB]: 7931
% 10.38/3.01 % (13228)Time elapsed: 0.076 s
% 10.38/3.01 % (13228)Instructions burned: 258 (million)
% 10.38/3.01 % (13228)------------------------------
% 10.38/3.01 % (13228)------------------------------
% 10.38/3.02 % (13231)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_12850 for (2986ds/373Mi)
% 12.51/3.08 % (13219)Instruction limit reached!
% 12.51/3.08 % (13219)------------------------------
% 12.51/3.08 % (13219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.51/3.08 % (13219)Termination reason: Unknown
% 12.51/3.08 % (13219)Termination phase: Saturation
% 12.51/3.08
% 12.51/3.08 % (13219)Memory used [KB]: 11641
% 12.51/3.08 % (13219)Time elapsed: 0.471 s
% 12.51/3.08 % (13219)Instructions burned: 1541 (million)
% 12.51/3.08 % (13219)------------------------------
% 12.51/3.08 % (13219)------------------------------
% 12.51/3.09 % (13232)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_12850 for (2985ds/253Mi)
% 12.51/3.09 % (13222)Instruction limit reached!
% 12.51/3.09 % (13222)------------------------------
% 12.51/3.09 % (13222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.51/3.09 % (13222)Termination reason: Unknown
% 12.51/3.09 % (13222)Termination phase: Saturation
% 12.51/3.09
% 12.51/3.09 % (13222)Memory used [KB]: 2942
% 12.51/3.09 % (13222)Time elapsed: 0.377 s
% 12.51/3.09 % (13222)Instructions burned: 1915 (million)
% 12.51/3.09 % (13222)------------------------------
% 12.51/3.09 % (13222)------------------------------
% 12.51/3.10 % (13233)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_12850 for (2985ds/832Mi)
% 13.07/3.13 % (13231)Instruction limit reached!
% 13.07/3.13 % (13231)------------------------------
% 13.07/3.13 % (13231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.07/3.13 % (13231)Termination reason: Unknown
% 13.07/3.13 % (13231)Termination phase: Saturation
% 13.07/3.13
% 13.07/3.13 % (13231)Memory used [KB]: 8315
% 13.07/3.13 % (13231)Time elapsed: 0.115 s
% 13.07/3.13 % (13231)Instructions burned: 373 (million)
% 13.07/3.13 % (13231)------------------------------
% 13.07/3.13 % (13231)------------------------------
% 13.07/3.14 % (13234)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_12850 for (2985ds/668Mi)
% 13.07/3.16 % (13232)Instruction limit reached!
% 13.07/3.16 % (13232)------------------------------
% 13.07/3.16 % (13232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.07/3.16 % (13232)Termination reason: Unknown
% 13.07/3.16 % (13232)Termination phase: Saturation
% 13.07/3.16
% 13.07/3.16 % (13232)Memory used [KB]: 7547
% 13.07/3.16 % (13232)Time elapsed: 0.070 s
% 13.07/3.16 % (13232)Instructions burned: 255 (million)
% 13.07/3.16 % (13232)------------------------------
% 13.07/3.16 % (13232)------------------------------
% 13.07/3.17 % (13235)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_12850 for (2985ds/40Mi)
% 13.07/3.18 % (13235)Instruction limit reached!
% 13.07/3.18 % (13235)------------------------------
% 13.07/3.18 % (13235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.07/3.18 % (13235)Termination reason: Unknown
% 13.07/3.18 % (13235)Termination phase: shuffling
% 13.07/3.18
% 13.07/3.18 % (13235)Memory used [KB]: 2174
% 13.07/3.18 % (13235)Time elapsed: 0.012 s
% 13.07/3.18 % (13235)Instructions burned: 40 (million)
% 13.07/3.18 % (13235)------------------------------
% 13.07/3.18 % (13235)------------------------------
% 13.07/3.19 % (13236)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_12850 for (2984ds/294Mi)
% 13.59/3.26 % (13230)Instruction limit reached!
% 13.59/3.26 % (13230)------------------------------
% 13.59/3.26 % (13230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.59/3.26 % (13230)Termination reason: Unknown
% 13.59/3.26 % (13230)Termination phase: Saturation
% 13.59/3.26
% 13.59/3.26 % (13230)Memory used [KB]: 10106
% 13.59/3.26 % (13230)Time elapsed: 0.291 s
% 13.59/3.26 % (13230)Instructions burned: 996 (million)
% 13.59/3.26 % (13230)------------------------------
% 13.59/3.26 % (13230)------------------------------
% 13.59/3.27 % (13237)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_12850 for (2984ds/187Mi)
% 13.59/3.27 % (13236)Instruction limit reached!
% 13.59/3.27 % (13236)------------------------------
% 13.59/3.27 % (13236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.59/3.27 % (13236)Termination reason: Unknown
% 13.59/3.27 % (13236)Termination phase: Saturation
% 13.59/3.27
% 13.59/3.27 % (13236)Memory used [KB]: 7675
% 13.59/3.27 % (13236)Time elapsed: 0.085 s
% 13.59/3.27 % (13236)Instructions burned: 295 (million)
% 13.59/3.27 % (13236)------------------------------
% 13.59/3.27 % (13236)------------------------------
% 13.59/3.28 % (13238)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_12850 for (2983ds/371Mi)
% 14.05/3.32 % (13237)Instruction limit reached!
% 14.05/3.32 % (13237)------------------------------
% 14.05/3.32 % (13237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.05/3.32 % (13237)Termination reason: Unknown
% 14.05/3.32 % (13237)Termination phase: Saturation
% 14.05/3.32
% 14.05/3.32 % (13237)Memory used [KB]: 7419
% 14.05/3.32 % (13237)Time elapsed: 0.055 s
% 14.05/3.32 % (13237)Instructions burned: 190 (million)
% 14.05/3.32 % (13237)------------------------------
% 14.05/3.32 % (13237)------------------------------
% 14.05/3.33 % (13239)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_12850 for (2983ds/1827Mi)
% 14.05/3.34 % (13234)Instruction limit reached!
% 14.05/3.34 % (13234)------------------------------
% 14.05/3.34 % (13234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.05/3.34 % (13234)Termination reason: Unknown
% 14.05/3.34 % (13234)Termination phase: Saturation
% 14.05/3.34
% 14.05/3.34 % (13234)Memory used [KB]: 13944
% 14.05/3.34 % (13234)Time elapsed: 0.196 s
% 14.05/3.34 % (13234)Instructions burned: 669 (million)
% 14.05/3.34 % (13234)------------------------------
% 14.05/3.34 % (13234)------------------------------
% 14.05/3.34 % (13240)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_12850 for (2983ds/70Mi)
% 14.05/3.35 % (13233)Instruction limit reached!
% 14.05/3.35 % (13233)------------------------------
% 14.05/3.35 % (13233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.05/3.35 % (13233)Termination reason: Unknown
% 14.05/3.35 % (13233)Termination phase: Saturation
% 14.05/3.35
% 14.05/3.35 % (13233)Memory used [KB]: 8955
% 14.05/3.35 % (13233)Time elapsed: 0.248 s
% 14.05/3.35 % (13233)Instructions burned: 834 (million)
% 14.05/3.35 % (13233)------------------------------
% 14.05/3.35 % (13233)------------------------------
% 14.05/3.36 % (13241)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_12850 for (2983ds/316Mi)
% 14.05/3.36 % (13240)Instruction limit reached!
% 14.05/3.36 % (13240)------------------------------
% 14.05/3.36 % (13240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.05/3.36 % (13240)Termination reason: Unknown
% 14.05/3.36 % (13240)Termination phase: Property scanning
% 14.05/3.36
% 14.05/3.36 % (13240)Memory used [KB]: 2430
% 14.05/3.36 % (13240)Time elapsed: 0.020 s
% 14.05/3.36 % (13240)Instructions burned: 70 (million)
% 14.05/3.36 % (13240)------------------------------
% 14.05/3.36 % (13240)------------------------------
% 14.05/3.37 % (13242)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_12850 for (2982ds/932Mi)
% 14.05/3.39 % (13238)Instruction limit reached!
% 14.05/3.39 % (13238)------------------------------
% 14.05/3.39 % (13238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.05/3.39 % (13238)Termination reason: Unknown
% 14.05/3.39 % (13238)Termination phase: Saturation
% 14.05/3.39
% 14.05/3.39 % (13238)Memory used [KB]: 8443
% 14.05/3.39 % (13238)Time elapsed: 0.114 s
% 14.05/3.39 % (13238)Instructions burned: 372 (million)
% 14.05/3.39 % (13238)------------------------------
% 14.05/3.39 % (13238)------------------------------
% 15.02/3.40 % (13243)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_12850 for (2982ds/4714Mi)
% 15.02/3.44 % (13241)Refutation not found, incomplete strategy
% 15.02/3.44 % (13241)------------------------------
% 15.02/3.44 % (13241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/3.44 % (13241)Termination reason: Refutation not found, incomplete strategy
% 15.02/3.44
% 15.02/3.44
% 15.02/3.44 % (13241)Memory used [KB]: 7931
% 15.02/3.44 % (13241)Time elapsed: 0.080 s
% 15.02/3.44 % (13241)Instructions burned: 286 (million)
% 15.02/3.44 % (13241)------------------------------
% 15.02/3.44 % (13241)------------------------------
% 15.02/3.45 % (13244)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_12850 for (2982ds/8250Mi)
% 15.02/3.50 % (13243)Refutation not found, incomplete strategy
% 15.02/3.50 % (13243)------------------------------
% 15.02/3.50 % (13243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/3.50 % (13243)Termination reason: Refutation not found, incomplete strategy
% 15.02/3.50
% 15.02/3.50
% 15.02/3.50 % (13243)Memory used [KB]: 8059
% 15.02/3.50 % (13243)Time elapsed: 0.094 s
% 15.02/3.50 % (13243)Instructions burned: 329 (million)
% 15.02/3.50 % (13243)------------------------------
% 15.02/3.50 % (13243)------------------------------
% 15.42/3.51 % (13245)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_12850 for (2981ds/770Mi)
% 15.82/3.65 % (13242)Instruction limit reached!
% 15.82/3.65 % (13242)------------------------------
% 15.82/3.65 % (13242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.82/3.65 % (13242)Termination reason: Unknown
% 15.82/3.65 % (13242)Termination phase: Saturation
% 15.82/3.65
% 15.82/3.65 % (13242)Memory used [KB]: 11385
% 15.82/3.65 % (13242)Time elapsed: 0.275 s
% 15.82/3.65 % (13242)Instructions burned: 933 (million)
% 15.82/3.65 % (13242)------------------------------
% 15.82/3.65 % (13242)------------------------------
% 15.82/3.66 % (13246)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_12850 for (2980ds/794Mi)
% 16.40/3.73 % (13245)Instruction limit reached!
% 16.40/3.73 % (13245)------------------------------
% 16.40/3.73 % (13245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.40/3.73 % (13245)Termination reason: Unknown
% 16.40/3.73 % (13245)Termination phase: Saturation
% 16.40/3.73
% 16.40/3.73 % (13245)Memory used [KB]: 8571
% 16.40/3.73 % (13245)Time elapsed: 0.226 s
% 16.40/3.73 % (13245)Instructions burned: 771 (million)
% 16.40/3.73 % (13245)------------------------------
% 16.40/3.73 % (13245)------------------------------
% 16.40/3.74 % (13247)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_12850 for (2979ds/464Mi)
% 16.94/3.88 % (13247)Instruction limit reached!
% 16.94/3.88 % (13247)------------------------------
% 16.94/3.88 % (13247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.94/3.88 % (13247)Termination reason: Unknown
% 16.94/3.88 % (13247)Termination phase: Saturation
% 16.94/3.88
% 16.94/3.88 % (13247)Memory used [KB]: 7931
% 16.94/3.88 % (13247)Time elapsed: 0.144 s
% 16.94/3.88 % (13247)Instructions burned: 467 (million)
% 16.94/3.88 % (13247)------------------------------
% 16.94/3.88 % (13247)------------------------------
% 16.94/3.89 % (13248)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_12850 for (2977ds/1376Mi)
% 17.39/3.91 % (13246)Instruction limit reached!
% 17.39/3.91 % (13246)------------------------------
% 17.39/3.91 % (13246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.39/3.91 % (13246)Termination reason: Unknown
% 17.39/3.91 % (13246)Termination phase: Saturation
% 17.39/3.91
% 17.39/3.91 % (13246)Memory used [KB]: 5500
% 17.39/3.91 % (13246)Time elapsed: 0.249 s
% 17.39/3.91 % (13246)Instructions burned: 796 (million)
% 17.39/3.91 % (13246)------------------------------
% 17.39/3.91 % (13246)------------------------------
% 17.39/3.91 % (13239)Instruction limit reached!
% 17.39/3.91 % (13239)------------------------------
% 17.39/3.91 % (13239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.39/3.91 % (13239)Termination reason: Unknown
% 17.39/3.91 % (13239)Termination phase: Saturation
% 17.39/3.91
% 17.39/3.91 % (13239)Memory used [KB]: 10106
% 17.39/3.91 % (13239)Time elapsed: 0.575 s
% 17.39/3.91 % (13239)Instructions burned: 1828 (million)
% 17.39/3.91 % (13239)------------------------------
% 17.39/3.91 % (13239)------------------------------
% 17.39/3.92 % (13249)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_12850 for (2977ds/906Mi)
% 17.39/3.92 % (13250)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_12850 for (2977ds/434Mi)
% 17.39/3.94 % (13218)Instruction limit reached!
% 17.39/3.94 % (13218)------------------------------
% 17.39/3.94 % (13218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.39/3.94 % (13218)Termination reason: Unknown
% 17.39/3.94 % (13218)Termination phase: Saturation
% 17.39/3.94
% 17.39/3.94 % (13218)Memory used [KB]: 13176
% 17.39/3.94 % (13218)Time elapsed: 1.361 s
% 17.39/3.94 % (13218)Instructions burned: 4437 (million)
% 17.39/3.94 % (13218)------------------------------
% 17.39/3.94 % (13218)------------------------------
% 17.39/3.95 % (13251)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_12850 for (2977ds/865Mi)
% 17.39/3.96 % (13223)Instruction limit reached!
% 17.39/3.96 % (13223)------------------------------
% 17.39/3.96 % (13223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.39/3.96 % (13223)Termination reason: Unknown
% 17.39/3.96 % (13223)Termination phase: Saturation
% 17.39/3.96
% 17.39/3.96 % (13223)Memory used [KB]: 12665
% 17.39/3.96 % (13223)Time elapsed: 1.205 s
% 17.39/3.96 % (13223)Instructions burned: 4352 (million)
% 17.39/3.96 % (13223)------------------------------
% 17.39/3.96 % (13223)------------------------------
% 17.39/3.97 % (13252)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_12850 for (2977ds/593Mi)
% 19.53/4.04 % (13250)Instruction limit reached!
% 19.53/4.04 % (13250)------------------------------
% 19.53/4.04 % (13250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.53/4.04 % (13250)Termination reason: Unknown
% 19.53/4.04 % (13250)Termination phase: Saturation
% 19.53/4.04
% 19.53/4.04 % (13250)Memory used [KB]: 8059
% 19.53/4.04 % (13250)Time elapsed: 0.123 s
% 19.53/4.04 % (13250)Instructions burned: 436 (million)
% 19.53/4.04 % (13250)------------------------------
% 19.53/4.04 % (13250)------------------------------
% 19.53/4.05 % (13253)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_12850 for (2976ds/443Mi)
% 20.18/4.14 % (13252)Instruction limit reached!
% 20.18/4.14 % (13252)------------------------------
% 20.18/4.14 % (13252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.18/4.14 % (13252)Termination reason: Unknown
% 20.18/4.14 % (13252)Termination phase: Saturation
% 20.18/4.14
% 20.18/4.14 % (13252)Memory used [KB]: 11129
% 20.18/4.14 % (13252)Time elapsed: 0.189 s
% 20.18/4.14 % (13252)Instructions burned: 594 (million)
% 20.18/4.14 % (13252)------------------------------
% 20.18/4.14 % (13252)------------------------------
% 20.18/4.15 % (13254)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_12850 for (2975ds/594Mi)
% 20.18/4.18 % (13253)Instruction limit reached!
% 20.18/4.18 % (13253)------------------------------
% 20.18/4.18 % (13253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.18/4.18 % (13253)Termination reason: Unknown
% 20.18/4.18 % (13253)Termination phase: Saturation
% 20.18/4.18
% 20.18/4.18 % (13253)Memory used [KB]: 7803
% 20.18/4.18 % (13253)Time elapsed: 0.136 s
% 20.18/4.18 % (13253)Instructions burned: 445 (million)
% 20.18/4.18 % (13253)------------------------------
% 20.18/4.18 % (13253)------------------------------
% 20.18/4.19 % (13255)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_12850 for (2974ds/327Mi)
% 20.71/4.20 % (13251)Instruction limit reached!
% 20.71/4.20 % (13251)------------------------------
% 20.71/4.20 % (13251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.71/4.20 % (13251)Termination reason: Unknown
% 20.71/4.20 % (13251)Termination phase: Saturation
% 20.71/4.20
% 20.71/4.20 % (13251)Memory used [KB]: 9210
% 20.71/4.20 % (13251)Time elapsed: 0.254 s
% 20.71/4.20 % (13251)Instructions burned: 868 (million)
% 20.71/4.20 % (13251)------------------------------
% 20.71/4.20 % (13251)------------------------------
% 20.71/4.21 % (13256)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_12850 for (2974ds/5411Mi)
% 20.71/4.22 % (13249)Instruction limit reached!
% 20.71/4.22 % (13249)------------------------------
% 20.71/4.22 % (13249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.71/4.22 % (13249)Termination reason: Unknown
% 20.71/4.22 % (13249)Termination phase: Saturation
% 20.71/4.22
% 20.71/4.22 % (13249)Memory used [KB]: 12537
% 20.71/4.22 % (13249)Time elapsed: 0.309 s
% 20.71/4.22 % (13249)Instructions burned: 907 (million)
% 20.71/4.22 % (13249)------------------------------
% 20.71/4.22 % (13249)------------------------------
% 20.71/4.23 % (13257)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_12850 for (2974ds/1762Mi)
% 20.71/4.24 % (13221)Instruction limit reached!
% 20.71/4.24 % (13221)------------------------------
% 20.71/4.24 % (13221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.71/4.24 % (13221)Termination reason: Unknown
% 20.71/4.24 % (13221)Termination phase: Saturation
% 20.71/4.24
% 20.71/4.24 % (13221)Memory used [KB]: 14072
% 20.71/4.24 % (13221)Time elapsed: 1.602 s
% 20.71/4.24 % (13221)Instructions burned: 5205 (million)
% 20.71/4.24 % (13221)------------------------------
% 20.71/4.24 % (13221)------------------------------
% 20.71/4.25 % (13258)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_12850 for (2974ds/96Mi)
% 20.71/4.28 % (13258)Instruction limit reached!
% 20.71/4.28 % (13258)------------------------------
% 20.71/4.28 % (13258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.71/4.28 % (13258)Termination reason: Unknown
% 20.71/4.28 % (13258)Termination phase: Preprocessing 1
% 20.71/4.28
% 20.71/4.28 % (13258)Memory used [KB]: 2686
% 20.71/4.28 % (13258)Time elapsed: 0.029 s
% 20.71/4.28 % (13258)Instructions burned: 97 (million)
% 20.71/4.28 % (13258)------------------------------
% 20.71/4.28 % (13258)------------------------------
% 20.71/4.29 % (13259)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_12850 for (2973ds/503Mi)
% 20.71/4.29 % (13255)Instruction limit reached!
% 20.71/4.29 % (13255)------------------------------
% 20.71/4.29 % (13255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.71/4.29 % (13255)Termination reason: Unknown
% 20.71/4.29 % (13255)Termination phase: Saturation
% 20.71/4.29
% 20.71/4.29 % (13255)Memory used [KB]: 8187
% 20.71/4.29 % (13255)Time elapsed: 0.102 s
% 20.71/4.29 % (13255)Instructions burned: 328 (million)
% 20.71/4.29 % (13255)------------------------------
% 20.71/4.29 % (13255)------------------------------
% 21.19/4.30 % (13260)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_12850 for (2973ds/90Mi)
% 21.19/4.31 % (13248)Instruction limit reached!
% 21.19/4.31 % (13248)------------------------------
% 21.19/4.31 % (13248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.19/4.31 % (13248)Termination reason: Unknown
% 21.19/4.31 % (13248)Termination phase: Saturation
% 21.19/4.31
% 21.19/4.31 % (13248)Memory used [KB]: 14072
% 21.19/4.31 % (13248)Time elapsed: 0.414 s
% 21.19/4.31 % (13248)Instructions burned: 1376 (million)
% 21.19/4.31 % (13248)------------------------------
% 21.19/4.31 % (13248)------------------------------
% 21.19/4.32 % (13261)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_12850 for (2973ds/593Mi)
% 21.19/4.33 % (13260)Instruction limit reached!
% 21.19/4.33 % (13260)------------------------------
% 21.19/4.33 % (13260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.19/4.33 % (13260)Termination reason: Unknown
% 21.19/4.33 % (13260)Termination phase: Property scanning
% 21.19/4.33
% 21.19/4.33 % (13260)Memory used [KB]: 2558
% 21.19/4.33 % (13260)Time elapsed: 0.030 s
% 21.19/4.33 % (13260)Instructions burned: 93 (million)
% 21.19/4.33 % (13260)------------------------------
% 21.19/4.33 % (13260)------------------------------
% 21.19/4.34 % (13254)Instruction limit reached!
% 21.19/4.34 % (13254)------------------------------
% 21.19/4.34 % (13254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.19/4.34 % (13254)Termination reason: Unknown
% 21.19/4.34 % (13254)Termination phase: Saturation
% 21.19/4.34
% 21.19/4.34 % (13254)Memory used [KB]: 8059
% 21.19/4.34 % (13254)Time elapsed: 0.187 s
% 21.19/4.34 % (13254)Instructions burned: 596 (million)
% 21.19/4.34 % (13254)------------------------------
% 21.19/4.34 % (13254)------------------------------
% 21.19/4.34 % (13262)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_12850 for (2973ds/1512Mi)
% 21.19/4.35 % (13263)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_12850 for (2973ds/569Mi)
% 21.54/4.44 % (13259)Instruction limit reached!
% 21.54/4.44 % (13259)------------------------------
% 21.54/4.44 % (13259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.54/4.44 % (13259)Termination reason: Unknown
% 21.54/4.44 % (13259)Termination phase: Saturation
% 21.54/4.44
% 21.54/4.44 % (13259)Memory used [KB]: 9594
% 21.54/4.44 % (13259)Time elapsed: 0.150 s
% 21.54/4.44 % (13259)Instructions burned: 503 (million)
% 21.54/4.44 % (13259)------------------------------
% 21.54/4.44 % (13259)------------------------------
% 21.54/4.45 % (13264)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_12850 for (2972ds/501Mi)
% 21.54/4.50 % (13261)Instruction limit reached!
% 21.54/4.50 % (13261)------------------------------
% 21.54/4.50 % (13261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.80/4.50 % (13261)Termination reason: Unknown
% 21.80/4.50 % (13261)Termination phase: Saturation
% 21.80/4.50
% 21.80/4.50 % (13261)Memory used [KB]: 8955
% 21.80/4.50 % (13261)Time elapsed: 0.181 s
% 21.80/4.50 % (13261)Instructions burned: 593 (million)
% 21.80/4.50 % (13261)------------------------------
% 21.80/4.50 % (13261)------------------------------
% 21.80/4.51 % (13265)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_12850 for (2971ds/562Mi)
% 21.80/4.51 % (13263)Instruction limit reached!
% 21.80/4.51 % (13263)------------------------------
% 21.80/4.51 % (13263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.80/4.51 % (13263)Termination reason: Unknown
% 21.80/4.51 % (13263)Termination phase: Saturation
% 21.80/4.51
% 21.80/4.51 % (13263)Memory used [KB]: 8955
% 21.80/4.51 % (13263)Time elapsed: 0.162 s
% 21.80/4.51 % (13263)Instructions burned: 571 (million)
% 21.80/4.51 % (13263)------------------------------
% 21.80/4.51 % (13263)------------------------------
% 21.80/4.52 % (13266)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_12850 for (2971ds/406Mi)
% 22.27/4.60 % (13264)Instruction limit reached!
% 22.27/4.60 % (13264)------------------------------
% 22.27/4.60 % (13264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.27/4.60 % (13264)Termination reason: Unknown
% 22.27/4.60 % (13264)Termination phase: Saturation
% 22.27/4.60
% 22.27/4.60 % (13264)Memory used [KB]: 9850
% 22.27/4.60 % (13264)Time elapsed: 0.148 s
% 22.27/4.60 % (13264)Instructions burned: 503 (million)
% 22.27/4.60 % (13264)------------------------------
% 22.27/4.60 % (13264)------------------------------
% 22.27/4.61 % (13267)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_12850 for (2970ds/582Mi)
% 22.27/4.65 % (13266)Instruction limit reached!
% 22.27/4.65 % (13266)------------------------------
% 22.27/4.65 % (13266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.27/4.65 % (13266)Termination reason: Unknown
% 22.27/4.65 % (13266)Termination phase: Saturation
% 22.27/4.65
% 22.27/4.65 % (13266)Memory used [KB]: 8571
% 22.27/4.65 % (13266)Time elapsed: 0.129 s
% 22.27/4.65 % (13266)Instructions burned: 406 (million)
% 22.27/4.65 % (13266)------------------------------
% 22.27/4.65 % (13266)------------------------------
% 22.27/4.66 % (13268)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_12850 for (2970ds/456Mi)
% 22.27/4.67 % (13265)Instruction limit reached!
% 22.27/4.67 % (13265)------------------------------
% 22.27/4.67 % (13265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.27/4.67 % (13265)Termination reason: Unknown
% 22.27/4.67 % (13265)Termination phase: Saturation
% 22.27/4.67
% 22.27/4.67 % (13265)Memory used [KB]: 8827
% 22.27/4.67 % (13265)Time elapsed: 0.169 s
% 22.27/4.67 % (13265)Instructions burned: 564 (million)
% 22.27/4.67 % (13265)------------------------------
% 22.27/4.67 % (13265)------------------------------
% 22.27/4.68 % (13269)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_12850 for (2969ds/393Mi)
% 22.85/4.73 % (13257)Instruction limit reached!
% 22.85/4.73 % (13257)------------------------------
% 22.85/4.73 % (13257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.85/4.73 % (13257)Termination reason: Unknown
% 22.85/4.73 % (13257)Termination phase: Saturation
% 22.85/4.73
% 22.85/4.73 % (13257)Memory used [KB]: 10234
% 22.85/4.73 % (13257)Time elapsed: 0.494 s
% 22.85/4.73 % (13257)Instructions burned: 1764 (million)
% 22.85/4.73 % (13257)------------------------------
% 22.85/4.73 % (13257)------------------------------
% 22.85/4.74 % (13270)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_12850 for (2969ds/1335Mi)
% 22.85/4.79 % (13267)Instruction limit reached!
% 22.85/4.79 % (13267)------------------------------
% 22.85/4.79 % (13267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.85/4.79 % (13267)Termination reason: Unknown
% 22.85/4.79 % (13267)Termination phase: Saturation
% 22.85/4.79
% 22.85/4.79 % (13267)Memory used [KB]: 8571
% 22.85/4.79 % (13267)Time elapsed: 0.182 s
% 22.85/4.79 % (13267)Instructions burned: 584 (million)
% 22.85/4.79 % (13267)------------------------------
% 22.85/4.79 % (13267)------------------------------
% 22.85/4.79 % (13269)Instruction limit reached!
% 22.85/4.79 % (13269)------------------------------
% 22.85/4.79 % (13269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.85/4.79 % (13269)Termination reason: Unknown
% 22.85/4.79 % (13269)Termination phase: Saturation
% 22.85/4.79
% 22.85/4.79 % (13269)Memory used [KB]: 7803
% 22.85/4.79 % (13269)Time elapsed: 0.109 s
% 22.85/4.79 % (13269)Instructions burned: 393 (million)
% 22.85/4.79 % (13269)------------------------------
% 22.85/4.79 % (13269)------------------------------
% 22.85/4.79 % (13268)Instruction limit reached!
% 22.85/4.79 % (13268)------------------------------
% 22.85/4.79 % (13268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.85/4.79 % (13268)Termination reason: Unknown
% 22.85/4.79 % (13268)Termination phase: Saturation
% 22.85/4.79
% 22.85/4.79 % (13268)Memory used [KB]: 8315
% 22.85/4.79 % (13268)Time elapsed: 0.138 s
% 22.85/4.79 % (13268)Instructions burned: 458 (million)
% 22.85/4.79 % (13268)------------------------------
% 22.85/4.79 % (13268)------------------------------
% 23.90/4.80 % (13271)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_12850 for (2968ds/3373Mi)
% 23.90/4.80 % (13272)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_12850 for (2968ds/474Mi)
% 23.90/4.80 % (13273)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_12850 for (2968ds/157Mi)
% 23.90/4.81 % (13262)Instruction limit reached!
% 23.90/4.81 % (13262)------------------------------
% 23.90/4.81 % (13262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.90/4.81 % (13262)Termination reason: Unknown
% 23.90/4.81 % (13262)Termination phase: Saturation
% 23.90/4.81
% 23.90/4.81 % (13262)Memory used [KB]: 10106
% 23.90/4.81 % (13262)Time elapsed: 0.465 s
% 23.90/4.81 % (13262)Instructions burned: 1513 (million)
% 23.90/4.81 % (13262)------------------------------
% 23.90/4.81 % (13262)------------------------------
% 23.90/4.82 % (13274)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_12850 for (2968ds/590Mi)
% 23.90/4.85 % (13273)Instruction limit reached!
% 23.90/4.85 % (13273)------------------------------
% 23.90/4.85 % (13273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.90/4.85 % (13273)Termination reason: Unknown
% 23.90/4.85 % (13273)Termination phase: Function definition elimination
% 23.90/4.85
% 23.90/4.85 % (13273)Memory used [KB]: 2686
% 23.90/4.85 % (13273)Time elapsed: 0.045 s
% 23.90/4.85 % (13273)Instructions burned: 157 (million)
% 23.90/4.85 % (13273)------------------------------
% 23.90/4.85 % (13273)------------------------------
% 23.90/4.86 % (13275)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_12850 for (2968ds/104Mi)
% 23.90/4.89 % (13275)Instruction limit reached!
% 23.90/4.89 % (13275)------------------------------
% 23.90/4.89 % (13275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.90/4.89 % (13275)Termination reason: Unknown
% 23.90/4.89 % (13275)Termination phase: Property scanning
% 23.90/4.89
% 23.90/4.89 % (13275)Memory used [KB]: 2558
% 23.90/4.89 % (13275)Time elapsed: 0.032 s
% 23.90/4.89 % (13275)Instructions burned: 106 (million)
% 23.90/4.89 % (13275)------------------------------
% 23.90/4.89 % (13275)------------------------------
% 23.90/4.90 % (13276)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_12850 for (2967ds/414Mi)
% 24.57/4.94 % (13272)Instruction limit reached!
% 24.57/4.94 % (13272)------------------------------
% 24.57/4.94 % (13272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.57/4.94 % (13272)Termination reason: Unknown
% 24.57/4.94 % (13272)Termination phase: Saturation
% 24.57/4.94
% 24.57/4.94 % (13272)Memory used [KB]: 8187
% 24.57/4.94 % (13272)Time elapsed: 0.141 s
% 24.57/4.94 % (13272)Instructions burned: 475 (million)
% 24.57/4.94 % (13272)------------------------------
% 24.57/4.94 % (13272)------------------------------
% 24.57/4.95 % (13277)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_12850 for (2967ds/715Mi)
% 24.57/4.99 % (13274)Instruction limit reached!
% 24.57/4.99 % (13274)------------------------------
% 24.57/4.99 % (13274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.57/4.99 % (13274)Termination reason: Unknown
% 24.57/4.99 % (13274)Termination phase: Saturation
% 24.57/4.99
% 24.57/4.99 % (13274)Memory used [KB]: 9083
% 24.57/4.99 % (13274)Time elapsed: 0.173 s
% 24.57/4.99 % (13274)Instructions burned: 592 (million)
% 24.57/4.99 % (13274)------------------------------
% 24.57/4.99 % (13274)------------------------------
% 24.57/5.00 % (13278)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_12850 for (2966ds/961Mi)
% 24.57/5.01 % (13276)Instruction limit reached!
% 24.57/5.01 % (13276)------------------------------
% 24.57/5.01 % (13276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.57/5.01 % (13276)Termination reason: Unknown
% 24.57/5.01 % (13276)Termination phase: Saturation
% 24.57/5.01
% 24.57/5.01 % (13276)Memory used [KB]: 8571
% 24.57/5.01 % (13276)Time elapsed: 0.114 s
% 24.57/5.01 % (13276)Instructions burned: 416 (million)
% 24.57/5.01 % (13276)------------------------------
% 24.57/5.01 % (13276)------------------------------
% 26.56/5.03 % (13279)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_12850 for (2966ds/1213Mi)
% 26.56/5.12 % (13270)Instruction limit reached!
% 26.56/5.12 % (13270)------------------------------
% 26.56/5.12 % (13270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.56/5.12 % (13270)Termination reason: Unknown
% 26.56/5.12 % (13270)Termination phase: Saturation
% 26.56/5.12
% 26.56/5.12 % (13270)Memory used [KB]: 9850
% 26.56/5.12 % (13270)Time elapsed: 0.385 s
% 26.56/5.12 % (13270)Instructions burned: 1338 (million)
% 26.56/5.12 % (13270)------------------------------
% 26.56/5.12 % (13270)------------------------------
% 27.19/5.13 % (13280)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_12850 for (2965ds/1979Mi)
% 27.19/5.17 % (13277)Instruction limit reached!
% 27.19/5.17 % (13277)------------------------------
% 27.19/5.17 % (13277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.19/5.17 % (13277)Termination reason: Unknown
% 27.19/5.17 % (13277)Termination phase: Saturation
% 27.19/5.17
% 27.19/5.17 % (13277)Memory used [KB]: 4221
% 27.19/5.17 % (13277)Time elapsed: 0.220 s
% 27.19/5.17 % (13277)Instructions burned: 718 (million)
% 27.19/5.17 % (13277)------------------------------
% 27.19/5.17 % (13277)------------------------------
% 27.19/5.18 % (13281)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_12850 for (2964ds/481Mi)
% 27.53/5.29 % (13278)Instruction limit reached!
% 27.53/5.29 % (13278)------------------------------
% 27.53/5.29 % (13278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.53/5.29 % (13278)Termination reason: Unknown
% 27.53/5.29 % (13278)Termination phase: Saturation
% 27.53/5.29
% 27.53/5.29 % (13278)Memory used [KB]: 8187
% 27.53/5.29 % (13278)Time elapsed: 0.294 s
% 27.53/5.29 % (13278)Instructions burned: 963 (million)
% 27.53/5.29 % (13278)------------------------------
% 27.53/5.29 % (13278)------------------------------
% 27.94/5.30 % (13282)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_12850 for (2963ds/783Mi)
% 27.94/5.32 % (13281)Instruction limit reached!
% 27.94/5.32 % (13281)------------------------------
% 27.94/5.32 % (13281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.94/5.32 % (13281)Termination reason: Unknown
% 27.94/5.32 % (13281)Termination phase: Saturation
% 27.94/5.32
% 27.94/5.32 % (13281)Memory used [KB]: 7803
% 27.94/5.32 % (13281)Time elapsed: 0.144 s
% 27.94/5.32 % (13281)Instructions burned: 481 (million)
% 27.94/5.32 % (13281)------------------------------
% 27.94/5.32 % (13281)------------------------------
% 27.94/5.33 % (13283)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_12850 for (2963ds/432Mi)
% 28.39/5.40 % (13279)Instruction limit reached!
% 28.39/5.40 % (13279)------------------------------
% 28.39/5.40 % (13279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.39/5.40 % (13279)Termination reason: Unknown
% 28.39/5.40 % (13279)Termination phase: Saturation
% 28.39/5.40
% 28.39/5.40 % (13279)Memory used [KB]: 9978
% 28.39/5.40 % (13279)Time elapsed: 0.379 s
% 28.39/5.40 % (13279)Instructions burned: 1215 (million)
% 28.39/5.40 % (13279)------------------------------
% 28.39/5.40 % (13279)------------------------------
% 28.39/5.41 % (13284)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_12850 for (2962ds/1670Mi)
% 28.39/5.47 % (13283)Instruction limit reached!
% 28.39/5.47 % (13283)------------------------------
% 28.39/5.47 % (13283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.39/5.47 % (13283)Termination reason: Unknown
% 28.39/5.47 % (13283)Termination phase: Saturation
% 28.39/5.47
% 28.39/5.47 % (13283)Memory used [KB]: 8059
% 28.39/5.47 % (13283)Time elapsed: 0.137 s
% 28.39/5.47 % (13283)Instructions burned: 432 (million)
% 28.39/5.47 % (13283)------------------------------
% 28.39/5.47 % (13283)------------------------------
% 28.39/5.48 % (13285)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_12850 for (2961ds/90Mi)
% 29.22/5.50 % (13285)Instruction limit reached!
% 29.22/5.50 % (13285)------------------------------
% 29.22/5.50 % (13285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.22/5.50 % (13285)Termination reason: Unknown
% 29.22/5.50 % (13285)Termination phase: Property scanning
% 29.22/5.50
% 29.22/5.50 % (13285)Memory used [KB]: 2558
% 29.22/5.50 % (13285)Time elapsed: 0.028 s
% 29.22/5.50 % (13285)Instructions burned: 91 (million)
% 29.22/5.50 % (13285)------------------------------
% 29.22/5.50 % (13285)------------------------------
% 29.22/5.51 % (13286)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_12850 for (2961ds/346Mi)
% 29.22/5.55 % (13282)Instruction limit reached!
% 29.22/5.55 % (13282)------------------------------
% 29.22/5.55 % (13282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.22/5.55 % (13282)Termination reason: Unknown
% 29.22/5.55 % (13282)Termination phase: Saturation
% 29.22/5.55
% 29.22/5.55 % (13282)Memory used [KB]: 9210
% 29.22/5.55 % (13282)Time elapsed: 0.246 s
% 29.22/5.55 % (13282)Instructions burned: 785 (million)
% 29.22/5.55 % (13282)------------------------------
% 29.22/5.55 % (13282)------------------------------
% 29.22/5.56 % (13287)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_12850 for (2961ds/401Mi)
% 29.82/5.62 % (13286)Instruction limit reached!
% 29.82/5.62 % (13286)------------------------------
% 29.82/5.62 % (13286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.82/5.62 % (13286)Termination reason: Unknown
% 29.82/5.62 % (13286)Termination phase: Saturation
% 29.82/5.62
% 29.82/5.62 % (13286)Memory used [KB]: 7803
% 29.82/5.62 % (13286)Time elapsed: 0.104 s
% 29.82/5.62 % (13286)Instructions burned: 346 (million)
% 29.82/5.62 % (13286)------------------------------
% 29.82/5.62 % (13286)------------------------------
% 29.82/5.62 % (13256)Instruction limit reached!
% 29.82/5.62 % (13256)------------------------------
% 29.82/5.62 % (13256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.82/5.62 % (13256)Termination reason: Unknown
% 29.82/5.62 % (13256)Termination phase: Saturation
% 29.82/5.62
% 29.82/5.62 % (13256)Memory used [KB]: 8571
% 29.82/5.62 % (13256)Time elapsed: 1.407 s
% 29.82/5.62 % (13256)Instructions burned: 5414 (million)
% 29.82/5.62 % (13256)------------------------------
% 29.82/5.62 % (13256)------------------------------
% 29.82/5.63 % (13288)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_12850 for (2960ds/6454Mi)
% 29.82/5.63 % (13289)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_12850 for (2960ds/283Mi)
% 29.82/5.67 % (13287)Instruction limit reached!
% 29.82/5.67 % (13287)------------------------------
% 29.82/5.67 % (13287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.82/5.67 % (13287)Termination reason: Unknown
% 29.82/5.67 % (13287)Termination phase: Saturation
% 29.82/5.67
% 29.82/5.67 % (13287)Memory used [KB]: 8955
% 29.82/5.67 % (13287)Time elapsed: 0.112 s
% 29.82/5.67 % (13287)Instructions burned: 402 (million)
% 29.82/5.67 % (13287)------------------------------
% 29.82/5.67 % (13287)------------------------------
% 29.82/5.68 % (13290)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_12850 for (2959ds/865Mi)
% 30.30/5.71 % (13280)Instruction limit reached!
% 30.30/5.71 % (13280)------------------------------
% 30.30/5.71 % (13280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.30/5.71 % (13280)Termination reason: Unknown
% 30.30/5.71 % (13280)Termination phase: Saturation
% 30.30/5.71
% 30.30/5.71 % (13280)Memory used [KB]: 8699
% 30.30/5.71 % (13280)Time elapsed: 0.583 s
% 30.30/5.71 % (13280)Instructions burned: 1981 (million)
% 30.30/5.71 % (13280)------------------------------
% 30.30/5.71 % (13280)------------------------------
% 30.30/5.72 % (13289)Instruction limit reached!
% 30.30/5.72 % (13289)------------------------------
% 30.30/5.72 % (13289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.30/5.72 % (13289)Termination reason: Unknown
% 30.30/5.72 % (13289)Termination phase: Saturation
% 30.30/5.72
% 30.30/5.72 % (13289)Memory used [KB]: 8059
% 30.30/5.72 % (13289)Time elapsed: 0.089 s
% 30.30/5.72 % (13289)Instructions burned: 284 (million)
% 30.30/5.72 % (13289)------------------------------
% 30.30/5.72 % (13289)------------------------------
% 30.30/5.72 % (13291)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_12850 for (2959ds/4528Mi)
% 30.30/5.73 % (13292)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_12850 for (2959ds/1001Mi)
% 31.18/5.84 % (13271)Instruction limit reached!
% 31.18/5.84 % (13271)------------------------------
% 31.18/5.84 % (13271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.18/5.84 % (13271)Termination reason: Unknown
% 31.18/5.84 % (13271)Termination phase: Saturation
% 31.18/5.84
% 31.18/5.84 % (13271)Memory used [KB]: 12281
% 31.18/5.84 % (13271)Time elapsed: 1.038 s
% 31.18/5.84 % (13271)Instructions burned: 3373 (million)
% 31.18/5.84 % (13271)------------------------------
% 31.18/5.84 % (13271)------------------------------
% 31.18/5.85 % (13293)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_12850 for (2958ds/102Mi)
% 31.18/5.87 % (13293)Instruction limit reached!
% 31.18/5.87 % (13293)------------------------------
% 31.18/5.87 % (13293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.18/5.87 % (13293)Termination reason: Unknown
% 31.18/5.87 % (13293)Termination phase: Preprocessing 3
% 31.18/5.87
% 31.18/5.87 % (13293)Memory used [KB]: 2686
% 31.18/5.87 % (13293)Time elapsed: 0.030 s
% 31.18/5.87 % (13293)Instructions burned: 104 (million)
% 31.18/5.87 % (13293)------------------------------
% 31.18/5.87 % (13293)------------------------------
% 31.18/5.88 % (13294)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_12850 for (2957ds/952Mi)
% 31.37/5.91 % (13284)Instruction limit reached!
% 31.37/5.91 % (13284)------------------------------
% 31.37/5.91 % (13284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.37/5.91 % (13284)Termination reason: Unknown
% 31.37/5.91 % (13284)Termination phase: Saturation
% 31.37/5.91
% 31.37/5.91 % (13284)Memory used [KB]: 12025
% 31.37/5.91 % (13284)Time elapsed: 0.493 s
% 31.37/5.91 % (13284)Instructions burned: 1670 (million)
% 31.37/5.91 % (13284)------------------------------
% 31.37/5.91 % (13284)------------------------------
% 31.37/5.92 % (13295)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_12850 for (2957ds/578Mi)
% 31.37/5.94 % (13290)Instruction limit reached!
% 31.37/5.94 % (13290)------------------------------
% 31.37/5.94 % (13290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.37/5.94 % (13290)Termination reason: Unknown
% 31.37/5.94 % (13290)Termination phase: Saturation
% 31.37/5.94
% 31.37/5.94 % (13290)Memory used [KB]: 9978
% 31.37/5.94 % (13290)Time elapsed: 0.262 s
% 31.37/5.94 % (13290)Instructions burned: 867 (million)
% 31.37/5.94 % (13290)------------------------------
% 31.37/5.94 % (13290)------------------------------
% 31.37/5.95 % (13296)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_12850 for (2957ds/643Mi)
% 31.37/5.96 % (13244)Instruction limit reached!
% 31.37/5.96 % (13244)------------------------------
% 31.37/5.96 % (13244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.37/5.96 % (13244)Termination reason: Unknown
% 31.37/5.96 % (13244)Termination phase: Saturation
% 31.37/5.96
% 31.37/5.96 % (13244)Memory used [KB]: 16502
% 31.37/5.96 % (13244)Time elapsed: 2.511 s
% 31.37/5.96 % (13244)Instructions burned: 8250 (million)
% 31.37/5.96 % (13244)------------------------------
% 31.37/5.96 % (13244)------------------------------
% 31.37/5.97 % (13297)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_12850 for (2957ds/865Mi)
% 31.37/5.98 % (13292)Instruction limit reached!
% 31.37/5.98 % (13292)------------------------------
% 31.37/5.98 % (13292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.37/5.98 % (13292)Termination reason: Unknown
% 31.37/5.98 % (13292)Termination phase: Saturation
% 31.37/5.98
% 31.37/5.98 % (13292)Memory used [KB]: 7931
% 31.37/5.98 % (13292)Time elapsed: 0.249 s
% 31.37/5.98 % (13292)Instructions burned: 1003 (million)
% 31.37/5.98 % (13292)------------------------------
% 31.37/5.98 % (13292)------------------------------
% 31.37/5.99 % (13298)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_12850 for (2956ds/1174Mi)
% 33.59/6.08 % (13295)Instruction limit reached!
% 33.59/6.08 % (13295)------------------------------
% 33.59/6.08 % (13295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.59/6.08 % (13295)Termination reason: Unknown
% 33.59/6.08 % (13295)Termination phase: Saturation
% 33.59/6.08
% 33.59/6.08 % (13295)Memory used [KB]: 9338
% 33.59/6.08 % (13295)Time elapsed: 0.168 s
% 33.59/6.08 % (13295)Instructions burned: 578 (million)
% 33.59/6.08 % (13295)------------------------------
% 33.59/6.08 % (13295)------------------------------
% 33.59/6.09 % (13299)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_12850 for (2955ds/644Mi)
% 34.27/6.14 % (13296)Instruction limit reached!
% 34.27/6.14 % (13296)------------------------------
% 34.27/6.14 % (13296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.27/6.14 % (13296)Termination reason: Unknown
% 34.27/6.14 % (13296)Termination phase: Saturation
% 34.27/6.14
% 34.27/6.14 % (13296)Memory used [KB]: 9722
% 34.27/6.14 % (13296)Time elapsed: 0.192 s
% 34.27/6.14 % (13296)Instructions burned: 645 (million)
% 34.27/6.14 % (13296)------------------------------
% 34.27/6.14 % (13296)------------------------------
% 34.27/6.15 % (13300)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_12850 for (2955ds/1201Mi)
% 34.27/6.18 % (13294)Instruction limit reached!
% 34.27/6.18 % (13294)------------------------------
% 34.27/6.18 % (13294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.27/6.18 % (13294)Termination reason: Unknown
% 34.27/6.18 % (13294)Termination phase: Saturation
% 34.27/6.18
% 34.27/6.18 % (13294)Memory used [KB]: 9850
% 34.27/6.18 % (13294)Time elapsed: 0.295 s
% 34.27/6.18 % (13294)Instructions burned: 955 (million)
% 34.27/6.18 % (13294)------------------------------
% 34.27/6.18 % (13294)------------------------------
% 34.27/6.19 % (13301)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_12850 for (2954ds/1046Mi)
% 34.65/6.24 % (13297)Instruction limit reached!
% 34.65/6.24 % (13297)------------------------------
% 34.65/6.24 % (13297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.65/6.24 % (13297)Termination reason: Unknown
% 34.65/6.24 % (13297)Termination phase: Saturation
% 34.65/6.24
% 34.65/6.24 % (13297)Memory used [KB]: 10234
% 34.65/6.24 % (13297)Time elapsed: 0.271 s
% 34.65/6.24 % (13297)Instructions burned: 865 (million)
% 34.65/6.24 % (13297)------------------------------
% 34.65/6.24 % (13297)------------------------------
% 34.65/6.25 % (13302)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_12850 for (2954ds/222Mi)
% 34.65/6.29 % (13299)Instruction limit reached!
% 34.65/6.29 % (13299)------------------------------
% 34.65/6.29 % (13299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.65/6.29 % (13299)Termination reason: Unknown
% 34.65/6.29 % (13299)Termination phase: Saturation
% 34.65/6.29
% 34.65/6.29 % (13299)Memory used [KB]: 9978
% 34.65/6.29 % (13299)Time elapsed: 0.199 s
% 34.65/6.29 % (13299)Instructions burned: 644 (million)
% 34.65/6.29 % (13299)------------------------------
% 34.65/6.29 % (13299)------------------------------
% 35.20/6.30 % (13303)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_12850 for (2953ds/68Mi)
% 35.20/6.31 % (13302)Instruction limit reached!
% 35.20/6.31 % (13302)------------------------------
% 35.20/6.31 % (13302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.20/6.31 % (13302)Termination reason: Unknown
% 35.20/6.31 % (13302)Termination phase: Saturation
% 35.20/6.31
% 35.20/6.31 % (13302)Memory used [KB]: 7291
% 35.20/6.31 % (13302)Time elapsed: 0.062 s
% 35.20/6.31 % (13302)Instructions burned: 225 (million)
% 35.20/6.31 % (13302)------------------------------
% 35.20/6.31 % (13302)------------------------------
% 35.20/6.32 % (13304)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_12850 for (2953ds/454Mi)
% 35.20/6.32 % (13303)Instruction limit reached!
% 35.20/6.32 % (13303)------------------------------
% 35.20/6.32 % (13303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.20/6.32 % (13303)Termination reason: Unknown
% 35.20/6.32 % (13303)Termination phase: Preprocessing 3
% 35.20/6.32
% 35.20/6.32 % (13303)Memory used [KB]: 2174
% 35.20/6.32 % (13303)Time elapsed: 0.023 s
% 35.20/6.32 % (13303)Instructions burned: 69 (million)
% 35.20/6.32 % (13303)------------------------------
% 35.20/6.32 % (13303)------------------------------
% 35.20/6.33 % (13305)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_12850 for (2953ds/360Mi)
% 35.20/6.35 % (13298)Instruction limit reached!
% 35.20/6.35 % (13298)------------------------------
% 35.20/6.35 % (13298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.20/6.35 % (13298)Termination reason: Unknown
% 35.20/6.35 % (13298)Termination phase: Saturation
% 35.20/6.35
% 35.20/6.35 % (13298)Memory used [KB]: 10746
% 35.20/6.35 % (13298)Time elapsed: 0.363 s
% 35.20/6.35 % (13298)Instructions burned: 1175 (million)
% 35.20/6.35 % (13298)------------------------------
% 35.20/6.35 % (13298)------------------------------
% 35.20/6.36 % (13306)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_12850 for (2953ds/157Mi)
% 35.57/6.40 % (13306)Instruction limit reached!
% 35.57/6.40 % (13306)------------------------------
% 35.57/6.40 % (13306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.57/6.40 % (13306)Termination reason: Unknown
% 35.57/6.40 % (13306)Termination phase: Function definition elimination
% 35.57/6.40
% 35.57/6.40 % (13306)Memory used [KB]: 2686
% 35.57/6.40 % (13306)Time elapsed: 0.046 s
% 35.57/6.40 % (13306)Instructions burned: 158 (million)
% 35.57/6.40 % (13306)------------------------------
% 35.57/6.40 % (13306)------------------------------
% 35.57/6.41 % (13307)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_12850 for (2952ds/5061Mi)
% 35.57/6.43 % (13305)Instruction limit reached!
% 35.57/6.43 % (13305)------------------------------
% 35.57/6.43 % (13305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.57/6.43 % (13305)Termination reason: Unknown
% 35.57/6.43 % (13305)Termination phase: Saturation
% 35.57/6.43
% 35.57/6.43 % (13305)Memory used [KB]: 8699
% 35.57/6.43 % (13305)Time elapsed: 0.101 s
% 35.57/6.43 % (13305)Instructions burned: 360 (million)
% 35.57/6.43 % (13305)------------------------------
% 35.57/6.43 % (13305)------------------------------
% 35.57/6.44 % (13308)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_12850 for (2952ds/2401Mi)
% 35.57/6.45 % (13304)Instruction limit reached!
% 35.57/6.45 % (13304)------------------------------
% 35.57/6.45 % (13304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.57/6.45 % (13304)Termination reason: Unknown
% 35.57/6.45 % (13304)Termination phase: Saturation
% 35.57/6.45
% 35.57/6.45 % (13304)Memory used [KB]: 13304
% 35.57/6.45 % (13304)Time elapsed: 0.131 s
% 35.57/6.45 % (13304)Instructions burned: 455 (million)
% 35.57/6.45 % (13304)------------------------------
% 35.57/6.45 % (13304)------------------------------
% 35.57/6.46 % (13309)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_12850 for (2952ds/5798Mi)
% 35.57/6.49 % (13300)Instruction limit reached!
% 35.57/6.49 % (13300)------------------------------
% 35.57/6.49 % (13300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.57/6.49 % (13300)Termination reason: Unknown
% 35.57/6.49 % (13300)Termination phase: Saturation
% 35.57/6.49
% 35.57/6.49 % (13300)Memory used [KB]: 9722
% 35.57/6.49 % (13300)Time elapsed: 0.339 s
% 35.57/6.49 % (13300)Instructions burned: 1204 (million)
% 35.57/6.49 % (13300)------------------------------
% 35.57/6.49 % (13300)------------------------------
% 35.57/6.49 % (13301)Instruction limit reached!
% 35.57/6.49 % (13301)------------------------------
% 35.57/6.49 % (13301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.57/6.49 % (13301)Termination reason: Unknown
% 35.57/6.49 % (13301)Termination phase: Saturation
% 35.57/6.49
% 35.57/6.49 % (13301)Memory used [KB]: 9338
% 35.57/6.49 % (13301)Time elapsed: 0.305 s
% 35.57/6.49 % (13301)Instructions burned: 1046 (million)
% 35.57/6.49 % (13301)------------------------------
% 35.57/6.49 % (13301)------------------------------
% 35.57/6.50 % (13310)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_12850 for (2951ds/346Mi)
% 36.73/6.50 % (13311)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_12850 for (2951ds/1321Mi)
% 36.94/6.60 % (13310)Instruction limit reached!
% 36.94/6.60 % (13310)------------------------------
% 36.94/6.60 % (13310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.94/6.60 % (13310)Termination reason: Unknown
% 36.94/6.60 % (13310)Termination phase: Saturation
% 36.94/6.60
% 36.94/6.60 % (13310)Memory used [KB]: 7803
% 36.94/6.60 % (13310)Time elapsed: 0.104 s
% 36.94/6.60 % (13310)Instructions burned: 348 (million)
% 36.94/6.60 % (13310)------------------------------
% 36.94/6.60 % (13310)------------------------------
% 36.94/6.61 % (13312)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_12850 for (2950ds/1312Mi)
% 37.46/6.88 % (13311)Instruction limit reached!
% 37.46/6.88 % (13311)------------------------------
% 37.46/6.88 % (13311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.46/6.88 % (13311)Termination reason: Unknown
% 37.46/6.88 % (13311)Termination phase: Saturation
% 37.46/6.88
% 37.46/6.88 % (13311)Memory used [KB]: 5628
% 37.46/6.88 % (13311)Time elapsed: 0.381 s
% 37.46/6.88 % (13311)Instructions burned: 1322 (million)
% 37.46/6.88 % (13311)------------------------------
% 37.46/6.88 % (13311)------------------------------
% 38.05/6.90 % (13313)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_12850 for (2947ds/672Mi)
% 38.05/6.96 % (13291)Instruction limit reached!
% 38.05/6.96 % (13291)------------------------------
% 38.05/6.96 % (13291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.05/6.96 % (13291)Termination reason: Unknown
% 38.05/6.96 % (13291)Termination phase: Saturation
% 38.05/6.96
% 38.05/6.96 % (13291)Memory used [KB]: 6652
% 38.05/6.96 % (13291)Time elapsed: 1.238 s
% 38.05/6.96 % (13291)Instructions burned: 4529 (million)
% 38.05/6.96 % (13291)------------------------------
% 38.05/6.96 % (13291)------------------------------
% 38.05/6.97 % (13314)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_12850 for (2947ds/1897Mi)
% 38.05/6.99 % (13312)Instruction limit reached!
% 38.05/6.99 % (13312)------------------------------
% 38.05/6.99 % (13312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.05/6.99 % (13312)Termination reason: Unknown
% 38.05/6.99 % (13312)Termination phase: Saturation
% 38.05/6.99
% 38.05/6.99 % (13312)Memory used [KB]: 9466
% 38.05/6.99 % (13312)Time elapsed: 0.381 s
% 38.05/6.99 % (13312)Instructions burned: 1314 (million)
% 38.05/6.99 % (13312)------------------------------
% 38.05/6.99 % (13312)------------------------------
% 38.05/7.00 % (13315)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_12850 for (2946ds/1202Mi)
% 41.30/7.15 % (13313)Instruction limit reached!
% 41.30/7.15 % (13313)------------------------------
% 41.30/7.15 % (13313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.30/7.15 % (13313)Termination reason: Unknown
% 41.30/7.15 % (13313)Termination phase: Saturation
% 41.30/7.15
% 41.30/7.15 % (13313)Memory used [KB]: 9594
% 41.30/7.15 % (13313)Time elapsed: 0.253 s
% 41.30/7.15 % (13313)Instructions burned: 672 (million)
% 41.30/7.15 % (13313)------------------------------
% 41.30/7.15 % (13313)------------------------------
% 41.30/7.16 % (13316)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_12850 for (2945ds/1493Mi)
% 41.30/7.16 % (13308)Instruction limit reached!
% 41.30/7.16 % (13308)------------------------------
% 41.30/7.16 % (13308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.30/7.16 % (13308)Termination reason: Unknown
% 41.30/7.16 % (13308)Termination phase: Saturation
% 41.30/7.16
% 41.30/7.16 % (13308)Memory used [KB]: 6652
% 41.30/7.16 % (13308)Time elapsed: 0.721 s
% 41.30/7.16 % (13308)Instructions burned: 2401 (million)
% 41.30/7.16 % (13308)------------------------------
% 41.30/7.16 % (13308)------------------------------
% 41.30/7.17 % (13317)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_12850 for (2944ds/7679Mi)
% 41.76/7.21 % (13316)Refutation not found, incomplete strategy
% 41.76/7.21 % (13316)------------------------------
% 41.76/7.21 % (13316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.76/7.21 % (13316)Termination reason: Refutation not found, incomplete strategy
% 41.76/7.21
% 41.76/7.21
% 41.76/7.21 % (13316)Memory used [KB]: 7419
% 41.76/7.21 % (13316)Time elapsed: 0.053 s
% 41.76/7.21 % (13316)Instructions burned: 183 (million)
% 41.76/7.21 % (13316)------------------------------
% 41.76/7.21 % (13316)------------------------------
% 41.76/7.22 % (13318)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_12850 for (2944ds/340Mi)
% 41.76/7.30 % (13288)Instruction limit reached!
% 41.76/7.30 % (13288)------------------------------
% 41.76/7.30 % (13288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.76/7.30 % (13288)Termination reason: Unknown
% 41.76/7.30 % (13288)Termination phase: Saturation
% 41.76/7.30
% 41.76/7.30 % (13288)Memory used [KB]: 8827
% 41.76/7.30 % (13288)Time elapsed: 1.670 s
% 41.76/7.30 % (13288)Instructions burned: 6460 (million)
% 41.76/7.30 % (13288)------------------------------
% 41.76/7.30 % (13288)------------------------------
% 42.32/7.31 % (13319)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_12850 for (2943ds/3672Mi)
% 42.32/7.33 % (13318)Instruction limit reached!
% 42.32/7.33 % (13318)------------------------------
% 42.32/7.33 % (13318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.32/7.33 % (13318)Termination reason: Unknown
% 42.32/7.33 % (13318)Termination phase: Saturation
% 42.32/7.33
% 42.32/7.33 % (13318)Memory used [KB]: 9338
% 42.32/7.33 % (13318)Time elapsed: 0.104 s
% 42.32/7.33 % (13318)Instructions burned: 340 (million)
% 42.32/7.33 % (13318)------------------------------
% 42.32/7.33 % (13318)------------------------------
% 42.32/7.34 % (13320)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_12850 for (2943ds/1535Mi)
% 42.32/7.37 % (13315)Instruction limit reached!
% 42.32/7.37 % (13315)------------------------------
% 42.32/7.37 % (13315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.32/7.37 % (13315)Termination reason: Unknown
% 42.32/7.37 % (13315)Termination phase: Saturation
% 42.32/7.37
% 42.32/7.37 % (13315)Memory used [KB]: 6268
% 42.32/7.37 % (13315)Time elapsed: 0.375 s
% 42.32/7.37 % (13315)Instructions burned: 1204 (million)
% 42.32/7.37 % (13315)------------------------------
% 42.32/7.37 % (13315)------------------------------
% 42.32/7.38 % (13321)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_12850 for (2942ds/4637Mi)
% 43.13/7.55 % (13314)Instruction limit reached!
% 43.13/7.55 % (13314)------------------------------
% 43.13/7.55 % (13314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.13/7.55 % (13314)Termination reason: Unknown
% 43.13/7.55 % (13314)Termination phase: Saturation
% 43.13/7.55
% 43.13/7.55 % (13314)Memory used [KB]: 10362
% 43.13/7.55 % (13314)Time elapsed: 0.580 s
% 43.13/7.55 % (13314)Instructions burned: 1897 (million)
% 43.13/7.55 % (13314)------------------------------
% 43.13/7.55 % (13314)------------------------------
% 43.13/7.56 % (13322)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_12850 for (2941ds/3174Mi)
% 43.80/7.80 % (13320)Instruction limit reached!
% 43.80/7.80 % (13320)------------------------------
% 43.80/7.80 % (13320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.80/7.80 % (13320)Termination reason: Unknown
% 43.80/7.80 % (13320)Termination phase: Saturation
% 43.80/7.80
% 43.80/7.80 % (13320)Memory used [KB]: 12025
% 43.80/7.80 % (13320)Time elapsed: 0.466 s
% 43.80/7.80 % (13320)Instructions burned: 1535 (million)
% 43.80/7.80 % (13320)------------------------------
% 43.80/7.80 % (13320)------------------------------
% 43.80/7.81 % (13323)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_12850 for (2938ds/307Mi)
% 43.80/7.89 % (13323)Instruction limit reached!
% 43.80/7.89 % (13323)------------------------------
% 43.80/7.89 % (13323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.80/7.89 % (13323)Termination reason: Unknown
% 43.80/7.89 % (13323)Termination phase: Saturation
% 43.80/7.89
% 43.80/7.89 % (13323)Memory used [KB]: 7675
% 43.80/7.89 % (13323)Time elapsed: 0.084 s
% 43.80/7.89 % (13323)Instructions burned: 307 (million)
% 43.80/7.89 % (13323)------------------------------
% 43.80/7.89 % (13323)------------------------------
% 44.58/7.90 % (13324)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_12850 for (2937ds/3619Mi)
% 44.58/7.96 % (13307)Instruction limit reached!
% 44.58/7.96 % (13307)------------------------------
% 44.58/7.96 % (13307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.58/7.96 % (13307)Termination reason: Unknown
% 44.58/7.96 % (13307)Termination phase: Saturation
% 44.58/7.96
% 44.58/7.96 % (13307)Memory used [KB]: 13560
% 44.58/7.96 % (13307)Time elapsed: 1.547 s
% 44.58/7.96 % (13307)Instructions burned: 5064 (million)
% 44.58/7.96 % (13307)------------------------------
% 44.58/7.96 % (13307)------------------------------
% 44.58/7.97 % (13325)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_12850 for (2936ds/2325Mi)
% 48.32/8.17 % (13309)Instruction limit reached!
% 48.32/8.17 % (13309)------------------------------
% 48.32/8.17 % (13309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.32/8.17 % (13309)Termination reason: Unknown
% 48.32/8.17 % (13309)Termination phase: Saturation
% 48.32/8.17
% 48.32/8.17 % (13309)Memory used [KB]: 13944
% 48.32/8.17 % (13309)Time elapsed: 1.714 s
% 48.32/8.17 % (13309)Instructions burned: 5800 (million)
% 48.32/8.17 % (13309)------------------------------
% 48.32/8.17 % (13309)------------------------------
% 48.32/8.18 % (13326)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_12850 for (2934ds/2341Mi)
% 49.43/8.36 % (13325)Refutation not found, non-redundant clauses discarded% (13325)------------------------------
% 49.43/8.36 % (13325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.43/8.36 % (13325)Termination reason: Refutation not found, non-redundant clauses discarded
% 49.43/8.36
% 49.43/8.36 % (13325)Memory used [KB]: 10490
% 49.43/8.36 % (13325)Time elapsed: 0.394 s
% 49.43/8.36 % (13325)Instructions burned: 1273 (million)
% 49.43/8.36 % (13325)------------------------------
% 49.43/8.36 % (13325)------------------------------
% 49.43/8.37 % (13327)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_12850 for (2932ds/7257Mi)
% 50.02/8.45 % (13319)Instruction limit reached!
% 50.02/8.45 % (13319)------------------------------
% 50.02/8.45 % (13319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.02/8.45 % (13319)Termination reason: Unknown
% 50.02/8.45 % (13319)Termination phase: Saturation
% 50.02/8.45
% 50.02/8.45 % (13319)Memory used [KB]: 11257
% 50.02/8.45 % (13319)Time elapsed: 1.143 s
% 50.02/8.45 % (13319)Instructions burned: 3672 (million)
% 50.02/8.45 % (13319)------------------------------
% 50.02/8.45 % (13319)------------------------------
% 50.02/8.46 % (13328)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_12850 for (2932ds/3710Mi)
% 50.02/8.48 % (13322)Instruction limit reached!
% 50.02/8.48 % (13322)------------------------------
% 50.02/8.48 % (13322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.02/8.48 % (13322)Termination reason: Unknown
% 50.02/8.48 % (13322)Termination phase: Saturation
% 50.02/8.48
% 50.02/8.48 % (13322)Memory used [KB]: 10874
% 50.02/8.48 % (13322)Time elapsed: 0.928 s
% 50.02/8.48 % (13322)Instructions burned: 3174 (million)
% 50.02/8.48 % (13322)------------------------------
% 50.02/8.48 % (13322)------------------------------
% 50.02/8.49 % (13329)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_12850 for (2931ds/326Mi)
% 50.79/8.60 % (13329)Instruction limit reached!
% 50.79/8.60 % (13329)------------------------------
% 50.79/8.60 % (13329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.79/8.60 % (13329)Termination reason: Unknown
% 50.79/8.60 % (13329)Termination phase: Saturation
% 50.79/8.60
% 50.79/8.60 % (13329)Memory used [KB]: 8059
% 50.79/8.60 % (13329)Time elapsed: 0.107 s
% 50.79/8.60 % (13329)Instructions burned: 327 (million)
% 50.79/8.60 % (13329)------------------------------
% 50.79/8.60 % (13329)------------------------------
% 50.79/8.61 % (13330)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_12850 for (2930ds/1100Mi)
% 51.49/8.80 % (13321)Instruction limit reached!
% 51.49/8.80 % (13321)------------------------------
% 51.49/8.80 % (13321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.49/8.80 % (13321)Termination reason: Unknown
% 51.49/8.80 % (13321)Termination phase: Saturation
% 51.49/8.80
% 51.49/8.80 % (13321)Memory used [KB]: 17910
% 51.49/8.80 % (13321)Time elapsed: 1.422 s
% 51.49/8.80 % (13321)Instructions burned: 4637 (million)
% 51.49/8.80 % (13321)------------------------------
% 51.49/8.80 % (13321)------------------------------
% 51.49/8.81 % (13331)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_12850 for (2928ds/406Mi)
% 51.73/8.92 % (13326)Instruction limit reached!
% 51.73/8.92 % (13326)------------------------------
% 51.73/8.92 % (13326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.73/8.92 % (13326)Termination reason: Unknown
% 51.73/8.92 % (13326)Termination phase: Saturation
% 51.73/8.92
% 51.73/8.92 % (13326)Memory used [KB]: 9210
% 51.73/8.92 % (13326)Time elapsed: 0.737 s
% 51.73/8.92 % (13326)Instructions burned: 2343 (million)
% 51.73/8.92 % (13326)------------------------------
% 51.73/8.92 % (13326)------------------------------
% 51.73/8.93 % (13332)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_12850 for (2927ds/1871Mi)
% 51.73/8.94 % (13331)Instruction limit reached!
% 51.73/8.94 % (13331)------------------------------
% 51.73/8.94 % (13331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.73/8.94 % (13331)Termination reason: Unknown
% 51.73/8.94 % (13331)Termination phase: Saturation
% 51.73/8.94
% 51.73/8.94 % (13331)Memory used [KB]: 8571
% 51.73/8.94 % (13331)Time elapsed: 0.130 s
% 51.73/8.94 % (13331)Instructions burned: 408 (million)
% 51.73/8.94 % (13331)------------------------------
% 51.73/8.94 % (13331)------------------------------
% 51.73/8.94 % (13324)Instruction limit reached!
% 51.73/8.94 % (13324)------------------------------
% 51.73/8.94 % (13324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.73/8.94 % (13324)Termination reason: Unknown
% 51.73/8.94 % (13324)Termination phase: Saturation
% 51.73/8.94
% 51.73/8.94 % (13324)Memory used [KB]: 9210
% 51.73/8.94 % (13324)Time elapsed: 1.040 s
% 51.73/8.94 % (13324)Instructions burned: 3620 (million)
% 51.73/8.94 % (13324)------------------------------
% 51.73/8.94 % (13324)------------------------------
% 51.73/8.95 % (13330)Instruction limit reached!
% 51.73/8.95 % (13330)------------------------------
% 51.73/8.95 % (13330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.73/8.95 % (13330)Termination reason: Unknown
% 51.73/8.95 % (13330)Termination phase: Saturation
% 51.73/8.95
% 51.73/8.95 % (13330)Memory used [KB]: 11641
% 51.73/8.95 % (13330)Time elapsed: 0.339 s
% 51.73/8.95 % (13330)Instructions burned: 1102 (million)
% 51.73/8.95 % (13330)------------------------------
% 51.73/8.95 % (13330)------------------------------
% 51.73/8.95 % (13333)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_12850 for (2927ds/1194Mi)
% 51.73/8.95 % (13334)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_12850 for (2927ds/474Mi)
% 51.73/8.96 % (13335)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_12850 for (2927ds/3115Mi)
% 54.64/9.09 % (13334)Instruction limit reached!
% 54.64/9.09 % (13334)------------------------------
% 54.64/9.09 % (13334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.64/9.09 % (13334)Termination reason: Unknown
% 54.64/9.09 % (13334)Termination phase: Saturation
% 54.64/9.09
% 54.64/9.09 % (13334)Memory used [KB]: 8187
% 54.64/9.09 % (13334)Time elapsed: 0.138 s
% 54.64/9.09 % (13334)Instructions burned: 475 (million)
% 54.64/9.09 % (13334)------------------------------
% 54.64/9.09 % (13334)------------------------------
% 54.64/9.10 % (13336)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_12850 for (2925ds/831Mi)
% 56.37/9.32 % (13333)Instruction limit reached!
% 56.37/9.32 % (13333)------------------------------
% 56.37/9.32 % (13333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.37/9.32 % (13333)Termination reason: Unknown
% 56.37/9.32 % (13333)Termination phase: Saturation
% 56.37/9.32
% 56.37/9.32 % (13333)Memory used [KB]: 9850
% 56.37/9.32 % (13333)Time elapsed: 0.370 s
% 56.37/9.32 % (13333)Instructions burned: 1197 (million)
% 56.37/9.32 % (13333)------------------------------
% 56.37/9.32 % (13333)------------------------------
% 56.37/9.33 % (13337)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_12850 for (2923ds/1188Mi)
% 56.37/9.35 % (13336)Instruction limit reached!
% 56.37/9.35 % (13336)------------------------------
% 56.37/9.35 % (13336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.37/9.35 % (13336)Termination reason: Unknown
% 56.37/9.35 % (13336)Termination phase: Saturation
% 56.37/9.35
% 56.37/9.35 % (13336)Memory used [KB]: 10362
% 56.37/9.35 % (13336)Time elapsed: 0.247 s
% 56.37/9.35 % (13336)Instructions burned: 833 (million)
% 56.37/9.35 % (13336)------------------------------
% 56.37/9.35 % (13336)------------------------------
% 56.37/9.36 % (13338)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_12850 for (2923ds/2868Mi)
% 57.17/9.41 % (13317)Instruction limit reached!
% 57.17/9.41 % (13317)------------------------------
% 57.17/9.41 % (13317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.17/9.41 % (13317)Termination reason: Unknown
% 57.17/9.41 % (13317)Termination phase: Saturation
% 57.17/9.41
% 57.17/9.41 % (13317)Memory used [KB]: 21108
% 57.17/9.41 % (13317)Time elapsed: 2.243 s
% 57.17/9.41 % (13317)Instructions burned: 7680 (million)
% 57.17/9.41 % (13317)------------------------------
% 57.17/9.41 % (13317)------------------------------
% 57.17/9.43 % (13340)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_12850 for (2922ds/1516Mi)
% 57.17/9.45 % (13338)Refutation not found, incomplete strategy
% 57.17/9.45 % (13338)------------------------------
% 57.17/9.45 % (13338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.17/9.45 % (13338)Termination reason: Refutation not found, incomplete strategy
% 57.17/9.45
% 57.17/9.45
% 57.17/9.45 % (13338)Memory used [KB]: 8699
% 57.17/9.45 % (13338)Time elapsed: 0.099 s
% 57.17/9.45 % (13338)Instructions burned: 353 (million)
% 57.17/9.45 % (13338)------------------------------
% 57.17/9.45 % (13338)------------------------------
% 57.17/9.46 % (13341)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_12850 for (2921ds/2321Mi)
% 57.71/9.51 % (13332)Instruction limit reached!
% 57.71/9.51 % (13332)------------------------------
% 57.71/9.51 % (13332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.71/9.51 % (13332)Termination reason: Unknown
% 57.71/9.51 % (13332)Termination phase: Saturation
% 57.71/9.51
% 57.71/9.51 % (13332)Memory used [KB]: 11257
% 57.71/9.51 % (13332)Time elapsed: 0.583 s
% 57.71/9.51 % (13332)Instructions burned: 1871 (million)
% 57.71/9.51 % (13332)------------------------------
% 57.71/9.51 % (13332)------------------------------
% 57.71/9.52 % (13342)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_12850 for (2921ds/2812Mi)
% 57.71/9.55 % (13328)Instruction limit reached!
% 57.71/9.55 % (13328)------------------------------
% 57.71/9.55 % (13328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.71/9.55 % (13328)Termination reason: Unknown
% 57.71/9.55 % (13328)Termination phase: Saturation
% 57.71/9.55
% 57.71/9.55 % (13328)Memory used [KB]: 19445
% 57.71/9.55 % (13328)Time elapsed: 1.097 s
% 57.71/9.55 % (13328)Instructions burned: 3712 (million)
% 57.71/9.55 % (13328)------------------------------
% 57.71/9.55 % (13328)------------------------------
% 57.71/9.56 % (13341)Refutation not found, incomplete strategy
% 57.71/9.56 % (13341)------------------------------
% 57.71/9.56 % (13341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.71/9.56 % (13341)Termination reason: Refutation not found, incomplete strategy
% 57.71/9.56
% 57.71/9.56
% 57.71/9.56 % (13341)Memory used [KB]: 8187
% 57.71/9.56 % (13341)Time elapsed: 0.093 s
% 57.71/9.56 % (13341)Instructions burned: 339 (million)
% 57.71/9.56 % (13341)------------------------------
% 57.71/9.56 % (13341)------------------------------
% 57.71/9.56 % (13343)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_12850 for (2920ds/4604Mi)
% 57.71/9.57 % (13344)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_12850 for (2920ds/2678Mi)
% 58.11/9.69 % (13337)Instruction limit reached!
% 58.11/9.69 % (13337)------------------------------
% 58.11/9.69 % (13337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.11/9.69 % (13337)Termination reason: Unknown
% 58.11/9.69 % (13337)Termination phase: Saturation
% 58.11/9.69
% 58.11/9.69 % (13337)Memory used [KB]: 9978
% 58.11/9.69 % (13337)Time elapsed: 0.363 s
% 58.11/9.69 % (13337)Instructions burned: 1188 (million)
% 58.11/9.69 % (13337)------------------------------
% 58.11/9.69 % (13337)------------------------------
% 58.67/9.70 % (13345)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_12850 for (2919ds/643Mi)
% 58.87/9.89 % (13345)Instruction limit reached!
% 58.87/9.89 % (13345)------------------------------
% 58.87/9.89 % (13345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.87/9.89 % (13345)Termination reason: Unknown
% 58.87/9.89 % (13345)Termination phase: Saturation
% 58.87/9.89
% 58.87/9.89 % (13345)Memory used [KB]: 9722
% 58.87/9.89 % (13345)Time elapsed: 0.188 s
% 58.87/9.89 % (13345)Instructions burned: 645 (million)
% 58.87/9.89 % (13345)------------------------------
% 58.87/9.89 % (13345)------------------------------
% 58.87/9.90 % (13340)Instruction limit reached!
% 58.87/9.90 % (13340)------------------------------
% 58.87/9.90 % (13340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.87/9.90 % (13340)Termination reason: Unknown
% 58.87/9.90 % (13340)Termination phase: Saturation
% 58.87/9.90
% 58.87/9.90 % (13340)Memory used [KB]: 8315
% 58.87/9.90 % (13340)Time elapsed: 0.472 s
% 58.87/9.90 % (13340)Instructions burned: 1517 (million)
% 58.87/9.90 % (13340)------------------------------
% 58.87/9.90 % (13340)------------------------------
% 59.28/9.90 % (13346)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_12850 for (2917ds/458Mi)
% 59.28/9.90 % (13335)Instruction limit reached!
% 59.28/9.90 % (13335)------------------------------
% 59.28/9.90 % (13335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.28/9.90 % (13335)Termination reason: Unknown
% 59.28/9.90 % (13335)Termination phase: Saturation
% 59.28/9.90
% 59.28/9.90 % (13335)Memory used [KB]: 11257
% 59.28/9.90 % (13335)Time elapsed: 0.944 s
% 59.28/9.90 % (13335)Instructions burned: 3115 (million)
% 59.28/9.90 % (13335)------------------------------
% 59.28/9.90 % (13335)------------------------------
% 59.28/9.91 % (13347)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_12850 for (2917ds/2546Mi)
% 59.28/9.91 % (13348)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_12850 for (2917ds/1432Mi)
% 61.67/10.03 % (13346)Instruction limit reached!
% 61.67/10.03 % (13346)------------------------------
% 61.67/10.03 % (13346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.67/10.03 % (13346)Termination reason: Unknown
% 61.67/10.03 % (13346)Termination phase: Saturation
% 61.67/10.03
% 61.67/10.03 % (13346)Memory used [KB]: 8571
% 61.67/10.03 % (13346)Time elapsed: 0.129 s
% 61.67/10.03 % (13346)Instructions burned: 460 (million)
% 61.67/10.03 % (13346)------------------------------
% 61.67/10.03 % (13346)------------------------------
% 61.67/10.04 % (13349)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_12850 for (2916ds/386Mi)
% 62.28/10.15 % (13349)Instruction limit reached!
% 62.28/10.15 % (13349)------------------------------
% 62.28/10.15 % (13349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.28/10.15 % (13349)Termination reason: Unknown
% 62.28/10.15 % (13349)Termination phase: Saturation
% 62.28/10.15
% 62.28/10.15 % (13349)Memory used [KB]: 8827
% 62.28/10.15 % (13349)Time elapsed: 0.110 s
% 62.28/10.15 % (13349)Instructions burned: 388 (million)
% 62.28/10.15 % (13349)------------------------------
% 62.28/10.15 % (13349)------------------------------
% 62.28/10.16 % (13350)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_12850 for (2915ds/360Mi)
% 62.84/10.26 % (13350)Instruction limit reached!
% 62.84/10.26 % (13350)------------------------------
% 62.84/10.26 % (13350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.84/10.26 % (13350)Termination reason: Unknown
% 62.84/10.26 % (13350)Termination phase: Saturation
% 62.84/10.26
% 62.84/10.26 % (13350)Memory used [KB]: 8827
% 62.84/10.26 % (13350)Time elapsed: 0.104 s
% 62.84/10.26 % (13350)Instructions burned: 363 (million)
% 62.84/10.26 % (13350)------------------------------
% 62.84/10.26 % (13350)------------------------------
% 62.84/10.27 % (13351)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_12850 for (2914ds/5446Mi)
% 63.55/10.35 % (13348)Instruction limit reached!
% 63.55/10.35 % (13348)------------------------------
% 63.55/10.35 % (13348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.55/10.35 % (13348)Termination reason: Unknown
% 63.55/10.35 % (13348)Termination phase: Saturation
% 63.55/10.35
% 63.55/10.35 % (13348)Memory used [KB]: 10746
% 63.55/10.35 % (13348)Time elapsed: 0.436 s
% 63.55/10.35 % (13348)Instructions burned: 1432 (million)
% 63.55/10.35 % (13348)------------------------------
% 63.55/10.35 % (13348)------------------------------
% 63.55/10.36 % (13352)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_12850 for (2913ds/2573Mi)
% 63.55/10.37 % (13344)Instruction limit reached!
% 63.55/10.37 % (13344)------------------------------
% 63.55/10.37 % (13344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.55/10.37 % (13344)Termination reason: Unknown
% 63.55/10.37 % (13344)Termination phase: Saturation
% 63.55/10.37
% 63.55/10.37 % (13344)Memory used [KB]: 12920
% 63.55/10.37 % (13344)Time elapsed: 0.801 s
% 63.55/10.37 % (13344)Instructions burned: 2678 (million)
% 63.55/10.37 % (13344)------------------------------
% 63.55/10.37 % (13344)------------------------------
% 63.55/10.38 % (13353)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_12850 for (2913ds/2655Mi)
% 64.11/10.40 % (13342)Instruction limit reached!
% 64.11/10.40 % (13342)------------------------------
% 64.11/10.40 % (13342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.11/10.40 % (13342)Termination reason: Unknown
% 64.11/10.40 % (13342)Termination phase: Saturation
% 64.11/10.40
% 64.11/10.40 % (13342)Memory used [KB]: 11129
% 64.11/10.40 % (13342)Time elapsed: 0.879 s
% 64.11/10.40 % (13342)Instructions burned: 2812 (million)
% 64.11/10.40 % (13342)------------------------------
% 64.11/10.40 % (13342)------------------------------
% 64.11/10.41 % (13354)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_12850 for (2912ds/2781Mi)
% 64.42/10.50 % (13327)Instruction limit reached!
% 64.42/10.50 % (13327)------------------------------
% 64.42/10.50 % (13327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.42/10.50 % (13327)Termination reason: Unknown
% 64.42/10.50 % (13327)Termination phase: Saturation
% 64.42/10.50
% 64.42/10.50 % (13327)Memory used [KB]: 20212
% 64.42/10.50 % (13327)Time elapsed: 2.133 s
% 64.42/10.50 % (13327)Instructions burned: 7257 (million)
% 64.42/10.50 % (13327)------------------------------
% 64.42/10.50 % (13327)------------------------------
% 64.42/10.52 % (13355)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_12850 for (2911ds/307Mi)
% 64.63/10.60 % (13355)Instruction limit reached!
% 64.63/10.60 % (13355)------------------------------
% 64.63/10.60 % (13355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.63/10.60 % (13355)Termination reason: Unknown
% 64.63/10.60 % (13355)Termination phase: Saturation
% 64.63/10.60
% 64.63/10.60 % (13355)Memory used [KB]: 7675
% 64.63/10.60 % (13355)Time elapsed: 0.084 s
% 64.63/10.60 % (13355)Instructions burned: 307 (million)
% 64.63/10.60 % (13355)------------------------------
% 64.63/10.60 % (13355)------------------------------
% 64.63/10.61 % (13356)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_12850 for (2910ds/1548Mi)
% 64.93/10.71 % (13347)Instruction limit reached!
% 64.93/10.71 % (13347)------------------------------
% 64.93/10.71 % (13347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.93/10.71 % (13347)Termination reason: Unknown
% 64.93/10.71 % (13347)Termination phase: Saturation
% 64.93/10.71
% 64.93/10.71 % (13347)Memory used [KB]: 11641
% 64.93/10.71 % (13347)Time elapsed: 0.802 s
% 64.93/10.71 % (13347)Instructions burned: 2548 (million)
% 64.93/10.71 % (13347)------------------------------
% 64.93/10.71 % (13347)------------------------------
% 64.93/10.72 % (13357)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_12850 for (2909ds/5214Mi)
% 65.16/10.90 % (13343)Instruction limit reached!
% 65.16/10.90 % (13343)------------------------------
% 65.16/10.90 % (13343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.16/10.90 % (13343)Termination reason: Unknown
% 65.16/10.90 % (13343)Termination phase: Saturation
% 65.16/10.90
% 65.16/10.90 % (13343)Memory used [KB]: 16375
% 65.16/10.90 % (13343)Time elapsed: 1.340 s
% 65.16/10.90 % (13343)Instructions burned: 4604 (million)
% 65.16/10.90 % (13343)------------------------------
% 65.16/10.90 % (13343)------------------------------
% 65.16/10.91 % (13358)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_12850 for (2907ds/3201Mi)
% 68.66/11.07 % (13356)Instruction limit reached!
% 68.66/11.07 % (13356)------------------------------
% 68.66/11.07 % (13356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.66/11.07 % (13356)Termination reason: Unknown
% 68.66/11.07 % (13356)Termination phase: Saturation
% 68.66/11.07
% 68.66/11.07 % (13356)Memory used [KB]: 8699
% 68.66/11.07 % (13356)Time elapsed: 0.466 s
% 68.66/11.07 % (13356)Instructions burned: 1551 (million)
% 68.66/11.07 % (13356)------------------------------
% 68.66/11.07 % (13356)------------------------------
% 68.66/11.08 % (13359)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_12850 for (2905ds/454Mi)
% 69.38/11.14 % (13352)Instruction limit reached!
% 69.38/11.14 % (13352)------------------------------
% 69.38/11.14 % (13352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.38/11.14 % (13352)Termination reason: Unknown
% 69.38/11.14 % (13352)Termination phase: Saturation
% 69.38/11.14
% 69.38/11.14 % (13352)Memory used [KB]: 11001
% 69.38/11.14 % (13352)Time elapsed: 0.808 s
% 69.38/11.14 % (13352)Instructions burned: 2573 (million)
% 69.38/11.14 % (13352)------------------------------
% 69.38/11.14 % (13352)------------------------------
% 69.38/11.15 % (13360)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_12850 for (2905ds/3049Mi)
% 69.38/11.17 % (13353)Instruction limit reached!
% 69.38/11.17 % (13353)------------------------------
% 69.38/11.17 % (13353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.38/11.17 % (13353)Termination reason: Unknown
% 69.38/11.17 % (13353)Termination phase: Saturation
% 69.38/11.17
% 69.38/11.17 % (13353)Memory used [KB]: 12537
% 69.38/11.17 % (13353)Time elapsed: 0.814 s
% 69.38/11.17 % (13353)Instructions burned: 2655 (million)
% 69.38/11.17 % (13353)------------------------------
% 69.38/11.17 % (13353)------------------------------
% 69.38/11.18 % (13361)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_12850 for (2905ds/7311Mi)
% 69.75/11.21 % (13359)Instruction limit reached!
% 69.75/11.21 % (13359)------------------------------
% 69.75/11.21 % (13359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.75/11.21 % (13359)Termination reason: Unknown
% 69.75/11.21 % (13359)Termination phase: Saturation
% 69.75/11.21
% 69.75/11.21 % (13359)Memory used [KB]: 13432
% 69.75/11.21 % (13359)Time elapsed: 0.132 s
% 69.75/11.21 % (13359)Instructions burned: 457 (million)
% 69.75/11.21 % (13359)------------------------------
% 69.75/11.21 % (13359)------------------------------
% 69.75/11.22 % (13362)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_12850 for (2904ds/6804Mi)
% 69.75/11.26 % (13354)Instruction limit reached!
% 69.75/11.26 % (13354)------------------------------
% 69.75/11.26 % (13354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.75/11.26 % (13354)Termination reason: Unknown
% 69.75/11.26 % (13354)Termination phase: Saturation
% 69.75/11.26
% 69.75/11.26 % (13354)Memory used [KB]: 6140
% 69.75/11.26 % (13354)Time elapsed: 0.878 s
% 69.75/11.26 % (13354)Instructions burned: 2781 (million)
% 69.75/11.26 % (13354)------------------------------
% 69.75/11.26 % (13354)------------------------------
% 69.75/11.27 % (13363)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_12850 for (2904ds/1683Mi)
% 71.47/11.79 % (13363)Instruction limit reached!
% 71.47/11.79 % (13363)------------------------------
% 71.47/11.79 % (13363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.47/11.79 % (13363)Termination reason: Unknown
% 71.47/11.79 % (13363)Termination phase: Saturation
% 71.47/11.79
% 71.47/11.79 % (13363)Memory used [KB]: 10106
% 71.47/11.79 % (13363)Time elapsed: 0.545 s
% 71.47/11.79 % (13363)Instructions burned: 1685 (million)
% 71.47/11.79 % (13363)------------------------------
% 71.47/11.79 % (13363)------------------------------
% 72.30/11.80 % (13364)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_12850 for (2898ds/4688Mi)
% 72.30/11.88 % (13358)Instruction limit reached!
% 72.30/11.88 % (13358)------------------------------
% 72.30/11.88 % (13358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.30/11.88 % (13358)Termination reason: Unknown
% 72.30/11.88 % (13358)Termination phase: Saturation
% 72.30/11.88
% 72.30/11.88 % (13358)Memory used [KB]: 11257
% 72.30/11.88 % (13358)Time elapsed: 0.965 s
% 72.30/11.88 % (13358)Instructions burned: 3201 (million)
% 72.30/11.88 % (13358)------------------------------
% 72.30/11.88 % (13358)------------------------------
% 72.30/11.89 % (13365)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_12850 for (2897ds/2207Mi)
% 72.58/11.99 % (13351)Instruction limit reached!
% 72.58/11.99 % (13351)------------------------------
% 72.58/11.99 % (13351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.58/11.99 % (13351)Termination reason: Unknown
% 72.58/11.99 % (13351)Termination phase: Saturation
% 72.58/11.99
% 72.58/11.99 % (13351)Memory used [KB]: 15223
% 72.58/11.99 % (13351)Time elapsed: 1.745 s
% 72.58/11.99 % (13351)Instructions burned: 5447 (million)
% 72.58/11.99 % (13351)------------------------------
% 72.58/11.99 % (13351)------------------------------
% 72.58/12.00 % (13366)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_12850 for (2896ds/8216Mi)
% 75.69/12.03 % (13360)Instruction limit reached!
% 75.69/12.03 % (13360)------------------------------
% 75.69/12.03 % (13360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.69/12.03 % (13360)Termination reason: Unknown
% 75.69/12.03 % (13360)Termination phase: Saturation
% 75.69/12.03
% 75.69/12.03 % (13360)Memory used [KB]: 9594
% 75.69/12.03 % (13360)Time elapsed: 0.901 s
% 75.69/12.03 % (13360)Instructions burned: 3049 (million)
% 75.69/12.03 % (13360)------------------------------
% 75.69/12.03 % (13360)------------------------------
% 75.69/12.04 % (13367)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_12850 for (2896ds/430Mi)
% 76.33/12.16 % (13367)Instruction limit reached!
% 76.33/12.16 % (13367)------------------------------
% 76.33/12.16 % (13367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.33/12.16 % (13367)Termination reason: Unknown
% 76.33/12.16 % (13367)Termination phase: Saturation
% 76.33/12.16
% 76.33/12.16 % (13367)Memory used [KB]: 8059
% 76.33/12.16 % (13367)Time elapsed: 0.121 s
% 76.33/12.16 % (13367)Instructions burned: 430 (million)
% 76.33/12.16 % (13367)------------------------------
% 76.33/12.16 % (13367)------------------------------
% 76.33/12.17 % (13368)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_12850 for (2895ds/2012Mi)
% 76.93/12.28 % (13357)Instruction limit reached!
% 76.93/12.28 % (13357)------------------------------
% 76.93/12.28 % (13357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.93/12.28 % (13357)Termination reason: Unknown
% 76.93/12.28 % (13357)Termination phase: Saturation
% 76.93/12.28
% 76.93/12.28 % (13357)Memory used [KB]: 24946
% 76.93/12.28 % (13357)Time elapsed: 1.564 s
% 76.93/12.28 % (13357)Instructions burned: 5214 (million)
% 76.93/12.28 % (13357)------------------------------
% 76.93/12.28 % (13357)------------------------------
% 76.93/12.29 % (13369)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_12850 for (2893ds/631Mi)
% 78.01/12.48 % (13369)Instruction limit reached!
% 78.01/12.48 % (13369)------------------------------
% 78.01/12.48 % (13369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.01/12.48 % (13369)Termination reason: Unknown
% 78.01/12.48 % (13369)Termination phase: Saturation
% 78.01/12.48
% 78.01/12.48 % (13369)Memory used [KB]: 10106
% 78.01/12.48 % (13369)Time elapsed: 0.190 s
% 78.01/12.48 % (13369)Instructions burned: 631 (million)
% 78.01/12.48 % (13369)------------------------------
% 78.01/12.48 % (13369)------------------------------
% 78.01/12.49 % (13370)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_12850 for (2891ds/8785Mi)
% 78.71/12.57 % (13365)Instruction limit reached!
% 78.71/12.57 % (13365)------------------------------
% 78.71/12.57 % (13365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.71/12.57 % (13365)Termination reason: Unknown
% 78.71/12.57 % (13365)Termination phase: Saturation
% 78.71/12.57
% 78.71/12.57 % (13365)Memory used [KB]: 10490
% 78.71/12.57 % (13365)Time elapsed: 0.686 s
% 78.71/12.57 % (13365)Instructions burned: 2207 (million)
% 78.71/12.57 % (13365)------------------------------
% 78.71/12.57 % (13365)------------------------------
% 78.71/12.58 % (13371)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_12850 for (2890ds/739Mi)
% 79.60/12.77 % (13368)Instruction limit reached!
% 79.60/12.77 % (13368)------------------------------
% 79.60/12.77 % (13368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.60/12.77 % (13368)Termination reason: Unknown
% 79.60/12.77 % (13368)Termination phase: Saturation
% 79.60/12.77
% 79.60/12.77 % (13368)Memory used [KB]: 15223
% 79.60/12.77 % (13368)Time elapsed: 0.599 s
% 79.60/12.77 % (13368)Instructions burned: 2013 (million)
% 79.60/12.77 % (13368)------------------------------
% 79.60/12.77 % (13368)------------------------------
% 79.60/12.78 % (13372)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_12850 for (2888ds/5473Mi)
% 80.60/12.81 % (13371)Instruction limit reached!
% 80.60/12.81 % (13371)------------------------------
% 80.60/12.81 % (13371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.60/12.81 % (13371)Termination reason: Unknown
% 80.60/12.81 % (13371)Termination phase: Saturation
% 80.60/12.81
% 80.60/12.81 % (13371)Memory used [KB]: 9338
% 80.60/12.81 % (13371)Time elapsed: 0.231 s
% 80.60/12.81 % (13371)Instructions burned: 740 (million)
% 80.60/12.81 % (13371)------------------------------
% 80.60/12.81 % (13371)------------------------------
% 80.60/12.82 % (13373)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_12850 for (2888ds/43570Mi)
% 83.45/13.17 % (13364)Instruction limit reached!
% 83.45/13.17 % (13364)------------------------------
% 83.45/13.17 % (13364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.45/13.17 % (13364)Termination reason: Unknown
% 83.45/13.17 % (13364)Termination phase: Saturation
% 83.45/13.17
% 83.45/13.17 % (13364)Memory used [KB]: 17270
% 83.45/13.17 % (13364)Time elapsed: 1.370 s
% 83.45/13.17 % (13364)Instructions burned: 4689 (million)
% 83.45/13.17 % (13364)------------------------------
% 83.45/13.17 % (13364)------------------------------
% 83.45/13.18 % (13374)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_12850 for (2884ds/8382Mi)
% 83.95/13.29 % (13362)Instruction limit reached!
% 83.95/13.29 % (13362)------------------------------
% 83.95/13.29 % (13362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.95/13.29 % (13362)Termination reason: Unknown
% 83.95/13.29 % (13362)Termination phase: Saturation
% 83.95/13.29
% 83.95/13.29 % (13362)Memory used [KB]: 12537
% 83.95/13.29 % (13362)Time elapsed: 2.093 s
% 83.95/13.29 % (13362)Instructions burned: 6805 (million)
% 83.95/13.29 % (13362)------------------------------
% 83.95/13.29 % (13362)------------------------------
% 84.55/13.30 % (13375)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_12850 for (2883ds/407Mi)
% 85.05/13.41 % (13361)Instruction limit reached!
% 85.05/13.41 % (13361)------------------------------
% 85.05/13.41 % (13361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.05/13.41 % (13361)Termination reason: Unknown
% 85.05/13.41 % (13361)Termination phase: Saturation
% 85.05/13.41
% 85.05/13.41 % (13361)Memory used [KB]: 17654
% 85.05/13.41 % (13361)Time elapsed: 2.251 s
% 85.05/13.41 % (13361)Instructions burned: 7311 (million)
% 85.05/13.41 % (13361)------------------------------
% 85.05/13.41 % (13361)------------------------------
% 85.05/13.42 % (13376)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_12850 for (2882ds/2971Mi)
% 85.05/13.43 % (13375)Instruction limit reached!
% 85.05/13.43 % (13375)------------------------------
% 85.05/13.43 % (13375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.05/13.43 % (13375)Termination reason: Unknown
% 85.05/13.43 % (13375)Termination phase: Saturation
% 85.05/13.43
% 85.05/13.43 % (13375)Memory used [KB]: 8059
% 85.05/13.43 % (13375)Time elapsed: 0.123 s
% 85.05/13.43 % (13375)Instructions burned: 407 (million)
% 85.05/13.43 % (13375)------------------------------
% 85.05/13.43 % (13375)------------------------------
% 85.05/13.43 % (13377)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_12850 for (2882ds/9822Mi)
% 85.60/13.51 % (13376)Refutation not found, incomplete strategy
% 85.60/13.51 % (13376)------------------------------
% 85.60/13.51 % (13376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.60/13.51 % (13376)Termination reason: Refutation not found, incomplete strategy
% 85.60/13.51
% 85.60/13.51
% 85.60/13.51 % (13376)Memory used [KB]: 8699
% 85.60/13.51 % (13376)Time elapsed: 0.098 s
% 85.60/13.51 % (13376)Instructions burned: 352 (million)
% 85.60/13.51 % (13376)------------------------------
% 85.60/13.51 % (13376)------------------------------
% 85.60/13.52 % (13378)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_12850 for (2881ds/8425Mi)
% 92.37/14.43 % (13372)Instruction limit reached!
% 92.37/14.43 % (13372)------------------------------
% 92.37/14.43 % (13372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.37/14.43 % (13372)Termination reason: Unknown
% 92.37/14.43 % (13372)Termination phase: Saturation
% 92.37/14.43
% 92.37/14.43 % (13372)Memory used [KB]: 8955
% 92.37/14.43 % (13372)Time elapsed: 1.650 s
% 92.37/14.43 % (13372)Instructions burned: 5473 (million)
% 92.37/14.43 % (13372)------------------------------
% 92.37/14.43 % (13372)------------------------------
% 92.37/14.44 % (13517)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_12850 for (2872ds/3107Mi)
% 92.37/14.49 % (13366)Instruction limit reached!
% 92.37/14.49 % (13366)------------------------------
% 92.37/14.49 % (13366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.37/14.49 % (13366)Termination reason: Unknown
% 92.37/14.49 % (13366)Termination phase: Saturation
% 92.37/14.49
% 92.37/14.49 % (13366)Memory used [KB]: 15223
% 92.37/14.49 % (13366)Time elapsed: 2.487 s
% 92.37/14.49 % (13366)Instructions burned: 8218 (million)
% 92.37/14.49 % (13366)------------------------------
% 92.37/14.49 % (13366)------------------------------
% 93.02/14.50 % (13537)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_12850 for (2871ds/7967Mi)
% 93.02/14.59 % (13537)Refutation not found, incomplete strategy
% 93.02/14.59 % (13537)------------------------------
% 93.02/14.59 % (13537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.02/14.59 % (13537)Termination reason: Refutation not found, incomplete strategy
% 93.02/14.59
% 93.02/14.59
% 93.02/14.59 % (13537)Memory used [KB]: 8059
% 93.02/14.59 % (13537)Time elapsed: 0.089 s
% 93.02/14.59 % (13537)Instructions burned: 321 (million)
% 93.02/14.59 % (13537)------------------------------
% 93.02/14.59 % (13537)------------------------------
% 93.64/14.60 % (13598)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_12850 for (2870ds/3629Mi)
% 97.61/15.16 % (13370)Instruction limit reached!
% 97.61/15.16 % (13370)------------------------------
% 97.61/15.16 % (13370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.61/15.16 % (13370)Termination reason: Unknown
% 97.61/15.16 % (13370)Termination phase: Saturation
% 97.61/15.16
% 97.61/15.16 % (13370)Memory used [KB]: 19061
% 97.61/15.16 % (13370)Time elapsed: 2.669 s
% 97.61/15.16 % (13370)Instructions burned: 8786 (million)
% 97.61/15.16 % (13370)------------------------------
% 97.61/15.16 % (13370)------------------------------
% 97.61/15.17 % (13808)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_12850 for (2865ds/939Mi)
% 98.57/15.37 % (13517)Instruction limit reached!
% 98.57/15.37 % (13517)------------------------------
% 98.57/15.37 % (13517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.57/15.37 % (13517)Termination reason: Unknown
% 98.57/15.37 % (13517)Termination phase: Saturation
% 98.57/15.37
% 98.57/15.37 % (13517)Memory used [KB]: 11897
% 98.57/15.37 % (13517)Time elapsed: 0.937 s
% 98.57/15.37 % (13517)Instructions burned: 3107 (million)
% 98.57/15.37 % (13517)------------------------------
% 98.57/15.37 % (13517)------------------------------
% 98.57/15.38 % (13853)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_12850 for (2862ds/1188Mi)
% 99.16/15.44 % (13808)Instruction limit reached!
% 99.16/15.44 % (13808)------------------------------
% 99.16/15.44 % (13808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.16/15.44 % (13808)Termination reason: Unknown
% 99.16/15.44 % (13808)Termination phase: Saturation
% 99.16/15.44
% 99.16/15.44 % (13808)Memory used [KB]: 9466
% 99.16/15.44 % (13808)Time elapsed: 0.276 s
% 99.16/15.44 % (13808)Instructions burned: 943 (million)
% 99.16/15.44 % (13808)------------------------------
% 99.16/15.44 % (13808)------------------------------
% 99.16/15.45 % (13854)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_12850 for (2862ds/3205Mi)
% 100.95/15.71 % (13598)Instruction limit reached!
% 100.95/15.71 % (13598)------------------------------
% 100.95/15.71 % (13598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.95/15.71 % (13598)Termination reason: Unknown
% 100.95/15.71 % (13598)Termination phase: Saturation
% 100.95/15.71
% 100.95/15.71 % (13598)Memory used [KB]: 12281
% 100.95/15.71 % (13598)Time elapsed: 1.115 s
% 100.95/15.71 % (13598)Instructions burned: 3630 (million)
% 100.95/15.71 % (13598)------------------------------
% 100.95/15.71 % (13598)------------------------------
% 100.95/15.72 % (13855)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_12850 for (2859ds/865Mi)
% 100.95/15.76 % (13374)Instruction limit reached!
% 100.95/15.76 % (13374)------------------------------
% 100.95/15.76 % (13374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.95/15.76 % (13374)Termination reason: Unknown
% 100.95/15.76 % (13374)Termination phase: Saturation
% 100.95/15.76
% 100.95/15.76 % (13374)Memory used [KB]: 18549
% 100.95/15.76 % (13374)Time elapsed: 2.581 s
% 100.95/15.76 % (13374)Instructions burned: 8382 (million)
% 100.95/15.76 % (13374)------------------------------
% 100.95/15.76 % (13374)------------------------------
% 100.95/15.77 % (13853)Instruction limit reached!
% 100.95/15.77 % (13853)------------------------------
% 100.95/15.77 % (13853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.95/15.77 % (13853)Termination reason: Unknown
% 100.95/15.77 % (13853)Termination phase: Saturation
% 100.95/15.77
% 100.95/15.77 % (13853)Memory used [KB]: 9850
% 100.95/15.77 % (13853)Time elapsed: 0.387 s
% 100.95/15.77 % (13853)Instructions burned: 1188 (million)
% 100.95/15.77 % (13853)------------------------------
% 100.95/15.77 % (13853)------------------------------
% 100.95/15.77 % (13856)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_12850 for (2858ds/7469Mi)
% 100.95/15.78 % (13857)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_12850 for (2858ds/4165Mi)
% 103.79/16.05 % (13378)Instruction limit reached!
% 103.79/16.05 % (13378)------------------------------
% 103.79/16.05 % (13378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 103.79/16.05 % (13378)Termination reason: Unknown
% 103.79/16.05 % (13378)Termination phase: Saturation
% 103.79/16.05
% 103.79/16.05 % (13378)Memory used [KB]: 17526
% 103.79/16.05 % (13378)Time elapsed: 2.529 s
% 103.79/16.05 % (13378)Instructions burned: 8427 (million)
% 103.79/16.05 % (13378)------------------------------
% 103.79/16.05 % (13378)------------------------------
% 103.79/16.06 % (13860)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_12850 for (2856ds/13468Mi)
% 103.79/16.07 % (13855)Instruction limit reached!
% 103.79/16.07 % (13855)------------------------------
% 103.79/16.07 % (13855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 103.79/16.07 % (13855)Termination reason: Unknown
% 103.79/16.07 % (13855)Termination phase: Saturation
% 103.79/16.07
% 103.79/16.07 % (13855)Memory used [KB]: 10234
% 103.79/16.07 % (13855)Time elapsed: 0.347 s
% 103.79/16.07 % (13855)Instructions burned: 866 (million)
% 103.79/16.07 % (13855)------------------------------
% 103.79/16.07 % (13855)------------------------------
% 103.79/16.08 % (13861)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_12850 for (2855ds/2635Mi)
% 106.75/16.62 % (13854)Instruction limit reached!
% 106.75/16.62 % (13854)------------------------------
% 106.75/16.62 % (13854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.75/16.62 % (13854)Termination reason: Unknown
% 106.75/16.62 % (13854)Termination phase: Saturation
% 106.75/16.62
% 106.75/16.62 % (13854)Memory used [KB]: 13048
% 106.75/16.62 % (13854)Time elapsed: 1.170 s
% 106.75/16.62 % (13854)Instructions burned: 3208 (million)
% 106.75/16.62 % (13854)------------------------------
% 106.75/16.62 % (13854)------------------------------
% 106.75/16.63 % (13910)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_12850 for (2850ds/631Mi)
% 107.20/16.79 % (13377)Instruction limit reached!
% 107.20/16.79 % (13377)------------------------------
% 107.20/16.79 % (13377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 107.20/16.79 % (13377)Termination reason: Unknown
% 107.20/16.79 % (13377)Termination phase: Saturation
% 107.20/16.79
% 107.20/16.79 % (13377)Memory used [KB]: 19573
% 107.20/16.79 % (13377)Time elapsed: 3.354 s
% 107.20/16.79 % (13377)Instructions burned: 9823 (million)
% 107.20/16.79 % (13377)------------------------------
% 107.20/16.79 % (13377)------------------------------
% 107.60/16.81 % (13921)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_12850 for (2848ds/15557Mi)
% 107.60/16.88 % (13910)Instruction limit reached!
% 107.60/16.88 % (13910)------------------------------
% 107.60/16.88 % (13910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 107.60/16.88 % (13910)Termination reason: Unknown
% 107.60/16.88 % (13910)Termination phase: Saturation
% 107.60/16.88
% 107.60/16.88 % (13910)Memory used [KB]: 9722
% 107.60/16.88 % (13910)Time elapsed: 0.247 s
% 107.60/16.88 % (13910)Instructions burned: 633 (million)
% 107.60/16.88 % (13910)------------------------------
% 107.60/16.88 % (13910)------------------------------
% 107.60/16.90 % (13930)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_12850 for (2847ds/2142Mi)
% 112.01/17.21 % (13861)Instruction limit reached!
% 112.01/17.21 % (13861)------------------------------
% 112.01/17.21 % (13861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 112.01/17.21 % (13861)Termination reason: Unknown
% 112.01/17.21 % (13861)Termination phase: Saturation
% 112.01/17.21
% 112.01/17.21 % (13861)Memory used [KB]: 12281
% 112.01/17.21 % (13861)Time elapsed: 1.132 s
% 112.01/17.21 % (13861)Instructions burned: 2636 (million)
% 112.01/17.21 % (13861)------------------------------
% 112.01/17.21 % (13861)------------------------------
% 112.01/17.23 % (13950)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_12850 for (2844ds/5624Mi)
% 113.25/17.48 % (13857)Instruction limit reached!
% 113.25/17.48 % (13857)------------------------------
% 113.25/17.48 % (13857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 113.25/17.48 % (13857)Termination reason: Unknown
% 113.25/17.48 % (13857)Termination phase: Saturation
% 113.25/17.48
% 113.25/17.48 % (13857)Memory used [KB]: 13688
% 113.25/17.48 % (13857)Time elapsed: 1.706 s
% 113.25/17.48 % (13857)Instructions burned: 4165 (million)
% 113.25/17.48 % (13857)------------------------------
% 113.25/17.48 % (13857)------------------------------
% 113.25/17.49 % (13966)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_12850 for (2841ds/1665Mi)
% 114.82/17.72 % (13930)Instruction limit reached!
% 114.82/17.72 % (13930)------------------------------
% 114.82/17.72 % (13930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.82/17.72 % (13930)Termination reason: Unknown
% 114.82/17.72 % (13930)Termination phase: Saturation
% 114.82/17.72
% 114.82/17.72 % (13930)Memory used [KB]: 9083
% 114.82/17.72 % (13930)Time elapsed: 0.827 s
% 114.82/17.72 % (13930)Instructions burned: 2144 (million)
% 114.82/17.72 % (13930)------------------------------
% 114.82/17.72 % (13930)------------------------------
% 114.82/17.73 % (14043)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_12850 for (2839ds/64912Mi)
% 115.66/18.00 % (13966)Instruction limit reached!
% 115.66/18.00 % (13966)------------------------------
% 115.66/18.00 % (13966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.66/18.00 % (13966)Termination reason: Unknown
% 115.66/18.00 % (13966)Termination phase: Saturation
% 115.66/18.00
% 115.66/18.00 % (13966)Memory used [KB]: 12153
% 115.66/18.00 % (13966)Time elapsed: 0.505 s
% 115.66/18.00 % (13966)Instructions burned: 1667 (million)
% 115.66/18.00 % (13966)------------------------------
% 115.66/18.00 % (13966)------------------------------
% 115.66/18.01 % (14153)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_12850 for (2836ds/7801Mi)
% 119.39/18.31 % (13856)Instruction limit reached!
% 119.39/18.31 % (13856)------------------------------
% 119.39/18.31 % (13856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.39/18.31 % (13856)Termination reason: Unknown
% 119.39/18.31 % (13856)Termination phase: Saturation
% 119.39/18.31
% 119.39/18.31 % (13856)Memory used [KB]: 9338
% 119.39/18.31 % (13856)Time elapsed: 2.532 s
% 119.39/18.31 % (13856)Instructions burned: 7471 (million)
% 119.39/18.31 % (13856)------------------------------
% 119.39/18.31 % (13856)------------------------------
% 119.39/18.32 % (14200)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_12850 for (2833ds/15194Mi)
% 124.80/19.08 % (13950)Instruction limit reached!
% 124.80/19.08 % (13950)------------------------------
% 124.80/19.08 % (13950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 124.80/19.08 % (13950)Termination reason: Unknown
% 124.80/19.08 % (13950)Termination phase: Saturation
% 124.80/19.08
% 124.80/19.08 % (13950)Memory used [KB]: 13048
% 124.80/19.08 % (13950)Time elapsed: 1.870 s
% 124.80/19.08 % (13950)Instructions burned: 5624 (million)
% 124.80/19.08 % (13950)------------------------------
% 124.80/19.08 % (13950)------------------------------
% 124.80/19.09 % (14201)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_12850 for (2825ds/6753Mi)
% 134.45/20.40 % (14153)Instruction limit reached!
% 134.45/20.40 % (14153)------------------------------
% 134.45/20.40 % (14153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 134.45/20.40 % (14153)Termination reason: Unknown
% 134.45/20.40 % (14153)Termination phase: Saturation
% 134.45/20.40
% 134.45/20.40 % (14153)Memory used [KB]: 11257
% 134.45/20.40 % (14153)Time elapsed: 2.415 s
% 134.45/20.40 % (14153)Instructions burned: 7802 (million)
% 134.45/20.40 % (14153)------------------------------
% 134.45/20.40 % (14153)------------------------------
% 134.45/20.41 % (14202)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_12850 for (2812ds/1003Mi)
% 135.66/20.61 % (13860)Instruction limit reached!
% 135.66/20.61 % (13860)------------------------------
% 135.66/20.61 % (13860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 135.66/20.61 % (13860)Termination reason: Unknown
% 135.66/20.61 % (13860)Termination phase: Saturation
% 135.66/20.61
% 135.66/20.61 % (13860)Memory used [KB]: 21748
% 135.66/20.61 % (13860)Time elapsed: 4.567 s
% 135.66/20.61 % (13860)Instructions burned: 13469 (million)
% 135.66/20.61 % (13860)------------------------------
% 135.66/20.61 % (13860)------------------------------
% 135.66/20.62 % (14203)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_12850 for (2810ds/13018Mi)
% 136.18/20.71 % (14202)Instruction limit reached!
% 136.18/20.71 % (14202)------------------------------
% 136.18/20.71 % (14202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 136.18/20.71 % (14202)Termination reason: Unknown
% 136.18/20.71 % (14202)Termination phase: Saturation
% 136.18/20.71
% 136.18/20.71 % (14202)Memory used [KB]: 9338
% 136.18/20.71 % (14202)Time elapsed: 0.301 s
% 136.18/20.71 % (14202)Instructions burned: 1004 (million)
% 136.18/20.71 % (14202)------------------------------
% 136.18/20.71 % (14202)------------------------------
% 136.18/20.72 % (14204)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_12850 for (2809ds/1267Mi)
% 139.54/21.13 % (14204)Instruction limit reached!
% 139.54/21.13 % (14204)------------------------------
% 139.54/21.13 % (14204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 139.54/21.13 % (14204)Termination reason: Unknown
% 139.54/21.13 % (14204)Termination phase: Saturation
% 139.54/21.13
% 139.54/21.13 % (14204)Memory used [KB]: 8059
% 139.54/21.13 % (14204)Time elapsed: 0.408 s
% 139.54/21.13 % (14204)Instructions burned: 1268 (million)
% 139.54/21.13 % (14204)------------------------------
% 139.54/21.13 % (14204)------------------------------
% 139.54/21.14 % (14205)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_12850 for (2805ds/2570Mi)
% 140.00/21.21 % (14201)Instruction limit reached!
% 140.00/21.21 % (14201)------------------------------
% 140.00/21.21 % (14201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 140.00/21.21 % (14201)Termination reason: Unknown
% 140.00/21.21 % (14201)Termination phase: Saturation
% 140.00/21.21
% 140.00/21.21 % (14201)Memory used [KB]: 12665
% 140.00/21.21 % (14201)Time elapsed: 2.120 s
% 140.00/21.21 % (14201)Instructions burned: 6753 (million)
% 140.00/21.21 % (14201)------------------------------
% 140.00/21.21 % (14201)------------------------------
% 140.00/21.22 % (14206)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_12850 for (2804ds/13163Mi)
% 143.02/21.86 % (14205)Instruction limit reached!
% 143.02/21.86 % (14205)------------------------------
% 143.02/21.86 % (14205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 143.02/21.86 % (14205)Termination reason: Unknown
% 143.02/21.86 % (14205)Termination phase: Saturation
% 143.02/21.86
% 143.02/21.86 % (14205)Memory used [KB]: 10618
% 143.02/21.86 % (14205)Time elapsed: 0.718 s
% 143.02/21.86 % (14205)Instructions burned: 2571 (million)
% 143.02/21.86 % (14205)------------------------------
% 143.02/21.86 % (14205)------------------------------
% 143.02/21.87 % (14207)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_12850 for (2797ds/5087Mi)
% 144.26/21.95 % (13921)Instruction limit reached!
% 144.26/21.95 % (13921)------------------------------
% 144.26/21.95 % (13921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 144.26/21.95 % (13921)Termination reason: Unknown
% 144.26/21.95 % (13921)Termination phase: Saturation
% 144.26/21.95
% 144.26/21.95 % (13921)Memory used [KB]: 20852
% 144.26/21.95 % (13921)Time elapsed: 5.127 s
% 144.26/21.95 % (13921)Instructions burned: 15559 (million)
% 144.26/21.95 % (13921)------------------------------
% 144.26/21.95 % (13921)------------------------------
% 144.26/21.96 % (14208)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_12850 for (2797ds/10380Mi)
% 150.57/22.80 % (14200)Instruction limit reached!
% 150.57/22.80 % (14200)------------------------------
% 150.57/22.80 % (14200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 150.57/22.80 % (14200)Termination reason: Unknown
% 150.57/22.80 % (14200)Termination phase: Saturation
% 150.57/22.80
% 150.57/22.80 % (14200)Memory used [KB]: 16247
% 150.57/22.80 % (14200)Time elapsed: 4.503 s
% 150.57/22.80 % (14200)Instructions burned: 15198 (million)
% 150.57/22.80 % (14200)------------------------------
% 150.57/22.80 % (14200)------------------------------
% 151.28/22.81 % (14209)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_12850 for (2788ds/4218Mi)
% 155.50/23.40 % (14207)Instruction limit reached!
% 155.50/23.40 % (14207)------------------------------
% 155.50/23.40 % (14207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.50/23.40 % (14207)Termination reason: Unknown
% 155.50/23.40 % (14207)Termination phase: Saturation
% 155.50/23.40
% 155.50/23.40 % (14207)Memory used [KB]: 15735
% 155.50/23.40 % (14207)Time elapsed: 1.539 s
% 155.50/23.40 % (14207)Instructions burned: 5088 (million)
% 155.50/23.40 % (14207)------------------------------
% 155.50/23.40 % (14207)------------------------------
% 155.50/23.41 % (14210)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_12850 for (2782ds/3971Mi)
% 156.72/23.61 % (13373)Instruction limit reached!
% 156.72/23.61 % (13373)------------------------------
% 156.72/23.61 % (13373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 156.72/23.61 % (13373)Termination reason: Unknown
% 156.72/23.61 % (13373)Termination phase: Saturation
% 156.72/23.61
% 156.72/23.61 % (13373)Memory used [KB]: 9978
% 156.72/23.61 % (13373)Time elapsed: 10.814 s
% 156.72/23.61 % (13373)Instructions burned: 43570 (million)
% 156.72/23.61 % (13373)------------------------------
% 156.72/23.61 % (13373)------------------------------
% 156.72/23.63 % (14211)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_12850 for (2780ds/14014Mi)
% 158.26/23.96 % (14209)Refutation not found, non-redundant clauses discarded% (14209)------------------------------
% 158.26/23.96 % (14209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 158.26/23.96 % (14209)Termination reason: Refutation not found, non-redundant clauses discarded
% 158.26/23.96
% 158.26/23.96 % (14209)Memory used [KB]: 13048
% 158.26/23.96 % (14209)Time elapsed: 1.159 s
% 158.26/23.96 % (14209)Instructions burned: 4191 (million)
% 158.26/23.96 % (14209)------------------------------
% 158.26/23.96 % (14209)------------------------------
% 158.26/23.97 % (14212)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_12850 for (2777ds/8517Mi)
% 163.22/24.52 % (14210)Instruction limit reached!
% 163.22/24.52 % (14210)------------------------------
% 163.22/24.52 % (14210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 163.22/24.52 % (14210)Termination reason: Unknown
% 163.22/24.52 % (14210)Termination phase: Saturation
% 163.22/24.52
% 163.22/24.52 % (14210)Memory used [KB]: 10746
% 163.22/24.52 % (14210)Time elapsed: 1.105 s
% 163.22/24.52 % (14210)Instructions burned: 3973 (million)
% 163.22/24.52 % (14210)------------------------------
% 163.22/24.52 % (14210)------------------------------
% 163.22/24.53 % (14213)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_12850 for (2771ds/10148Mi)
% 163.85/24.69 % (14208)Instruction limit reached!
% 163.85/24.69 % (14208)------------------------------
% 163.85/24.69 % (14208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 163.85/24.69 % (14208)Termination reason: Unknown
% 163.85/24.69 % (14208)Termination phase: Saturation
% 163.85/24.69
% 163.85/24.69 % (14208)Memory used [KB]: 8187
% 163.85/24.69 % (14208)Time elapsed: 2.736 s
% 163.85/24.69 % (14208)Instructions burned: 10380 (million)
% 163.85/24.69 % (14208)------------------------------
% 163.85/24.69 % (14208)------------------------------
% 164.46/24.70 % (14214)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_12850 for (2769ds/9078Mi)
% 164.46/24.72 % (14203)Instruction limit reached!
% 164.46/24.72 % (14203)------------------------------
% 164.46/24.72 % (14203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 164.46/24.72 % (14203)Termination reason: Unknown
% 164.46/24.72 % (14203)Termination phase: Saturation
% 164.46/24.72
% 164.46/24.72 % (14203)Memory used [KB]: 27376
% 164.46/24.72 % (14203)Time elapsed: 4.101 s
% 164.46/24.72 % (14203)Instructions burned: 13020 (million)
% 164.46/24.72 % (14203)------------------------------
% 164.46/24.72 % (14203)------------------------------
% 164.46/24.73 % (14215)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_12850 for (2769ds/16164Mi)
% 168.14/25.27 % (14206)Instruction limit reached!
% 168.14/25.27 % (14206)------------------------------
% 168.14/25.27 % (14206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 168.14/25.27 % (14206)Termination reason: Unknown
% 168.14/25.27 % (14206)Termination phase: Saturation
% 168.14/25.27
% 168.14/25.27 % (14206)Memory used [KB]: 21108
% 168.14/25.27 % (14206)Time elapsed: 4.053 s
% 168.14/25.27 % (14206)Instructions burned: 13164 (million)
% 168.14/25.27 % (14206)------------------------------
% 168.14/25.27 % (14206)------------------------------
% 168.14/25.28 % (14216)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_12850 for (2763ds/6102Mi)
% 176.58/26.41 % (14214)Instruction limit reached!
% 176.58/26.41 % (14214)------------------------------
% 176.58/26.41 % (14214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 176.58/26.41 % (14214)Termination reason: Unknown
% 176.58/26.41 % (14214)Termination phase: Saturation
% 176.58/26.41
% 176.58/26.41 % (14214)Memory used [KB]: 9594
% 176.58/26.41 % (14214)Time elapsed: 1.710 s
% 176.58/26.41 % (14214)Instructions burned: 9079 (million)
% 176.58/26.41 % (14214)------------------------------
% 176.58/26.41 % (14214)------------------------------
% 176.58/26.42 % (14217)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_12850 for (2752ds/10308Mi)
% 177.20/26.52 % (14212)Instruction limit reached!
% 177.20/26.52 % (14212)------------------------------
% 177.20/26.52 % (14212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 177.20/26.52 % (14212)Termination reason: Unknown
% 177.20/26.52 % (14212)Termination phase: Saturation
% 177.20/26.52
% 177.20/26.52 % (14212)Memory used [KB]: 20852
% 177.20/26.52 % (14212)Time elapsed: 2.566 s
% 177.20/26.52 % (14212)Instructions burned: 8517 (million)
% 177.20/26.52 % (14212)------------------------------
% 177.20/26.52 % (14212)------------------------------
% 177.20/26.53 % (14218)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_12850 for (2751ds/4041Mi)
% 179.24/26.98 % (14216)Instruction limit reached!
% 179.24/26.98 % (14216)------------------------------
% 179.24/26.98 % (14216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 179.24/26.98 % (14216)Termination reason: Unknown
% 179.24/26.98 % (14216)Termination phase: Saturation
% 179.24/26.98
% 179.24/26.98 % (14216)Memory used [KB]: 22771
% 179.24/26.98 % (14216)Time elapsed: 1.699 s
% 179.24/26.98 % (14216)Instructions burned: 6102 (million)
% 179.24/26.98 % (14216)------------------------------
% 179.24/26.98 % (14216)------------------------------
% 179.24/26.99 % (14219)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_12850 for (2746ds/6901Mi)
% 184.30/27.52 % (14213)Instruction limit reached!
% 184.30/27.52 % (14213)------------------------------
% 184.30/27.52 % (14213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 184.30/27.52 % (14213)Termination reason: Unknown
% 184.30/27.52 % (14213)Termination phase: Saturation
% 184.30/27.52
% 184.30/27.52 % (14213)Memory used [KB]: 18677
% 184.30/27.52 % (14213)Time elapsed: 2.993 s
% 184.30/27.52 % (14213)Instructions burned: 10148 (million)
% 184.30/27.52 % (14213)------------------------------
% 184.30/27.52 % (14213)------------------------------
% 184.30/27.53 % (14220)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on DTF2THF_12850 for (2741ds/5576Mi)
% 185.55/27.72 % (14218)Instruction limit reached!
% 185.55/27.72 % (14218)------------------------------
% 185.55/27.72 % (14218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 185.55/27.72 % (14218)Termination reason: Unknown
% 185.55/27.72 % (14218)Termination phase: Saturation
% 185.55/27.72
% 185.55/27.72 % (14218)Memory used [KB]: 12537
% 185.55/27.72 % (14218)Time elapsed: 1.196 s
% 185.55/27.72 % (14218)Instructions burned: 4042 (million)
% 185.55/27.72 % (14218)------------------------------
% 185.55/27.72 % (14218)------------------------------
% 185.55/27.73 % (14221)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=2014:si=on:rtra=on_0 on DTF2THF_12850 for (2739ds/2014Mi)
% 186.61/27.92 % (14211)Instruction limit reached!
% 186.61/27.92 % (14211)------------------------------
% 186.61/27.92 % (14211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 186.61/27.92 % (14211)Termination reason: Unknown
% 186.61/27.92 % (14211)Termination phase: Saturation
% 186.61/27.92
% 186.61/27.92 % (14211)Memory used [KB]: 17910
% 186.61/27.92 % (14211)Time elapsed: 4.322 s
% 186.61/27.92 % (14211)Instructions burned: 14017 (million)
% 186.61/27.92 % (14211)------------------------------
% 186.61/27.92 % (14211)------------------------------
% 186.61/27.94 % (14222)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_12850 for (2737ds/5115Mi)
% 189.94/28.34 % (14221)Instruction limit reached!
% 189.94/28.34 % (14221)------------------------------
% 189.94/28.34 % (14221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 189.94/28.34 % (14221)Termination reason: Unknown
% 189.94/28.34 % (14221)Termination phase: Saturation
% 189.94/28.34
% 189.94/28.34 % (14221)Memory used [KB]: 9722
% 189.94/28.34 % (14221)Time elapsed: 0.605 s
% 189.94/28.34 % (14221)Instructions burned: 2014 (million)
% 189.94/28.34 % (14221)------------------------------
% 189.94/28.34 % (14221)------------------------------
% 189.94/28.35 % (14223)lrs+2_1:1_au=on:cnfonf=lazy_pi_sigma_gen:sos=on:ss=axioms:i=13001:si=on:rtra=on_0 on DTF2THF_12850 for (2733ds/13001Mi)
% 190.59/28.40 % (14223)Refutation not found, incomplete strategy
% 190.59/28.40 % (14223)------------------------------
% 190.59/28.40 % (14223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 190.59/28.40 % (14223)Termination reason: Refutation not found, incomplete strategy
% 190.59/28.40
% 190.59/28.40
% 190.59/28.40 % (14223)Memory used [KB]: 7419
% 190.59/28.40 % (14223)Time elapsed: 0.072 s
% 190.59/28.40 % (14223)Instructions burned: 180 (million)
% 190.59/28.40 % (14223)------------------------------
% 190.59/28.40 % (14223)------------------------------
% 190.59/28.41 % (14224)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_12850 for (2732ds/11105Mi)
% 191.84/28.62 % (14215)Instruction limit reached!
% 191.84/28.62 % (14215)------------------------------
% 191.84/28.62 % (14215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 191.84/28.62 % (14215)Termination reason: Unknown
% 191.84/28.62 % (14215)Termination phase: Saturation
% 191.84/28.62
% 191.84/28.62 % (14215)Memory used [KB]: 12665
% 191.84/28.62 % (14215)Time elapsed: 3.898 s
% 191.84/28.62 % (14215)Instructions burned: 16166 (million)
% 191.84/28.62 % (14215)------------------------------
% 191.84/28.62 % (14215)------------------------------
% 191.84/28.64 % (14225)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_12850 for (2730ds/13832Mi)
% 195.03/29.08 % (14220)Refutation not found, non-redundant clauses discarded% (14220)------------------------------
% 195.03/29.08 % (14220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 195.03/29.08 % (14220)Termination reason: Refutation not found, non-redundant clauses discarded
% 195.03/29.08
% 195.03/29.08 % (14220)Memory used [KB]: 10618
% 195.03/29.08 % (14220)Time elapsed: 1.547 s
% 195.03/29.08 % (14220)Instructions burned: 5478 (million)
% 195.03/29.08 % (14220)------------------------------
% 195.03/29.08 % (14220)------------------------------
% 195.03/29.09 % (14238)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=32887:si=on:rtra=on_0 on DTF2THF_12850 for (2725ds/32887Mi)
% 195.03/29.09 % (14219)Instruction limit reached!
% 195.03/29.09 % (14219)------------------------------
% 195.03/29.09 % (14219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 195.03/29.09 % (14219)Termination reason: Unknown
% 195.03/29.09 % (14219)Termination phase: Saturation
% 195.03/29.09
% 195.03/29.09 % (14219)Memory used [KB]: 14328
% 195.03/29.09 % (14219)Time elapsed: 2.105 s
% 195.03/29.09 % (14219)Instructions burned: 6901 (million)
% 195.03/29.09 % (14219)------------------------------
% 195.03/29.09 % (14219)------------------------------
% 195.03/29.11 % (14241)dis+1010_2:1_avsq=on:fde=unused:prag=on:i=3362:si=on:rtra=on_0 on DTF2THF_12850 for (2725ds/3362Mi)
% 197.05/29.43 % (14222)Instruction limit reached!
% 197.05/29.43 % (14222)------------------------------
% 197.05/29.43 % (14222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 197.05/29.43 % (14222)Termination reason: Unknown
% 197.05/29.43 % (14222)Termination phase: Saturation
% 197.05/29.43
% 197.05/29.43 % (14222)Memory used [KB]: 26225
% 197.05/29.43 % (14222)Time elapsed: 1.495 s
% 197.05/29.43 % (14222)Instructions burned: 5115 (million)
% 197.05/29.43 % (14222)------------------------------
% 197.05/29.43 % (14222)------------------------------
% 197.05/29.44 % (14362)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_12850 for (2722ds/24965Mi)
% 197.92/29.62 % (14217)Instruction limit reached!
% 197.92/29.62 % (14217)------------------------------
% 197.92/29.62 % (14217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 197.92/29.62 % (14217)Termination reason: Unknown
% 197.92/29.62 % (14217)Termination phase: Saturation
% 197.92/29.62
% 197.92/29.62 % (14217)Memory used [KB]: 14200
% 197.92/29.62 % (14217)Time elapsed: 3.199 s
% 197.92/29.62 % (14217)Instructions burned: 10311 (million)
% 197.92/29.62 % (14217)------------------------------
% 197.92/29.62 % (14217)------------------------------
% 197.92/29.63 % (14449)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_12850 for (2720ds/15705Mi)
% 202.79/30.14 % (14241)Instruction limit reached!
% 202.79/30.14 % (14241)------------------------------
% 202.79/30.14 % (14241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 202.79/30.14 % (14241)Termination reason: Unknown
% 202.79/30.14 % (14241)Termination phase: Saturation
% 202.79/30.14
% 202.79/30.14 % (14241)Memory used [KB]: 13944
% 202.79/30.14 % (14241)Time elapsed: 1.032 s
% 202.79/30.14 % (14241)Instructions burned: 3363 (million)
% 202.79/30.14 % (14241)------------------------------
% 202.79/30.14 % (14241)------------------------------
% 202.79/30.15 % (14667)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_12850 for (2715ds/1536Mi)
% 205.02/30.57 % (14667)Instruction limit reached!
% 205.02/30.57 % (14667)------------------------------
% 205.02/30.57 % (14667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 205.02/30.57 % (14667)Termination reason: Unknown
% 205.02/30.57 % (14667)Termination phase: Saturation
% 205.02/30.57
% 205.02/30.57 % (14667)Memory used [KB]: 9850
% 205.02/30.57 % (14667)Time elapsed: 0.428 s
% 205.02/30.57 % (14667)Instructions burned: 1537 (million)
% 205.02/30.57 % (14667)------------------------------
% 205.02/30.57 % (14667)------------------------------
% 205.02/30.58 % (14812)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_12850 for (2710ds/23684Mi)
% 214.48/31.83 % (14224)Instruction limit reached!
% 214.48/31.83 % (14224)------------------------------
% 214.48/31.83 % (14224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 214.48/31.83 % (14224)Termination reason: Unknown
% 214.48/31.83 % (14224)Termination phase: Saturation
% 214.48/31.83
% 214.48/31.83 % (14224)Memory used [KB]: 25330
% 214.48/31.83 % (14224)Time elapsed: 3.442 s
% 214.48/31.83 % (14224)Instructions burned: 11106 (million)
% 214.48/31.83 % (14224)------------------------------
% 214.48/31.83 % (14224)------------------------------
% 214.48/31.84 % (14813)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_12850 for (2698ds/4925Mi)
% 220.13/32.69 % (14225)Instruction limit reached!
% 220.13/32.69 % (14225)------------------------------
% 220.13/32.69 % (14225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 220.13/32.69 % (14225)Termination reason: Unknown
% 220.13/32.69 % (14225)Termination phase: Saturation
% 220.13/32.69
% 220.13/32.69 % (14225)Memory used [KB]: 32494
% 220.13/32.69 % (14225)Time elapsed: 4.082 s
% 220.13/32.69 % (14225)Instructions burned: 13834 (million)
% 220.13/32.69 % (14225)------------------------------
% 220.13/32.69 % (14225)------------------------------
% 220.84/32.71 % (14814)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_12850 for (2689ds/14666Mi)
% 225.04/33.31 % (14813)Instruction limit reached!
% 225.04/33.31 % (14813)------------------------------
% 225.04/33.31 % (14813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 225.04/33.31 % (14813)Termination reason: Unknown
% 225.04/33.31 % (14813)Termination phase: Saturation
% 225.04/33.31
% 225.04/33.31 % (14813)Memory used [KB]: 13688
% 225.04/33.31 % (14813)Time elapsed: 1.469 s
% 225.04/33.31 % (14813)Instructions burned: 4927 (million)
% 225.04/33.31 % (14813)------------------------------
% 225.04/33.31 % (14813)------------------------------
% 225.04/33.32 % (14815)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_12850 for (2683ds/3322Mi)
% 231.34/34.27 % (14815)Instruction limit reached!
% 231.34/34.27 % (14815)------------------------------
% 231.34/34.27 % (14815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 231.34/34.27 % (14815)Termination reason: Unknown
% 231.34/34.27 % (14815)Termination phase: Saturation
% 231.34/34.27
% 231.34/34.27 % (14815)Memory used [KB]: 9210
% 231.34/34.27 % (14815)Time elapsed: 0.953 s
% 231.34/34.27 % (14815)Instructions burned: 3323 (million)
% 231.34/34.27 % (14815)------------------------------
% 231.34/34.27 % (14815)------------------------------
% 231.34/34.28 % (14816)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1810:si=on:rtra=on_0 on DTF2THF_12850 for (2673ds/1810Mi)
% 232.64/34.45 % (14449)Instruction limit reached!
% 232.64/34.45 % (14449)------------------------------
% 232.64/34.45 % (14449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 232.64/34.45 % (14449)Termination reason: Unknown
% 232.64/34.45 % (14449)Termination phase: Saturation
% 232.64/34.45
% 232.64/34.45 % (14449)Memory used [KB]: 37739
% 232.64/34.45 % (14449)Time elapsed: 4.825 s
% 232.64/34.45 % (14449)Instructions burned: 15707 (million)
% 232.64/34.45 % (14449)------------------------------
% 232.64/34.45 % (14449)------------------------------
% 232.64/34.47 % (14817)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_12850 for (2671ds/2465Mi)
% 233.21/34.58 % (14817)Refutation not found, incomplete strategy
% 233.21/34.58 % (14817)------------------------------
% 233.21/34.58 % (14817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 233.21/34.58 % (14817)Termination reason: Refutation not found, incomplete strategy
% 233.21/34.58
% 233.21/34.58
% 233.21/34.58 % (14817)Memory used [KB]: 8955
% 233.21/34.58 % (14817)Time elapsed: 0.113 s
% 233.21/34.58 % (14817)Instructions burned: 399 (million)
% 233.21/34.58 % (14817)------------------------------
% 233.21/34.58 % (14817)------------------------------
% 233.21/34.59 % (14818)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_12850 for (2670ds/41234Mi)
% 233.82/34.68 % (14043)Instruction limit reached!
% 233.82/34.68 % (14043)------------------------------
% 233.82/34.68 % (14043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 233.82/34.68 % (14043)Termination reason: Unknown
% 233.82/34.68 % (14043)Termination phase: Saturation
% 233.82/34.68
% 233.82/34.68 % (14043)Memory used [KB]: 15223
% 233.82/34.68 % (14043)Time elapsed: 16.974 s
% 233.82/34.68 % (14043)Instructions burned: 64912 (million)
% 233.82/34.68 % (14043)------------------------------
% 233.82/34.68 % (14043)------------------------------
% 233.82/34.69 % (14819)dis+1002_1:1_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:nm=0:i=14027:si=on:rtra=on_0 on DTF2THF_12850 for (2669ds/14027Mi)
% 234.73/34.81 % (14816)Instruction limit reached!
% 234.73/34.81 % (14816)------------------------------
% 234.73/34.81 % (14816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 234.73/34.81 % (14816)Termination reason: Unknown
% 234.73/34.81 % (14816)Termination phase: Saturation
% 234.73/34.81
% 234.73/34.81 % (14816)Memory used [KB]: 9978
% 234.73/34.81 % (14816)Time elapsed: 0.532 s
% 234.73/34.81 % (14816)Instructions burned: 1811 (million)
% 234.73/34.81 % (14816)------------------------------
% 234.73/34.81 % (14816)------------------------------
% 234.73/34.82 % (14820)dis+1010_1:1_au=on:cnfonf=conj_eager:nwc=10.0:sac=on:i=27021:si=on:rtra=on_0 on DTF2THF_12850 for (2668ds/27021Mi)
% 240.49/35.58 % (14238)Instruction limit reached!
% 240.49/35.58 % (14238)------------------------------
% 240.49/35.58 % (14238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 240.49/35.58 % (14238)Termination reason: Unknown
% 240.49/35.58 % (14238)Termination phase: Saturation
% 240.49/35.58
% 240.49/35.58 % (14238)Memory used [KB]: 8955
% 240.49/35.58 % (14238)Time elapsed: 6.496 s
% 240.49/35.58 % (14238)Instructions burned: 32891 (million)
% 240.49/35.58 % (14238)------------------------------
% 240.49/35.58 % (14238)------------------------------
% 240.49/35.59 % (14821)dis-1666_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:i=5643:si=on:rtra=on_0 on DTF2THF_12850 for (2660ds/5643Mi)
% 248.91/36.77 % (14814)Instruction limit reached!
% 248.91/36.77 % (14814)------------------------------
% 248.91/36.77 % (14814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 248.91/36.77 % (14814)Termination reason: Unknown
% 248.91/36.77 % (14814)Termination phase: Saturation
% 248.91/36.77
% 248.91/36.77 % (14814)Memory used [KB]: 17142
% 248.91/36.77 % (14814)Time elapsed: 4.069 s
% 248.91/36.77 % (14814)Instructions burned: 14666 (million)
% 248.91/36.77 % (14814)------------------------------
% 248.91/36.77 % (14814)------------------------------
% 248.91/36.78 % (14822)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_12850 for (2648ds/8612Mi)
% 249.60/36.81 % (14362)Instruction limit reached!
% 249.60/36.81 % (14362)------------------------------
% 249.60/36.81 % (14362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 249.60/36.81 % (14362)Termination reason: Unknown
% 249.60/36.81 % (14362)Termination phase: Saturation
% 249.60/36.81
% 249.60/36.81 % (14362)Memory used [KB]: 25713
% 249.60/36.81 % (14362)Time elapsed: 7.366 s
% 249.60/36.81 % (14362)Instructions burned: 24967 (million)
% 249.60/36.81 % (14362)------------------------------
% 249.60/36.81 % (14362)------------------------------
% 249.60/36.82 % (14823)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_12850 for (2648ds/3743Mi)
% 253.12/37.37 % (14821)Instruction limit reached!
% 253.12/37.37 % (14821)------------------------------
% 253.12/37.37 % (14821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 253.12/37.37 % (14821)Termination reason: Unknown
% 253.12/37.37 % (14821)Termination phase: Saturation
% 253.12/37.37
% 253.12/37.37 % (14821)Memory used [KB]: 13816
% 253.12/37.37 % (14821)Time elapsed: 1.773 s
% 253.12/37.37 % (14821)Instructions burned: 5643 (million)
% 253.12/37.37 % (14821)------------------------------
% 253.12/37.37 % (14821)------------------------------
% 253.12/37.38 % (14824)dis+10_1:2_amm=off:bd=preordered:cnfonf=off:e2e=on:fe=off:fsr=off:hud=5:nm=3:s2a=on:sos=on:i=2571:si=on:rtra=on_0 on DTF2THF_12850 for (2643ds/2571Mi)
% 255.02/37.64 % (14812)Instruction limit reached!
% 255.02/37.64 % (14812)------------------------------
% 255.02/37.64 % (14812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 255.02/37.64 % (14812)Termination reason: Unknown
% 255.02/37.64 % (14812)Termination phase: Saturation
% 255.02/37.64
% 255.02/37.64 % (14812)Memory used [KB]: 40681
% 255.02/37.64 % (14812)Time elapsed: 7.062 s
% 255.02/37.64 % (14812)Instructions burned: 23685 (million)
% 255.02/37.64 % (14812)------------------------------
% 255.02/37.64 % (14812)------------------------------
% 255.02/37.66 % (14825)dis+1010_1:16_cbe=off:cnfonf=conj_eager:fe=off:hud=15:nwc=3.0:piset=pi_sigma:prag=on:sd=5:sp=weighted_frequency:ss=axioms:st=2.0:i=35728:si=on:rtra=on_0 on DTF2THF_12850 for (2640ds/35728Mi)
% 256.58/37.98 % (14823)Instruction limit reached!
% 256.58/37.98 % (14823)------------------------------
% 256.58/37.98 % (14823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 256.58/37.98 % (14823)Termination reason: Unknown
% 256.58/37.98 % (14823)Termination phase: Saturation
% 256.58/37.98
% 256.58/37.98 % (14823)Memory used [KB]: 13304
% 256.58/37.98 % (14823)Time elapsed: 1.166 s
% 256.58/37.98 % (14823)Instructions burned: 3745 (million)
% 256.58/37.98 % (14823)------------------------------
% 256.58/37.98 % (14823)------------------------------
% 256.58/37.99 % (14826)lrs+1004_1:24_i=5433:si=on:rtra=on_0 on DTF2THF_12850 for (2636ds/5433Mi)
% 258.20/38.09 % (14824)Instruction limit reached!
% 258.20/38.09 % (14824)------------------------------
% 258.20/38.09 % (14824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 258.20/38.09 % (14824)Termination reason: Unknown
% 258.20/38.09 % (14824)Termination phase: Saturation
% 258.20/38.09
% 258.20/38.09 % (14824)Memory used [KB]: 13944
% 258.20/38.09 % (14824)Time elapsed: 0.739 s
% 258.20/38.09 % (14824)Instructions burned: 2572 (million)
% 258.20/38.09 % (14824)------------------------------
% 258.20/38.09 % (14824)------------------------------
% 258.20/38.10 % (14827)ott+1002_1:1_anc=all_dependent:au=on:avsq=on:cnfonf=lazy_pi_sigma_gen:piset=not:i=27944:si=on:rtra=on_0 on DTF2THF_12850 for (2635ds/27944Mi)
% 263.57/38.91 % (14819)Instruction limit reached!
% 263.57/38.91 % (14819)------------------------------
% 263.57/38.91 % (14819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 263.57/38.91 % (14819)Termination reason: Unknown
% 263.57/38.91 % (14819)Termination phase: Saturation
% 263.57/38.91
% 263.57/38.91 % (14819)Memory used [KB]: 14072
% 263.57/38.91 % (14819)Time elapsed: 4.221 s
% 263.57/38.91 % (14819)Instructions burned: 14029 (million)
% 263.57/38.91 % (14819)------------------------------
% 263.57/38.91 % (14819)------------------------------
% 263.57/38.93 % (14828)ott+10_1:10_cnfonf=lazy_gen:fde=none:sp=const_frequency:i=15814:si=on:rtra=on_0 on DTF2THF_12850 for (2627ds/15814Mi)
% 267.90/39.44 % (14822)Instruction limit reached!
% 267.90/39.44 % (14822)------------------------------
% 267.90/39.44 % (14822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 267.90/39.44 % (14822)Termination reason: Unknown
% 267.90/39.44 % (14822)Termination phase: Saturation
% 267.90/39.44
% 267.90/39.44 % (14822)Memory used [KB]: 13816
% 267.90/39.44 % (14822)Time elapsed: 2.661 s
% 267.90/39.44 % (14822)Instructions burned: 8612 (million)
% 267.90/39.44 % (14822)------------------------------
% 267.90/39.44 % (14822)------------------------------
% 267.90/39.46 % (14829)lrs+1002_1:128_atotf=0.1:au=on:cbe=off:ntd=on:sp=const_frequency:i=9867:si=on:rtra=on_0 on DTF2THF_12850 for (2622ds/9867Mi)
% 268.54/39.59 % (14826)Instruction limit reached!
% 268.54/39.59 % (14826)------------------------------
% 268.54/39.59 % (14826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 268.54/39.59 % (14826)Termination reason: Unknown
% 268.54/39.59 % (14826)Termination phase: Saturation
% 268.54/39.59
% 268.54/39.59 % (14826)Memory used [KB]: 10618
% 268.54/39.59 % (14826)Time elapsed: 1.597 s
% 268.54/39.59 % (14826)Instructions burned: 5436 (million)
% 268.54/39.59 % (14826)------------------------------
% 268.54/39.59 % (14826)------------------------------
% 269.13/39.60 % (14830)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=5419:si=on:rtra=on_0 on DTF2THF_12850 for (2620ds/5419Mi)
% 269.64/39.71 % (14820)Instruction limit reached!
% 269.64/39.71 % (14820)------------------------------
% 269.64/39.71 % (14820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 269.64/39.71 % (14820)Termination reason: Unknown
% 269.64/39.71 % (14820)Termination phase: Saturation
% 269.64/39.71
% 269.64/39.71 % (14820)Memory used [KB]: 12025
% 269.64/39.71 % (14820)Time elapsed: 4.896 s
% 269.64/39.71 % (14820)Instructions burned: 27021 (million)
% 269.64/39.71 % (14820)------------------------------
% 269.64/39.71 % (14820)------------------------------
% 269.64/39.73 % (14831)dis+1010_1:28_au=on:cnfonf=off:e2e=on:fde=none:nicw=on:s2a=on:s2at=5.0:tgt=full:i=15386:si=on:rtra=on_0 on DTF2THF_12850 for (2619ds/15386Mi)
% 280.52/41.21 % (14830)Instruction limit reached!
% 280.52/41.21 % (14830)------------------------------
% 280.52/41.21 % (14830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 280.52/41.21 % (14830)Termination reason: Unknown
% 280.52/41.21 % (14830)Termination phase: Saturation
% 280.52/41.21
% 280.52/41.21 % (14830)Memory used [KB]: 12792
% 280.52/41.21 % (14830)Time elapsed: 1.616 s
% 280.52/41.21 % (14830)Instructions burned: 5420 (million)
% 280.52/41.21 % (14830)------------------------------
% 280.52/41.21 % (14830)------------------------------
% 280.52/41.22 % (14832)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_12850 for (2604ds/4714Mi)
% 281.14/41.31 % (14832)Refutation not found, incomplete strategy
% 281.14/41.31 % (14832)------------------------------
% 281.14/41.31 % (14832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 281.14/41.31 % (14832)Termination reason: Refutation not found, incomplete strategy
% 281.14/41.31
% 281.14/41.31
% 281.14/41.31 % (14832)Memory used [KB]: 8059
% 281.14/41.31 % (14832)Time elapsed: 0.091 s
% 281.14/41.31 % (14832)Instructions burned: 328 (million)
% 281.14/41.31 % (14832)------------------------------
% 281.14/41.31 % (14832)------------------------------
% 281.14/41.32 % (14833)lrs+10_1:1_bd=off:c=on:fsr=off:ntd=on:prag=on:sd=1:sos=all:ss=axioms:st=5.0:i=42749:si=on:rtra=on_0 on DTF2THF_12850 for (2603ds/42749Mi)
% 283.65/41.71 % (14833)First to succeed.
% 283.65/41.71 % (14833)Refutation found. Thanks to Tanya!
% 283.65/41.71 % SZS status Theorem for DTF2THF_12850
% 283.65/41.71 % SZS output start Proof for DTF2THF_12850
% 283.65/41.71 thf(type_def_6, type, list: ($tType) > $tType).
% 283.65/41.71 thf(type_def_7, type, set: ($tType) > $tType).
% 283.65/41.71 thf(type_def_8, type, nat: $tType).
% 283.65/41.71 thf(type_def_9, type, product_prod: ($tType * $tType) > $tType).
% 283.65/41.71 thf(type_def_10, type, prover_Mirabelle_U: $tType).
% 283.65/41.71 thf(type_def_11, type, prover2006609834e_form: $tType).
% 283.65/41.71 thf(func_def_0, type, prover2006609834e_form: $tType).
% 283.65/41.71 thf(func_def_1, type, prover_Mirabelle_U: $tType).
% 283.65/41.71 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 283.65/41.71 thf(func_def_3, type, list: ($tType) > $tType).
% 283.65/41.71 thf(func_def_4, type, set: ($tType) > $tType).
% 283.65/41.71 thf(func_def_5, type, nat: $tType).
% 283.65/41.71 thf(func_def_6, type, type: !>[X0: $tType]:($o)).
% 283.65/41.71 thf(func_def_7, type, ord: !>[X0: $tType]:($o)).
% 283.65/41.71 thf(func_def_8, type, linorder: !>[X0: $tType]:($o)).
% 283.65/41.71 thf(func_def_9, type, zero_zero: !>[X0: $tType]:(X0)).
% 283.65/41.71 thf(func_def_10, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 283.65/41.71 thf(func_def_11, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_12, type, bind: !>[X0: $tType, X1: $tType]:(list @ X0 > (X0 > list @ X1) > list @ X1)).
% 283.65/41.71 thf(func_def_13, type, butlast: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_14, type, can_select: !>[X0: $tType]:((X0 > $o) > set @ X0 > $o)).
% 283.65/41.71 thf(func_def_15, type, concat: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_16, type, count_list: !>[X0: $tType]:(list @ X0 > X0 > nat)).
% 283.65/41.71 thf(func_def_17, type, gen_length: !>[X0: $tType]:(nat > list @ X0 > nat)).
% 283.65/41.71 thf(func_def_18, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_19, type, last: !>[X0: $tType]:(list @ X0 > X0)).
% 283.65/41.71 thf(func_def_20, type, lenlex: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0)).
% 283.65/41.71 thf(func_def_21, type, lex: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0)).
% 283.65/41.71 thf(func_def_22, type, lexord: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0)).
% 283.65/41.71 thf(func_def_23, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_24, type, nil: !>[X0: $tType]:(list @ X0)).
% 283.65/41.71 thf(func_def_25, type, set2: !>[X0: $tType]:(list @ X0 > set @ X0)).
% 283.65/41.71 thf(func_def_26, type, list_ex1: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 283.65/41.71 thf(func_def_27, type, list_update: !>[X0: $tType]:(list @ X0 > nat > X0 > list @ X0)).
% 283.65/41.71 thf(func_def_28, type, listrel: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X1 > set @ product_prod @ list @ X0 @ list @ X1)).
% 283.65/41.71 thf(func_def_29, type, listrel1: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0)).
% 283.65/41.71 thf(func_def_30, type, maps: !>[X0: $tType, X1: $tType]:((X0 > list @ X1) > list @ X0 > list @ X1)).
% 283.65/41.71 thf(func_def_31, type, measures: !>[X0: $tType]:(list @ (X0 > nat) > set @ product_prod @ X0 @ X0)).
% 283.65/41.71 thf(func_def_32, type, n_lists: !>[X0: $tType]:(nat > list @ X0 > list @ list @ X0)).
% 283.65/41.71 thf(func_def_33, type, nth: !>[X0: $tType]:(list @ X0 > nat > X0)).
% 283.65/41.71 thf(func_def_34, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 283.65/41.71 thf(func_def_35, type, rotate1: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_36, type, subseqs: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 283.65/41.71 thf(func_def_37, type, take: !>[X0: $tType]:(nat > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_38, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 283.65/41.71 thf(func_def_39, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 283.65/41.71 thf(func_def_40, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 283.65/41.71 thf(func_def_41, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 283.65/41.71 thf(func_def_42, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 283.65/41.71 thf(func_def_43, type, prover1899965912_SEval: product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) > (nat > prover_Mirabelle_U) > list @ prover2006609834e_form > $o).
% 283.65/41.71 thf(func_def_44, type, prover1090191840Svalid: list @ prover2006609834e_form > $o).
% 283.65/41.71 thf(func_def_45, type, prover48307765_finst: prover2006609834e_form > nat > prover2006609834e_form).
% 283.65/41.71 thf(func_def_46, type, prover12291693latten: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_47, type, prover946642470e_FAll: prover2006609834e_form > prover2006609834e_form).
% 283.65/41.71 thf(func_def_48, type, prover_Mirabelle_fv: prover2006609834e_form > list @ nat).
% 283.65/41.71 thf(func_def_49, type, prover1043414700is_env: product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) > (nat > prover_Mirabelle_U) > $o).
% 283.65/41.71 thf(func_def_50, type, prover572158330maxvar: list @ nat > nat).
% 283.65/41.71 thf(func_def_51, type, prover1646808149preSuc: list @ nat > list @ nat).
% 283.65/41.71 thf(func_def_52, type, prover_Mirabelle_sfv: list @ prover2006609834e_form > list @ nat).
% 283.65/41.71 thf(func_def_53, type, irrefl: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 283.65/41.71 thf(func_def_54, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 283.65/41.71 thf(func_def_55, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 283.65/41.71 thf(func_def_56, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 283.65/41.71 thf(func_def_57, type, a: set @ prover_Mirabelle_U).
% 283.65/41.71 thf(func_def_58, type, b: nat > list @ prover_Mirabelle_U > $o).
% 283.65/41.71 thf(func_def_59, type, f: prover2006609834e_form).
% 283.65/41.71 thf(func_def_60, type, s: list @ prover2006609834e_form).
% 283.65/41.71 thf(func_def_61, type, u: nat).
% 283.65/41.71 thf(func_def_77, type, sK0: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_78, type, sK1: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_79, type, sK2: nat > prover_Mirabelle_U).
% 283.65/41.71 thf(func_def_80, type, sK3: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 283.65/41.71 thf(func_def_81, type, sK4: !>[X0: $tType]:(list @ X0 > X0)).
% 283.65/41.71 thf(func_def_82, type, sK5: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_83, type, sK6: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_84, type, sK7: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_85, type, sK8: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_86, type, sK9: !>[X0: $tType]:(list @ X0 > X0)).
% 283.65/41.71 thf(func_def_87, type, sK10: !>[X0: $tType]:(list @ X0 > X0)).
% 283.65/41.71 thf(func_def_88, type, sK11: !>[X0: $tType]:(list @ X0 > X0)).
% 283.65/41.71 thf(func_def_89, type, sK12: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_90, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > X1)).
% 283.65/41.71 thf(func_def_91, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X1)).
% 283.65/41.71 thf(func_def_92, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > X0)).
% 283.65/41.71 thf(func_def_93, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_94, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > X2)).
% 283.65/41.71 thf(func_def_95, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X2)).
% 283.65/41.71 thf(func_def_96, type, sK19: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_97, type, sK20: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_98, type, sK21: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_99, type, sK22: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_100, type, sK23: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 283.65/41.71 thf(func_def_101, type, sK24: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 283.65/41.71 thf(func_def_102, type, sK25: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > X0)).
% 283.65/41.71 thf(func_def_103, type, sK26: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > X0)).
% 283.65/41.71 thf(func_def_104, type, sK27: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > list @ X0 > X0)).
% 283.65/41.71 thf(func_def_105, type, sK28: !>[X0: $tType]:((X0 > $o) > list @ X0 > nat)).
% 283.65/41.71 thf(func_def_106, type, sK29: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 283.65/41.71 thf(func_def_107, type, sK30: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_108, type, sK31: !>[X0: $tType]:(list @ X0 > list @ X0 > nat)).
% 283.65/41.71 thf(func_def_109, type, sK32: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_110, type, sK33: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 283.65/41.71 thf(func_def_111, type, sK34: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_112, type, sK35: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 283.65/41.71 thf(func_def_113, type, sK36: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_114, type, sK37: !>[X0: $tType]:(list @ X0 > X0 > X0)).
% 283.65/41.71 thf(func_def_115, type, sK38: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 283.65/41.71 thf(func_def_116, type, sK39: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 283.65/41.71 thf(func_def_117, type, sK40: (nat > prover_Mirabelle_U) > (nat > prover_Mirabelle_U) > list @ prover2006609834e_form > nat).
% 283.65/41.71 thf(func_def_118, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 283.65/41.71 thf(func_def_119, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 283.65/41.71 thf(func_def_120, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 283.65/41.71 thf(func_def_121, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 283.65/41.71 thf(func_def_122, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 283.65/41.71 thf(func_def_123, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 283.65/41.71 thf(func_def_124, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 283.65/41.71 thf(func_def_125, type, sK48: !>[X0: $tType]:(nat > list @ X0)).
% 283.65/41.71 thf(func_def_126, type, sK49: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 283.65/41.71 thf(func_def_127, type, sK50: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_128, type, sK51: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_129, type, sK52: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 283.65/41.71 thf(func_def_130, type, sK53: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_131, type, sK54: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 283.65/41.71 thf(func_def_132, type, sK55: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_133, type, sK56: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 283.65/41.71 thf(func_def_134, type, sK57: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_135, type, sK58: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_136, type, sK59: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 283.65/41.71 thf(func_def_137, type, sK60: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 283.65/41.71 thf(func_def_138, type, sK61: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 283.65/41.71 thf(func_def_139, type, sK62: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 283.65/41.71 thf(func_def_140, type, sK63: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 283.65/41.71 thf(func_def_141, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 283.65/41.71 thf(func_def_142, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 283.65/41.71 thf(func_def_143, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 283.65/41.71 thf(func_def_144, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 283.65/41.71 thf(func_def_145, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_146, type, sK69: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_147, type, sK70: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 283.65/41.71 thf(func_def_148, type, sK71: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_149, type, sK72: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_150, type, sK73: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 283.65/41.71 thf(func_def_151, type, sK74: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_152, type, sK75: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 283.65/41.71 thf(func_def_153, type, sK76: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_154, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 283.65/41.71 thf(func_def_155, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 283.65/41.71 thf(func_def_156, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 283.65/41.71 thf(func_def_157, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 283.65/41.71 thf(func_def_158, type, sK81: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_159, type, sK82: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 283.65/41.71 thf(func_def_160, type, sK83: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_161, type, sK84: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_162, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 283.65/41.71 thf(func_def_163, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 283.65/41.71 thf(func_def_164, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 283.65/41.71 thf(func_def_165, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 283.65/41.71 thf(func_def_166, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 283.65/41.71 thf(func_def_167, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_168, type, sK91: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_169, type, sK92: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_170, type, sK93: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_171, type, sK94: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_172, type, sK95: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 283.65/41.71 thf(func_def_173, type, sK96: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 283.65/41.71 thf(func_def_174, type, sK97: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_175, type, sK98: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 283.65/41.71 thf(func_def_176, type, sK99: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_177, type, sK100: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_178, type, sK101: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_179, type, sK102: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_180, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 283.65/41.71 thf(func_def_181, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 283.65/41.71 thf(func_def_182, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 283.65/41.71 thf(func_def_183, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 283.65/41.71 thf(func_def_184, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 283.65/41.71 thf(func_def_185, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 283.65/41.71 thf(func_def_186, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_187, type, sK110: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_188, type, sK111: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 283.65/41.71 thf(func_def_189, type, sK112: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_190, type, sK113: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_191, type, sK114: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_192, type, sK115: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_193, type, sK116: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_194, type, sK117: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_195, type, sK118: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_196, type, sK119: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_197, type, sK120: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 283.65/41.71 thf(func_def_198, type, sK121: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_199, type, sK122: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_200, type, sK123: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_201, type, sK124: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 283.65/41.71 thf(func_def_202, type, sK125: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 283.65/41.71 thf(func_def_203, type, sK126: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_204, type, sK127: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1)).
% 283.65/41.71 thf(func_def_205, type, sK128: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1)).
% 283.65/41.71 thf(func_def_206, type, sK129: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1)).
% 283.65/41.71 thf(func_def_207, type, sK130: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0)).
% 283.65/41.71 thf(func_def_208, type, sK131: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X0)).
% 283.65/41.71 thf(func_def_209, type, sK132: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1)).
% 283.65/41.71 thf(func_def_210, type, sK133: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 283.65/41.71 thf(func_def_211, type, sK134: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 283.65/41.71 thf(func_def_212, type, sK135: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 283.65/41.71 thf(func_def_213, type, sK136: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 283.65/41.71 thf(func_def_214, type, sK137: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 283.65/41.71 thf(func_def_215, type, sK138: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 283.65/41.71 thf(func_def_216, type, sK139: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 283.65/41.71 thf(func_def_217, type, sK140: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 283.65/41.71 thf(func_def_218, type, sK141: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_219, type, sK142: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 283.65/41.71 thf(func_def_220, type, sK143: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_221, type, sK144: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 283.65/41.71 thf(func_def_222, type, sK145: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 283.65/41.71 thf(func_def_223, type, sK146: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_224, type, sK147: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 283.65/41.71 thf(func_def_225, type, sK148: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_226, type, sK149: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 283.65/41.71 thf(func_def_227, type, sK150: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 283.65/41.71 thf(func_def_228, type, sK151: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 283.65/41.71 thf(func_def_229, type, sK152: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_230, type, sK153: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 283.65/41.71 thf(func_def_231, type, sK154: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_232, type, sK155: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 283.65/41.71 thf(func_def_233, type, sK156: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 283.65/41.71 thf(func_def_234, type, sK157: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_235, type, sK158: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 283.65/41.71 thf(func_def_236, type, sK159: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 283.65/41.71 thf(func_def_237, type, sK160: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 283.65/41.71 thf(func_def_238, type, sK161: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 283.65/41.71 thf(func_def_239, type, sK162: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 283.65/41.71 thf(func_def_240, type, sK163: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_241, type, sK164: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 283.65/41.71 thf(func_def_242, type, sK165: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 283.65/41.71 thf(func_def_243, type, sK166: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 283.65/41.71 thf(func_def_244, type, sK167: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_245, type, sK168: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 283.65/41.71 thf(func_def_246, type, sK169: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o)).
% 283.65/41.71 thf(func_def_247, type, sK170: !>[X0: $tType]:(product_prod @ (X0 > X0 > $o) @ list @ X0 > X0)).
% 283.65/41.71 thf(func_def_248, type, sK171: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 283.65/41.71 thf(func_def_249, type, sK172: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_250, type, sK173: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 283.65/41.71 thf(func_def_251, type, sK174: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 283.65/41.71 thf(func_def_252, type, sK175: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_253, type, sK176: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 283.65/41.71 thf(func_def_254, type, sK177: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_255, type, sK178: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_256, type, sK179: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_257, type, sK180: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_258, type, sK181: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_259, type, sK182: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_260, type, sK183: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 283.65/41.71 thf(func_def_261, type, sK184: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 283.65/41.71 thf(func_def_262, type, sK185: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 283.65/41.71 thf(func_def_263, type, sK186: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 283.65/41.71 thf(func_def_264, type, sK187: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 283.65/41.71 thf(func_def_265, type, sK188: !>[X0: $tType]:(list @ X0 > X0)).
% 283.65/41.71 thf(func_def_266, type, sK189: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 283.65/41.71 thf(func_def_267, type, sK190: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 283.65/41.71 thf(func_def_268, type, sK191: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 283.65/41.71 thf(func_def_269, type, sK192: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 283.65/41.71 thf(func_def_270, type, sK193: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 283.65/41.71 thf(func_def_271, type, sK194: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 283.65/41.71 thf(func_def_272, type, sK195: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 283.65/41.71 thf(func_def_273, type, sK196: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 283.65/41.71 thf(func_def_274, type, sK197: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 283.65/41.71 thf(func_def_275, type, sK198: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 283.65/41.71 thf(func_def_276, type, sK199: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 283.65/41.71 thf(func_def_277, type, sK200: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 283.65/41.71 thf(func_def_278, type, sK201: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 283.65/41.71 thf(func_def_279, type, sK202: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 283.65/41.71 thf(func_def_281, type, ph204: !>[X0: $tType]:(X0)).
% 283.65/41.71 thf(func_def_282, type, sK205: nat > prover_Mirabelle_U).
% 283.65/41.71 thf(func_def_283, type, sK206: product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)).
% 283.65/41.71 thf(func_def_284, type, sK207: nat > prover_Mirabelle_U).
% 283.65/41.71 thf(func_def_285, type, sK208: product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)).
% 283.65/41.71 thf(func_def_286, type, sK209: nat > prover_Mirabelle_U).
% 283.65/41.71 thf(func_def_287, type, sK210: product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)).
% 283.65/41.71 thf(f1989,plain,(
% 283.65/41.71 $false),
% 283.65/41.71 inference(avatar_sat_refutation,[status(thm)],[f1156,f1161,f1933,f1988])).
% 283.65/41.71 thf(f1988,plain,(
% 283.65/41.71 ~spl203_1 | ~spl203_3),
% 283.65/41.71 inference(avatar_contradiction_clause,[status(thm)],[f1987])).
% 283.65/41.71 thf(f1987,plain,(
% 283.65/41.71 $false | (~spl203_1 | ~spl203_3)),
% 283.65/41.71 inference(trivial_inequality_removal,[status(thm)],[f1986])).
% 283.65/41.71 thf(f1986,plain,(
% 283.65/41.71 ($true = $false) | (~spl203_1 | ~spl203_3)),
% 283.65/41.71 inference(forward_demodulation,[status(thm)],[f1985,f1152])).
% 283.65/41.71 thf(f1152,plain,(
% 283.65/41.71 ($false = (prover1899965912_SEval @ sK206 @ sK205 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form)))) | ~spl203_1),
% 283.65/41.71 inference(avatar_component_clause,[status(thm)],[f1150])).
% 283.65/41.71 thf(f1150,definition,(
% 283.65/41.71 spl203_1 <=> ($false = (prover1899965912_SEval @ sK206 @ sK205 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form))))),
% 283.65/41.71 introduced(definition,[new_symbols(naming,[spl203_1])],[avatar_definition])).
% 283.65/41.71 thf(f1985,plain,(
% 283.65/41.71 ($true = (prover1899965912_SEval @ sK206 @ sK205 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form)))) | ~spl203_3),
% 283.65/41.71 inference(trivial_inequality_removal,[status(thm)],[f1984])).
% 283.65/41.71 thf(f1984,plain,(
% 283.65/41.71 ($true = (prover1899965912_SEval @ sK206 @ sK205 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form)))) | ($true != $true) | ~spl203_3),
% 283.65/41.71 inference(superposition,[status(thm)],[f1325,f1160])).
% 283.65/41.71 thf(f1160,plain,(
% 283.65/41.71 ($true = (prover1043414700is_env @ sK206 @ sK205)) | ~spl203_3),
% 283.65/41.71 inference(avatar_component_clause,[status(thm)],[f1158])).
% 283.65/41.71 thf(f1158,definition,(
% 283.65/41.71 spl203_3 <=> ($true = (prover1043414700is_env @ sK206 @ sK205))),
% 283.65/41.71 introduced(definition,[new_symbols(naming,[spl203_3])],[avatar_definition])).
% 283.65/41.71 thf(f1325,plain,(
% 283.65/41.71 ( ! [X0 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o),X1 : nat > prover_Mirabelle_U] : (((prover1043414700is_env @ X0 @ X1) != $true) | ($true = (prover1899965912_SEval @ X0 @ X1 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form))))) )),
% 283.65/41.71 inference(superposition,[status(thm)],[f991,f1064])).
% 283.65/41.71 thf(f1064,plain,(
% 283.65/41.71 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod @ X0 @ X1] : (((product_Pair @ X0 @ X1 @ (sK159 @ X0 @ X1 @ X2) @ (sK160 @ X0 @ X1 @ X2)) = X2)) )),
% 283.65/41.71 inference(cnf_transformation,[status(thm)],[f908])).
% 283.65/41.71 thf(f908,plain,(
% 283.65/41.71 ! [X0 : $tType,X1 : $tType,X2 : product_prod @ X0 @ X1] : ((product_Pair @ X0 @ X1 @ (sK159 @ X0 @ X1 @ X2) @ (sK160 @ X0 @ X1 @ X2)) = X2)),
% 283.65/41.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK159,sK160])],[f643,f907])).
% 283.65/41.71 thf(f907,plain,(
% 283.65/41.71 ! [X1 : $tType,X0 : $tType,X2 : product_prod @ X0 @ X1] : (? [X3 : X0,X4 : X1] : ((product_Pair @ X0 @ X1 @ X3 @ X4) = X2) => ((product_Pair @ X0 @ X1 @ (sK159 @ X0 @ X1 @ X2) @ (sK160 @ X0 @ X1 @ X2)) = X2))),
% 283.65/41.71 introduced(definition,[],[choice_axiom])).
% 283.65/41.71 thf(f643,plain,(
% 283.65/41.71 ! [X0 : $tType,X1 : $tType,X2 : product_prod @ X0 @ X1] : ? [X3 : X0,X4 : X1] : ((product_Pair @ X0 @ X1 @ X3 @ X4) = X2)),
% 283.65/41.71 inference(rectify,[status(thm)],[f107])).
% 283.65/41.71 thf(f107,axiom,(
% 283.65/41.71 ! [X0 : $tType,X1 : $tType,X75 : product_prod @ X0 @ X1] : ? [X11 : X0,X46 : X1] : ((product_Pair @ X0 @ X1 @ X11 @ X46) = X75)),
% 283.65/41.71 file('/export/starexec/sandbox2/tmp/tmp.6AU5jlErjD/DTF2THF_12850.p',fact_106_surj__pair)).
% 283.65/41.71 thf(f991,plain,(
% 283.65/41.71 ( ! [X2 : nat > prover_Mirabelle_U,X0 : set @ prover_Mirabelle_U,X1 : nat > list @ prover_Mirabelle_U > $o] : (($true != (prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ X0 @ X1) @ X2)) | ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ X0 @ X1) @ X2 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form))) = $true)) )),
% 283.65/41.71 inference(cnf_transformation,[status(thm)],[f688])).
% 283.65/41.71 thf(f688,plain,(
% 283.65/41.71 ! [X0 : set @ prover_Mirabelle_U,X1 : nat > list @ prover_Mirabelle_U > $o,X2 : nat > prover_Mirabelle_U] : (($true != (prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ X0 @ X1) @ X2)) | ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ X0 @ X1) @ X2 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form))) = $true))),
% 283.65/41.71 inference(ennf_transformation,[status(thm)],[f333])).
% 283.65/41.71 thf(f333,plain,(
% 283.65/41.71 ! [X0 : set @ prover_Mirabelle_U,X1 : nat > list @ prover_Mirabelle_U > $o,X2 : nat > prover_Mirabelle_U] : (($true = (prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ X0 @ X1) @ X2)) => ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ X0 @ X1) @ X2 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form))) = $true))),
% 283.65/41.71 inference(fool_elimination,[status(thm)],[f332])).
% 283.65/41.71 thf(f332,plain,(
% 283.65/41.71 ! [X0 : set @ prover_Mirabelle_U,X1 : nat > list @ prover_Mirabelle_U > $o,X2 : nat > prover_Mirabelle_U] : ((prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ X0 @ X1) @ X2) => (prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ X0 @ X1) @ X2 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form))))),
% 283.65/41.71 inference(rectify,[status(thm)],[f266])).
% 283.65/41.71 thf(f266,axiom,(
% 283.65/41.71 ! [X129 : set @ prover_Mirabelle_U,X101 : nat > list @ prover_Mirabelle_U > $o,X130 : nat > prover_Mirabelle_U] : ((prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ X129 @ X101) @ X130) => (prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ X129 @ X101) @ X130 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form))))),
% 283.65/41.71 file('/export/starexec/sandbox2/tmp/tmp.6AU5jlErjD/DTF2THF_12850.p',conj_1)).
% 283.65/41.71 thf(f1933,plain,(
% 283.65/41.71 ~spl203_2),
% 283.65/41.71 inference(avatar_contradiction_clause,[status(thm)],[f1932])).
% 283.65/41.71 thf(f1932,plain,(
% 283.65/41.71 $false | ~spl203_2),
% 283.65/41.71 inference(trivial_inequality_removal,[status(thm)],[f1925])).
% 283.65/41.71 thf(f1925,plain,(
% 283.65/41.71 ($true = $false) | ~spl203_2),
% 283.65/41.71 inference(superposition,[status(thm)],[f1687,f944])).
% 283.65/41.71 thf(f944,plain,(
% 283.65/41.71 ((prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ sK2) = $true)),
% 283.65/41.71 inference(cnf_transformation,[status(thm)],[f784])).
% 283.65/41.71 thf(f784,plain,(
% 283.65/41.71 ((prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ sK2) = $true) & ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ sK2 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)) != $true)),
% 283.65/41.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f719,f783])).
% 283.65/41.71 thf(f783,plain,(
% 283.65/41.71 ? [X0 : nat > prover_Mirabelle_U] : (($true = (prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X0)) & ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X0 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)) != $true)) => (((prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ sK2) = $true) & ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ sK2 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)) != $true))),
% 283.65/41.71 introduced(definition,[],[choice_axiom])).
% 283.65/41.71 thf(f719,plain,(
% 283.65/41.71 ? [X0 : nat > prover_Mirabelle_U] : (($true = (prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X0)) & ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X0 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)) != $true))),
% 283.65/41.71 inference(ennf_transformation,[status(thm)],[f628])).
% 283.65/41.71 thf(f628,plain,(
% 283.65/41.71 ~! [X0 : nat > prover_Mirabelle_U] : (($true != (prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X0)) | ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X0 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)) = $true))),
% 283.65/41.71 inference(flattening,[status(thm)],[f395])).
% 283.65/41.71 thf(f395,plain,(
% 283.65/41.71 ~! [X0 : nat > prover_Mirabelle_U] : (((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X0 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)) = $true) | ~($true = (prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X0)))),
% 283.65/41.71 inference(fool_elimination,[status(thm)],[f394])).
% 283.65/41.71 thf(f394,plain,(
% 283.65/41.71 ~! [X0 : nat > prover_Mirabelle_U] : ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X0 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)) | ~(prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X0))),
% 283.65/41.71 inference(rectify,[status(thm)],[f268])).
% 283.65/41.71 thf(f268,negated_conjecture,(
% 283.65/41.71 ~! [X81 : nat > prover_Mirabelle_U] : ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X81 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)) | ~(prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X81))),
% 283.65/41.71 inference(negated_conjecture,[status(cth)],[f267])).
% 283.65/41.71 thf(f267,conjecture,(
% 283.65/41.71 ! [X81 : nat > prover_Mirabelle_U] : ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X81 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)) | ~(prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ X81))),
% 283.65/41.71 file('/export/starexec/sandbox2/tmp/tmp.6AU5jlErjD/DTF2THF_12850.p',conj_2)).
% 283.65/41.71 thf(f1687,plain,(
% 283.65/41.71 ((prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ sK2) = $false) | ~spl203_2),
% 283.65/41.71 inference(trivial_inequality_removal,[status(thm)],[f1670])).
% 283.65/41.71 thf(f1670,plain,(
% 283.65/41.71 ((prover1043414700is_env @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ sK2) = $false) | ($true = $false) | ~spl203_2),
% 283.65/41.71 inference(superposition,[status(thm)],[f1155,f1289])).
% 283.65/41.71 thf(f1289,plain,(
% 283.65/41.71 ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ sK2 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)) = $false)),
% 283.65/41.71 inference(trivial_inequality_removal,[status(thm)],[f1282])).
% 283.65/41.71 thf(f1282,plain,(
% 283.65/41.71 ($true != $true) | ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ sK2 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)) = $false)),
% 283.65/41.71 inference(fool_paramodulation,[status(thm)],[f943])).
% 283.65/41.71 thf(f943,plain,(
% 283.65/41.71 ((prover1899965912_SEval @ (product_Pair @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ a @ b) @ sK2 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)) != $true)),
% 283.65/41.71 inference(cnf_transformation,[status(thm)],[f784])).
% 283.65/41.71 thf(f1155,plain,(
% 283.65/41.71 ( ! [X2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o),X1 : nat > prover_Mirabelle_U] : (($true = (prover1899965912_SEval @ X2 @ X1 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s))) | ((prover1043414700is_env @ X2 @ X1) = $false)) ) | ~spl203_2),
% 283.65/41.71 inference(avatar_component_clause,[status(thm)],[f1154])).
% 283.65/41.71 thf(f1154,definition,(
% 283.65/41.71 spl203_2 <=> ! [X2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o),X1 : nat > prover_Mirabelle_U] : (($true = (prover1899965912_SEval @ X2 @ X1 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s))) | ((prover1043414700is_env @ X2 @ X1) = $false))),
% 283.65/41.71 introduced(definition,[new_symbols(naming,[spl203_2])],[avatar_definition])).
% 283.65/41.71 thf(f1161,plain,(
% 283.65/41.71 spl203_3 | spl203_2),
% 283.65/41.71 inference(avatar_split_clause,[status(thm)],[f1136,f1154,f1158])).
% 283.65/41.71 thf(f1136,plain,(
% 283.65/41.71 ( ! [X2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o),X1 : nat > prover_Mirabelle_U] : (((prover1043414700is_env @ X2 @ X1) = $false) | ($true = (prover1043414700is_env @ sK206 @ sK205)) | ($true = (prover1899965912_SEval @ X2 @ X1 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)))) )),
% 283.65/41.71 inference(binary_proxy_clausification,[status(thm)],[f1134])).
% 283.65/41.71 thf(f1134,plain,(
% 283.65/41.71 ( ! [X2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o),X1 : nat > prover_Mirabelle_U] : ((((prover1043414700is_env @ sK206 @ sK205) => (prover1899965912_SEval @ sK206 @ sK205 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form)))) = $false) | ((prover1043414700is_env @ X2 @ X1) = $false) | ($true = (prover1899965912_SEval @ X2 @ X1 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)))) )),
% 283.65/41.71 inference(beta_eta_normalization,[status(thm)],[f1133])).
% 283.65/41.71 thf(f1133,plain,(
% 283.65/41.71 ( ! [X2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o),X1 : nat > prover_Mirabelle_U] : ((((^[Y0 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y0 @ sK205) => (prover1899965912_SEval @ Y0 @ sK205 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form))))) @ sK206) = $false) | ($true = (prover1899965912_SEval @ X2 @ X1 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s))) | ((prover1043414700is_env @ X2 @ X1) = $false)) )),
% 283.65/41.71 inference(sigma_clausification,[status(thm)],[f1132])).
% 283.65/41.71 thf(f1132,plain,(
% 283.65/41.71 ( ! [X2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o),X1 : nat > prover_Mirabelle_U] : (($true = (prover1899965912_SEval @ X2 @ X1 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s))) | ((!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y0 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y0 @ sK205) => (prover1899965912_SEval @ Y0 @ sK205 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form)))))) = $false) | ((prover1043414700is_env @ X2 @ X1) = $false)) )),
% 283.65/41.71 inference(binary_proxy_clausification,[status(thm)],[f1131])).
% 283.65/41.71 thf(f1131,plain,(
% 283.65/41.71 ( ! [X2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o),X1 : nat > prover_Mirabelle_U] : (($true = ((prover1043414700is_env @ X2 @ X1) => (prover1899965912_SEval @ X2 @ X1 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)))) | ((!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y0 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y0 @ sK205) => (prover1899965912_SEval @ Y0 @ sK205 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form)))))) = $false)) )),
% 283.65/41.71 inference(beta_eta_normalization,[status(thm)],[f1130])).
% 283.65/41.71 thf(f1130,plain,(
% 283.65/41.71 ( ! [X2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o),X1 : nat > prover_Mirabelle_U] : (($true = ((^[Y0 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y0 @ X1) => (prover1899965912_SEval @ Y0 @ X1 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)))) @ X2)) | ((!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y0 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y0 @ sK205) => (prover1899965912_SEval @ Y0 @ sK205 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form)))))) = $false)) )),
% 283.65/41.71 inference(pi_clausification,[status(thm)],[f1129])).
% 283.65/41.71 thf(f1129,plain,(
% 283.65/41.71 ( ! [X1 : nat > prover_Mirabelle_U] : (((!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y0 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y0 @ X1) => (prover1899965912_SEval @ Y0 @ X1 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s))))) = $true) | ((!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y0 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y0 @ sK205) => (prover1899965912_SEval @ Y0 @ sK205 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form)))))) = $false)) )),
% 283.65/41.71 inference(beta_eta_normalization,[status(thm)],[f1128])).
% 283.65/41.71 thf(f1128,plain,(
% 283.65/41.71 ( ! [X1 : nat > prover_Mirabelle_U] : ((((^[Y0 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y1 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y1 @ Y0) => (prover1899965912_SEval @ Y1 @ Y0 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form))))))) @ sK205) = $false) | ((!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y0 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y0 @ X1) => (prover1899965912_SEval @ Y0 @ X1 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s))))) = $true)) )),
% 283.65/41.71 inference(sigma_clausification,[status(thm)],[f1127])).
% 283.65/41.71 thf(f1127,plain,(
% 283.65/41.71 ( ! [X1 : nat > prover_Mirabelle_U] : (($true != (!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y1 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y1 @ Y0) => (prover1899965912_SEval @ Y1 @ Y0 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form))))))))) | ((!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y0 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y0 @ X1) => (prover1899965912_SEval @ Y0 @ X1 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s))))) = $true)) )),
% 283.65/41.71 inference(beta_eta_normalization,[status(thm)],[f1126])).
% 283.65/41.71 thf(f1126,plain,(
% 283.65/41.71 ( ! [X1 : nat > prover_Mirabelle_U] : (($true != (!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y1 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y1 @ Y0) => (prover1899965912_SEval @ Y1 @ Y0 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form))))))))) | (((^[Y0 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y1 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y1 @ Y0) => (prover1899965912_SEval @ Y1 @ Y0 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)))))) @ X1) = $true)) )),
% 283.65/41.71 inference(pi_clausification,[status(thm)],[f1125])).
% 283.65/41.71 thf(f1125,plain,(
% 283.65/41.71 ((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y1 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y1 @ Y0) => (prover1899965912_SEval @ Y1 @ Y0 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s))))))) = $true) | ($true != (!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y1 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y1 @ Y0) => (prover1899965912_SEval @ Y1 @ Y0 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form)))))))))),
% 283.65/41.71 inference(trivial_inequality_removal,[status(thm)],[f1106])).
% 283.65/41.71 thf(f1106,plain,(
% 283.65/41.71 ((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y1 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y1 @ Y0) => (prover1899965912_SEval @ Y1 @ Y0 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s))))))) = $true) | ($true != $true) | ($true != (!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y1 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y1 @ Y0) => (prover1899965912_SEval @ Y1 @ Y0 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form)))))))))),
% 283.65/41.71 inference(superposition,[status(thm)],[f999,f1104])).
% 283.65/41.71 thf(f1104,plain,(
% 283.65/41.71 ( ! [X2 : list @ prover2006609834e_form,X0 : nat,X1 : prover2006609834e_form] : (((member @ nat @ X0 @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2)))) = $true) | ($true != (!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y1 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y1 @ Y0) => (prover1899965912_SEval @ Y1 @ Y0 @ (append @ prover2006609834e_form @ X2 @ (cons @ prover2006609834e_form @ (prover48307765_finst @ X1 @ X0) @ nil @ prover2006609834e_form))))))))) | ($true = (!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y1 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y1 @ Y0) => (prover1899965912_SEval @ Y1 @ Y0 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2))))))))) )),
% 283.65/41.71 inference(beta_eta_normalization,[status(thm)],[f1096])).
% 283.65/41.71 thf(f1096,plain,(
% 283.65/41.71 ( ! [X2 : list @ prover2006609834e_form,X0 : nat,X1 : prover2006609834e_form] : (((member @ nat @ X0 @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2)))) = $true) | (((^[Y0 : list @ prover2006609834e_form]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y2 @ Y1) => (prover1899965912_SEval @ Y2 @ Y1 @ Y0))))))) @ (append @ prover2006609834e_form @ X2 @ (cons @ prover2006609834e_form @ (prover48307765_finst @ X1 @ X0) @ nil @ prover2006609834e_form))) != $true) | ($true = ((^[Y0 : list @ prover2006609834e_form]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y2 @ Y1) => (prover1899965912_SEval @ Y2 @ Y1 @ Y0))))))) @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2)))) )),
% 283.65/41.71 inference(definition_unfolding,[status(thm)],[f952,f992,f992])).
% 283.65/41.71 thf(f992,plain,(
% 283.65/41.71 (prover1090191840Svalid = (^[Y0 : list @ prover2006609834e_form]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y2 @ Y1) => (prover1899965912_SEval @ Y2 @ Y1 @ Y0))))))))),
% 283.65/41.71 inference(cnf_transformation,[status(thm)],[f465])).
% 283.65/41.71 thf(f465,plain,(
% 283.65/41.71 (prover1090191840Svalid = (^[Y0 : list @ prover2006609834e_form]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: (!! @ product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o) @ (^[Y2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o)]: ((prover1043414700is_env @ Y2 @ Y1) => (prover1899965912_SEval @ Y2 @ Y1 @ Y0))))))))),
% 283.65/41.71 inference(fool_elimination,[status(thm)],[f464])).
% 283.65/41.71 thf(f464,plain,(
% 283.65/41.71 ((^[X0 : list @ prover2006609834e_form] : (! [X1 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o),X2 : nat > prover_Mirabelle_U] : ((prover1043414700is_env @ X1 @ X2) => (prover1899965912_SEval @ X1 @ X2 @ X0)))) = prover1090191840Svalid)),
% 283.65/41.71 inference(rectify,[status(thm)],[f15])).
% 283.65/41.71 thf(f15,axiom,(
% 283.65/41.71 ((^[X19 : list @ prover2006609834e_form] : (! [X20 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o),X21 : nat > prover_Mirabelle_U] : ((prover1043414700is_env @ X20 @ X21) => (prover1899965912_SEval @ X20 @ X21 @ X19)))) = prover1090191840Svalid)),
% 283.65/41.71 file('/export/starexec/sandbox2/tmp/tmp.6AU5jlErjD/DTF2THF_12850.p',fact_14_Svalid__def)).
% 283.65/41.71 thf(f952,plain,(
% 283.65/41.71 ( ! [X2 : list @ prover2006609834e_form,X0 : nat,X1 : prover2006609834e_form] : (((member @ nat @ X0 @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2)))) = $true) | ($true != (prover1090191840Svalid @ (append @ prover2006609834e_form @ X2 @ (cons @ prover2006609834e_form @ (prover48307765_finst @ X1 @ X0) @ nil @ prover2006609834e_form)))) | ($true = (prover1090191840Svalid @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2)))) )),
% 283.65/41.71 inference(cnf_transformation,[status(thm)],[f718])).
% 283.65/41.71 thf(f718,plain,(
% 283.65/41.71 ! [X0 : nat,X1 : prover2006609834e_form,X2 : list @ prover2006609834e_form] : (((member @ nat @ X0 @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2)))) = $true) | ($true != (prover1090191840Svalid @ (append @ prover2006609834e_form @ X2 @ (cons @ prover2006609834e_form @ (prover48307765_finst @ X1 @ X0) @ nil @ prover2006609834e_form)))) | ($true = (prover1090191840Svalid @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2))))),
% 283.65/41.71 inference(flattening,[status(thm)],[f717])).
% 283.65/41.71 thf(f717,plain,(
% 283.65/41.71 ! [X0 : nat,X1 : prover2006609834e_form,X2 : list @ prover2006609834e_form] : ((($true = (prover1090191840Svalid @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2))) | ($true != (prover1090191840Svalid @ (append @ prover2006609834e_form @ X2 @ (cons @ prover2006609834e_form @ (prover48307765_finst @ X1 @ X0) @ nil @ prover2006609834e_form))))) | ((member @ nat @ X0 @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2)))) = $true))),
% 283.65/41.71 inference(ennf_transformation,[status(thm)],[f675])).
% 283.65/41.71 thf(f675,plain,(
% 283.65/41.71 ! [X0 : nat,X1 : prover2006609834e_form,X2 : list @ prover2006609834e_form] : (((member @ nat @ X0 @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2)))) != $true) => (($true = (prover1090191840Svalid @ (append @ prover2006609834e_form @ X2 @ (cons @ prover2006609834e_form @ (prover48307765_finst @ X1 @ X0) @ nil @ prover2006609834e_form)))) => ($true = (prover1090191840Svalid @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2)))))),
% 283.65/41.71 inference(flattening,[status(thm)],[f605])).
% 283.65/41.71 thf(f605,plain,(
% 283.65/41.71 ! [X0 : nat,X1 : prover2006609834e_form,X2 : list @ prover2006609834e_form] : (~((member @ nat @ X0 @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2)))) = $true) => (($true = (prover1090191840Svalid @ (append @ prover2006609834e_form @ X2 @ (cons @ prover2006609834e_form @ (prover48307765_finst @ X1 @ X0) @ nil @ prover2006609834e_form)))) => ($true = (prover1090191840Svalid @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2)))))),
% 283.65/41.71 inference(fool_elimination,[status(thm)],[f604])).
% 283.65/41.71 thf(f604,plain,(
% 283.65/41.71 ! [X0 : nat,X1 : prover2006609834e_form,X2 : list @ prover2006609834e_form] : (~(member @ nat @ X0 @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2)))) => ((prover1090191840Svalid @ (append @ prover2006609834e_form @ X2 @ (cons @ prover2006609834e_form @ (prover48307765_finst @ X1 @ X0) @ nil @ prover2006609834e_form))) => (prover1090191840Svalid @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X1) @ X2))))),
% 283.65/41.71 inference(rectify,[status(thm)],[f5])).
% 283.65/41.71 thf(f5,axiom,(
% 283.65/41.71 ! [X14 : nat,X15 : prover2006609834e_form,X8 : list @ prover2006609834e_form] : (~(member @ nat @ X14 @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X15) @ X8)))) => ((prover1090191840Svalid @ (append @ prover2006609834e_form @ X8 @ (cons @ prover2006609834e_form @ (prover48307765_finst @ X15 @ X14) @ nil @ prover2006609834e_form))) => (prover1090191840Svalid @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ X15) @ X8))))),
% 283.65/41.71 file('/export/starexec/sandbox2/tmp/tmp.6AU5jlErjD/DTF2THF_12850.p',fact_4_sound__FAll)).
% 283.65/41.71 thf(f999,plain,(
% 283.65/41.71 ((member @ nat @ u @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)))) != $true)),
% 283.65/41.71 inference(cnf_transformation,[status(thm)],[f629])).
% 283.65/41.71 thf(f629,plain,(
% 283.65/41.71 ((member @ nat @ u @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)))) != $true)),
% 283.65/41.71 inference(flattening,[status(thm)],[f613])).
% 283.65/41.71 thf(f613,plain,(
% 283.65/41.71 ~((member @ nat @ u @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s)))) = $true)),
% 283.65/41.71 inference(fool_elimination,[status(thm)],[f612])).
% 283.65/41.71 thf(f612,plain,(
% 283.65/41.71 ~(member @ nat @ u @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s))))),
% 283.65/41.71 inference(rectify,[status(thm)],[f265])).
% 283.65/41.71 thf(f265,axiom,(
% 283.65/41.71 ~(member @ nat @ u @ (set2 @ nat @ (prover_Mirabelle_sfv @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s))))),
% 283.65/41.71 file('/export/starexec/sandbox2/tmp/tmp.6AU5jlErjD/DTF2THF_12850.p',conj_0)).
% 283.65/41.71 thf(f1156,plain,(
% 283.65/41.71 spl203_1 | spl203_2),
% 283.65/41.71 inference(avatar_split_clause,[status(thm)],[f1135,f1154,f1150])).
% 283.65/41.71 thf(f1135,plain,(
% 283.65/41.71 ( ! [X2 : product_prod @ set @ prover_Mirabelle_U @ (nat > list @ prover_Mirabelle_U > $o),X1 : nat > prover_Mirabelle_U] : (($true = (prover1899965912_SEval @ X2 @ X1 @ (cons @ prover2006609834e_form @ (prover946642470e_FAll @ f) @ s))) | ((prover1043414700is_env @ X2 @ X1) = $false) | ($false = (prover1899965912_SEval @ sK206 @ sK205 @ (append @ prover2006609834e_form @ s @ (cons @ prover2006609834e_form @ (prover48307765_finst @ f @ u) @ nil @ prover2006609834e_form))))) )),
% 283.65/41.71 inference(binary_proxy_clausification,[status(thm)],[f1134])).
% 283.65/41.71 % SZS output end Proof for DTF2THF_12850
% 283.65/41.71 % (14833)------------------------------
% 283.65/41.71 % (14833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 283.65/41.71 % (14833)Termination reason: Refutation
% 283.65/41.71
% 283.65/41.71 % (14833)Memory used [KB]: 10234
% 283.65/41.71 % (14833)Time elapsed: 0.387 s
% 283.65/41.71 % (14833)Instructions burned: 1358 (million)
% 283.65/41.71 % (14833)------------------------------
% 283.65/41.71 % (14833)------------------------------
% 283.65/41.71 % (13121)Success in time 40.057 s
%------------------------------------------------------------------------------