%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP118^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 08:55:42 AM UTC 2026
% Result : Theorem 232.52s 34.90s
% Output : Refutation 232.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP118^2 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n006.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 08:26:45 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : ITP118^2 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.46 % Domain : Interactive Theorem Proving
% 0.19/0.46 % Problem : Sledgehammer Minkowskis_Theorem problem prob_62__6246984_1
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Des21]
% 0.19/0.46 % Names : Minkowskis_Theorem/prob_62__6246984_1 [Des21]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.00 v8.1.0, 0.25 v7.5.0
% 0.19/0.46 % Syntax : Number of formulae : 435 ( 100 unt; 68 typ; 0 def)
% 0.19/0.46 % Number of atoms : 1027 ( 200 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.19/0.46 % Number of connectives : 3681 ( 54 ~; 13 |; 75 &;3055 @)
% 0.19/0.46 % ( 0 <=>; 484 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 21 ( 7 avg)
% 0.19/0.46 % Number of types : 5 ( 4 usr)
% 0.19/0.46 % Number of type conns : 94 ( 94 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 67 ( 64 usr; 7 con; 0-6 aty)
% 0.19/0.46 % Number of variables : 1013 ( 65 ^; 864 !; 18 ?;1013 :)
% 0.19/0.46 % ( 66 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.46 % SPC : TH1_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:28:18.191
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % Could-be-implicit typings (6)
% 0.19/0.46 thf(ty_t_Finite__Cartesian__Product_Ovec,type,
% 0.19/0.46 finite_Cartesian_vec: $tType > $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Numeral__Type_Onum1,type,
% 0.19/0.46 numeral_num1: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Real_Oreal,type,
% 0.19/0.46 real: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Set_Oset,type,
% 0.19/0.46 set: $tType > $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_t_Int_Oint,type,
% 0.19/0.46 int: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_tf_n,type,
% 0.19/0.46 n: $tType ).
% 0.19/0.46
% 0.19/0.46 % Explicit typings (62)
% 0.19/0.46 thf(sy_cl_Cardinality_OCARD__1,type,
% 0.19/0.46 cARD_1:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_HOL_Otype,type,
% 0.19/0.46 type:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Groups_Oone,type,
% 0.19/0.46 one:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Rings_Oring,type,
% 0.19/0.46 ring:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Groups_Ozero,type,
% 0.19/0.46 zero:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Fields_Ofield,type,
% 0.19/0.46 field:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Groups_Ominus,type,
% 0.19/0.46 minus:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Rings_Oring__1,type,
% 0.19/0.46 ring_1:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.19/0.46 ord:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Nat_Oring__char__0,type,
% 0.19/0.46 ring_char_0:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.19/0.46 order:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.19/0.46 group_add:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Ono__bot,type,
% 0.19/0.46 no_bot:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Ono__top,type,
% 0.19/0.46 no_top:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.19/0.46 finite_finite:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Groups_Omonoid__mult,type,
% 0.19/0.46 monoid_mult:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.19/0.46 linorder:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.19/0.46 preorder:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Rings_Oidom__abs__sgn,type,
% 0.19/0.46 idom_abs_sgn:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Owellorder,type,
% 0.19/0.46 wellorder:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Odense__order,type,
% 0.19/0.46 dense_order:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.19/0.46 linordered_idom:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.19/0.46 dense_linorder:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.19/0.46 ordered_ab_group_add:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Real__Vector__Spaces_Odist__norm,type,
% 0.19/0.46 real_V1639655670t_norm:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.19/0.46 cancel146912293up_add:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Archimedean__Field_Ofloor__ceiling,type,
% 0.19/0.46 archim1727834104eiling:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Groups_Oordered__ab__group__add__abs,type,
% 0.19/0.46 ordere142940540dd_abs:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Real__Vector__Spaces_Ometric__space,type,
% 0.19/0.46 real_V2090557954_space:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.19/0.46 linord1659791738miring:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Archimedean__Field_Oarchimedean__field,type,
% 0.19/0.46 archim1804426504_field:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector,type,
% 0.19/0.46 real_V55928688vector:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__algebra__1,type,
% 0.19/0.46 real_V1229719638ebra_1:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Ordered__Euclidean__Space_Oordered__euclidean__space,type,
% 0.19/0.46 ordere890947078_space:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.19/0.46 condit1656338222tinuum:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.19/0.46 condit1037483654norder:
% 0.19/0.46 !>[A: $tType] : $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Archimedean__Field_Oceiling,type,
% 0.19/0.46 archimedean_ceiling:
% 0.19/0.46 !>[A: $tType] : ( A > int ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor,type,
% 0.19/0.46 archim2085082626_floor:
% 0.19/0.46 !>[A: $tType] : ( A > int ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Finite__Cartesian__Product_Oaxis,type,
% 0.19/0.46 finite1218308419n_axis:
% 0.19/0.46 !>[B: $tType,A: $tType] : ( B > A > ( finite_Cartesian_vec @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Finite__Cartesian__Product_Oaxis__index,type,
% 0.19/0.46 finite1115014511_index:
% 0.19/0.46 !>[A: $tType,N: $tType] : ( ( finite_Cartesian_vec @ A @ N ) > N ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Finite__Cartesian__Product_Omap__matrix,type,
% 0.19/0.46 finite1614961371matrix:
% 0.19/0.46 !>[A: $tType,B: $tType,I: $tType,J: $tType] : ( ( A > B ) > ( finite_Cartesian_vec @ ( finite_Cartesian_vec @ A @ I ) @ J ) > ( finite_Cartesian_vec @ ( finite_Cartesian_vec @ B @ I ) @ J ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Finite__Cartesian__Product_Ovec,type,
% 0.19/0.46 finite_Cartesian_vec2:
% 0.19/0.47 !>[A: $tType,B: $tType] : ( A > ( finite_Cartesian_vec @ A @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Finite__Cartesian__Product_Ovec_Ovec__nth,type,
% 0.19/0.47 finite1433825200ec_nth:
% 0.19/0.47 !>[A: $tType,B: $tType] : ( ( finite_Cartesian_vec @ A @ B ) > B > A ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Finite__Cartesian__Product_Ovector__scalar__mult,type,
% 0.19/0.47 finite431509953r_mult:
% 0.19/0.47 !>[A: $tType,N: $tType] : ( A > ( finite_Cartesian_vec @ A @ N ) > ( finite_Cartesian_vec @ A @ N ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Groups_Oabs__class_Oabs,type,
% 0.19/0.47 abs_abs:
% 0.19/0.47 !>[A: $tType] : ( A > A ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.19/0.47 minus_minus:
% 0.19/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.19/0.47 one_one:
% 0.19/0.47 !>[A: $tType] : A ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_If,type,
% 0.19/0.47 if:
% 0.19/0.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Int_Oring__1__class_OInts,type,
% 0.19/0.47 ring_1_Ints:
% 0.19/0.47 !>[A: $tType] : ( set @ A ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Int_Oring__1__class_Oof__int,type,
% 0.19/0.47 ring_1_of_int:
% 0.19/0.47 !>[A: $tType] : ( int > A ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Minkowskis__Theorem__Mirabelle__jpyvdnlcjd_Oof__int__vec,type,
% 0.19/0.47 minkow1937162798nt_vec:
% 0.19/0.47 !>[B: $tType,A: $tType] : ( ( finite_Cartesian_vec @ int @ B ) > ( finite_Cartesian_vec @ A @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.19/0.47 ord_less:
% 0.19/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.19/0.47 ord_less_eq:
% 0.19/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist,type,
% 0.19/0.47 real_V2000881966t_dist:
% 0.19/0.47 !>[A: $tType] : ( A > A > real ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm,type,
% 0.19/0.47 real_V1127708846m_norm:
% 0.19/0.47 !>[A: $tType] : ( A > real ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Set_OCollect,type,
% 0.19/0.47 collect:
% 0.19/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_member,type,
% 0.19/0.47 member:
% 0.19/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_A,type,
% 0.19/0.47 a: set @ ( finite_Cartesian_vec @ real @ n ) ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_i____,type,
% 0.19/0.47 i: n ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_m____,type,
% 0.19/0.47 m: int ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_x____,type,
% 0.19/0.47 x: finite_Cartesian_vec @ real @ n ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_y____,type,
% 0.19/0.47 y: finite_Cartesian_vec @ real @ n ).
% 0.19/0.47
% 0.19/0.47 % Relevant facts (255)
% 0.19/0.47 thf(fact_0__C1_C_I2_J,axiom,
% 0.19/0.47 member @ ( finite_Cartesian_vec @ real @ n ) @ y @ a ).
% 0.19/0.47
% 0.19/0.47 % "1"(2)
% 0.19/0.47 thf(fact_1__C1_C_I1_J,axiom,
% 0.19/0.47 member @ ( finite_Cartesian_vec @ real @ n ) @ x @ a ).
% 0.19/0.47
% 0.19/0.47 % "1"(1)
% 0.19/0.47 thf(fact_2_m,axiom,
% 0.19/0.47 ( ( ring_1_of_int @ real @ m )
% 0.19/0.47 = ( minus_minus @ real @ ( finite1433825200ec_nth @ real @ n @ x @ i ) @ ( finite1433825200ec_nth @ real @ n @ y @ i ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % m
% 0.19/0.47 thf(fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.19/0.47 ~ ! [M: int] :
% 0.19/0.47 ( ( ring_1_of_int @ real @ M )
% 0.19/0.47 != ( minus_minus @ real @ ( finite1433825200ec_nth @ real @ n @ x @ i ) @ ( finite1433825200ec_nth @ real @ n @ y @ i ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % \<open>\<And>thesis. (\<And>m. real_of_int m = x $ i - y $ i \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.19/0.47 thf(fact_4_vector__minus__component,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType] :
% 0.19/0.47 ( ( ( finite_finite @ B )
% 0.19/0.47 & ( minus @ A ) )
% 0.19/0.47 => ! [X: finite_Cartesian_vec @ A @ B,Y: finite_Cartesian_vec @ A @ B,I2: B] :
% 0.19/0.47 ( ( finite1433825200ec_nth @ A @ B @ ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ X @ Y ) @ I2 )
% 0.19/0.47 = ( minus_minus @ A @ ( finite1433825200ec_nth @ A @ B @ X @ I2 ) @ ( finite1433825200ec_nth @ A @ B @ Y @ I2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % vector_minus_component
% 0.19/0.47 thf(fact_5_of__int__abs,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( linordered_idom @ A )
% 0.19/0.47 => ! [X: int] :
% 0.19/0.47 ( ( ring_1_of_int @ A @ ( abs_abs @ int @ X ) )
% 0.19/0.47 = ( abs_abs @ A @ ( ring_1_of_int @ A @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % of_int_abs
% 0.19/0.47 thf(fact_6_of__int__diff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ring_1 @ A )
% 0.19/0.47 => ! [W: int,Z: int] :
% 0.19/0.47 ( ( ring_1_of_int @ A @ ( minus_minus @ int @ W @ Z ) )
% 0.19/0.47 = ( minus_minus @ A @ ( ring_1_of_int @ A @ W ) @ ( ring_1_of_int @ A @ Z ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % of_int_diff
% 0.19/0.47 thf(fact_7__092_060open_062x_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060in_062_A_092_060int_062_092_060close_062,axiom,
% 0.19/0.47 member @ real @ ( minus_minus @ real @ ( finite1433825200ec_nth @ real @ n @ x @ i ) @ ( finite1433825200ec_nth @ real @ n @ y @ i ) ) @ ( ring_1_Ints @ real ) ).
% 0.19/0.47
% 0.19/0.47 % \<open>x $ i - y $ i \<in> \<int>\<close>
% 0.19/0.47 thf(fact_8_of__int__vec__nth,axiom,
% 0.19/0.47 ! [A: $tType,B: $tType] :
% 0.19/0.47 ( ( ( finite_finite @ B )
% 0.19/0.47 & ( ring_1 @ A ) )
% 0.19/0.47 => ! [V: finite_Cartesian_vec @ int @ B,N2: B] :
% 0.19/0.47 ( ( finite1433825200ec_nth @ A @ B @ ( minkow1937162798nt_vec @ B @ A @ V ) @ N2 )
% 0.19/0.47 = ( ring_1_of_int @ A @ ( finite1433825200ec_nth @ int @ B @ V @ N2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % of_int_vec_nth
% 0.19/0.47 thf(fact_9_of__int__eq__iff,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ring_char_0 @ A )
% 0.19/0.47 => ! [W: int,Z: int] :
% 0.19/0.47 ( ( ( ring_1_of_int @ A @ W )
% 0.19/0.47 = ( ring_1_of_int @ A @ Z ) )
% 0.19/0.47 = ( W = Z ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % of_int_eq_iff
% 0.19/0.47 thf(fact_10_abs__abs,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( idom_abs_sgn @ A )
% 0.19/0.47 => ! [A2: A] :
% 0.19/0.47 ( ( abs_abs @ A @ ( abs_abs @ A @ A2 ) )
% 0.19/0.47 = ( abs_abs @ A @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_abs
% 0.19/0.47 thf(fact_11_abs__idempotent,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ordere142940540dd_abs @ A )
% 0.19/0.47 => ! [A2: A] :
% 0.19/0.47 ( ( abs_abs @ A @ ( abs_abs @ A @ A2 ) )
% 0.19/0.47 = ( abs_abs @ A @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_idempotent
% 0.19/0.47 thf(fact_12_minus__apply,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( minus @ B )
% 0.19/0.47 => ( ( minus_minus @ ( A > B ) )
% 0.19/0.47 = ( ^ [A3: A > B,B2: A > B,X2: A] : ( minus_minus @ B @ ( A3 @ X2 ) @ ( B2 @ X2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % minus_apply
% 0.19/0.47 thf(fact_13_abs__minus__commute,axiom,
% 0.19/0.47 ! [A: $tType] :
% 0.19/0.47 ( ( ordere142940540dd_abs @ A )
% 0.19/0.47 => ! [A2: A,B3: A] :
% 0.19/0.47 ( ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B3 ) )
% 0.19/0.47 = ( abs_abs @ A @ ( minus_minus @ A @ B3 @ A2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_minus_commute
% 0.19/0.47 thf(fact_14_lambda__skolem,axiom,
% 0.19/0.47 ! [N: $tType,A: $tType] :
% 0.19/0.47 ( ( finite_finite @ N )
% 0.19/0.47 => ! [P: N > A > $o] :
% 0.19/0.47 ( ( ! [I3: N] :
% 0.19/0.47 ? [X3: A] : ( P @ I3 @ X3 ) )
% 0.19/0.47 = ( ? [X2: finite_Cartesian_vec @ A @ N] :
% 0.19/0.47 ! [I3: N] : ( P @ I3 @ ( finite1433825200ec_nth @ A @ N @ X2 @ I3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % lambda_skolem
% 0.19/0.47 thf(fact_15_vec__eq__iff,axiom,
% 0.19/0.47 ! [B: $tType,A: $tType] :
% 0.19/0.47 ( ( finite_finite @ B )
% 0.19/0.47 => ( ( ^ [Y2: finite_Cartesian_vec @ A @ B,Z2: finite_Cartesian_vec @ A @ B] : ( Y2 = Z2 ) )
% 0.19/0.47 = ( ^ [X2: finite_Cartesian_vec @ A @ B,Y3: finite_Cartesian_vec @ A @ B] :
% 0.19/0.47 ! [I3: B] :
% 0.19/0.47 ( ( finite1433825200ec_nth @ A @ B @ X2 @ I3 )
% 0.19/0.47 = ( finite1433825200ec_nth @ A @ B @ Y3 @ I3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % vec_eq_iff
% 0.19/0.47 thf(fact_16_assms,axiom,
% 0.19/0.47 ! [V: finite_Cartesian_vec @ real @ n,I2: n] :
% 0.19/0.47 ( ( member @ ( finite_Cartesian_vec @ real @ n ) @ V @ a )
% 0.19/0.47 => ( member @ real @ ( finite1433825200ec_nth @ real @ n @ V @ I2 ) @ ( ring_1_Ints @ real ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % assms
% 0.19/0.47 thf(fact_17_of__int__vec__eq__iff,axiom,
% 0.19/0.47 ! [A: $tType,N: $tType] :
% 0.19/0.47 ( ( ( finite_finite @ N )
% 0.19/0.47 & ( ring_char_0 @ A ) )
% 0.19/0.47 => ! [A2: finite_Cartesian_vec @ int @ N,B3: finite_Cartesian_vec @ int @ N] :
% 0.31/0.47 ( ( ( minkow1937162798nt_vec @ N @ A @ A2 )
% 0.31/0.47 = ( minkow1937162798nt_vec @ N @ A @ B3 ) )
% 0.31/0.47 = ( A2 = B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_vec_eq_iff
% 0.31/0.47 thf(fact_18_Ints__diff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring_1 @ A )
% 0.31/0.47 => ! [A2: A,B3: A] :
% 0.31/0.47 ( ( member @ A @ A2 @ ( ring_1_Ints @ A ) )
% 0.31/0.47 => ( ( member @ A @ B3 @ ( ring_1_Ints @ A ) )
% 0.31/0.47 => ( member @ A @ ( minus_minus @ A @ A2 @ B3 ) @ ( ring_1_Ints @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Ints_diff
% 0.31/0.47 thf(fact_19_Ints__abs,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( member @ A @ A2 @ ( ring_1_Ints @ A ) )
% 0.31/0.47 => ( member @ A @ ( abs_abs @ A @ A2 ) @ ( ring_1_Ints @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Ints_abs
% 0.31/0.47 thf(fact_20_Ints__of__int,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring_1 @ A )
% 0.31/0.47 => ! [Z: int] : ( member @ A @ ( ring_1_of_int @ A @ Z ) @ ( ring_1_Ints @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Ints_of_int
% 0.31/0.47 thf(fact_21_Ints__induct,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring_1 @ A )
% 0.31/0.47 => ! [Q: A,P: A > $o] :
% 0.31/0.47 ( ( member @ A @ Q @ ( ring_1_Ints @ A ) )
% 0.31/0.47 => ( ! [Z3: int] : ( P @ ( ring_1_of_int @ A @ Z3 ) )
% 0.31/0.47 => ( P @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Ints_induct
% 0.31/0.47 thf(fact_22_Ints__cases,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring_1 @ A )
% 0.31/0.47 => ! [Q: A] :
% 0.31/0.47 ( ( member @ A @ Q @ ( ring_1_Ints @ A ) )
% 0.31/0.47 => ~ ! [Z3: int] :
% 0.31/0.47 ( Q
% 0.31/0.47 != ( ring_1_of_int @ A @ Z3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Ints_cases
% 0.31/0.47 thf(fact_23_diff__right__commute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel146912293up_add @ A )
% 0.31/0.47 => ! [A2: A,C: A,B3: A] :
% 0.31/0.47 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B3 )
% 0.31/0.47 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B3 ) @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_right_commute
% 0.31/0.47 thf(fact_24_diff__eq__diff__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A,D: A] :
% 0.31/0.47 ( ( ( minus_minus @ A @ A2 @ B3 )
% 0.31/0.47 = ( minus_minus @ A @ C @ D ) )
% 0.31/0.47 => ( ( A2 = B3 )
% 0.31/0.47 = ( C = D ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_eq_diff_eq
% 0.31/0.47 thf(fact_25_fun__diff__def,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( minus @ B )
% 0.31/0.47 => ( ( minus_minus @ ( A > B ) )
% 0.31/0.47 = ( ^ [A3: A > B,B2: A > B,X2: A] : ( minus_minus @ B @ ( A3 @ X2 ) @ ( B2 @ X2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_diff_def
% 0.31/0.47 thf(fact_26_vec__nth__inject,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( finite_finite @ B )
% 0.31/0.47 => ! [X: finite_Cartesian_vec @ A @ B,Y: finite_Cartesian_vec @ A @ B] :
% 0.31/0.47 ( ( ( finite1433825200ec_nth @ A @ B @ X )
% 0.31/0.47 = ( finite1433825200ec_nth @ A @ B @ Y ) )
% 0.31/0.47 = ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % vec_nth_inject
% 0.31/0.47 thf(fact_27_cond__component,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( finite_finite @ B )
% 0.31/0.47 => ! [B3: $o,X: finite_Cartesian_vec @ A @ B,Y: finite_Cartesian_vec @ A @ B,I2: B] :
% 0.31/0.47 ( ( B3
% 0.31/0.47 => ( ( finite1433825200ec_nth @ A @ B @ ( if @ ( finite_Cartesian_vec @ A @ B ) @ B3 @ X @ Y ) @ I2 )
% 0.31/0.47 = ( finite1433825200ec_nth @ A @ B @ X @ I2 ) ) )
% 0.31/0.47 & ( ~ B3
% 0.31/0.47 => ( ( finite1433825200ec_nth @ A @ B @ ( if @ ( finite_Cartesian_vec @ A @ B ) @ B3 @ X @ Y ) @ I2 )
% 0.31/0.47 = ( finite1433825200ec_nth @ A @ B @ Y @ I2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % cond_component
% 0.31/0.47 thf(fact_28_nth__map__matrix,axiom,
% 0.31/0.47 ! [A: $tType,C2: $tType,D2: $tType,B: $tType] :
% 0.31/0.47 ( ( ( finite_finite @ B )
% 0.31/0.47 & ( finite_finite @ C2 ) )
% 0.31/0.47 => ! [F: D2 > A,X: finite_Cartesian_vec @ ( finite_Cartesian_vec @ D2 @ B ) @ C2,I2: C2,J2: B] :
% 0.31/0.47 ( ( finite1433825200ec_nth @ A @ B @ ( finite1433825200ec_nth @ ( finite_Cartesian_vec @ A @ B ) @ C2 @ ( finite1614961371matrix @ D2 @ A @ B @ C2 @ F @ X ) @ I2 ) @ J2 )
% 0.31/0.47 = ( F @ ( finite1433825200ec_nth @ D2 @ B @ ( finite1433825200ec_nth @ ( finite_Cartesian_vec @ D2 @ B ) @ C2 @ X @ I2 ) @ J2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nth_map_matrix
% 0.31/0.47 thf(fact_29_dist__of__int,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V1229719638ebra_1 @ A )
% 0.31/0.47 => ! [M2: int,N2: int] :
% 0.31/0.47 ( ( real_V2000881966t_dist @ A @ ( ring_1_of_int @ A @ M2 ) @ ( ring_1_of_int @ A @ N2 ) )
% 0.31/0.47 = ( ring_1_of_int @ real @ ( abs_abs @ int @ ( minus_minus @ int @ M2 @ N2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dist_of_int
% 0.31/0.47 thf(fact_30_vec__sub,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( minus @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( finite_Cartesian_vec2 @ A @ B @ ( minus_minus @ A @ X @ Y ) )
% 0.31/0.47 = ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ ( finite_Cartesian_vec2 @ A @ B @ X ) @ ( finite_Cartesian_vec2 @ A @ B @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % vec_sub
% 0.31/0.47 thf(fact_31_vector__sub__rdistrib,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( ring @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ! [A2: A,B3: A,X: finite_Cartesian_vec @ A @ B] :
% 0.31/0.47 ( ( finite431509953r_mult @ A @ B @ ( minus_minus @ A @ A2 @ B3 ) @ X )
% 0.31/0.47 = ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ ( finite431509953r_mult @ A @ B @ A2 @ X ) @ ( finite431509953r_mult @ A @ B @ B3 @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % vector_sub_rdistrib
% 0.31/0.47 thf(fact_32__C1_C_I3_J,axiom,
% 0.31/0.47 ord_less @ real @ ( real_V2000881966t_dist @ ( finite_Cartesian_vec @ real @ n ) @ y @ x ) @ ( one_one @ real ) ).
% 0.31/0.47
% 0.31/0.47 % "1"(3)
% 0.31/0.47 thf(fact_33_norm__of__int,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V1229719638ebra_1 @ A )
% 0.31/0.47 => ! [Z: int] :
% 0.31/0.47 ( ( real_V1127708846m_norm @ A @ ( ring_1_of_int @ A @ Z ) )
% 0.31/0.47 = ( abs_abs @ real @ ( ring_1_of_int @ real @ Z ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % norm_of_int
% 0.31/0.47 thf(fact_34_ceiling__diff__of__int,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A,Z: int] :
% 0.31/0.47 ( ( archimedean_ceiling @ A @ ( minus_minus @ A @ X @ ( ring_1_of_int @ A @ Z ) ) )
% 0.31/0.47 = ( minus_minus @ int @ ( archimedean_ceiling @ A @ X ) @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_diff_of_int
% 0.31/0.47 thf(fact_35_axis__nth,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( zero @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ! [I2: B,X: A] :
% 0.31/0.47 ( ( finite1433825200ec_nth @ A @ B @ ( finite1218308419n_axis @ B @ A @ I2 @ X ) @ I2 )
% 0.31/0.47 = X ) ) ).
% 0.31/0.47
% 0.31/0.47 % axis_nth
% 0.31/0.47 thf(fact_36_vec_Oscale__left__diff__distrib,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( field @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ! [A2: A,B3: A,X: finite_Cartesian_vec @ A @ B] :
% 0.31/0.47 ( ( finite431509953r_mult @ A @ B @ ( minus_minus @ A @ A2 @ B3 ) @ X )
% 0.31/0.47 = ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ ( finite431509953r_mult @ A @ B @ A2 @ X ) @ ( finite431509953r_mult @ A @ B @ B3 @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % vec.scale_left_diff_distrib
% 0.31/0.47 thf(fact_37_floor__diff__of__int,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A,Z: int] :
% 0.31/0.47 ( ( archim2085082626_floor @ A @ ( minus_minus @ A @ X @ ( ring_1_of_int @ A @ Z ) ) )
% 0.31/0.47 = ( minus_minus @ int @ ( archim2085082626_floor @ A @ X ) @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % floor_diff_of_int
% 0.31/0.47 thf(fact_38_norm__axis__1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( finite_finite @ A )
% 0.31/0.47 => ! [M2: A] :
% 0.31/0.47 ( ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ real @ A ) @ ( finite1218308419n_axis @ A @ real @ M2 @ ( one_one @ real ) ) )
% 0.31/0.47 = ( one_one @ real ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % norm_axis_1
% 0.31/0.47 thf(fact_39_vec__eq,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( finite_finite @ B )
% 0.31/0.47 => ! [M2: A,N2: A] :
% 0.31/0.47 ( ( ( finite_Cartesian_vec2 @ A @ B @ M2 )
% 0.31/0.47 = ( finite_Cartesian_vec2 @ A @ B @ N2 ) )
% 0.31/0.47 = ( M2 = N2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % vec_eq
% 0.31/0.47 thf(fact_40_vec__inj,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( finite_finite @ B )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ( finite_Cartesian_vec2 @ A @ B @ X )
% 0.31/0.47 = ( finite_Cartesian_vec2 @ A @ B @ Y ) )
% 0.31/0.47 = ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % vec_inj
% 0.31/0.47 thf(fact_41_vec_Oscale__one,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( field @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ! [X: finite_Cartesian_vec @ A @ B] :
% 0.31/0.47 ( ( finite431509953r_mult @ A @ B @ ( one_one @ A ) @ X )
% 0.31/0.47 = X ) ) ).
% 0.31/0.47
% 0.31/0.47 % vec.scale_one
% 0.31/0.47 thf(fact_42_vector__smult__lid,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( monoid_mult @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ! [X: finite_Cartesian_vec @ A @ B] :
% 0.31/0.47 ( ( finite431509953r_mult @ A @ B @ ( one_one @ A ) @ X )
% 0.31/0.47 = X ) ) ).
% 0.31/0.47
% 0.31/0.47 % vector_smult_lid
% 0.31/0.47 thf(fact_43_abs__1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( idom_abs_sgn @ A )
% 0.31/0.47 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 0.31/0.47 = ( one_one @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_1
% 0.31/0.47 thf(fact_44_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.31/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.31/0.47 = ( P @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_45_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A: $tType,A4: set @ A] :
% 0.31/0.47 ( ( collect @ A
% 0.31/0.47 @ ^ [X2: A] : ( member @ A @ X2 @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_46_Collect__cong,axiom,
% 0.31/0.47 ! [A: $tType,P: A > $o,Q2: A > $o] :
% 0.31/0.47 ( ! [X4: A] :
% 0.31/0.47 ( ( P @ X4 )
% 0.31/0.47 = ( Q2 @ X4 ) )
% 0.31/0.47 => ( ( collect @ A @ P )
% 0.31/0.47 = ( collect @ A @ Q2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_cong
% 0.31/0.47 thf(fact_47_ext,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.31/0.47 ( ! [X4: A] :
% 0.31/0.47 ( ( F @ X4 )
% 0.31/0.47 = ( G @ X4 ) )
% 0.31/0.47 => ( F = G ) ) ).
% 0.31/0.47
% 0.31/0.47 % ext
% 0.31/0.47 thf(fact_48_of__int__less__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ! [W: int,Z: int] :
% 0.31/0.47 ( ( ord_less @ A @ ( ring_1_of_int @ A @ W ) @ ( ring_1_of_int @ A @ Z ) )
% 0.31/0.47 = ( ord_less @ int @ W @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_less_iff
% 0.31/0.47 thf(fact_49_one__index,axiom,
% 0.31/0.47 ! [N: $tType,A: $tType] :
% 0.31/0.47 ( ( ( one @ A )
% 0.31/0.47 & ( finite_finite @ N ) )
% 0.31/0.47 => ! [I2: N] :
% 0.31/0.47 ( ( finite1433825200ec_nth @ A @ N @ ( one_one @ ( finite_Cartesian_vec @ A @ N ) ) @ I2 )
% 0.31/0.47 = ( one_one @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % one_index
% 0.31/0.47 thf(fact_50_of__int__eq__1__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring_char_0 @ A )
% 0.31/0.47 => ! [Z: int] :
% 0.31/0.47 ( ( ( ring_1_of_int @ A @ Z )
% 0.31/0.47 = ( one_one @ A ) )
% 0.31/0.47 = ( Z
% 0.31/0.47 = ( one_one @ int ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_eq_1_iff
% 0.31/0.47 thf(fact_51_of__int__1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring_1 @ A )
% 0.31/0.47 => ( ( ring_1_of_int @ A @ ( one_one @ int ) )
% 0.31/0.47 = ( one_one @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_1
% 0.31/0.47 thf(fact_52_abs__norm__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V55928688vector @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( abs_abs @ real @ ( real_V1127708846m_norm @ A @ A2 ) )
% 0.31/0.47 = ( real_V1127708846m_norm @ A @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_norm_cancel
% 0.31/0.47 thf(fact_53_floor__one,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ( ( archim2085082626_floor @ A @ ( one_one @ A ) )
% 0.31/0.47 = ( one_one @ int ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % floor_one
% 0.31/0.47 thf(fact_54_ceiling__one,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ( ( archimedean_ceiling @ A @ ( one_one @ A ) )
% 0.31/0.47 = ( one_one @ int ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_one
% 0.31/0.47 thf(fact_55_vec__1,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( one @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ( ( finite_Cartesian_vec2 @ A @ B @ ( one_one @ A ) )
% 0.31/0.47 = ( one_one @ ( finite_Cartesian_vec @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % vec_1
% 0.31/0.47 thf(fact_56_floor__of__int,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [Z: int] :
% 0.31/0.47 ( ( archim2085082626_floor @ A @ ( ring_1_of_int @ A @ Z ) )
% 0.31/0.47 = Z ) ) ).
% 0.31/0.47
% 0.31/0.47 % floor_of_int
% 0.31/0.47 thf(fact_57_ceiling__of__int,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [Z: int] :
% 0.31/0.47 ( ( archimedean_ceiling @ A @ ( ring_1_of_int @ A @ Z ) )
% 0.31/0.47 = Z ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_of_int
% 0.31/0.47 thf(fact_58_vec__component,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( finite_finite @ B )
% 0.31/0.47 => ! [X: A,I2: B] :
% 0.31/0.47 ( ( finite1433825200ec_nth @ A @ B @ ( finite_Cartesian_vec2 @ A @ B @ X ) @ I2 )
% 0.31/0.47 = X ) ) ).
% 0.31/0.47
% 0.31/0.47 % vec_component
% 0.31/0.47 thf(fact_59_vector__ssub__ldistrib,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( ring @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ! [C: A,X: finite_Cartesian_vec @ A @ B,Y: finite_Cartesian_vec @ A @ B] :
% 0.31/0.47 ( ( finite431509953r_mult @ A @ B @ C @ ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ X @ Y ) )
% 0.31/0.47 = ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ ( finite431509953r_mult @ A @ B @ C @ X ) @ ( finite431509953r_mult @ A @ B @ C @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % vector_ssub_ldistrib
% 0.31/0.47 thf(fact_60_of__int__1__less__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ! [Z: int] :
% 0.31/0.47 ( ( ord_less @ A @ ( one_one @ A ) @ ( ring_1_of_int @ A @ Z ) )
% 0.31/0.47 = ( ord_less @ int @ ( one_one @ int ) @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_1_less_iff
% 0.31/0.47 thf(fact_61_of__int__less__1__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ! [Z: int] :
% 0.31/0.47 ( ( ord_less @ A @ ( ring_1_of_int @ A @ Z ) @ ( one_one @ A ) )
% 0.31/0.47 = ( ord_less @ int @ Z @ ( one_one @ int ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_less_1_iff
% 0.31/0.47 thf(fact_62_norm__one,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V1229719638ebra_1 @ A )
% 0.31/0.47 => ( ( real_V1127708846m_norm @ A @ ( one_one @ A ) )
% 0.31/0.47 = ( one_one @ real ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % norm_one
% 0.31/0.47 thf(fact_63_dist__diff_I2_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V55928688vector @ A )
% 0.31/0.47 => ! [A2: A,B3: A] :
% 0.31/0.47 ( ( real_V2000881966t_dist @ A @ ( minus_minus @ A @ A2 @ B3 ) @ A2 )
% 0.31/0.47 = ( real_V1127708846m_norm @ A @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dist_diff(2)
% 0.31/0.47 thf(fact_64_dist__diff_I1_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V55928688vector @ A )
% 0.31/0.47 => ! [A2: A,B3: A] :
% 0.31/0.47 ( ( real_V2000881966t_dist @ A @ A2 @ ( minus_minus @ A @ A2 @ B3 ) )
% 0.31/0.47 = ( real_V1127708846m_norm @ A @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dist_diff(1)
% 0.31/0.47 thf(fact_65_floor__less__one,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( ord_less @ int @ ( archim2085082626_floor @ A @ X ) @ ( one_one @ int ) )
% 0.31/0.47 = ( ord_less @ A @ X @ ( one_one @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % floor_less_one
% 0.31/0.47 thf(fact_66_one__less__ceiling,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( ord_less @ int @ ( one_one @ int ) @ ( archimedean_ceiling @ A @ X ) )
% 0.31/0.47 = ( ord_less @ A @ ( one_one @ A ) @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % one_less_ceiling
% 0.31/0.47 thf(fact_67_floor__diff__one,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( archim2085082626_floor @ A @ ( minus_minus @ A @ X @ ( one_one @ A ) ) )
% 0.31/0.47 = ( minus_minus @ int @ ( archim2085082626_floor @ A @ X ) @ ( one_one @ int ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % floor_diff_one
% 0.31/0.47 thf(fact_68_ceiling__diff__one,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( archimedean_ceiling @ A @ ( minus_minus @ A @ X @ ( one_one @ A ) ) )
% 0.31/0.47 = ( minus_minus @ int @ ( archimedean_ceiling @ A @ X ) @ ( one_one @ int ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_diff_one
% 0.31/0.47 thf(fact_69_one__reorient,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( one @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( ( one_one @ A )
% 0.31/0.47 = X )
% 0.31/0.47 = ( X
% 0.31/0.47 = ( one_one @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % one_reorient
% 0.31/0.47 thf(fact_70_floor__less__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A,Z: int] :
% 0.31/0.47 ( ( ord_less @ int @ ( archim2085082626_floor @ A @ X ) @ Z )
% 0.31/0.47 = ( ord_less @ A @ X @ ( ring_1_of_int @ A @ Z ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % floor_less_iff
% 0.31/0.47 thf(fact_71_less__ceiling__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [Z: int,X: A] :
% 0.31/0.47 ( ( ord_less @ int @ Z @ ( archimedean_ceiling @ A @ X ) )
% 0.31/0.47 = ( ord_less @ A @ ( ring_1_of_int @ A @ Z ) @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_ceiling_iff
% 0.31/0.47 thf(fact_72_vec_Oscale__left__commute,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( field @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ! [A2: A,B3: A,X: finite_Cartesian_vec @ A @ B] :
% 0.31/0.47 ( ( finite431509953r_mult @ A @ B @ A2 @ ( finite431509953r_mult @ A @ B @ B3 @ X ) )
% 0.31/0.47 = ( finite431509953r_mult @ A @ B @ B3 @ ( finite431509953r_mult @ A @ B @ A2 @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % vec.scale_left_commute
% 0.31/0.47 thf(fact_73_dist__norm,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V1639655670t_norm @ A )
% 0.31/0.47 => ( ( real_V2000881966t_dist @ A )
% 0.31/0.47 = ( ^ [X2: A,Y3: A] : ( real_V1127708846m_norm @ A @ ( minus_minus @ A @ X2 @ Y3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dist_norm
% 0.31/0.47 thf(fact_74_linorder__neqE__linordered__idom,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( X != Y )
% 0.31/0.47 => ( ~ ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_neqE_linordered_idom
% 0.31/0.47 thf(fact_75_dist__commute__lessI,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V2090557954_space @ A )
% 0.31/0.47 => ! [Y: A,X: A,E: real] :
% 0.31/0.47 ( ( ord_less @ real @ ( real_V2000881966t_dist @ A @ Y @ X ) @ E )
% 0.31/0.47 => ( ord_less @ real @ ( real_V2000881966t_dist @ A @ X @ Y ) @ E ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dist_commute_lessI
% 0.31/0.47 thf(fact_76_dist__commute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V2090557954_space @ A )
% 0.31/0.47 => ( ( real_V2000881966t_dist @ A )
% 0.31/0.47 = ( ^ [X2: A,Y3: A] : ( real_V2000881966t_dist @ A @ Y3 @ X2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dist_commute
% 0.31/0.47 thf(fact_77_ceiling__less__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ int @ ( archimedean_ceiling @ A @ X ) @ ( archimedean_ceiling @ A @ Y ) )
% 0.31/0.47 => ( ord_less @ A @ X @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_less_cancel
% 0.31/0.47 thf(fact_78_floor__less__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ int @ ( archim2085082626_floor @ A @ X ) @ ( archim2085082626_floor @ A @ Y ) )
% 0.31/0.47 => ( ord_less @ A @ X @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % floor_less_cancel
% 0.31/0.47 thf(fact_79_norm__minus__commute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V55928688vector @ A )
% 0.31/0.47 => ! [A2: A,B3: A] :
% 0.31/0.47 ( ( real_V1127708846m_norm @ A @ ( minus_minus @ A @ A2 @ B3 ) )
% 0.31/0.47 = ( real_V1127708846m_norm @ A @ ( minus_minus @ A @ B3 @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % norm_minus_commute
% 0.31/0.47 thf(fact_80_real__norm__def,axiom,
% 0.31/0.47 ( ( real_V1127708846m_norm @ real )
% 0.31/0.47 = ( abs_abs @ real ) ) ).
% 0.31/0.47
% 0.31/0.47 % real_norm_def
% 0.31/0.47 thf(fact_81_ex__less__of__int,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1804426504_field @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ? [Z3: int] : ( ord_less @ A @ X @ ( ring_1_of_int @ A @ Z3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_less_of_int
% 0.31/0.47 thf(fact_82_ex__of__int__less,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1804426504_field @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ? [Z3: int] : ( ord_less @ A @ ( ring_1_of_int @ A @ Z3 ) @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_of_int_less
% 0.31/0.47 thf(fact_83_norm__bound__component__lt__cart,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( finite_finite @ A )
% 0.31/0.47 => ! [X: finite_Cartesian_vec @ real @ A,E: real,I2: A] :
% 0.31/0.47 ( ( ord_less @ real @ ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ real @ A ) @ X ) @ E )
% 0.31/0.47 => ( ord_less @ real @ ( abs_abs @ real @ ( finite1433825200ec_nth @ real @ A @ X @ I2 ) ) @ E ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % norm_bound_component_lt_cart
% 0.31/0.47 thf(fact_84_diff__strict__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [A2: A,B3: A,D: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ord_less @ A @ D @ C )
% 0.31/0.47 => ( ord_less @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_strict_mono
% 0.31/0.47 thf(fact_85_diff__eq__diff__less,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A,D: A] :
% 0.31/0.47 ( ( ( minus_minus @ A @ A2 @ B3 )
% 0.31/0.47 = ( minus_minus @ A @ C @ D ) )
% 0.31/0.47 => ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 = ( ord_less @ A @ C @ D ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_eq_diff_less
% 0.31/0.47 thf(fact_86_diff__strict__left__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [B3: A,A2: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.31/0.47 => ( ord_less @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_strict_left_mono
% 0.31/0.47 thf(fact_87_diff__strict__right__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ( ord_less @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B3 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_strict_right_mono
% 0.31/0.47 thf(fact_88_abs__one,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 0.31/0.47 = ( one_one @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_one
% 0.31/0.47 thf(fact_89_dist__real__def,axiom,
% 0.31/0.47 ( ( real_V2000881966t_dist @ real )
% 0.31/0.47 = ( ^ [X2: real,Y3: real] : ( abs_abs @ real @ ( minus_minus @ real @ X2 @ Y3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dist_real_def
% 0.31/0.47 thf(fact_90_Ints__1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring_1 @ A )
% 0.31/0.47 => ( member @ A @ ( one_one @ A ) @ ( ring_1_Ints @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Ints_1
% 0.31/0.47 thf(fact_91_vec_Oscale__right__diff__distrib,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( field @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ! [A2: A,X: finite_Cartesian_vec @ A @ B,Y: finite_Cartesian_vec @ A @ B] :
% 0.31/0.47 ( ( finite431509953r_mult @ A @ B @ A2 @ ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ X @ Y ) )
% 0.31/0.47 = ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ ( finite431509953r_mult @ A @ B @ A2 @ X ) @ ( finite431509953r_mult @ A @ B @ A2 @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % vec.scale_right_diff_distrib
% 0.31/0.47 thf(fact_92_Ints__eq__abs__less1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( member @ A @ X @ ( ring_1_Ints @ A ) )
% 0.31/0.47 => ( ( member @ A @ Y @ ( ring_1_Ints @ A ) )
% 0.31/0.47 => ( ( X = Y )
% 0.31/0.47 = ( ord_less @ A @ ( abs_abs @ A @ ( minus_minus @ A @ X @ Y ) ) @ ( one_one @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Ints_eq_abs_less1
% 0.31/0.47 thf(fact_93_of__int__ceiling__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( ( ring_1_of_int @ A @ ( archimedean_ceiling @ A @ X ) )
% 0.31/0.47 = X )
% 0.31/0.47 = ( ? [N3: int] :
% 0.31/0.47 ( X
% 0.31/0.47 = ( ring_1_of_int @ A @ N3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_ceiling_cancel
% 0.31/0.47 thf(fact_94_of__int__floor__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( ( ring_1_of_int @ A @ ( archim2085082626_floor @ A @ X ) )
% 0.31/0.47 = X )
% 0.31/0.47 = ( ? [N3: int] :
% 0.31/0.47 ( X
% 0.31/0.47 = ( ring_1_of_int @ A @ N3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_floor_cancel
% 0.31/0.47 thf(fact_95_real__of__int__floor__gt__diff__one,axiom,
% 0.31/0.47 ! [R: real] : ( ord_less @ real @ ( minus_minus @ real @ R @ ( one_one @ real ) ) @ ( ring_1_of_int @ real @ ( archim2085082626_floor @ real @ R ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % real_of_int_floor_gt_diff_one
% 0.31/0.47 thf(fact_96_real__abs__dist,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V2090557954_space @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( abs_abs @ real @ ( real_V2000881966t_dist @ A @ X @ Y ) )
% 0.31/0.47 = ( real_V2000881966t_dist @ A @ X @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % real_abs_dist
% 0.31/0.47 thf(fact_97_less__numeral__extra_I4_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linord1659791738miring @ A )
% 0.31/0.47 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_numeral_extra(4)
% 0.31/0.47 thf(fact_98_axis__index__axis,axiom,
% 0.31/0.47 ! [N: $tType] :
% 0.31/0.47 ( ( finite_finite @ N )
% 0.31/0.47 => ! [U: N] :
% 0.31/0.47 ( ( finite1115014511_index @ real @ N @ ( finite1218308419n_axis @ N @ real @ U @ ( one_one @ real ) ) )
% 0.31/0.47 = U ) ) ).
% 0.31/0.47
% 0.31/0.47 % axis_index_axis
% 0.31/0.47 thf(fact_99_le__ceiling__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [Z: int,X: A] :
% 0.31/0.47 ( ( ord_less_eq @ int @ Z @ ( archimedean_ceiling @ A @ X ) )
% 0.31/0.47 = ( ord_less @ A @ ( minus_minus @ A @ ( ring_1_of_int @ A @ Z ) @ ( one_one @ A ) ) @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_ceiling_iff
% 0.31/0.47 thf(fact_100_ceiling__split,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [P: int > $o,T: A] :
% 0.31/0.47 ( ( P @ ( archimedean_ceiling @ A @ T ) )
% 0.31/0.47 = ( ! [I3: int] :
% 0.31/0.47 ( ( ( ord_less @ A @ ( minus_minus @ A @ ( ring_1_of_int @ A @ I3 ) @ ( one_one @ A ) ) @ T )
% 0.31/0.47 & ( ord_less_eq @ A @ T @ ( ring_1_of_int @ A @ I3 ) ) )
% 0.31/0.47 => ( P @ I3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_split
% 0.31/0.47 thf(fact_101_ceiling__eq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A,A2: int] :
% 0.31/0.47 ( ( ( archimedean_ceiling @ A @ X )
% 0.31/0.47 = A2 )
% 0.31/0.47 = ( ( ord_less @ A @ ( minus_minus @ A @ ( ring_1_of_int @ A @ A2 ) @ ( one_one @ A ) ) @ X )
% 0.31/0.47 & ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ A2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_eq_iff
% 0.31/0.47 thf(fact_102_of__int__le__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ! [W: int,Z: int] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( ring_1_of_int @ A @ W ) @ ( ring_1_of_int @ A @ Z ) )
% 0.31/0.47 = ( ord_less_eq @ int @ W @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_le_iff
% 0.31/0.47 thf(fact_103_zle__diff1__eq,axiom,
% 0.31/0.47 ! [W: int,Z: int] :
% 0.31/0.47 ( ( ord_less_eq @ int @ W @ ( minus_minus @ int @ Z @ ( one_one @ int ) ) )
% 0.31/0.47 = ( ord_less @ int @ W @ Z ) ) ).
% 0.31/0.47
% 0.31/0.47 % zle_diff1_eq
% 0.31/0.47 thf(fact_104_of__int__le__1__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ! [Z: int] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( ring_1_of_int @ A @ Z ) @ ( one_one @ A ) )
% 0.31/0.47 = ( ord_less_eq @ int @ Z @ ( one_one @ int ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_le_1_iff
% 0.31/0.47 thf(fact_105_of__int__1__le__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ! [Z: int] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( one_one @ A ) @ ( ring_1_of_int @ A @ Z ) )
% 0.31/0.47 = ( ord_less_eq @ int @ ( one_one @ int ) @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_1_le_iff
% 0.31/0.47 thf(fact_106_one__le__floor,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( ord_less_eq @ int @ ( one_one @ int ) @ ( archim2085082626_floor @ A @ X ) )
% 0.31/0.47 = ( ord_less_eq @ A @ ( one_one @ A ) @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % one_le_floor
% 0.31/0.47 thf(fact_107_ceiling__le__one,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( ord_less_eq @ int @ ( archimedean_ceiling @ A @ X ) @ ( one_one @ int ) )
% 0.31/0.47 = ( ord_less_eq @ A @ X @ ( one_one @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_le_one
% 0.31/0.47 thf(fact_108_ceiling__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [Y: A,X: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ Y @ X )
% 0.31/0.47 => ( ord_less_eq @ int @ ( archimedean_ceiling @ A @ Y ) @ ( archimedean_ceiling @ A @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_mono
% 0.31/0.47 thf(fact_109_floor__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ( ord_less_eq @ int @ ( archim2085082626_floor @ A @ X ) @ ( archim2085082626_floor @ A @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % floor_mono
% 0.31/0.47 thf(fact_110_less__eq__real__def,axiom,
% 0.31/0.47 ( ( ord_less_eq @ real )
% 0.31/0.47 = ( ^ [X2: real,Y3: real] :
% 0.31/0.47 ( ( ord_less @ real @ X2 @ Y3 )
% 0.31/0.47 | ( X2 = Y3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_eq_real_def
% 0.31/0.47 thf(fact_111_le__numeral__extra_I4_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linord1659791738miring @ A )
% 0.31/0.47 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_numeral_extra(4)
% 0.31/0.47 thf(fact_112_less__eq__vec__def,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( ord @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ( ( ord_less_eq @ ( finite_Cartesian_vec @ A @ B ) )
% 0.31/0.47 = ( ^ [X2: finite_Cartesian_vec @ A @ B,Y3: finite_Cartesian_vec @ A @ B] :
% 0.31/0.47 ! [I3: B] : ( ord_less_eq @ A @ ( finite1433825200ec_nth @ A @ B @ X2 @ I3 ) @ ( finite1433825200ec_nth @ A @ B @ Y3 @ I3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_eq_vec_def
% 0.31/0.47 thf(fact_113_int__less__induct,axiom,
% 0.31/0.47 ! [I2: int,K: int,P: int > $o] :
% 0.31/0.47 ( ( ord_less @ int @ I2 @ K )
% 0.31/0.47 => ( ( P @ ( minus_minus @ int @ K @ ( one_one @ int ) ) )
% 0.31/0.47 => ( ! [I4: int] :
% 0.31/0.47 ( ( ord_less @ int @ I4 @ K )
% 0.31/0.47 => ( ( P @ I4 )
% 0.31/0.47 => ( P @ ( minus_minus @ int @ I4 @ ( one_one @ int ) ) ) ) )
% 0.31/0.47 => ( P @ I2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % int_less_induct
% 0.31/0.47 thf(fact_114_int__le__induct,axiom,
% 0.31/0.47 ! [I2: int,K: int,P: int > $o] :
% 0.31/0.47 ( ( ord_less_eq @ int @ I2 @ K )
% 0.31/0.47 => ( ( P @ K )
% 0.31/0.47 => ( ! [I4: int] :
% 0.31/0.47 ( ( ord_less_eq @ int @ I4 @ K )
% 0.31/0.47 => ( ( P @ I4 )
% 0.31/0.47 => ( P @ ( minus_minus @ int @ I4 @ ( one_one @ int ) ) ) ) )
% 0.31/0.47 => ( P @ I2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % int_le_induct
% 0.31/0.47 thf(fact_115_ceiling__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A,A2: int] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ A2 ) )
% 0.31/0.47 => ( ord_less_eq @ int @ ( archimedean_ceiling @ A @ X ) @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_le
% 0.31/0.47 thf(fact_116_le__floor__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [Z: int,X: A] :
% 0.31/0.47 ( ( ord_less_eq @ int @ Z @ ( archim2085082626_floor @ A @ X ) )
% 0.31/0.47 = ( ord_less_eq @ A @ ( ring_1_of_int @ A @ Z ) @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_floor_iff
% 0.31/0.47 thf(fact_117_ceiling__le__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A,Z: int] :
% 0.31/0.47 ( ( ord_less_eq @ int @ ( archimedean_ceiling @ A @ X ) @ Z )
% 0.31/0.47 = ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ Z ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_le_iff
% 0.31/0.47 thf(fact_118_diff__eq__diff__less__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A,D: A] :
% 0.31/0.47 ( ( ( minus_minus @ A @ A2 @ B3 )
% 0.31/0.47 = ( minus_minus @ A @ C @ D ) )
% 0.31/0.47 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_eq_diff_less_eq
% 0.31/0.47 thf(fact_119_diff__right__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B3 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_right_mono
% 0.31/0.47 thf(fact_120_diff__left__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [B3: A,A2: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.31/0.47 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_left_mono
% 0.31/0.47 thf(fact_121_diff__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [A2: A,B3: A,D: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ D @ C )
% 0.31/0.47 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_mono
% 0.31/0.47 thf(fact_122_abs__ge__self,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ ( abs_abs @ A @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_ge_self
% 0.31/0.47 thf(fact_123_abs__le__D1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( abs_abs @ A @ A2 ) @ B3 )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_le_D1
% 0.31/0.47 thf(fact_124_norm__vector__1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V55928688vector @ A )
% 0.31/0.47 => ( ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ A @ numeral_num1 ) )
% 0.31/0.47 = ( ^ [X2: finite_Cartesian_vec @ A @ numeral_num1] : ( real_V1127708846m_norm @ A @ ( finite1433825200ec_nth @ A @ numeral_num1 @ X2 @ ( one_one @ numeral_num1 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % norm_vector_1
% 0.31/0.47 thf(fact_125_ex__le__of__int,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1804426504_field @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ? [Z3: int] : ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ Z3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_le_of_int
% 0.31/0.47 thf(fact_126_dist__vector__1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V55928688vector @ A )
% 0.31/0.47 => ( ( real_V2000881966t_dist @ ( finite_Cartesian_vec @ A @ numeral_num1 ) )
% 0.31/0.47 = ( ^ [X2: finite_Cartesian_vec @ A @ numeral_num1,Y3: finite_Cartesian_vec @ A @ numeral_num1] : ( real_V2000881966t_dist @ A @ ( finite1433825200ec_nth @ A @ numeral_num1 @ X2 @ ( one_one @ numeral_num1 ) ) @ ( finite1433825200ec_nth @ A @ numeral_num1 @ Y3 @ ( one_one @ numeral_num1 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dist_vector_1
% 0.31/0.47 thf(fact_127_norm__real,axiom,
% 0.31/0.47 ( ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ real @ numeral_num1 ) )
% 0.31/0.47 = ( ^ [X2: finite_Cartesian_vec @ real @ numeral_num1] : ( abs_abs @ real @ ( finite1433825200ec_nth @ real @ numeral_num1 @ X2 @ ( one_one @ numeral_num1 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % norm_real
% 0.31/0.47 thf(fact_128_ceiling__diff__floor__le__1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] : ( ord_less_eq @ int @ ( minus_minus @ int @ ( archimedean_ceiling @ A @ X ) @ ( archim2085082626_floor @ A @ X ) ) @ ( one_one @ int ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_diff_floor_le_1
% 0.31/0.47 thf(fact_129_ceiling__less__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A,Z: int] :
% 0.31/0.47 ( ( ord_less @ int @ ( archimedean_ceiling @ A @ X ) @ Z )
% 0.31/0.47 = ( ord_less_eq @ A @ X @ ( minus_minus @ A @ ( ring_1_of_int @ A @ Z ) @ ( one_one @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_less_iff
% 0.31/0.47 thf(fact_130_abs__triangle__ineq2__sym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B3: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B3 ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ B3 @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_triangle_ineq2_sym
% 0.31/0.47 thf(fact_131_abs__triangle__ineq3,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B3: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B3 ) ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_triangle_ineq3
% 0.31/0.47 thf(fact_132_abs__triangle__ineq2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B3: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B3 ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_triangle_ineq2
% 0.31/0.47 thf(fact_133_norm__le__componentwise__cart,axiom,
% 0.31/0.47 ! [A: $tType,N: $tType,B: $tType] :
% 0.31/0.47 ( ( ( real_V55928688vector @ B )
% 0.31/0.47 & ( finite_finite @ N )
% 0.31/0.47 & ( real_V55928688vector @ A ) )
% 0.31/0.47 => ! [X: finite_Cartesian_vec @ A @ N,Y: finite_Cartesian_vec @ B @ N] :
% 0.31/0.47 ( ! [I4: N] : ( ord_less_eq @ real @ ( real_V1127708846m_norm @ A @ ( finite1433825200ec_nth @ A @ N @ X @ I4 ) ) @ ( real_V1127708846m_norm @ B @ ( finite1433825200ec_nth @ B @ N @ Y @ I4 ) ) )
% 0.31/0.47 => ( ord_less_eq @ real @ ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ A @ N ) @ X ) @ ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ B @ N ) @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % norm_le_componentwise_cart
% 0.31/0.47 thf(fact_134_Finite__Cartesian__Product_Onorm__nth__le,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( real_V55928688vector @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ! [X: finite_Cartesian_vec @ A @ B,I2: B] : ( ord_less_eq @ real @ ( real_V1127708846m_norm @ A @ ( finite1433825200ec_nth @ A @ B @ X @ I2 ) ) @ ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ A @ B ) @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Finite_Cartesian_Product.norm_nth_le
% 0.31/0.47 thf(fact_135_real__of__int__floor__ge__diff__one,axiom,
% 0.31/0.47 ! [R: real] : ( ord_less_eq @ real @ ( minus_minus @ real @ R @ ( one_one @ real ) ) @ ( ring_1_of_int @ real @ ( archim2085082626_floor @ real @ R ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % real_of_int_floor_ge_diff_one
% 0.31/0.47 thf(fact_136_of__int__floor__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] : ( ord_less_eq @ A @ ( ring_1_of_int @ A @ ( archim2085082626_floor @ A @ X ) ) @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_floor_le
% 0.31/0.47 thf(fact_137_le__of__int__ceiling,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] : ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ ( archimedean_ceiling @ A @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_of_int_ceiling
% 0.31/0.47 thf(fact_138_norm__bound__component__le__cart,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( finite_finite @ A )
% 0.31/0.47 => ! [X: finite_Cartesian_vec @ real @ A,E: real,I2: A] :
% 0.31/0.47 ( ( ord_less_eq @ real @ ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ real @ A ) @ X ) @ E )
% 0.31/0.47 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( finite1433825200ec_nth @ real @ A @ X @ I2 ) ) @ E ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % norm_bound_component_le_cart
% 0.31/0.47 thf(fact_139_component__le__norm__cart,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( finite_finite @ A )
% 0.31/0.47 => ! [X: finite_Cartesian_vec @ real @ A,I2: A] : ( ord_less_eq @ real @ ( abs_abs @ real @ ( finite1433825200ec_nth @ real @ A @ X @ I2 ) ) @ ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ real @ A ) @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % component_le_norm_cart
% 0.31/0.47 thf(fact_140_dist__real,axiom,
% 0.31/0.47 ( ( real_V2000881966t_dist @ ( finite_Cartesian_vec @ real @ numeral_num1 ) )
% 0.31/0.47 = ( ^ [X2: finite_Cartesian_vec @ real @ numeral_num1,Y3: finite_Cartesian_vec @ real @ numeral_num1] : ( abs_abs @ real @ ( minus_minus @ real @ ( finite1433825200ec_nth @ real @ numeral_num1 @ X2 @ ( one_one @ numeral_num1 ) ) @ ( finite1433825200ec_nth @ real @ numeral_num1 @ Y3 @ ( one_one @ numeral_num1 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dist_real
% 0.31/0.47 thf(fact_141_floor__le__ceiling,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] : ( ord_less_eq @ int @ ( archim2085082626_floor @ A @ X ) @ ( archimedean_ceiling @ A @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % floor_le_ceiling
% 0.31/0.47 thf(fact_142_of__int__ceiling__diff__one__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [R: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( ring_1_of_int @ A @ ( archimedean_ceiling @ A @ R ) ) @ ( one_one @ A ) ) @ R ) ) ).
% 0.31/0.47
% 0.31/0.47 % of_int_ceiling_diff_one_le
% 0.31/0.47 thf(fact_143_norm__triangle__ineq2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V55928688vector @ A )
% 0.31/0.47 => ! [A2: A,B3: A] : ( ord_less_eq @ real @ ( minus_minus @ real @ ( real_V1127708846m_norm @ A @ A2 ) @ ( real_V1127708846m_norm @ A @ B3 ) ) @ ( real_V1127708846m_norm @ A @ ( minus_minus @ A @ A2 @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % norm_triangle_ineq2
% 0.31/0.47 thf(fact_144_abs__dist__diff__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V2090557954_space @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A] : ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( real_V2000881966t_dist @ A @ A2 @ B3 ) @ ( real_V2000881966t_dist @ A @ B3 @ C ) ) ) @ ( real_V2000881966t_dist @ A @ A2 @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_dist_diff_le
% 0.31/0.47 thf(fact_145_metric__eq__thm,axiom,
% 0.31/0.47 ! [A5: $tType] :
% 0.31/0.47 ( ( real_V2090557954_space @ A5 )
% 0.31/0.47 => ! [X5: A5,S: set @ A5,Y4: A5] :
% 0.31/0.47 ( ( member @ A5 @ X5 @ S )
% 0.31/0.47 => ( ( member @ A5 @ Y4 @ S )
% 0.31/0.47 => ( ( X5 = Y4 )
% 0.31/0.47 = ( ! [X2: A5] :
% 0.31/0.47 ( ( member @ A5 @ X2 @ S )
% 0.31/0.47 => ( ( real_V2000881966t_dist @ A5 @ X5 @ X2 )
% 0.31/0.47 = ( real_V2000881966t_dist @ A5 @ Y4 @ X2 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % metric_eq_thm
% 0.31/0.47 thf(fact_146_dist__vec__nth__le,axiom,
% 0.31/0.47 ! [D2: $tType,C2: $tType] :
% 0.31/0.47 ( ( ( real_V2090557954_space @ C2 )
% 0.31/0.47 & ( finite_finite @ D2 ) )
% 0.31/0.47 => ! [X: finite_Cartesian_vec @ C2 @ D2,I2: D2,Y: finite_Cartesian_vec @ C2 @ D2] : ( ord_less_eq @ real @ ( real_V2000881966t_dist @ C2 @ ( finite1433825200ec_nth @ C2 @ D2 @ X @ I2 ) @ ( finite1433825200ec_nth @ C2 @ D2 @ Y @ I2 ) ) @ ( real_V2000881966t_dist @ ( finite_Cartesian_vec @ C2 @ D2 ) @ X @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dist_vec_nth_le
% 0.31/0.47 thf(fact_147_norm__triangle__ineq3,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( real_V55928688vector @ A )
% 0.31/0.47 => ! [A2: A,B3: A] : ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( real_V1127708846m_norm @ A @ A2 ) @ ( real_V1127708846m_norm @ A @ B3 ) ) ) @ ( real_V1127708846m_norm @ A @ ( minus_minus @ A @ A2 @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % norm_triangle_ineq3
% 0.31/0.47 thf(fact_148_ceiling__correct,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( ord_less @ A @ ( minus_minus @ A @ ( ring_1_of_int @ A @ ( archimedean_ceiling @ A @ X ) ) @ ( one_one @ A ) ) @ X )
% 0.31/0.47 & ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ ( archimedean_ceiling @ A @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_correct
% 0.31/0.47 thf(fact_149_ceiling__unique,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( archim1727834104eiling @ A )
% 0.31/0.47 => ! [Z: int,X: A] :
% 0.31/0.47 ( ( ord_less @ A @ ( minus_minus @ A @ ( ring_1_of_int @ A @ Z ) @ ( one_one @ A ) ) @ X )
% 0.31/0.47 => ( ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ Z ) )
% 0.31/0.47 => ( ( archimedean_ceiling @ A @ X )
% 0.31/0.47 = Z ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ceiling_unique
% 0.31/0.47 thf(fact_150_order__refl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_refl
% 0.31/0.47 thf(fact_151_complete__interval,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( condit1037483654norder @ A )
% 0.31/0.47 => ! [A2: A,B3: A,P: A > $o] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( P @ A2 )
% 0.31/0.47 => ( ~ ( P @ B3 )
% 0.31/0.47 => ? [C3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ C3 )
% 0.31/0.47 & ( ord_less_eq @ A @ C3 @ B3 )
% 0.31/0.47 & ! [X6: A] :
% 0.31/0.47 ( ( ( ord_less_eq @ A @ A2 @ X6 )
% 0.31/0.47 & ( ord_less @ A @ X6 @ C3 ) )
% 0.31/0.47 => ( P @ X6 ) )
% 0.31/0.47 & ! [D3: A] :
% 0.31/0.47 ( ! [X4: A] :
% 0.31/0.47 ( ( ( ord_less_eq @ A @ A2 @ X4 )
% 0.31/0.47 & ( ord_less @ A @ X4 @ D3 ) )
% 0.31/0.47 => ( P @ X4 ) )
% 0.31/0.47 => ( ord_less_eq @ A @ D3 @ C3 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % complete_interval
% 0.31/0.47 thf(fact_152_eucl__less__le__not__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere890947078_space @ A )
% 0.31/0.47 => ( ( ord_less @ A )
% 0.31/0.47 = ( ^ [X2: A,Y3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/0.47 & ~ ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eucl_less_le_not_le
% 0.31/0.47 thf(fact_153_order_Onot__eq__order__implies__strict,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B3: A] :
% 0.31/0.47 ( ( A2 != B3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 => ( ord_less @ A @ A2 @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.not_eq_order_implies_strict
% 0.31/0.47 thf(fact_154_dual__order_Ostrict__implies__order,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B3: A,A2: A] :
% 0.31/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.31/0.47 => ( ord_less_eq @ A @ B3 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_implies_order
% 0.31/0.47 thf(fact_155_vector__one__nth,axiom,
% 0.31/0.47 ! [A: $tType,X: finite_Cartesian_vec @ A @ numeral_num1] :
% 0.31/0.47 ( ( finite_Cartesian_vec2 @ A @ numeral_num1 @ ( finite1433825200ec_nth @ A @ numeral_num1 @ X @ ( one_one @ numeral_num1 ) ) )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 % vector_one_nth
% 0.31/0.47 thf(fact_156_less__vec__def,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ( ord @ A )
% 0.31/0.47 & ( finite_finite @ B ) )
% 0.31/0.47 => ( ( ord_less @ ( finite_Cartesian_vec @ A @ B ) )
% 0.31/0.47 = ( ^ [X2: finite_Cartesian_vec @ A @ B,Y3: finite_Cartesian_vec @ A @ B] :
% 0.31/0.47 ( ( ord_less_eq @ ( finite_Cartesian_vec @ A @ B ) @ X2 @ Y3 )
% 0.31/0.47 & ~ ( ord_less_eq @ ( finite_Cartesian_vec @ A @ B ) @ Y3 @ X2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_vec_def
% 0.31/0.47 thf(fact_157_complete__real,axiom,
% 0.31/0.47 ! [S2: set @ real] :
% 0.31/0.47 ( ? [X6: real] : ( member @ real @ X6 @ S2 )
% 0.31/0.47 => ( ? [Z4: real] :
% 0.31/0.47 ! [X4: real] :
% 0.31/0.47 ( ( member @ real @ X4 @ S2 )
% 0.31/0.47 => ( ord_less_eq @ real @ X4 @ Z4 ) )
% 0.31/0.47 => ? [Y5: real] :
% 0.31/0.47 ( ! [X6: real] :
% 0.31/0.47 ( ( member @ real @ X6 @ S2 )
% 0.31/0.47 => ( ord_less_eq @ real @ X6 @ Y5 ) )
% 0.31/0.47 & ! [Z4: real] :
% 0.31/0.47 ( ! [X4: real] :
% 0.31/0.47 ( ( member @ real @ X4 @ S2 )
% 0.31/0.47 => ( ord_less_eq @ real @ X4 @ Z4 ) )
% 0.31/0.47 => ( ord_less_eq @ real @ Y5 @ Z4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % complete_real
% 0.31/0.47 thf(fact_158_dual__order_Oantisym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B3: A,A2: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 => ( A2 = B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.antisym
% 0.31/0.47 thf(fact_159_dual__order_Oeq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 0.31/0.47 = ( ^ [A6: A,B4: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B4 @ A6 )
% 0.31/0.47 & ( ord_less_eq @ A @ A6 @ B4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.eq_iff
% 0.31/0.47 thf(fact_160_dual__order_Otrans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B3: A,A2: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.31/0.47 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.trans
% 0.31/0.47 thf(fact_161_linorder__wlog,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [P: A > A > $o,A2: A,B3: A] :
% 0.31/0.47 ( ! [A7: A,B5: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A7 @ B5 )
% 0.31/0.47 => ( P @ A7 @ B5 ) )
% 0.31/0.47 => ( ! [A7: A,B5: A] :
% 0.31/0.47 ( ( P @ B5 @ A7 )
% 0.31/0.47 => ( P @ A7 @ B5 ) )
% 0.31/0.47 => ( P @ A2 @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_wlog
% 0.31/0.47 thf(fact_162_dual__order_Orefl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.refl
% 0.31/0.47 thf(fact_163_order__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A,Y: A,Z: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.31/0.47 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_trans
% 0.31/0.47 thf(fact_164_order__class_Oorder_Oantisym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.31/0.47 => ( A2 = B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_class.order.antisym
% 0.31/0.47 thf(fact_165_ord__le__eq__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( B3 = C )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_le_eq_trans
% 0.31/0.47 thf(fact_166_ord__eq__le__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A] :
% 0.31/0.47 ( ( A2 = B3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_le_trans
% 0.31/0.47 thf(fact_167_order__class_Oorder_Oeq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 0.31/0.47 = ( ^ [A6: A,B4: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A6 @ B4 )
% 0.31/0.47 & ( ord_less_eq @ A @ B4 @ A6 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_class.order.eq_iff
% 0.31/0.47 thf(fact_168_antisym__conv,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [Y: A,X: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ Y @ X )
% 0.31/0.47 => ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 = ( X = Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym_conv
% 0.31/0.47 thf(fact_169_le__cases3,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A,Z: A] :
% 0.31/0.47 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.31/0.47 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 0.31/0.47 => ( ( ( ord_less_eq @ A @ X @ Z )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.31/0.47 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.31/0.47 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 0.31/0.47 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_cases3
% 0.31/0.47 thf(fact_170_order_Otrans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.trans
% 0.31/0.47 thf(fact_171_le__cases,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_cases
% 0.31/0.47 thf(fact_172_eq__refl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( X = Y )
% 0.31/0.47 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_refl
% 0.31/0.47 thf(fact_173_linear,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linear
% 0.31/0.47 thf(fact_174_antisym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ( ( ord_less_eq @ A @ Y @ X )
% 0.31/0.47 => ( X = Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym
% 0.31/0.47 thf(fact_175_eq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 0.31/0.47 = ( ^ [X2: A,Y3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/0.47 & ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_iff
% 0.31/0.47 thf(fact_176_ord__le__eq__subst,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( ( ord @ B )
% 0.31/0.47 & ( ord @ A ) )
% 0.31/0.47 => ! [A2: A,B3: A,F: A > B,C: B] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ( F @ B3 )
% 0.31/0.47 = C )
% 0.31/0.47 => ( ! [X4: A,Y5: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.31/0.47 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_le_eq_subst
% 0.31/0.47 thf(fact_177_ord__eq__le__subst,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( ( ord @ B )
% 0.31/0.47 & ( ord @ A ) )
% 0.31/0.47 => ! [A2: A,F: B > A,B3: B,C: B] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( F @ B3 ) )
% 0.31/0.47 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.31/0.47 => ( ! [X4: B,Y5: B] :
% 0.31/0.47 ( ( ord_less_eq @ B @ X4 @ Y5 )
% 0.31/0.47 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_le_subst
% 0.31/0.47 thf(fact_178_order__subst2,axiom,
% 0.31/0.47 ! [A: $tType,C2: $tType] :
% 0.31/0.47 ( ( ( order @ C2 )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,B3: A,F: A > C2,C: C2] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ord_less_eq @ C2 @ ( F @ B3 ) @ C )
% 0.31/0.47 => ( ! [X4: A,Y5: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.31/0.47 => ( ord_less_eq @ C2 @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_subst2
% 0.31/0.47 thf(fact_179_order__subst1,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( ( order @ B )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,F: B > A,B3: B,C: B] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 0.31/0.47 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.31/0.47 => ( ! [X4: B,Y5: B] :
% 0.31/0.47 ( ( ord_less_eq @ B @ X4 @ Y5 )
% 0.31/0.47 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_subst1
% 0.31/0.47 thf(fact_180_le__fun__def,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B )
% 0.31/0.47 => ( ( ord_less_eq @ ( A > B ) )
% 0.31/0.47 = ( ^ [F2: A > B,G2: A > B] :
% 0.31/0.47 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_fun_def
% 0.31/0.47 thf(fact_181_le__funI,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B )
% 0.31/0.47 => ! [F: A > B,G: A > B] :
% 0.31/0.47 ( ! [X4: A] : ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.31/0.47 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_funI
% 0.31/0.47 thf(fact_182_le__funE,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B )
% 0.31/0.47 => ! [F: A > B,G: A > B,X: A] :
% 0.31/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.31/0.47 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_funE
% 0.31/0.47 thf(fact_183_le__funD,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B )
% 0.31/0.47 => ! [F: A > B,G: A > B,X: A] :
% 0.31/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.31/0.47 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_funD
% 0.31/0.47 thf(fact_184_ex__gt__or__lt,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( condit1656338222tinuum @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ? [B5: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B5 )
% 0.31/0.47 | ( ord_less @ A @ B5 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_gt_or_lt
% 0.31/0.47 thf(fact_185_dual__order_Ostrict__implies__not__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B3: A,A2: A] :
% 0.31/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.31/0.47 => ( A2 != B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_implies_not_eq
% 0.31/0.47 thf(fact_186_order_Ostrict__implies__not__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B3: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ( A2 != B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_implies_not_eq
% 0.31/0.47 thf(fact_187_not__less__iff__gr__or__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.31/0.47 = ( ( ord_less @ A @ Y @ X )
% 0.31/0.47 | ( X = Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_less_iff_gr_or_eq
% 0.31/0.47 thf(fact_188_dual__order_Ostrict__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B3: A,A2: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.31/0.47 => ( ( ord_less @ A @ C @ B3 )
% 0.31/0.47 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_trans
% 0.31/0.47 thf(fact_189_linorder__less__wlog,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [P: A > A > $o,A2: A,B3: A] :
% 0.31/0.47 ( ! [A7: A,B5: A] :
% 0.31/0.47 ( ( ord_less @ A @ A7 @ B5 )
% 0.31/0.47 => ( P @ A7 @ B5 ) )
% 0.31/0.47 => ( ! [A7: A] : ( P @ A7 @ A7 )
% 0.31/0.47 => ( ! [A7: A,B5: A] :
% 0.31/0.47 ( ( P @ B5 @ A7 )
% 0.31/0.47 => ( P @ A7 @ B5 ) )
% 0.31/0.47 => ( P @ A2 @ B3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_less_wlog
% 0.31/0.47 thf(fact_190_exists__least__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( wellorder @ A )
% 0.31/0.47 => ( ( ^ [P2: A > $o] :
% 0.31/0.47 ? [X3: A] : ( P2 @ X3 ) )
% 0.31/0.47 = ( ^ [P3: A > $o] :
% 0.31/0.47 ? [N3: A] :
% 0.31/0.47 ( ( P3 @ N3 )
% 0.31/0.47 & ! [M3: A] :
% 0.31/0.47 ( ( ord_less @ A @ M3 @ N3 )
% 0.31/0.47 => ~ ( P3 @ M3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % exists_least_iff
% 0.31/0.47 thf(fact_191_less__imp__not__less,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_not_less
% 0.31/0.47 thf(fact_192_order_Ostrict__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ord_less @ A @ B3 @ C )
% 0.31/0.47 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_trans
% 0.31/0.47 thf(fact_193_dual__order_Oirrefl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.irrefl
% 0.31/0.47 thf(fact_194_linorder__cases,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ~ ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( ( X != Y )
% 0.31/0.47 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_cases
% 0.31/0.47 thf(fact_195_less__imp__triv,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A,Y: A,P: $o] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( ( ord_less @ A @ Y @ X )
% 0.31/0.47 => P ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_triv
% 0.31/0.47 thf(fact_196_less__imp__not__eq2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( Y != X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_not_eq2
% 0.31/0.47 thf(fact_197_antisym__conv3,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [Y: A,X: A] :
% 0.31/0.47 ( ~ ( ord_less @ A @ Y @ X )
% 0.31/0.47 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.31/0.47 = ( X = Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym_conv3
% 0.31/0.47 thf(fact_198_less__induct,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( wellorder @ A )
% 0.31/0.47 => ! [P: A > $o,A2: A] :
% 0.31/0.47 ( ! [X4: A] :
% 0.31/0.47 ( ! [Y6: A] :
% 0.31/0.47 ( ( ord_less @ A @ Y6 @ X4 )
% 0.31/0.47 => ( P @ Y6 ) )
% 0.31/0.47 => ( P @ X4 ) )
% 0.31/0.47 => ( P @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_induct
% 0.31/0.47 thf(fact_199_less__not__sym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_not_sym
% 0.31/0.47 thf(fact_200_less__imp__not__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( X != Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_not_eq
% 0.31/0.47 thf(fact_201_dual__order_Oasym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B3: A,A2: A] :
% 0.31/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.31/0.47 => ~ ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.asym
% 0.31/0.47 thf(fact_202_ord__less__eq__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( B3 = C )
% 0.31/0.47 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_less_eq_trans
% 0.31/0.47 thf(fact_203_ord__eq__less__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A] :
% 0.31/0.47 ( ( A2 = B3 )
% 0.31/0.47 => ( ( ord_less @ A @ B3 @ C )
% 0.31/0.47 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_less_trans
% 0.31/0.47 thf(fact_204_less__irrefl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_irrefl
% 0.31/0.47 thf(fact_205_less__linear,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 | ( X = Y )
% 0.31/0.47 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_linear
% 0.31/0.47 thf(fact_206_less__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A,Y: A,Z: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( ( ord_less @ A @ Y @ Z )
% 0.31/0.47 => ( ord_less @ A @ X @ Z ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_trans
% 0.31/0.47 thf(fact_207_less__asym_H,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [A2: A,B3: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_asym'
% 0.31/0.47 thf(fact_208_less__asym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_asym
% 0.31/0.47 thf(fact_209_less__imp__neq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( X != Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_neq
% 0.31/0.47 thf(fact_210_dense,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( dense_order @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ? [Z3: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Z3 )
% 0.31/0.47 & ( ord_less @ A @ Z3 @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dense
% 0.31/0.47 thf(fact_211_order_Oasym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B3: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.asym
% 0.31/0.47 thf(fact_212_neq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( X != Y )
% 0.31/0.47 = ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_iff
% 0.31/0.47 thf(fact_213_neqE,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( X != Y )
% 0.31/0.47 => ( ~ ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neqE
% 0.31/0.47 thf(fact_214_gt__ex,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( no_top @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ? [X_1: A] : ( ord_less @ A @ X @ X_1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % gt_ex
% 0.31/0.47 thf(fact_215_lt__ex,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( no_bot @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ? [Y5: A] : ( ord_less @ A @ Y5 @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % lt_ex
% 0.31/0.47 thf(fact_216_order__less__subst2,axiom,
% 0.31/0.47 ! [A: $tType,C2: $tType] :
% 0.31/0.47 ( ( ( order @ C2 )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,B3: A,F: A > C2,C: C2] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ord_less @ C2 @ ( F @ B3 ) @ C )
% 0.31/0.47 => ( ! [X4: A,Y5: A] :
% 0.31/0.47 ( ( ord_less @ A @ X4 @ Y5 )
% 0.31/0.47 => ( ord_less @ C2 @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_less_subst2
% 0.31/0.47 thf(fact_217_order__less__subst1,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( ( order @ B )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,F: B > A,B3: B,C: B] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ ( F @ B3 ) )
% 0.31/0.47 => ( ( ord_less @ B @ B3 @ C )
% 0.31/0.47 => ( ! [X4: B,Y5: B] :
% 0.31/0.47 ( ( ord_less @ B @ X4 @ Y5 )
% 0.31/0.47 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_less_subst1
% 0.31/0.47 thf(fact_218_ord__less__eq__subst,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( ( ord @ B )
% 0.31/0.47 & ( ord @ A ) )
% 0.31/0.47 => ! [A2: A,B3: A,F: A > B,C: B] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ( F @ B3 )
% 0.31/0.47 = C )
% 0.31/0.47 => ( ! [X4: A,Y5: A] :
% 0.31/0.47 ( ( ord_less @ A @ X4 @ Y5 )
% 0.31/0.47 => ( ord_less @ B @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_less_eq_subst
% 0.31/0.47 thf(fact_219_ord__eq__less__subst,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( ( ord @ B )
% 0.31/0.47 & ( ord @ A ) )
% 0.31/0.47 => ! [A2: A,F: B > A,B3: B,C: B] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( F @ B3 ) )
% 0.31/0.47 => ( ( ord_less @ B @ B3 @ C )
% 0.31/0.47 => ( ! [X4: B,Y5: B] :
% 0.31/0.47 ( ( ord_less @ B @ X4 @ Y5 )
% 0.31/0.47 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_less_subst
% 0.31/0.47 thf(fact_220_leD,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [Y: A,X: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ Y @ X )
% 0.31/0.47 => ~ ( ord_less @ A @ X @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % leD
% 0.31/0.47 thf(fact_221_leI,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ~ ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % leI
% 0.31/0.47 thf(fact_222_le__less,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ord_less_eq @ A )
% 0.31/0.47 = ( ^ [X2: A,Y3: A] :
% 0.31/0.47 ( ( ord_less @ A @ X2 @ Y3 )
% 0.31/0.47 | ( X2 = Y3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_less
% 0.31/0.47 thf(fact_223_less__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ord_less @ A )
% 0.31/0.47 = ( ^ [X2: A,Y3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/0.47 & ( X2 != Y3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_le
% 0.31/0.47 thf(fact_224_order__le__less__subst1,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( ( order @ B )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,F: B > A,B3: B,C: B] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 0.31/0.47 => ( ( ord_less @ B @ B3 @ C )
% 0.31/0.47 => ( ! [X4: B,Y5: B] :
% 0.31/0.47 ( ( ord_less @ B @ X4 @ Y5 )
% 0.31/0.47 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_le_less_subst1
% 0.31/0.47 thf(fact_225_order__le__less__subst2,axiom,
% 0.31/0.47 ! [A: $tType,C2: $tType] :
% 0.31/0.47 ( ( ( order @ C2 )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,B3: A,F: A > C2,C: C2] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ord_less @ C2 @ ( F @ B3 ) @ C )
% 0.31/0.47 => ( ! [X4: A,Y5: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.31/0.47 => ( ord_less_eq @ C2 @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_le_less_subst2
% 0.31/0.47 thf(fact_226_order__less__le__subst1,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( ( order @ B )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,F: B > A,B3: B,C: B] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ ( F @ B3 ) )
% 0.31/0.47 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.31/0.47 => ( ! [X4: B,Y5: B] :
% 0.31/0.47 ( ( ord_less_eq @ B @ X4 @ Y5 )
% 0.31/0.47 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_less_le_subst1
% 0.31/0.47 thf(fact_227_order__less__le__subst2,axiom,
% 0.31/0.47 ! [A: $tType,C2: $tType] :
% 0.31/0.47 ( ( ( order @ C2 )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,B3: A,F: A > C2,C: C2] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ord_less_eq @ C2 @ ( F @ B3 ) @ C )
% 0.31/0.47 => ( ! [X4: A,Y5: A] :
% 0.31/0.47 ( ( ord_less @ A @ X4 @ Y5 )
% 0.31/0.47 => ( ord_less @ C2 @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_less_le_subst2
% 0.31/0.47 thf(fact_228_not__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ~ ( ord_less_eq @ A @ X @ Y ) )
% 0.31/0.47 = ( ord_less @ A @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_le
% 0.31/0.47 thf(fact_229_not__less,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.31/0.47 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_less
% 0.31/0.47 thf(fact_230_le__neq__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( A2 != B3 )
% 0.31/0.47 => ( ord_less @ A @ A2 @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_neq_trans
% 0.31/0.47 thf(fact_231_antisym__conv1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ~ ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 = ( X = Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym_conv1
% 0.31/0.47 thf(fact_232_antisym__conv2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.31/0.47 = ( X = Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym_conv2
% 0.31/0.47 thf(fact_233_less__imp__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_le
% 0.31/0.47 thf(fact_234_le__less__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A,Y: A,Z: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ( ( ord_less @ A @ Y @ Z )
% 0.31/0.47 => ( ord_less @ A @ X @ Z ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_less_trans
% 0.31/0.47 thf(fact_235_less__le__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A,Y: A,Z: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.31/0.47 => ( ord_less @ A @ X @ Z ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_le_trans
% 0.31/0.47 thf(fact_236_dense__ge,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( dense_linorder @ A )
% 0.31/0.47 => ! [Z: A,Y: A] :
% 0.31/0.47 ( ! [X4: A] :
% 0.31/0.47 ( ( ord_less @ A @ Z @ X4 )
% 0.31/0.47 => ( ord_less_eq @ A @ Y @ X4 ) )
% 0.31/0.47 => ( ord_less_eq @ A @ Y @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dense_ge
% 0.31/0.47 thf(fact_237_dense__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( dense_linorder @ A )
% 0.31/0.47 => ! [Y: A,Z: A] :
% 0.31/0.47 ( ! [X4: A] :
% 0.31/0.47 ( ( ord_less @ A @ X4 @ Y )
% 0.31/0.47 => ( ord_less_eq @ A @ X4 @ Z ) )
% 0.31/0.47 => ( ord_less_eq @ A @ Y @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dense_le
% 0.31/0.47 thf(fact_238_le__less__linear,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_less_linear
% 0.31/0.47 thf(fact_239_le__imp__less__or__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 | ( X = Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_imp_less_or_eq
% 0.31/0.47 thf(fact_240_less__le__not__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ( ( ord_less @ A )
% 0.31/0.47 = ( ^ [X2: A,Y3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/0.47 & ~ ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_le_not_le
% 0.31/0.47 thf(fact_241_not__le__imp__less,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [Y: A,X: A] :
% 0.31/0.47 ( ~ ( ord_less_eq @ A @ Y @ X )
% 0.31/0.47 => ( ord_less @ A @ X @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_le_imp_less
% 0.31/0.47 thf(fact_242_order_Ostrict__trans1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ord_less @ A @ B3 @ C )
% 0.31/0.47 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_trans1
% 0.31/0.47 thf(fact_243_order_Ostrict__trans2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B3: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.31/0.47 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_trans2
% 0.31/0.47 thf(fact_244_order_Oorder__iff__strict,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ord_less_eq @ A )
% 0.31/0.47 = ( ^ [A6: A,B4: A] :
% 0.31/0.47 ( ( ord_less @ A @ A6 @ B4 )
% 0.31/0.47 | ( A6 = B4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.order_iff_strict
% 0.31/0.47 thf(fact_245_order_Ostrict__iff__order,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ord_less @ A )
% 0.31/0.47 = ( ^ [A6: A,B4: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A6 @ B4 )
% 0.31/0.47 & ( A6 != B4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_iff_order
% 0.31/0.47 thf(fact_246_dual__order_Ostrict__trans1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B3: A,A2: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.31/0.47 => ( ( ord_less @ A @ C @ B3 )
% 0.31/0.47 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_trans1
% 0.31/0.47 thf(fact_247_dual__order_Ostrict__trans2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B3: A,A2: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.31/0.47 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_trans2
% 0.31/0.47 thf(fact_248_dense__ge__bounded,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( dense_linorder @ A )
% 0.31/0.47 => ! [Z: A,X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ A @ Z @ X )
% 0.31/0.47 => ( ! [W2: A] :
% 0.31/0.47 ( ( ord_less @ A @ Z @ W2 )
% 0.31/0.47 => ( ( ord_less @ A @ W2 @ X )
% 0.31/0.47 => ( ord_less_eq @ A @ Y @ W2 ) ) )
% 0.31/0.47 => ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dense_ge_bounded
% 0.31/0.47 thf(fact_249_dense__le__bounded,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( dense_linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A,Z: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( ! [W2: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ W2 )
% 0.31/0.47 => ( ( ord_less @ A @ W2 @ Y )
% 0.31/0.47 => ( ord_less_eq @ A @ W2 @ Z ) ) )
% 0.31/0.47 => ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dense_le_bounded
% 0.31/0.47 thf(fact_250_order_Ostrict__implies__order,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B3: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_implies_order
% 0.31/0.47 thf(fact_251_dual__order_Oorder__iff__strict,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ord_less_eq @ A )
% 0.31/0.47 = ( ^ [B4: A,A6: A] :
% 0.31/0.47 ( ( ord_less @ A @ B4 @ A6 )
% 0.31/0.47 | ( A6 = B4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.order_iff_strict
% 0.31/0.47 thf(fact_252_dual__order_Ostrict__iff__order,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ord_less @ A )
% 0.31/0.47 = ( ^ [B4: A,A6: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B4 @ A6 )
% 0.31/0.47 & ( A6 != B4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_iff_order
% 0.31/0.47 thf(fact_253_forall__1,axiom,
% 0.31/0.47 ( ( ^ [P2: numeral_num1 > $o] :
% 0.31/0.47 ! [X3: numeral_num1] : ( P2 @ X3 ) )
% 0.31/0.47 = ( ^ [P3: numeral_num1 > $o] : ( P3 @ ( one_one @ numeral_num1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % forall_1
% 0.31/0.47 thf(fact_254_ex__1,axiom,
% 0.31/0.47 ( ( ^ [P2: numeral_num1 > $o] :
% 0.31/0.47 ? [X3: numeral_num1] : ( P2 @ X3 ) )
% 0.31/0.47 = ( ^ [P3: numeral_num1 > $o] : ( P3 @ ( one_one @ numeral_num1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_1
% 0.31/0.47
% 0.31/0.47 % Subclasses (1)
% 0.31/0.47 thf(subcl_Finite__Set_Ofinite___HOL_Otype,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( finite_finite @ A )
% 0.31/0.47 => ( type @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % Type constructors (106)
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Cardinality_OCARD__1,axiom,
% 0.31/0.47 cARD_1 @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( preorder @ A8 )
% 0.31/0.47 => ( preorder @ ( A5 > A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( finite_finite @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( finite_finite @ ( A5 > A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( order @ A8 )
% 0.31/0.47 => ( order @ ( A5 > A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ord @ A8 )
% 0.31/0.47 => ( ord @ ( A5 > A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Groups_Ominus,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( minus @ A8 )
% 0.31/0.47 => ( minus @ ( A5 > A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.31/0.47 condit1037483654norder @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Rings_Olinordered__nonzero__semiring,axiom,
% 0.31/0.47 linord1659791738miring @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add__abs,axiom,
% 0.31/0.47 ordere142940540dd_abs @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.31/0.47 cancel146912293up_add @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add,axiom,
% 0.31/0.47 ordered_ab_group_add @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Rings_Olinordered__idom,axiom,
% 0.31/0.47 linordered_idom @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Rings_Oidom__abs__sgn,axiom,
% 0.31/0.47 idom_abs_sgn @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Orderings_Opreorder_1,axiom,
% 0.31/0.47 preorder @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Orderings_Olinorder,axiom,
% 0.31/0.47 linorder @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Groups_Omonoid__mult,axiom,
% 0.31/0.47 monoid_mult @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Orderings_Ono__top,axiom,
% 0.31/0.47 no_top @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Orderings_Ono__bot,axiom,
% 0.31/0.47 no_bot @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Groups_Ogroup__add,axiom,
% 0.31/0.47 group_add @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Orderings_Oorder_2,axiom,
% 0.31/0.47 order @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Nat_Oring__char__0,axiom,
% 0.31/0.47 ring_char_0 @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Orderings_Oord_3,axiom,
% 0.31/0.47 ord @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Rings_Oring__1,axiom,
% 0.31/0.47 ring_1 @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Groups_Ominus_4,axiom,
% 0.31/0.47 minus @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Groups_Ozero,axiom,
% 0.31/0.47 zero @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Rings_Oring,axiom,
% 0.31/0.47 ring @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Int_Oint___Groups_Oone,axiom,
% 0.31/0.47 one @ int ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 0.31/0.47 ! [A5: $tType] : ( preorder @ ( set @ A5 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Groups_Omonoid__mult_6,axiom,
% 0.31/0.47 ! [A5: $tType] :
% 0.31/0.47 ( ( monoid_mult @ A5 )
% 0.31/0.47 => ( monoid_mult @ ( set @ A5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Finite__Set_Ofinite_7,axiom,
% 0.31/0.47 ! [A5: $tType] :
% 0.31/0.47 ( ( finite_finite @ A5 )
% 0.31/0.47 => ( finite_finite @ ( set @ A5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Oorder_8,axiom,
% 0.31/0.47 ! [A5: $tType] : ( order @ ( set @ A5 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Oord_9,axiom,
% 0.31/0.47 ! [A5: $tType] : ( ord @ ( set @ A5 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Groups_Ominus_10,axiom,
% 0.31/0.47 ! [A5: $tType] : ( minus @ ( set @ A5 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Groups_Ozero_11,axiom,
% 0.31/0.47 ! [A5: $tType] :
% 0.31/0.47 ( ( zero @ A5 )
% 0.31/0.47 => ( zero @ ( set @ A5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Groups_Oone_12,axiom,
% 0.31/0.47 ! [A5: $tType] :
% 0.31/0.47 ( ( one @ A5 )
% 0.31/0.47 => ( one @ ( set @ A5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_13,axiom,
% 0.31/0.47 preorder @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_14,axiom,
% 0.31/0.47 linorder @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Finite__Set_Ofinite_15,axiom,
% 0.31/0.47 finite_finite @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_16,axiom,
% 0.31/0.47 order @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Oord_17,axiom,
% 0.31/0.47 ord @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Groups_Ominus_18,axiom,
% 0.31/0.47 minus @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_19,axiom,
% 0.31/0.47 condit1037483654norder @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Olinear__continuum,axiom,
% 0.31/0.47 condit1656338222tinuum @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space,axiom,
% 0.31/0.47 ordere890947078_space @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__algebra__1,axiom,
% 0.31/0.47 real_V1229719638ebra_1 @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector,axiom,
% 0.31/0.47 real_V55928688vector @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Archimedean__Field_Oarchimedean__field,axiom,
% 0.31/0.47 archim1804426504_field @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_20,axiom,
% 0.31/0.47 linord1659791738miring @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space,axiom,
% 0.31/0.47 real_V2090557954_space @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs_21,axiom,
% 0.31/0.47 ordere142940540dd_abs @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Archimedean__Field_Ofloor__ceiling,axiom,
% 0.31/0.47 archim1727834104eiling @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_22,axiom,
% 0.31/0.47 cancel146912293up_add @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Real__Vector__Spaces_Odist__norm,axiom,
% 0.31/0.47 real_V1639655670t_norm @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add_23,axiom,
% 0.31/0.47 ordered_ab_group_add @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Orderings_Odense__linorder,axiom,
% 0.31/0.47 dense_linorder @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__idom_24,axiom,
% 0.31/0.47 linordered_idom @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Orderings_Odense__order,axiom,
% 0.31/0.47 dense_order @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Rings_Oidom__abs__sgn_25,axiom,
% 0.31/0.47 idom_abs_sgn @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Orderings_Opreorder_26,axiom,
% 0.31/0.47 preorder @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Orderings_Olinorder_27,axiom,
% 0.31/0.47 linorder @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Omonoid__mult_28,axiom,
% 0.31/0.47 monoid_mult @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Orderings_Ono__top_29,axiom,
% 0.31/0.47 no_top @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Orderings_Ono__bot_30,axiom,
% 0.31/0.47 no_bot @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Ogroup__add_31,axiom,
% 0.31/0.47 group_add @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Orderings_Oorder_32,axiom,
% 0.31/0.47 order @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Nat_Oring__char__0_33,axiom,
% 0.31/0.47 ring_char_0 @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Orderings_Oord_34,axiom,
% 0.31/0.47 ord @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Rings_Oring__1_35,axiom,
% 0.31/0.47 ring_1 @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Ominus_36,axiom,
% 0.31/0.47 minus @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Fields_Ofield,axiom,
% 0.31/0.47 field @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Ozero_37,axiom,
% 0.31/0.47 zero @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Rings_Oring_38,axiom,
% 0.31/0.47 ring @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Oone_39,axiom,
% 0.31/0.47 one @ real ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Groups_Ocancel__ab__semigroup__add_40,axiom,
% 0.31/0.47 cancel146912293up_add @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Orderings_Owellorder,axiom,
% 0.31/0.47 wellorder @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Orderings_Opreorder_41,axiom,
% 0.31/0.47 preorder @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Orderings_Olinorder_42,axiom,
% 0.31/0.47 linorder @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Groups_Omonoid__mult_43,axiom,
% 0.31/0.47 monoid_mult @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Finite__Set_Ofinite_44,axiom,
% 0.31/0.47 finite_finite @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Groups_Ogroup__add_45,axiom,
% 0.31/0.47 group_add @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Orderings_Oorder_46,axiom,
% 0.31/0.47 order @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Orderings_Oord_47,axiom,
% 0.31/0.47 ord @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Groups_Ominus_48,axiom,
% 0.31/0.47 minus @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Groups_Ozero_49,axiom,
% 0.31/0.47 zero @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Rings_Oring_50,axiom,
% 0.31/0.47 ring @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Numeral__Type_Onum1___Groups_Oone_51,axiom,
% 0.31/0.47 one @ numeral_num1 ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space_52,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( ordere890947078_space @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( ordere890947078_space @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_53,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( real_V55928688vector @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( real_V55928688vector @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Ometric__space_54,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( real_V2090557954_space @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( real_V2090557954_space @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add__abs_55,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( ordere890947078_space @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( ordere142940540dd_abs @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__ab__semigroup__add_56,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( cancel146912293up_add @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( cancel146912293up_add @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Odist__norm_57,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( real_V55928688vector @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( real_V1639655670t_norm @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add_58,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( ordere890947078_space @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( ordered_ab_group_add @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Opreorder_59,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( order @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( preorder @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Olinorder_60,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( linorder @ A5 )
% 0.31/0.47 & ( cARD_1 @ A8 ) )
% 0.31/0.47 => ( linorder @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Omonoid__mult_61,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( monoid_mult @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( monoid_mult @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_62,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( finite_finite @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( finite_finite @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ogroup__add_63,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( group_add @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( group_add @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oorder_64,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( order @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( order @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Nat_Oring__char__0_65,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( ring_char_0 @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( ring_char_0 @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oord_66,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( ord @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( ord @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Rings_Oring__1_67,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( ring_1 @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( ring_1 @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ominus_68,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( minus @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( minus @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ozero_69,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( zero @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( zero @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Rings_Oring_70,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( ring @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( ring @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oone_71,axiom,
% 0.31/0.47 ! [A5: $tType,A8: $tType] :
% 0.31/0.47 ( ( ( one @ A5 )
% 0.31/0.47 & ( finite_finite @ A8 ) )
% 0.31/0.47 => ( one @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Helper facts (3)
% 0.31/0.47 thf(help_If_3_1_T,axiom,
% 0.31/0.47 ! [P: $o] :
% 0.31/0.47 ( ( P = $true )
% 0.31/0.47 | ( P = $false ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_2_1_T,axiom,
% 0.31/0.47 ! [A: $tType,X: A,Y: A] :
% 0.31/0.47 ( ( if @ A @ $false @ X @ Y )
% 0.31/0.47 = Y ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_1_1_T,axiom,
% 0.31/0.47 ! [A: $tType,X: A,Y: A] :
% 0.31/0.47 ( ( if @ A @ $true @ X @ Y )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 % Free types (1)
% 0.31/0.47 thf(tfree_0,hypothesis,
% 0.31/0.47 finite_finite @ n ).
% 0.31/0.47
% 0.31/0.47 % Conjectures (1)
% 0.31/0.47 thf(conj_0,conjecture,
% 0.31/0.47 ( ( ring_1_of_int @ real @ ( abs_abs @ int @ m ) )
% 0.31/0.47 = ( abs_abs @ real @ ( finite1433825200ec_nth @ real @ n @ ( minus_minus @ ( finite_Cartesian_vec @ real @ n ) @ x @ y ) @ i ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 3.74/1.77 ---- Embedded in THF ---
% 3.74/1.77 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.74/1.77 %%% Generated on Tue Feb 24 08:26:46 EST 2026
% 3.74/1.77 %%% using '$$dhol' embedding, version 1.3.0.
% 3.74/1.77 %%% Logic specification used:
% 3.74/1.77 %%% thf(spec, logic, $$dhol).
% 3.74/1.77
% 3.74/1.77 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2DTF8750.p
% 3.74/1.77 thf(ty_t_Finite__Cartesian__Product_Ovec, type, finite_Cartesian_vec: ($tType > ($tType > $tType))).
% 3.74/1.77 thf(ty_t_Numeral__Type_Onum1, type, numeral_num1: $tType).
% 3.74/1.77 thf(ty_t_Real_Oreal, type, real: $tType).
% 3.74/1.77 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.74/1.77 thf(ty_t_Int_Oint, type, int: $tType).
% 3.74/1.77 thf(ty_tf_n, type, n: $tType).
% 3.74/1.77 thf(sy_cl_Cardinality_OCARD__1, type, cARD_1: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Rings_Oring, type, ring: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Fields_Ofield, type, field: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Groups_Ominus, type, minus: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Rings_Oring__1, type, ring_1: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Nat_Oring__char__0, type, ring_char_0: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Groups_Omonoid__mult, type, monoid_mult: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Rings_Oidom__abs__sgn, type, idom_abs_sgn: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Real__Vector__Spaces_Odist__norm, type, real_V1639655670t_norm: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Archimedean__Field_Ofloor__ceiling, type, archim1727834104eiling: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Groups_Oordered__ab__group__add__abs, type, ordere142940540dd_abs: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Real__Vector__Spaces_Ometric__space, type, real_V2090557954_space: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Archimedean__Field_Oarchimedean__field, type, archim1804426504_field: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector, type, real_V55928688vector: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__algebra__1, type, real_V1229719638ebra_1: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Ordered__Euclidean__Space_Oordered__euclidean__space, type, ordere890947078_space: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum, type, condit1656338222tinuum: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder, type, condit1037483654norder: (!> [A:$tType]: ($o))).
% 3.74/1.77 thf(sy_c_Archimedean__Field_Oceiling, type, archimedean_ceiling: (!> [A:$tType]: ((A > int)))).
% 3.74/1.77 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor, type, archim2085082626_floor: (!> [A:$tType]: ((A > int)))).
% 3.74/1.77 thf(sy_c_Finite__Cartesian__Product_Oaxis, type, finite1218308419n_axis: (!> [B:$tType,A:$tType]: ((B > (A > ((finite_Cartesian_vec @ A) @ B)))))).
% 3.74/1.77 thf(sy_c_Finite__Cartesian__Product_Oaxis__index, type, finite1115014511_index: (!> [A:$tType,N:$tType]: ((((finite_Cartesian_vec @ A) @ N) > N)))).
% 3.74/1.77 thf(sy_c_Finite__Cartesian__Product_Omap__matrix, type, finite1614961371matrix: (!> [A:$tType,B:$tType,I:$tType,J:$tType]: (((A > B) > (((finite_Cartesian_vec @ ((finite_Cartesian_vec @ A) @ I)) @ J) > ((finite_Cartesian_vec @ ((finite_Cartesian_vec @ B) @ I)) @ J)))))).
% 3.74/1.77 thf(sy_c_Finite__Cartesian__Product_Ovec, type, finite_Cartesian_vec2: (!> [A:$tType,B:$tType]: ((A > ((finite_Cartesian_vec @ A) @ B))))).
% 3.74/1.77 thf(sy_c_Finite__Cartesian__Product_Ovec_Ovec__nth, type, finite1433825200ec_nth: (!> [A:$tType,B:$tType]: ((((finite_Cartesian_vec @ A) @ B) > (B > A))))).
% 3.74/1.77 thf(sy_c_Finite__Cartesian__Product_Ovector__scalar__mult, type, finite431509953r_mult: (!> [A:$tType,N:$tType]: ((A > (((finite_Cartesian_vec @ A) @ N) > ((finite_Cartesian_vec @ A) @ N)))))).
% 3.74/1.77 thf(sy_c_Groups_Oabs__class_Oabs, type, abs_abs: (!> [A:$tType]: ((A > A)))).
% 3.74/1.77 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 3.74/1.77 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 3.74/1.77 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.74/1.77 thf(sy_c_Int_Oring__1__class_OInts, type, ring_1_Ints: (!> [A:$tType]: ((set @ A)))).
% 3.74/1.77 thf(sy_c_Int_Oring__1__class_Oof__int, type, ring_1_of_int: (!> [A:$tType]: ((int > A)))).
% 3.74/1.77 thf(sy_c_Minkowskis__Theorem__Mirabelle__jpyvdnlcjd_Oof__int__vec, type, minkow1937162798nt_vec: (!> [B:$tType,A:$tType]: ((((finite_Cartesian_vec @ int) @ B) > ((finite_Cartesian_vec @ A) @ B))))).
% 3.74/1.77 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 3.74/1.77 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.74/1.77 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist, type, real_V2000881966t_dist: (!> [A:$tType]: ((A > (A > real))))).
% 3.74/1.77 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm, type, real_V1127708846m_norm: (!> [A:$tType]: ((A > real)))).
% 3.74/1.77 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.74/1.77 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.74/1.77 thf(sy_v_A, type, a: (set @ ((finite_Cartesian_vec @ real) @ n))).
% 3.74/1.77 thf(sy_v_i____, type, i: n).
% 3.74/1.77 thf(sy_v_m____, type, m: int).
% 3.74/1.77 thf(sy_v_x____, type, x: ((finite_Cartesian_vec @ real) @ n)).
% 3.74/1.77 thf(sy_v_y____, type, y: ((finite_Cartesian_vec @ real) @ n)).
% 3.74/1.77 thf(fact_0__C1_C_I2_J, axiom, (((member @ ((finite_Cartesian_vec @ real) @ n)) @ y) @ a)).
% 3.74/1.77 thf(fact_1__C1_C_I1_J, axiom, (((member @ ((finite_Cartesian_vec @ real) @ n)) @ x) @ a)).
% 3.74/1.77 thf(fact_2_m, axiom, (((ring_1_of_int @ real) @ m) = (((minus_minus @ real) @ ((((finite1433825200ec_nth @ real) @ n) @ x) @ i)) @ ((((finite1433825200ec_nth @ real) @ n) @ y) @ i)))).
% 3.74/1.77 thf(fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [M:int]: ((((ring_1_of_int @ real) @ M) != (((minus_minus @ real) @ ((((finite1433825200ec_nth @ real) @ n) @ x) @ i)) @ ((((finite1433825200ec_nth @ real) @ n) @ y) @ i)))))))).
% 3.74/1.77 thf(fact_4_vector__minus__component, axiom, (! [A:$tType,B:$tType]: ((((finite_finite @ B) & (minus @ A)) => (! [X:((finite_Cartesian_vec @ A) @ B),Y:((finite_Cartesian_vec @ A) @ B),I2:B]: ((((((finite1433825200ec_nth @ A) @ B) @ (((minus_minus @ ((finite_Cartesian_vec @ A) @ B)) @ X) @ Y)) @ I2) = (((minus_minus @ A) @ ((((finite1433825200ec_nth @ A) @ B) @ X) @ I2)) @ ((((finite1433825200ec_nth @ A) @ B) @ Y) @ I2))))))))).
% 3.74/1.77 thf(fact_5_of__int__abs, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:int]: ((((ring_1_of_int @ A) @ ((abs_abs @ int) @ X)) = ((abs_abs @ A) @ ((ring_1_of_int @ A) @ X))))))))).
% 3.74/1.77 thf(fact_6_of__int__diff, axiom, (! [A:$tType]: (((ring_1 @ A) => (! [W:int,Z:int]: ((((ring_1_of_int @ A) @ (((minus_minus @ int) @ W) @ Z)) = (((minus_minus @ A) @ ((ring_1_of_int @ A) @ W)) @ ((ring_1_of_int @ A) @ Z))))))))).
% 3.74/1.77 thf(fact_7__092_060open_062x_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060in_062_A_092_060int_062_092_060close_062, axiom, (((member @ real) @ (((minus_minus @ real) @ ((((finite1433825200ec_nth @ real) @ n) @ x) @ i)) @ ((((finite1433825200ec_nth @ real) @ n) @ y) @ i))) @ (ring_1_Ints @ real))).
% 3.74/1.77 thf(fact_8_of__int__vec__nth, axiom, (! [A:$tType,B:$tType]: ((((finite_finite @ B) & (ring_1 @ A)) => (! [V:((finite_Cartesian_vec @ int) @ B),N2:B]: ((((((finite1433825200ec_nth @ A) @ B) @ (((minkow1937162798nt_vec @ B) @ A) @ V)) @ N2) = ((ring_1_of_int @ A) @ ((((finite1433825200ec_nth @ int) @ B) @ V) @ N2))))))))).
% 3.74/1.77 thf(fact_9_of__int__eq__iff, axiom, (! [A:$tType]: (((ring_char_0 @ A) => (! [W:int,Z:int]: (((((ring_1_of_int @ A) @ W) = ((ring_1_of_int @ A) @ Z)) = (W = Z)))))))).
% 3.74/1.77 thf(fact_10_abs__abs, axiom, (! [A:$tType]: (((idom_abs_sgn @ A) => (! [A2:A]: ((((abs_abs @ A) @ ((abs_abs @ A) @ A2)) = ((abs_abs @ A) @ A2)))))))).
% 3.74/1.77 thf(fact_11_abs__idempotent, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A]: ((((abs_abs @ A) @ ((abs_abs @ A) @ A2)) = ((abs_abs @ A) @ A2)))))))).
% 3.74/1.77 thf(fact_12_minus__apply, axiom, (! [B:$tType,A:$tType]: (((minus @ B) => ((minus_minus @ (A > B)) = (^ [A3:(A > B),B2:(A > B),X2:A]: ((((minus_minus @ B) @ (A3 @ X2)) @ (B2 @ X2))))))))).
% 3.74/1.77 thf(fact_13_abs__minus__commute, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B3:A]: ((((abs_abs @ A) @ (((minus_minus @ A) @ A2) @ B3)) = ((abs_abs @ A) @ (((minus_minus @ A) @ B3) @ A2))))))))).
% 3.74/1.77 thf(fact_14_lambda__skolem, axiom, (! [N:$tType,A:$tType]: (((finite_finite @ N) => (! [P:(N > (A > $o))]: (((! [I3:N]: ((? [X3:A]: (((P @ I3) @ X3))))) = (? [X2:((finite_Cartesian_vec @ A) @ N)]: ((! [I3:N]: (((P @ I3) @ ((((finite1433825200ec_nth @ A) @ N) @ X2) @ I3))))))))))))).
% 3.74/1.77 thf(fact_15_vec__eq__iff, axiom, (! [B:$tType,A:$tType]: (((finite_finite @ B) => ((^ [Y2:((finite_Cartesian_vec @ A) @ B),Z2:((finite_Cartesian_vec @ A) @ B)]: ((Y2 = Z2))) = (^ [X2:((finite_Cartesian_vec @ A) @ B),Y3:((finite_Cartesian_vec @ A) @ B)]: ((! [I3:B]: ((((((finite1433825200ec_nth @ A) @ B) @ X2) @ I3) = ((((finite1433825200ec_nth @ A) @ B) @ Y3) @ I3))))))))))).
% 3.74/1.77 thf(fact_16_assms, axiom, (! [V:((finite_Cartesian_vec @ real) @ n),I2:n]: (((((member @ ((finite_Cartesian_vec @ real) @ n)) @ V) @ a) => (((member @ real) @ ((((finite1433825200ec_nth @ real) @ n) @ V) @ I2)) @ (ring_1_Ints @ real)))))).
% 3.74/1.77 thf(fact_17_of__int__vec__eq__iff, axiom, (! [A:$tType,N:$tType]: ((((finite_finite @ N) & (ring_char_0 @ A)) => (! [A2:((finite_Cartesian_vec @ int) @ N),B3:((finite_Cartesian_vec @ int) @ N)]: ((((((minkow1937162798nt_vec @ N) @ A) @ A2) = (((minkow1937162798nt_vec @ N) @ A) @ B3)) = (A2 = B3)))))))).
% 3.74/1.77 thf(fact_18_Ints__diff, axiom, (! [A:$tType]: (((ring_1 @ A) => (! [A2:A,B3:A]: (((((member @ A) @ A2) @ (ring_1_Ints @ A)) => ((((member @ A) @ B3) @ (ring_1_Ints @ A)) => (((member @ A) @ (((minus_minus @ A) @ A2) @ B3)) @ (ring_1_Ints @ A)))))))))).
% 3.74/1.77 thf(fact_19_Ints__abs, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [A2:A]: (((((member @ A) @ A2) @ (ring_1_Ints @ A)) => (((member @ A) @ ((abs_abs @ A) @ A2)) @ (ring_1_Ints @ A))))))))).
% 3.74/1.77 thf(fact_20_Ints__of__int, axiom, (! [A:$tType]: (((ring_1 @ A) => (! [Z:int]: ((((member @ A) @ ((ring_1_of_int @ A) @ Z)) @ (ring_1_Ints @ A)))))))).
% 3.74/1.77 thf(fact_21_Ints__induct, axiom, (! [A:$tType]: (((ring_1 @ A) => (! [Q:A,P:(A > $o)]: (((((member @ A) @ Q) @ (ring_1_Ints @ A)) => ((! [Z3:int]: ((P @ ((ring_1_of_int @ A) @ Z3)))) => (P @ Q))))))))).
% 3.74/1.77 thf(fact_22_Ints__cases, axiom, (! [A:$tType]: (((ring_1 @ A) => (! [Q:A]: (((((member @ A) @ Q) @ (ring_1_Ints @ A)) => (~ ((! [Z3:int]: ((Q != ((ring_1_of_int @ A) @ Z3))))))))))))).
% 3.74/1.77 thf(fact_23_diff__right__commute, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A2:A,C:A,B3:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ C)) @ B3) = (((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ B3)) @ C)))))))).
% 3.74/1.77 thf(fact_24_diff__eq__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B3:A,C:A,D:A]: ((((((minus_minus @ A) @ A2) @ B3) = (((minus_minus @ A) @ C) @ D)) => ((A2 = B3) = (C = D))))))))).
% 3.74/1.77 thf(fact_25_fun__diff__def, axiom, (! [B:$tType,A:$tType]: (((minus @ B) => ((minus_minus @ (A > B)) = (^ [A3:(A > B),B2:(A > B),X2:A]: ((((minus_minus @ B) @ (A3 @ X2)) @ (B2 @ X2))))))))).
% 3.74/1.77 thf(fact_26_vec__nth__inject, axiom, (! [B:$tType,A:$tType]: (((finite_finite @ B) => (! [X:((finite_Cartesian_vec @ A) @ B),Y:((finite_Cartesian_vec @ A) @ B)]: ((((((finite1433825200ec_nth @ A) @ B) @ X) = (((finite1433825200ec_nth @ A) @ B) @ Y)) = (X = Y)))))))).
% 3.74/1.77 thf(fact_27_cond__component, axiom, (! [A:$tType,B:$tType]: (((finite_finite @ B) => (! [B3:$o,X:((finite_Cartesian_vec @ A) @ B),Y:((finite_Cartesian_vec @ A) @ B),I2:B]: (((B3 => (((((finite1433825200ec_nth @ A) @ B) @ ((((if @ ((finite_Cartesian_vec @ A) @ B)) @ B3) @ X) @ Y)) @ I2) = ((((finite1433825200ec_nth @ A) @ B) @ X) @ I2))) & ((~ (B3)) => (((((finite1433825200ec_nth @ A) @ B) @ ((((if @ ((finite_Cartesian_vec @ A) @ B)) @ B3) @ X) @ Y)) @ I2) = ((((finite1433825200ec_nth @ A) @ B) @ Y) @ I2)))))))))).
% 3.74/1.77 thf(fact_28_nth__map__matrix, axiom, (! [A:$tType,C2:$tType,D2:$tType,B:$tType]: ((((finite_finite @ B) & (finite_finite @ C2)) => (! [F:(D2 > A),X:((finite_Cartesian_vec @ ((finite_Cartesian_vec @ D2) @ B)) @ C2),I2:C2,J2:B]: ((((((finite1433825200ec_nth @ A) @ B) @ ((((finite1433825200ec_nth @ ((finite_Cartesian_vec @ A) @ B)) @ C2) @ ((((((finite1614961371matrix @ D2) @ A) @ B) @ C2) @ F) @ X)) @ I2)) @ J2) = (F @ ((((finite1433825200ec_nth @ D2) @ B) @ ((((finite1433825200ec_nth @ ((finite_Cartesian_vec @ D2) @ B)) @ C2) @ X) @ I2)) @ J2))))))))).
% 3.74/1.77 thf(fact_29_dist__of__int, axiom, (! [A:$tType]: (((real_V1229719638ebra_1 @ A) => (! [M2:int,N2:int]: (((((real_V2000881966t_dist @ A) @ ((ring_1_of_int @ A) @ M2)) @ ((ring_1_of_int @ A) @ N2)) = ((ring_1_of_int @ real) @ ((abs_abs @ int) @ (((minus_minus @ int) @ M2) @ N2)))))))))).
% 3.74/1.77 thf(fact_30_vec__sub, axiom, (! [B:$tType,A:$tType]: ((((minus @ A) & (finite_finite @ B)) => (! [X:A,Y:A]: (((((finite_Cartesian_vec2 @ A) @ B) @ (((minus_minus @ A) @ X) @ Y)) = (((minus_minus @ ((finite_Cartesian_vec @ A) @ B)) @ (((finite_Cartesian_vec2 @ A) @ B) @ X)) @ (((finite_Cartesian_vec2 @ A) @ B) @ Y))))))))).
% 3.74/1.77 thf(fact_31_vector__sub__rdistrib, axiom, (! [B:$tType,A:$tType]: ((((ring @ A) & (finite_finite @ B)) => (! [A2:A,B3:A,X:((finite_Cartesian_vec @ A) @ B)]: ((((((finite431509953r_mult @ A) @ B) @ (((minus_minus @ A) @ A2) @ B3)) @ X) = (((minus_minus @ ((finite_Cartesian_vec @ A) @ B)) @ ((((finite431509953r_mult @ A) @ B) @ A2) @ X)) @ ((((finite431509953r_mult @ A) @ B) @ B3) @ X))))))))).
% 3.74/1.77 thf(fact_32__C1_C_I3_J, axiom, (((ord_less @ real) @ (((real_V2000881966t_dist @ ((finite_Cartesian_vec @ real) @ n)) @ y) @ x)) @ (one_one @ real))).
% 3.74/1.77 thf(fact_33_norm__of__int, axiom, (! [A:$tType]: (((real_V1229719638ebra_1 @ A) => (! [Z:int]: ((((real_V1127708846m_norm @ A) @ ((ring_1_of_int @ A) @ Z)) = ((abs_abs @ real) @ ((ring_1_of_int @ real) @ Z))))))))).
% 3.74/1.77 thf(fact_34_ceiling__diff__of__int, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A,Z:int]: ((((archimedean_ceiling @ A) @ (((minus_minus @ A) @ X) @ ((ring_1_of_int @ A) @ Z))) = (((minus_minus @ int) @ ((archimedean_ceiling @ A) @ X)) @ Z)))))))).
% 3.74/1.77 thf(fact_35_axis__nth, axiom, (! [B:$tType,A:$tType]: ((((zero @ A) & (finite_finite @ B)) => (! [I2:B,X:A]: ((((((finite1433825200ec_nth @ A) @ B) @ ((((finite1218308419n_axis @ B) @ A) @ I2) @ X)) @ I2) = X))))))).
% 3.74/1.77 thf(fact_36_vec_Oscale__left__diff__distrib, axiom, (! [B:$tType,A:$tType]: ((((field @ A) & (finite_finite @ B)) => (! [A2:A,B3:A,X:((finite_Cartesian_vec @ A) @ B)]: ((((((finite431509953r_mult @ A) @ B) @ (((minus_minus @ A) @ A2) @ B3)) @ X) = (((minus_minus @ ((finite_Cartesian_vec @ A) @ B)) @ ((((finite431509953r_mult @ A) @ B) @ A2) @ X)) @ ((((finite431509953r_mult @ A) @ B) @ B3) @ X))))))))).
% 3.74/1.77 thf(fact_37_floor__diff__of__int, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A,Z:int]: ((((archim2085082626_floor @ A) @ (((minus_minus @ A) @ X) @ ((ring_1_of_int @ A) @ Z))) = (((minus_minus @ int) @ ((archim2085082626_floor @ A) @ X)) @ Z)))))))).
% 3.74/1.77 thf(fact_38_norm__axis__1, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [M2:A]: ((((real_V1127708846m_norm @ ((finite_Cartesian_vec @ real) @ A)) @ ((((finite1218308419n_axis @ A) @ real) @ M2) @ (one_one @ real))) = (one_one @ real)))))))).
% 3.74/1.77 thf(fact_39_vec__eq, axiom, (! [B:$tType,A:$tType]: (((finite_finite @ B) => (! [M2:A,N2:A]: ((((((finite_Cartesian_vec2 @ A) @ B) @ M2) = (((finite_Cartesian_vec2 @ A) @ B) @ N2)) = (M2 = N2)))))))).
% 3.74/1.77 thf(fact_40_vec__inj, axiom, (! [B:$tType,A:$tType]: (((finite_finite @ B) => (! [X:A,Y:A]: ((((((finite_Cartesian_vec2 @ A) @ B) @ X) = (((finite_Cartesian_vec2 @ A) @ B) @ Y)) = (X = Y)))))))).
% 3.74/1.77 thf(fact_41_vec_Oscale__one, axiom, (! [B:$tType,A:$tType]: ((((field @ A) & (finite_finite @ B)) => (! [X:((finite_Cartesian_vec @ A) @ B)]: ((((((finite431509953r_mult @ A) @ B) @ (one_one @ A)) @ X) = X))))))).
% 3.74/1.77 thf(fact_42_vector__smult__lid, axiom, (! [B:$tType,A:$tType]: ((((monoid_mult @ A) & (finite_finite @ B)) => (! [X:((finite_Cartesian_vec @ A) @ B)]: ((((((finite431509953r_mult @ A) @ B) @ (one_one @ A)) @ X) = X))))))).
% 3.74/1.77 thf(fact_43_abs__1, axiom, (! [A:$tType]: (((idom_abs_sgn @ A) => (((abs_abs @ A) @ (one_one @ A)) = (one_one @ A)))))).
% 3.74/1.77 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 3.74/1.77 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A4)))) = A4)))).
% 3.74/1.77 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q2:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q2 @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q2)))))).
% 3.74/1.77 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 3.74/1.77 thf(fact_48_of__int__less__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [W:int,Z:int]: (((((ord_less @ A) @ ((ring_1_of_int @ A) @ W)) @ ((ring_1_of_int @ A) @ Z)) = (((ord_less @ int) @ W) @ Z)))))))).
% 3.74/1.77 thf(fact_49_one__index, axiom, (! [N:$tType,A:$tType]: ((((one @ A) & (finite_finite @ N)) => (! [I2:N]: ((((((finite1433825200ec_nth @ A) @ N) @ (one_one @ ((finite_Cartesian_vec @ A) @ N))) @ I2) = (one_one @ A)))))))).
% 3.74/1.77 thf(fact_50_of__int__eq__1__iff, axiom, (! [A:$tType]: (((ring_char_0 @ A) => (! [Z:int]: (((((ring_1_of_int @ A) @ Z) = (one_one @ A)) = (Z = (one_one @ int))))))))).
% 3.74/1.77 thf(fact_51_of__int__1, axiom, (! [A:$tType]: (((ring_1 @ A) => (((ring_1_of_int @ A) @ (one_one @ int)) = (one_one @ A)))))).
% 3.74/1.77 thf(fact_52_abs__norm__cancel, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [A2:A]: ((((abs_abs @ real) @ ((real_V1127708846m_norm @ A) @ A2)) = ((real_V1127708846m_norm @ A) @ A2)))))))).
% 3.74/1.77 thf(fact_53_floor__one, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (((archim2085082626_floor @ A) @ (one_one @ A)) = (one_one @ int)))))).
% 3.74/1.77 thf(fact_54_ceiling__one, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (((archimedean_ceiling @ A) @ (one_one @ A)) = (one_one @ int)))))).
% 3.74/1.77 thf(fact_55_vec__1, axiom, (! [B:$tType,A:$tType]: ((((one @ A) & (finite_finite @ B)) => ((((finite_Cartesian_vec2 @ A) @ B) @ (one_one @ A)) = (one_one @ ((finite_Cartesian_vec @ A) @ B))))))).
% 3.74/1.77 thf(fact_56_floor__of__int, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [Z:int]: ((((archim2085082626_floor @ A) @ ((ring_1_of_int @ A) @ Z)) = Z))))))).
% 3.74/1.77 thf(fact_57_ceiling__of__int, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [Z:int]: ((((archimedean_ceiling @ A) @ ((ring_1_of_int @ A) @ Z)) = Z))))))).
% 3.74/1.77 thf(fact_58_vec__component, axiom, (! [B:$tType,A:$tType]: (((finite_finite @ B) => (! [X:A,I2:B]: ((((((finite1433825200ec_nth @ A) @ B) @ (((finite_Cartesian_vec2 @ A) @ B) @ X)) @ I2) = X))))))).
% 3.74/1.77 thf(fact_59_vector__ssub__ldistrib, axiom, (! [B:$tType,A:$tType]: ((((ring @ A) & (finite_finite @ B)) => (! [C:A,X:((finite_Cartesian_vec @ A) @ B),Y:((finite_Cartesian_vec @ A) @ B)]: ((((((finite431509953r_mult @ A) @ B) @ C) @ (((minus_minus @ ((finite_Cartesian_vec @ A) @ B)) @ X) @ Y)) = (((minus_minus @ ((finite_Cartesian_vec @ A) @ B)) @ ((((finite431509953r_mult @ A) @ B) @ C) @ X)) @ ((((finite431509953r_mult @ A) @ B) @ C) @ Y))))))))).
% 3.74/1.77 thf(fact_60_of__int__1__less__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z:int]: (((((ord_less @ A) @ (one_one @ A)) @ ((ring_1_of_int @ A) @ Z)) = (((ord_less @ int) @ (one_one @ int)) @ Z)))))))).
% 3.74/1.77 thf(fact_61_of__int__less__1__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z:int]: (((((ord_less @ A) @ ((ring_1_of_int @ A) @ Z)) @ (one_one @ A)) = (((ord_less @ int) @ Z) @ (one_one @ int))))))))).
% 3.74/1.77 thf(fact_62_norm__one, axiom, (! [A:$tType]: (((real_V1229719638ebra_1 @ A) => (((real_V1127708846m_norm @ A) @ (one_one @ A)) = (one_one @ real)))))).
% 3.74/1.77 thf(fact_63_dist__diff_I2_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [A2:A,B3:A]: (((((real_V2000881966t_dist @ A) @ (((minus_minus @ A) @ A2) @ B3)) @ A2) = ((real_V1127708846m_norm @ A) @ B3)))))))).
% 3.74/1.77 thf(fact_64_dist__diff_I1_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [A2:A,B3:A]: (((((real_V2000881966t_dist @ A) @ A2) @ (((minus_minus @ A) @ A2) @ B3)) = ((real_V1127708846m_norm @ A) @ B3)))))))).
% 3.74/1.77 thf(fact_65_floor__less__one, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: (((((ord_less @ int) @ ((archim2085082626_floor @ A) @ X)) @ (one_one @ int)) = (((ord_less @ A) @ X) @ (one_one @ A))))))))).
% 3.74/1.77 thf(fact_66_one__less__ceiling, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: (((((ord_less @ int) @ (one_one @ int)) @ ((archimedean_ceiling @ A) @ X)) = (((ord_less @ A) @ (one_one @ A)) @ X)))))))).
% 3.74/1.77 thf(fact_67_floor__diff__one, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: ((((archim2085082626_floor @ A) @ (((minus_minus @ A) @ X) @ (one_one @ A))) = (((minus_minus @ int) @ ((archim2085082626_floor @ A) @ X)) @ (one_one @ int))))))))).
% 3.74/1.77 thf(fact_68_ceiling__diff__one, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: ((((archimedean_ceiling @ A) @ (((minus_minus @ A) @ X) @ (one_one @ A))) = (((minus_minus @ int) @ ((archimedean_ceiling @ A) @ X)) @ (one_one @ int))))))))).
% 3.74/1.77 thf(fact_69_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 3.74/1.77 thf(fact_70_floor__less__iff, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A,Z:int]: (((((ord_less @ int) @ ((archim2085082626_floor @ A) @ X)) @ Z) = (((ord_less @ A) @ X) @ ((ring_1_of_int @ A) @ Z))))))))).
% 3.74/1.77 thf(fact_71_less__ceiling__iff, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [Z:int,X:A]: (((((ord_less @ int) @ Z) @ ((archimedean_ceiling @ A) @ X)) = (((ord_less @ A) @ ((ring_1_of_int @ A) @ Z)) @ X)))))))).
% 3.74/1.77 thf(fact_72_vec_Oscale__left__commute, axiom, (! [B:$tType,A:$tType]: ((((field @ A) & (finite_finite @ B)) => (! [A2:A,B3:A,X:((finite_Cartesian_vec @ A) @ B)]: ((((((finite431509953r_mult @ A) @ B) @ A2) @ ((((finite431509953r_mult @ A) @ B) @ B3) @ X)) = ((((finite431509953r_mult @ A) @ B) @ B3) @ ((((finite431509953r_mult @ A) @ B) @ A2) @ X))))))))).
% 3.74/1.77 thf(fact_73_dist__norm, axiom, (! [A:$tType]: (((real_V1639655670t_norm @ A) => ((real_V2000881966t_dist @ A) = (^ [X2:A,Y3:A]: (((real_V1127708846m_norm @ A) @ (((minus_minus @ A) @ X2) @ Y3))))))))).
% 3.74/1.77 thf(fact_74_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 3.74/1.77 thf(fact_75_dist__commute__lessI, axiom, (! [A:$tType]: (((real_V2090557954_space @ A) => (! [Y:A,X:A,E:real]: (((((ord_less @ real) @ (((real_V2000881966t_dist @ A) @ Y) @ X)) @ E) => (((ord_less @ real) @ (((real_V2000881966t_dist @ A) @ X) @ Y)) @ E)))))))).
% 3.74/1.77 thf(fact_76_dist__commute, axiom, (! [A:$tType]: (((real_V2090557954_space @ A) => ((real_V2000881966t_dist @ A) = (^ [X2:A,Y3:A]: ((((real_V2000881966t_dist @ A) @ Y3) @ X2)))))))).
% 3.74/1.77 thf(fact_77_ceiling__less__cancel, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A,Y:A]: (((((ord_less @ int) @ ((archimedean_ceiling @ A) @ X)) @ ((archimedean_ceiling @ A) @ Y)) => (((ord_less @ A) @ X) @ Y)))))))).
% 3.74/1.77 thf(fact_78_floor__less__cancel, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A,Y:A]: (((((ord_less @ int) @ ((archim2085082626_floor @ A) @ X)) @ ((archim2085082626_floor @ A) @ Y)) => (((ord_less @ A) @ X) @ Y)))))))).
% 3.74/1.77 thf(fact_79_norm__minus__commute, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [A2:A,B3:A]: ((((real_V1127708846m_norm @ A) @ (((minus_minus @ A) @ A2) @ B3)) = ((real_V1127708846m_norm @ A) @ (((minus_minus @ A) @ B3) @ A2))))))))).
% 3.74/1.77 thf(fact_80_real__norm__def, axiom, ((real_V1127708846m_norm @ real) = (abs_abs @ real))).
% 3.74/1.77 thf(fact_81_ex__less__of__int, axiom, (! [A:$tType]: (((archim1804426504_field @ A) => (! [X:A]: ((? [Z3:int]: ((((ord_less @ A) @ X) @ ((ring_1_of_int @ A) @ Z3)))))))))).
% 3.74/1.77 thf(fact_82_ex__of__int__less, axiom, (! [A:$tType]: (((archim1804426504_field @ A) => (! [X:A]: ((? [Z3:int]: ((((ord_less @ A) @ ((ring_1_of_int @ A) @ Z3)) @ X))))))))).
% 3.74/1.77 thf(fact_83_norm__bound__component__lt__cart, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [X:((finite_Cartesian_vec @ real) @ A),E:real,I2:A]: (((((ord_less @ real) @ ((real_V1127708846m_norm @ ((finite_Cartesian_vec @ real) @ A)) @ X)) @ E) => (((ord_less @ real) @ ((abs_abs @ real) @ ((((finite1433825200ec_nth @ real) @ A) @ X) @ I2))) @ E)))))))).
% 3.74/1.77 thf(fact_84_diff__strict__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B3:A,D:A,C:A]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less @ A) @ D) @ C) => (((ord_less @ A) @ (((minus_minus @ A) @ A2) @ C)) @ (((minus_minus @ A) @ B3) @ D)))))))))).
% 3.74/1.77 thf(fact_85_diff__eq__diff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B3:A,C:A,D:A]: ((((((minus_minus @ A) @ A2) @ B3) = (((minus_minus @ A) @ C) @ D)) => ((((ord_less @ A) @ A2) @ B3) = (((ord_less @ A) @ C) @ D))))))))).
% 3.74/1.77 thf(fact_86_diff__strict__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B3:A,A2:A,C:A]: (((((ord_less @ A) @ B3) @ A2) => (((ord_less @ A) @ (((minus_minus @ A) @ C) @ A2)) @ (((minus_minus @ A) @ C) @ B3))))))))).
% 3.74/1.77 thf(fact_87_diff__strict__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B3:A,C:A]: (((((ord_less @ A) @ A2) @ B3) => (((ord_less @ A) @ (((minus_minus @ A) @ A2) @ C)) @ (((minus_minus @ A) @ B3) @ C))))))))).
% 3.74/1.77 thf(fact_88_abs__one, axiom, (! [A:$tType]: (((linordered_idom @ A) => (((abs_abs @ A) @ (one_one @ A)) = (one_one @ A)))))).
% 3.74/1.77 thf(fact_89_dist__real__def, axiom, ((real_V2000881966t_dist @ real) = (^ [X2:real,Y3:real]: (((abs_abs @ real) @ (((minus_minus @ real) @ X2) @ Y3)))))).
% 3.74/1.77 thf(fact_90_Ints__1, axiom, (! [A:$tType]: (((ring_1 @ A) => (((member @ A) @ (one_one @ A)) @ (ring_1_Ints @ A)))))).
% 3.74/1.77 thf(fact_91_vec_Oscale__right__diff__distrib, axiom, (! [B:$tType,A:$tType]: ((((field @ A) & (finite_finite @ B)) => (! [A2:A,X:((finite_Cartesian_vec @ A) @ B),Y:((finite_Cartesian_vec @ A) @ B)]: ((((((finite431509953r_mult @ A) @ B) @ A2) @ (((minus_minus @ ((finite_Cartesian_vec @ A) @ B)) @ X) @ Y)) = (((minus_minus @ ((finite_Cartesian_vec @ A) @ B)) @ ((((finite431509953r_mult @ A) @ B) @ A2) @ X)) @ ((((finite431509953r_mult @ A) @ B) @ A2) @ Y))))))))).
% 3.74/1.77 thf(fact_92_Ints__eq__abs__less1, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:A,Y:A]: (((((member @ A) @ X) @ (ring_1_Ints @ A)) => ((((member @ A) @ Y) @ (ring_1_Ints @ A)) => ((X = Y) = (((ord_less @ A) @ ((abs_abs @ A) @ (((minus_minus @ A) @ X) @ Y))) @ (one_one @ A))))))))))).
% 3.74/1.77 thf(fact_93_of__int__ceiling__cancel, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: (((((ring_1_of_int @ A) @ ((archimedean_ceiling @ A) @ X)) = X) = (? [N3:int]: ((X = ((ring_1_of_int @ A) @ N3))))))))))).
% 3.74/1.77 thf(fact_94_of__int__floor__cancel, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: (((((ring_1_of_int @ A) @ ((archim2085082626_floor @ A) @ X)) = X) = (? [N3:int]: ((X = ((ring_1_of_int @ A) @ N3))))))))))).
% 3.74/1.77 thf(fact_95_real__of__int__floor__gt__diff__one, axiom, (! [R:real]: ((((ord_less @ real) @ (((minus_minus @ real) @ R) @ (one_one @ real))) @ ((ring_1_of_int @ real) @ ((archim2085082626_floor @ real) @ R)))))).
% 3.74/1.77 thf(fact_96_real__abs__dist, axiom, (! [A:$tType]: (((real_V2090557954_space @ A) => (! [X:A,Y:A]: ((((abs_abs @ real) @ (((real_V2000881966t_dist @ A) @ X) @ Y)) = (((real_V2000881966t_dist @ A) @ X) @ Y)))))))).
% 3.74/1.77 thf(fact_97_less__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 3.74/1.77 thf(fact_98_axis__index__axis, axiom, (! [N:$tType]: (((finite_finite @ N) => (! [U:N]: (((((finite1115014511_index @ real) @ N) @ ((((finite1218308419n_axis @ N) @ real) @ U) @ (one_one @ real))) = U))))))).
% 3.74/1.77 thf(fact_99_le__ceiling__iff, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [Z:int,X:A]: (((((ord_less_eq @ int) @ Z) @ ((archimedean_ceiling @ A) @ X)) = (((ord_less @ A) @ (((minus_minus @ A) @ ((ring_1_of_int @ A) @ Z)) @ (one_one @ A))) @ X)))))))).
% 3.74/1.77 thf(fact_100_ceiling__split, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [P:(int > $o),T:A]: (((P @ ((archimedean_ceiling @ A) @ T)) = (! [I3:int]: ((((((ord_less @ A) @ (((minus_minus @ A) @ ((ring_1_of_int @ A) @ I3)) @ (one_one @ A))) @ T) & (((ord_less_eq @ A) @ T) @ ((ring_1_of_int @ A) @ I3))) => (P @ I3))))))))))).
% 3.74/1.77 thf(fact_101_ceiling__eq__iff, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A,A2:int]: (((((archimedean_ceiling @ A) @ X) = A2) = ((((ord_less @ A) @ (((minus_minus @ A) @ ((ring_1_of_int @ A) @ A2)) @ (one_one @ A))) @ X) & (((ord_less_eq @ A) @ X) @ ((ring_1_of_int @ A) @ A2)))))))))).
% 3.74/1.77 thf(fact_102_of__int__le__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [W:int,Z:int]: (((((ord_less_eq @ A) @ ((ring_1_of_int @ A) @ W)) @ ((ring_1_of_int @ A) @ Z)) = (((ord_less_eq @ int) @ W) @ Z)))))))).
% 3.74/1.77 thf(fact_103_zle__diff1__eq, axiom, (! [W:int,Z:int]: (((((ord_less_eq @ int) @ W) @ (((minus_minus @ int) @ Z) @ (one_one @ int))) = (((ord_less @ int) @ W) @ Z))))).
% 3.74/1.77 thf(fact_104_of__int__le__1__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z:int]: (((((ord_less_eq @ A) @ ((ring_1_of_int @ A) @ Z)) @ (one_one @ A)) = (((ord_less_eq @ int) @ Z) @ (one_one @ int))))))))).
% 3.74/1.77 thf(fact_105_of__int__1__le__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z:int]: (((((ord_less_eq @ A) @ (one_one @ A)) @ ((ring_1_of_int @ A) @ Z)) = (((ord_less_eq @ int) @ (one_one @ int)) @ Z)))))))).
% 3.74/1.77 thf(fact_106_one__le__floor, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: (((((ord_less_eq @ int) @ (one_one @ int)) @ ((archim2085082626_floor @ A) @ X)) = (((ord_less_eq @ A) @ (one_one @ A)) @ X)))))))).
% 3.74/1.77 thf(fact_107_ceiling__le__one, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: (((((ord_less_eq @ int) @ ((archimedean_ceiling @ A) @ X)) @ (one_one @ int)) = (((ord_less_eq @ A) @ X) @ (one_one @ A))))))))).
% 3.74/1.77 thf(fact_108_ceiling__mono, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => (((ord_less_eq @ int) @ ((archimedean_ceiling @ A) @ Y)) @ ((archimedean_ceiling @ A) @ X))))))))).
% 3.74/1.77 thf(fact_109_floor__mono, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => (((ord_less_eq @ int) @ ((archim2085082626_floor @ A) @ X)) @ ((archim2085082626_floor @ A) @ Y))))))))).
% 3.74/1.77 thf(fact_110_less__eq__real__def, axiom, ((ord_less_eq @ real) = (^ [X2:real,Y3:real]: (((((ord_less @ real) @ X2) @ Y3) | (X2 = Y3)))))).
% 3.74/1.77 thf(fact_111_le__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 3.74/1.77 thf(fact_112_less__eq__vec__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) & (finite_finite @ B)) => ((ord_less_eq @ ((finite_Cartesian_vec @ A) @ B)) = (^ [X2:((finite_Cartesian_vec @ A) @ B),Y3:((finite_Cartesian_vec @ A) @ B)]: ((! [I3:B]: ((((ord_less_eq @ A) @ ((((finite1433825200ec_nth @ A) @ B) @ X2) @ I3)) @ ((((finite1433825200ec_nth @ A) @ B) @ Y3) @ I3))))))))))).
% 3.74/1.77 thf(fact_113_int__less__induct, axiom, (! [I2:int,K:int,P:(int > $o)]: (((((ord_less @ int) @ I2) @ K) => ((P @ (((minus_minus @ int) @ K) @ (one_one @ int))) => ((! [I4:int]: (((((ord_less @ int) @ I4) @ K) => ((P @ I4) => (P @ (((minus_minus @ int) @ I4) @ (one_one @ int))))))) => (P @ I2))))))).
% 3.74/1.77 thf(fact_114_int__le__induct, axiom, (! [I2:int,K:int,P:(int > $o)]: (((((ord_less_eq @ int) @ I2) @ K) => ((P @ K) => ((! [I4:int]: (((((ord_less_eq @ int) @ I4) @ K) => ((P @ I4) => (P @ (((minus_minus @ int) @ I4) @ (one_one @ int))))))) => (P @ I2))))))).
% 3.74/1.77 thf(fact_115_ceiling__le, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A,A2:int]: (((((ord_less_eq @ A) @ X) @ ((ring_1_of_int @ A) @ A2)) => (((ord_less_eq @ int) @ ((archimedean_ceiling @ A) @ X)) @ A2)))))))).
% 3.74/1.77 thf(fact_116_le__floor__iff, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [Z:int,X:A]: (((((ord_less_eq @ int) @ Z) @ ((archim2085082626_floor @ A) @ X)) = (((ord_less_eq @ A) @ ((ring_1_of_int @ A) @ Z)) @ X)))))))).
% 3.74/1.77 thf(fact_117_ceiling__le__iff, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A,Z:int]: (((((ord_less_eq @ int) @ ((archimedean_ceiling @ A) @ X)) @ Z) = (((ord_less_eq @ A) @ X) @ ((ring_1_of_int @ A) @ Z))))))))).
% 3.74/1.77 thf(fact_118_diff__eq__diff__less__eq, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B3:A,C:A,D:A]: ((((((minus_minus @ A) @ A2) @ B3) = (((minus_minus @ A) @ C) @ D)) => ((((ord_less_eq @ A) @ A2) @ B3) = (((ord_less_eq @ A) @ C) @ D))))))))).
% 3.74/1.77 thf(fact_119_diff__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B3) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A2) @ C)) @ (((minus_minus @ A) @ B3) @ C))))))))).
% 3.74/1.77 thf(fact_120_diff__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B3:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B3) @ A2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ C) @ A2)) @ (((minus_minus @ A) @ C) @ B3))))))))).
% 3.74/1.77 thf(fact_121_diff__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B3:A,D:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ D) @ C) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A2) @ C)) @ (((minus_minus @ A) @ B3) @ D)))))))))).
% 3.74/1.77 thf(fact_122_abs__ge__self, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ ((abs_abs @ A) @ A2)))))))).
% 3.74/1.77 thf(fact_123_abs__le__D1, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B3:A]: (((((ord_less_eq @ A) @ ((abs_abs @ A) @ A2)) @ B3) => (((ord_less_eq @ A) @ A2) @ B3)))))))).
% 3.74/1.77 thf(fact_124_norm__vector__1, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => ((real_V1127708846m_norm @ ((finite_Cartesian_vec @ A) @ numeral_num1)) = (^ [X2:((finite_Cartesian_vec @ A) @ numeral_num1)]: (((real_V1127708846m_norm @ A) @ ((((finite1433825200ec_nth @ A) @ numeral_num1) @ X2) @ (one_one @ numeral_num1)))))))))).
% 3.74/1.77 thf(fact_125_ex__le__of__int, axiom, (! [A:$tType]: (((archim1804426504_field @ A) => (! [X:A]: ((? [Z3:int]: ((((ord_less_eq @ A) @ X) @ ((ring_1_of_int @ A) @ Z3)))))))))).
% 3.74/1.77 thf(fact_126_dist__vector__1, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => ((real_V2000881966t_dist @ ((finite_Cartesian_vec @ A) @ numeral_num1)) = (^ [X2:((finite_Cartesian_vec @ A) @ numeral_num1),Y3:((finite_Cartesian_vec @ A) @ numeral_num1)]: ((((real_V2000881966t_dist @ A) @ ((((finite1433825200ec_nth @ A) @ numeral_num1) @ X2) @ (one_one @ numeral_num1))) @ ((((finite1433825200ec_nth @ A) @ numeral_num1) @ Y3) @ (one_one @ numeral_num1)))))))))).
% 3.74/1.77 thf(fact_127_norm__real, axiom, ((real_V1127708846m_norm @ ((finite_Cartesian_vec @ real) @ numeral_num1)) = (^ [X2:((finite_Cartesian_vec @ real) @ numeral_num1)]: (((abs_abs @ real) @ ((((finite1433825200ec_nth @ real) @ numeral_num1) @ X2) @ (one_one @ numeral_num1))))))).
% 3.74/1.77 thf(fact_128_ceiling__diff__floor__le__1, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: ((((ord_less_eq @ int) @ (((minus_minus @ int) @ ((archimedean_ceiling @ A) @ X)) @ ((archim2085082626_floor @ A) @ X))) @ (one_one @ int)))))))).
% 3.74/1.77 thf(fact_129_ceiling__less__iff, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A,Z:int]: (((((ord_less @ int) @ ((archimedean_ceiling @ A) @ X)) @ Z) = (((ord_less_eq @ A) @ X) @ (((minus_minus @ A) @ ((ring_1_of_int @ A) @ Z)) @ (one_one @ A)))))))))).
% 3.74/1.77 thf(fact_130_abs__triangle__ineq2__sym, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B3:A]: ((((ord_less_eq @ A) @ (((minus_minus @ A) @ ((abs_abs @ A) @ A2)) @ ((abs_abs @ A) @ B3))) @ ((abs_abs @ A) @ (((minus_minus @ A) @ B3) @ A2))))))))).
% 3.74/1.77 thf(fact_131_abs__triangle__ineq3, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B3:A]: ((((ord_less_eq @ A) @ ((abs_abs @ A) @ (((minus_minus @ A) @ ((abs_abs @ A) @ A2)) @ ((abs_abs @ A) @ B3)))) @ ((abs_abs @ A) @ (((minus_minus @ A) @ A2) @ B3))))))))).
% 3.74/1.77 thf(fact_132_abs__triangle__ineq2, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B3:A]: ((((ord_less_eq @ A) @ (((minus_minus @ A) @ ((abs_abs @ A) @ A2)) @ ((abs_abs @ A) @ B3))) @ ((abs_abs @ A) @ (((minus_minus @ A) @ A2) @ B3))))))))).
% 3.74/1.77 thf(fact_133_norm__le__componentwise__cart, axiom, (! [A:$tType,N:$tType,B:$tType]: ((((real_V55928688vector @ B) & ((finite_finite @ N) & (real_V55928688vector @ A))) => (! [X:((finite_Cartesian_vec @ A) @ N),Y:((finite_Cartesian_vec @ B) @ N)]: (((! [I4:N]: ((((ord_less_eq @ real) @ ((real_V1127708846m_norm @ A) @ ((((finite1433825200ec_nth @ A) @ N) @ X) @ I4))) @ ((real_V1127708846m_norm @ B) @ ((((finite1433825200ec_nth @ B) @ N) @ Y) @ I4))))) => (((ord_less_eq @ real) @ ((real_V1127708846m_norm @ ((finite_Cartesian_vec @ A) @ N)) @ X)) @ ((real_V1127708846m_norm @ ((finite_Cartesian_vec @ B) @ N)) @ Y))))))))).
% 3.74/1.77 thf(fact_134_Finite__Cartesian__Product_Onorm__nth__le, axiom, (! [B:$tType,A:$tType]: ((((real_V55928688vector @ A) & (finite_finite @ B)) => (! [X:((finite_Cartesian_vec @ A) @ B),I2:B]: ((((ord_less_eq @ real) @ ((real_V1127708846m_norm @ A) @ ((((finite1433825200ec_nth @ A) @ B) @ X) @ I2))) @ ((real_V1127708846m_norm @ ((finite_Cartesian_vec @ A) @ B)) @ X)))))))).
% 3.74/1.77 thf(fact_135_real__of__int__floor__ge__diff__one, axiom, (! [R:real]: ((((ord_less_eq @ real) @ (((minus_minus @ real) @ R) @ (one_one @ real))) @ ((ring_1_of_int @ real) @ ((archim2085082626_floor @ real) @ R)))))).
% 3.74/1.77 thf(fact_136_of__int__floor__le, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: ((((ord_less_eq @ A) @ ((ring_1_of_int @ A) @ ((archim2085082626_floor @ A) @ X))) @ X))))))).
% 3.74/1.77 thf(fact_137_le__of__int__ceiling, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ ((ring_1_of_int @ A) @ ((archimedean_ceiling @ A) @ X))))))))).
% 3.74/1.77 thf(fact_138_norm__bound__component__le__cart, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [X:((finite_Cartesian_vec @ real) @ A),E:real,I2:A]: (((((ord_less_eq @ real) @ ((real_V1127708846m_norm @ ((finite_Cartesian_vec @ real) @ A)) @ X)) @ E) => (((ord_less_eq @ real) @ ((abs_abs @ real) @ ((((finite1433825200ec_nth @ real) @ A) @ X) @ I2))) @ E)))))))).
% 3.74/1.77 thf(fact_139_component__le__norm__cart, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [X:((finite_Cartesian_vec @ real) @ A),I2:A]: ((((ord_less_eq @ real) @ ((abs_abs @ real) @ ((((finite1433825200ec_nth @ real) @ A) @ X) @ I2))) @ ((real_V1127708846m_norm @ ((finite_Cartesian_vec @ real) @ A)) @ X)))))))).
% 3.74/1.77 thf(fact_140_dist__real, axiom, ((real_V2000881966t_dist @ ((finite_Cartesian_vec @ real) @ numeral_num1)) = (^ [X2:((finite_Cartesian_vec @ real) @ numeral_num1),Y3:((finite_Cartesian_vec @ real) @ numeral_num1)]: (((abs_abs @ real) @ (((minus_minus @ real) @ ((((finite1433825200ec_nth @ real) @ numeral_num1) @ X2) @ (one_one @ numeral_num1))) @ ((((finite1433825200ec_nth @ real) @ numeral_num1) @ Y3) @ (one_one @ numeral_num1)))))))).
% 3.74/1.77 thf(fact_141_floor__le__ceiling, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: ((((ord_less_eq @ int) @ ((archim2085082626_floor @ A) @ X)) @ ((archimedean_ceiling @ A) @ X)))))))).
% 3.74/1.77 thf(fact_142_of__int__ceiling__diff__one__le, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [R:A]: ((((ord_less_eq @ A) @ (((minus_minus @ A) @ ((ring_1_of_int @ A) @ ((archimedean_ceiling @ A) @ R))) @ (one_one @ A))) @ R))))))).
% 3.74/1.77 thf(fact_143_norm__triangle__ineq2, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [A2:A,B3:A]: ((((ord_less_eq @ real) @ (((minus_minus @ real) @ ((real_V1127708846m_norm @ A) @ A2)) @ ((real_V1127708846m_norm @ A) @ B3))) @ ((real_V1127708846m_norm @ A) @ (((minus_minus @ A) @ A2) @ B3))))))))).
% 3.74/1.77 thf(fact_144_abs__dist__diff__le, axiom, (! [A:$tType]: (((real_V2090557954_space @ A) => (! [A2:A,B3:A,C:A]: ((((ord_less_eq @ real) @ ((abs_abs @ real) @ (((minus_minus @ real) @ (((real_V2000881966t_dist @ A) @ A2) @ B3)) @ (((real_V2000881966t_dist @ A) @ B3) @ C)))) @ (((real_V2000881966t_dist @ A) @ A2) @ C)))))))).
% 3.74/1.77 thf(fact_145_metric__eq__thm, axiom, (! [A5:$tType]: (((real_V2090557954_space @ A5) => (! [X5:A5,S:(set @ A5),Y4:A5]: (((((member @ A5) @ X5) @ S) => ((((member @ A5) @ Y4) @ S) => ((X5 = Y4) = (! [X2:A5]: (((((member @ A5) @ X2) @ S) => ((((real_V2000881966t_dist @ A5) @ X5) @ X2) = (((real_V2000881966t_dist @ A5) @ Y4) @ X2)))))))))))))).
% 3.74/1.77 thf(fact_146_dist__vec__nth__le, axiom, (! [D2:$tType,C2:$tType]: ((((real_V2090557954_space @ C2) & (finite_finite @ D2)) => (! [X:((finite_Cartesian_vec @ C2) @ D2),I2:D2,Y:((finite_Cartesian_vec @ C2) @ D2)]: ((((ord_less_eq @ real) @ (((real_V2000881966t_dist @ C2) @ ((((finite1433825200ec_nth @ C2) @ D2) @ X) @ I2)) @ ((((finite1433825200ec_nth @ C2) @ D2) @ Y) @ I2))) @ (((real_V2000881966t_dist @ ((finite_Cartesian_vec @ C2) @ D2)) @ X) @ Y)))))))).
% 3.74/1.77 thf(fact_147_norm__triangle__ineq3, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [A2:A,B3:A]: ((((ord_less_eq @ real) @ ((abs_abs @ real) @ (((minus_minus @ real) @ ((real_V1127708846m_norm @ A) @ A2)) @ ((real_V1127708846m_norm @ A) @ B3)))) @ ((real_V1127708846m_norm @ A) @ (((minus_minus @ A) @ A2) @ B3))))))))).
% 3.74/1.77 thf(fact_148_ceiling__correct, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [X:A]: (((((ord_less @ A) @ (((minus_minus @ A) @ ((ring_1_of_int @ A) @ ((archimedean_ceiling @ A) @ X))) @ (one_one @ A))) @ X) & (((ord_less_eq @ A) @ X) @ ((ring_1_of_int @ A) @ ((archimedean_ceiling @ A) @ X)))))))))).
% 3.74/1.77 thf(fact_149_ceiling__unique, axiom, (! [A:$tType]: (((archim1727834104eiling @ A) => (! [Z:int,X:A]: (((((ord_less @ A) @ (((minus_minus @ A) @ ((ring_1_of_int @ A) @ Z)) @ (one_one @ A))) @ X) => ((((ord_less_eq @ A) @ X) @ ((ring_1_of_int @ A) @ Z)) => (((archimedean_ceiling @ A) @ X) = Z))))))))).
% 3.74/1.77 thf(fact_150_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 3.74/1.77 thf(fact_151_complete__interval, axiom, (! [A:$tType]: (((condit1037483654norder @ A) => (! [A2:A,B3:A,P:(A > $o)]: (((((ord_less @ A) @ A2) @ B3) => ((P @ A2) => ((~ ((P @ B3))) => (? [C3:A]: (((((ord_less_eq @ A) @ A2) @ C3) & ((((ord_less_eq @ A) @ C3) @ B3) & ((! [X6:A]: ((((((ord_less_eq @ A) @ A2) @ X6) & (((ord_less @ A) @ X6) @ C3)) => (P @ X6)))) & (! [D3:A]: (((! [X4:A]: ((((((ord_less_eq @ A) @ A2) @ X4) & (((ord_less @ A) @ X4) @ D3)) => (P @ X4)))) => (((ord_less_eq @ A) @ D3) @ C3)))))))))))))))))).
% 3.74/1.77 thf(fact_152_eucl__less__le__not__le, axiom, (! [A:$tType]: (((ordere890947078_space @ A) => ((ord_less @ A) = (^ [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) & (~ ((((ord_less_eq @ A) @ Y3) @ X2))))))))))).
% 3.74/1.77 thf(fact_153_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A]: (((A2 != B3) => ((((ord_less_eq @ A) @ A2) @ B3) => (((ord_less @ A) @ A2) @ B3))))))))).
% 3.74/1.77 thf(fact_154_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A]: (((((ord_less @ A) @ B3) @ A2) => (((ord_less_eq @ A) @ B3) @ A2)))))))).
% 3.74/1.77 thf(fact_155_vector__one__nth, axiom, (! [A:$tType,X:((finite_Cartesian_vec @ A) @ numeral_num1)]: (((((finite_Cartesian_vec2 @ A) @ numeral_num1) @ ((((finite1433825200ec_nth @ A) @ numeral_num1) @ X) @ (one_one @ numeral_num1))) = X)))).
% 3.74/1.77 thf(fact_156_less__vec__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) & (finite_finite @ B)) => ((ord_less @ ((finite_Cartesian_vec @ A) @ B)) = (^ [X2:((finite_Cartesian_vec @ A) @ B),Y3:((finite_Cartesian_vec @ A) @ B)]: (((((ord_less_eq @ ((finite_Cartesian_vec @ A) @ B)) @ X2) @ Y3) & (~ ((((ord_less_eq @ ((finite_Cartesian_vec @ A) @ B)) @ Y3) @ X2))))))))))).
% 3.74/1.77 thf(fact_157_complete__real, axiom, (! [S2:(set @ real)]: (((? [X6:real]: ((((member @ real) @ X6) @ S2))) => ((? [Z4:real]: ((! [X4:real]: (((((member @ real) @ X4) @ S2) => (((ord_less_eq @ real) @ X4) @ Z4)))))) => (? [Y5:real]: (((! [X6:real]: (((((member @ real) @ X6) @ S2) => (((ord_less_eq @ real) @ X6) @ Y5)))) & (! [Z4:real]: (((! [X4:real]: (((((member @ real) @ X4) @ S2) => (((ord_less_eq @ real) @ X4) @ Z4)))) => (((ord_less_eq @ real) @ Y5) @ Z4)))))))))))).
% 3.74/1.77 thf(fact_158_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ A2) @ B3) => (A2 = B3))))))))).
% 3.74/1.77 thf(fact_159_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y2:A,Z2:A]: ((Y2 = Z2))) = (^ [A6:A,B4:A]: (((((ord_less_eq @ A) @ B4) @ A6) & (((ord_less_eq @ A) @ A6) @ B4))))))))).
% 3.74/1.77 thf(fact_160_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ C) @ B3) => (((ord_less_eq @ A) @ C) @ A2))))))))).
% 3.74/1.77 thf(fact_161_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B3:A]: (((! [A7:A,B5:A]: (((((ord_less_eq @ A) @ A7) @ B5) => ((P @ A7) @ B5)))) => ((! [A7:A,B5:A]: ((((P @ B5) @ A7) => ((P @ A7) @ B5)))) => ((P @ A2) @ B3))))))))).
% 3.74/1.77 thf(fact_162_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 3.74/1.77 thf(fact_163_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less_eq @ A) @ X) @ Z))))))))).
% 3.74/1.77 thf(fact_164_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ A2) => (A2 = B3))))))))).
% 3.74/1.77 thf(fact_165_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((B3 = C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 3.74/1.77 thf(fact_166_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B3:A,C:A]: (((A2 = B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 3.74/1.77 thf(fact_167_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y2:A,Z2:A]: ((Y2 = Z2))) = (^ [A6:A,B4:A]: (((((ord_less_eq @ A) @ A6) @ B4) & (((ord_less_eq @ A) @ B4) @ A6))))))))).
% 3.74/1.77 thf(fact_168_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 3.74/1.77 thf(fact_169_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A,Z:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z)))) => (((((ord_less_eq @ A) @ X) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ Y)))) => (((((ord_less_eq @ A) @ Z) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ X)))) => (~ (((((ord_less_eq @ A) @ Z) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 3.74/1.77 thf(fact_170_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 3.74/1.77 thf(fact_171_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 3.74/1.77 thf(fact_172_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 3.74/1.77 thf(fact_173_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 3.74/1.77 thf(fact_174_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 3.74/1.77 thf(fact_175_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y2:A,Z2:A]: ((Y2 = Z2))) = (^ [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) & (((ord_less_eq @ A) @ Y3) @ X2))))))))).
% 3.74/1.77 thf(fact_176_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B3:A,F:(A > B),C:B]: (((((ord_less_eq @ A) @ A2) @ B3) => (((F @ B3) = C) => ((! [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) => (((ord_less_eq @ B) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C)))))))))).
% 3.74/1.77 thf(fact_177_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B3:B,C:B]: (((A2 = (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C) => ((! [X4:B,Y5:B]: (((((ord_less_eq @ B) @ X4) @ Y5) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 3.74/1.77 thf(fact_178_order__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A2:A,B3:A,F:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ C2) @ (F @ B3)) @ C) => ((! [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) => (((ord_less_eq @ C2) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less_eq @ C2) @ (F @ A2)) @ C)))))))))).
% 3.74/1.77 thf(fact_179_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B3:B,C:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C) => ((! [X4:B,Y5:B]: (((((ord_less_eq @ B) @ X4) @ Y5) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 3.74/1.77 thf(fact_180_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X2:A]: ((((ord_less_eq @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))))).
% 3.74/1.77 thf(fact_181_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X4:A]: ((((ord_less_eq @ B) @ (F @ X4)) @ (G @ X4)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 3.74/1.77 thf(fact_182_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 3.74/1.77 thf(fact_183_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 3.74/1.77 thf(fact_184_ex__gt__or__lt, axiom, (! [A:$tType]: (((condit1656338222tinuum @ A) => (! [A2:A]: ((? [B5:A]: (((((ord_less @ A) @ A2) @ B5) | (((ord_less @ A) @ B5) @ A2)))))))))).
% 3.74/1.77 thf(fact_185_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A]: (((((ord_less @ A) @ B3) @ A2) => (A2 != B3)))))))).
% 3.74/1.77 thf(fact_186_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (A2 != B3)))))))).
% 3.74/1.77 thf(fact_187_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) = ((((ord_less @ A) @ Y) @ X) | (X = Y))))))))).
% 3.74/1.77 thf(fact_188_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A,C:A]: (((((ord_less @ A) @ B3) @ A2) => ((((ord_less @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ A2))))))))).
% 3.74/1.77 thf(fact_189_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B3:A]: (((! [A7:A,B5:A]: (((((ord_less @ A) @ A7) @ B5) => ((P @ A7) @ B5)))) => ((! [A7:A]: (((P @ A7) @ A7))) => ((! [A7:A,B5:A]: ((((P @ B5) @ A7) => ((P @ A7) @ B5)))) => ((P @ A2) @ B3)))))))))).
% 3.74/1.77 thf(fact_190_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P2:(A > $o)]: ((? [X3:A]: ((P2 @ X3))))) = (^ [P3:(A > $o)]: ((? [N3:A]: (((P3 @ N3) & (! [M3:A]: (((((ord_less @ A) @ M3) @ N3) => (~ ((P3 @ M3)))))))))))))))).
% 3.74/1.77 thf(fact_191_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 3.74/1.77 thf(fact_192_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A,C:A]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less @ A) @ B3) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 3.74/1.77 thf(fact_193_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 3.74/1.77 thf(fact_194_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((X != Y) => (((ord_less @ A) @ Y) @ X))))))))).
% 3.74/1.77 thf(fact_195_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,P:$o]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ X) => P)))))))).
% 3.74/1.77 thf(fact_196_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (Y != X)))))))).
% 3.74/1.77 thf(fact_197_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y:A,X:A]: (((~ ((((ord_less @ A) @ Y) @ X))) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 3.74/1.77 thf(fact_198_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P:(A > $o),A2:A]: (((! [X4:A]: (((! [Y6:A]: (((((ord_less @ A) @ Y6) @ X4) => (P @ Y6)))) => (P @ X4)))) => (P @ A2)))))))).
% 3.74/1.77 thf(fact_199_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 3.74/1.77 thf(fact_200_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 3.74/1.77 thf(fact_201_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A]: (((((ord_less @ A) @ B3) @ A2) => (~ ((((ord_less @ A) @ A2) @ B3)))))))))).
% 3.74/1.77 thf(fact_202_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B3:A,C:A]: (((((ord_less @ A) @ A2) @ B3) => ((B3 = C) => (((ord_less @ A) @ A2) @ C))))))))).
% 3.74/1.77 thf(fact_203_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B3:A,C:A]: (((A2 = B3) => ((((ord_less @ A) @ B3) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 3.74/1.77 thf(fact_204_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((~ ((((ord_less @ A) @ X) @ X))))))))).
% 3.74/1.77 thf(fact_205_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) | ((X = Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 3.74/1.77 thf(fact_206_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z) => (((ord_less @ A) @ X) @ Z))))))))).
% 3.74/1.77 thf(fact_207_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (~ ((((ord_less @ A) @ B3) @ A2)))))))))).
% 3.74/1.77 thf(fact_208_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 3.74/1.77 thf(fact_209_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 3.74/1.77 thf(fact_210_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (? [Z3:A]: (((((ord_less @ A) @ X) @ Z3) & (((ord_less @ A) @ Z3) @ Y))))))))))).
% 3.74/1.77 thf(fact_211_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (~ ((((ord_less @ A) @ B3) @ A2)))))))))).
% 3.74/1.77 thf(fact_212_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((X != Y) = ((((ord_less @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 3.74/1.77 thf(fact_213_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 3.74/1.77 thf(fact_214_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X:A]: ((? [X_1:A]: ((((ord_less @ A) @ X) @ X_1))))))))).
% 3.74/1.77 thf(fact_215_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X:A]: ((? [Y5:A]: ((((ord_less @ A) @ Y5) @ X))))))))).
% 3.74/1.77 thf(fact_216_order__less__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A2:A,B3:A,F:(A > C2),C:C2]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less @ C2) @ (F @ B3)) @ C) => ((! [X4:A,Y5:A]: (((((ord_less @ A) @ X4) @ Y5) => (((ord_less @ C2) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less @ C2) @ (F @ A2)) @ C)))))))))).
% 3.74/1.77 thf(fact_217_order__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B3:B,C:B]: (((((ord_less @ A) @ A2) @ (F @ B3)) => ((((ord_less @ B) @ B3) @ C) => ((! [X4:B,Y5:B]: (((((ord_less @ B) @ X4) @ Y5) => (((ord_less @ A) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 3.74/1.77 thf(fact_218_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B3:A,F:(A > B),C:B]: (((((ord_less @ A) @ A2) @ B3) => (((F @ B3) = C) => ((! [X4:A,Y5:A]: (((((ord_less @ A) @ X4) @ Y5) => (((ord_less @ B) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less @ B) @ (F @ A2)) @ C)))))))))).
% 3.74/1.77 thf(fact_219_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B3:B,C:B]: (((A2 = (F @ B3)) => ((((ord_less @ B) @ B3) @ C) => ((! [X4:B,Y5:B]: (((((ord_less @ B) @ X4) @ Y5) => (((ord_less @ A) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 3.74/1.77 thf(fact_220_leD, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less @ A) @ X) @ Y)))))))))).
% 3.74/1.77 thf(fact_221_leI, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 3.74/1.77 thf(fact_222_le__less, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [X2:A,Y3:A]: (((((ord_less @ A) @ X2) @ Y3) | (X2 = Y3))))))))).
% 3.74/1.77 thf(fact_223_less__le, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) & (X2 != Y3))))))))).
% 3.74/1.77 thf(fact_224_order__le__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B3:B,C:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B3)) => ((((ord_less @ B) @ B3) @ C) => ((! [X4:B,Y5:B]: (((((ord_less @ B) @ X4) @ Y5) => (((ord_less @ A) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 3.74/1.77 thf(fact_225_order__le__less__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A2:A,B3:A,F:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less @ C2) @ (F @ B3)) @ C) => ((! [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) => (((ord_less_eq @ C2) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less @ C2) @ (F @ A2)) @ C)))))))))).
% 3.74/1.77 thf(fact_226_order__less__le__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B3:B,C:B]: (((((ord_less @ A) @ A2) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C) => ((! [X4:B,Y5:B]: (((((ord_less_eq @ B) @ X4) @ Y5) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 3.74/1.77 thf(fact_227_order__less__le__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A2:A,B3:A,F:(A > C2),C:C2]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less_eq @ C2) @ (F @ B3)) @ C) => ((! [X4:A,Y5:A]: (((((ord_less @ A) @ X4) @ Y5) => (((ord_less @ C2) @ (F @ X4)) @ (F @ Y5))))) => (((ord_less @ C2) @ (F @ A2)) @ C)))))))))).
% 3.74/1.77 thf(fact_228_not__le, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) = (((ord_less @ A) @ Y) @ X)))))))).
% 3.74/1.77 thf(fact_229_not__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) = (((ord_less_eq @ A) @ Y) @ X)))))))).
% 3.74/1.77 thf(fact_230_le__neq__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((A2 != B3) => (((ord_less @ A) @ A2) @ B3))))))))).
% 3.74/1.77 thf(fact_231_antisym__conv1, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 3.74/1.77 thf(fact_232_antisym__conv2, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 3.74/1.77 thf(fact_233_less__imp__le, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 3.74/1.77 thf(fact_234_le__less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z) => (((ord_less @ A) @ X) @ Z))))))))).
% 3.74/1.77 thf(fact_235_less__le__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less @ A) @ X) @ Z))))))))).
% 3.74/1.77 thf(fact_236_dense__ge, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z:A,Y:A]: (((! [X4:A]: (((((ord_less @ A) @ Z) @ X4) => (((ord_less_eq @ A) @ Y) @ X4)))) => (((ord_less_eq @ A) @ Y) @ Z)))))))).
% 3.74/1.77 thf(fact_237_dense__le, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Y:A,Z:A]: (((! [X4:A]: (((((ord_less @ A) @ X4) @ Y) => (((ord_less_eq @ A) @ X4) @ Z)))) => (((ord_less_eq @ A) @ Y) @ Z)))))))).
% 3.74/1.77 thf(fact_238_le__less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X)))))))).
% 3.74/1.77 thf(fact_239_le__imp__less__or__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less @ A) @ X) @ Y) | (X = Y))))))))).
% 3.74/1.77 thf(fact_240_less__le__not__le, axiom, (! [A:$tType]: (((preorder @ A) => ((ord_less @ A) = (^ [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) & (~ ((((ord_less_eq @ A) @ Y3) @ X2))))))))))).
% 3.74/1.77 thf(fact_241_not__le__imp__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y:A,X:A]: (((~ ((((ord_less_eq @ A) @ Y) @ X))) => (((ord_less @ A) @ X) @ Y)))))))).
% 3.74/1.77 thf(fact_242_order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less @ A) @ B3) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 3.74/1.77 thf(fact_243_order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A,C:A]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 3.74/1.77 thf(fact_244_order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [A6:A,B4:A]: (((((ord_less @ A) @ A6) @ B4) | (A6 = B4))))))))).
% 3.74/1.77 thf(fact_245_order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [A6:A,B4:A]: (((((ord_less_eq @ A) @ A6) @ B4) & (A6 != B4))))))))).
% 3.74/1.77 thf(fact_246_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ A2))))))))).
% 3.74/1.77 thf(fact_247_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A,C:A]: (((((ord_less @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ A2))))))))).
% 3.74/1.77 thf(fact_248_dense__ge__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z:A,X:A,Y:A]: (((((ord_less @ A) @ Z) @ X) => ((! [W2:A]: (((((ord_less @ A) @ Z) @ W2) => ((((ord_less @ A) @ W2) @ X) => (((ord_less_eq @ A) @ Y) @ W2))))) => (((ord_less_eq @ A) @ Y) @ Z))))))))).
% 3.74/1.77 thf(fact_249_dense__le__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [X:A,Y:A,Z:A]: (((((ord_less @ A) @ X) @ Y) => ((! [W2:A]: (((((ord_less @ A) @ X) @ W2) => ((((ord_less @ A) @ W2) @ Y) => (((ord_less_eq @ A) @ W2) @ Z))))) => (((ord_less_eq @ A) @ Y) @ Z))))))))).
% 3.74/1.77 thf(fact_250_order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (((ord_less_eq @ A) @ A2) @ B3)))))))).
% 3.74/1.77 thf(fact_251_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [B4:A,A6:A]: (((((ord_less @ A) @ B4) @ A6) | (A6 = B4))))))))).
% 3.74/1.77 thf(fact_252_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [B4:A,A6:A]: (((((ord_less_eq @ A) @ B4) @ A6) & (A6 != B4))))))))).
% 3.74/1.77 thf(fact_253_forall__1, axiom, ((^ [P2:(numeral_num1 > $o)]: ((! [X3:numeral_num1]: ((P2 @ X3))))) = (^ [P3:(numeral_num1 > $o)]: ((P3 @ (one_one @ numeral_num1)))))).
% 3.74/1.77 thf(fact_254_ex__1, axiom, ((^ [P2:(numeral_num1 > $o)]: ((? [X3:numeral_num1]: ((P2 @ X3))))) = (^ [P3:(numeral_num1 > $o)]: ((P3 @ (one_one @ numeral_num1)))))).
% 3.74/1.77 thf(subcl_Finite__Set_Ofinite___HOL_Otype, axiom, (! [A:$tType]: (((finite_finite @ A) => (type @ A))))).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Cardinality_OCARD__1, axiom, (cARD_1 @ numeral_num1)).
% 3.74/1.77 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A5:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A5 > A8)))))).
% 3.74/1.77 thf(tcon_fun___Finite__Set_Ofinite, axiom, (! [A5:$tType,A8:$tType]: ((((finite_finite @ A5) & (finite_finite @ A8)) => (finite_finite @ (A5 > A8)))))).
% 3.74/1.77 thf(tcon_fun___Orderings_Oorder, axiom, (! [A5:$tType,A8:$tType]: (((order @ A8) => (order @ (A5 > A8)))))).
% 3.74/1.77 thf(tcon_fun___Orderings_Oord, axiom, (! [A5:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A5 > A8)))))).
% 3.74/1.77 thf(tcon_fun___Groups_Ominus, axiom, (! [A5:$tType,A8:$tType]: (((minus @ A8) => (minus @ (A5 > A8)))))).
% 3.74/1.77 thf(tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, axiom, (condit1037483654norder @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add__abs, axiom, (ordere142940540dd_abs @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add, axiom, (cancel146912293up_add @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add, axiom, (ordered_ab_group_add @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Rings_Olinordered__idom, axiom, (linordered_idom @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Rings_Oidom__abs__sgn, axiom, (idom_abs_sgn @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Orderings_Opreorder_1, axiom, (preorder @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Orderings_Olinorder, axiom, (linorder @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Groups_Omonoid__mult, axiom, (monoid_mult @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Orderings_Ono__top, axiom, (no_top @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Orderings_Ono__bot, axiom, (no_bot @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Groups_Ogroup__add, axiom, (group_add @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Orderings_Oorder_2, axiom, (order @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Nat_Oring__char__0, axiom, (ring_char_0 @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Orderings_Oord_3, axiom, (ord @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Rings_Oring__1, axiom, (ring_1 @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Groups_Ominus_4, axiom, (minus @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Groups_Ozero, axiom, (zero @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Rings_Oring, axiom, (ring @ int)).
% 3.74/1.77 thf(tcon_Int_Oint___Groups_Oone, axiom, (one @ int)).
% 3.74/1.77 thf(tcon_Set_Oset___Orderings_Opreorder_5, axiom, (! [A5:$tType]: ((preorder @ (set @ A5))))).
% 3.74/1.77 thf(tcon_Set_Oset___Groups_Omonoid__mult_6, axiom, (! [A5:$tType]: (((monoid_mult @ A5) => (monoid_mult @ (set @ A5)))))).
% 3.74/1.77 thf(tcon_Set_Oset___Finite__Set_Ofinite_7, axiom, (! [A5:$tType]: (((finite_finite @ A5) => (finite_finite @ (set @ A5)))))).
% 3.74/1.77 thf(tcon_Set_Oset___Orderings_Oorder_8, axiom, (! [A5:$tType]: ((order @ (set @ A5))))).
% 3.74/1.77 thf(tcon_Set_Oset___Orderings_Oord_9, axiom, (! [A5:$tType]: ((ord @ (set @ A5))))).
% 3.74/1.77 thf(tcon_Set_Oset___Groups_Ominus_10, axiom, (! [A5:$tType]: ((minus @ (set @ A5))))).
% 3.74/1.77 thf(tcon_Set_Oset___Groups_Ozero_11, axiom, (! [A5:$tType]: (((zero @ A5) => (zero @ (set @ A5)))))).
% 3.74/1.77 thf(tcon_Set_Oset___Groups_Oone_12, axiom, (! [A5:$tType]: (((one @ A5) => (one @ (set @ A5)))))).
% 3.74/1.77 thf(tcon_HOL_Obool___Orderings_Opreorder_13, axiom, (preorder @ $o)).
% 3.74/1.77 thf(tcon_HOL_Obool___Orderings_Olinorder_14, axiom, (linorder @ $o)).
% 3.74/1.77 thf(tcon_HOL_Obool___Finite__Set_Ofinite_15, axiom, (finite_finite @ $o)).
% 3.74/1.77 thf(tcon_HOL_Obool___Orderings_Oorder_16, axiom, (order @ $o)).
% 3.74/1.77 thf(tcon_HOL_Obool___Orderings_Oord_17, axiom, (ord @ $o)).
% 3.74/1.77 thf(tcon_HOL_Obool___Groups_Ominus_18, axiom, (minus @ $o)).
% 3.74/1.77 thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_19, axiom, (condit1037483654norder @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Olinear__continuum, axiom, (condit1656338222tinuum @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space, axiom, (ordere890947078_space @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__algebra__1, axiom, (real_V1229719638ebra_1 @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector, axiom, (real_V55928688vector @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Archimedean__Field_Oarchimedean__field, axiom, (archim1804426504_field @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_20, axiom, (linord1659791738miring @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space, axiom, (real_V2090557954_space @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs_21, axiom, (ordere142940540dd_abs @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Archimedean__Field_Ofloor__ceiling, axiom, (archim1727834104eiling @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_22, axiom, (cancel146912293up_add @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Real__Vector__Spaces_Odist__norm, axiom, (real_V1639655670t_norm @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add_23, axiom, (ordered_ab_group_add @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Orderings_Odense__linorder, axiom, (dense_linorder @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Rings_Olinordered__idom_24, axiom, (linordered_idom @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Orderings_Odense__order, axiom, (dense_order @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Rings_Oidom__abs__sgn_25, axiom, (idom_abs_sgn @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Orderings_Opreorder_26, axiom, (preorder @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Orderings_Olinorder_27, axiom, (linorder @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Groups_Omonoid__mult_28, axiom, (monoid_mult @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Orderings_Ono__top_29, axiom, (no_top @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Orderings_Ono__bot_30, axiom, (no_bot @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Groups_Ogroup__add_31, axiom, (group_add @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Orderings_Oorder_32, axiom, (order @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Nat_Oring__char__0_33, axiom, (ring_char_0 @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Orderings_Oord_34, axiom, (ord @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Rings_Oring__1_35, axiom, (ring_1 @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Groups_Ominus_36, axiom, (minus @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Fields_Ofield, axiom, (field @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Groups_Ozero_37, axiom, (zero @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Rings_Oring_38, axiom, (ring @ real)).
% 3.74/1.77 thf(tcon_Real_Oreal___Groups_Oone_39, axiom, (one @ real)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Groups_Ocancel__ab__semigroup__add_40, axiom, (cancel146912293up_add @ numeral_num1)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Orderings_Owellorder, axiom, (wellorder @ numeral_num1)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Orderings_Opreorder_41, axiom, (preorder @ numeral_num1)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Orderings_Olinorder_42, axiom, (linorder @ numeral_num1)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Groups_Omonoid__mult_43, axiom, (monoid_mult @ numeral_num1)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Finite__Set_Ofinite_44, axiom, (finite_finite @ numeral_num1)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Groups_Ogroup__add_45, axiom, (group_add @ numeral_num1)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Orderings_Oorder_46, axiom, (order @ numeral_num1)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Orderings_Oord_47, axiom, (ord @ numeral_num1)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Groups_Ominus_48, axiom, (minus @ numeral_num1)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Groups_Ozero_49, axiom, (zero @ numeral_num1)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Rings_Oring_50, axiom, (ring @ numeral_num1)).
% 3.74/1.77 thf(tcon_Numeral__Type_Onum1___Groups_Oone_51, axiom, (one @ numeral_num1)).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space_52, axiom, (! [A5:$tType,A8:$tType]: ((((ordere890947078_space @ A5) & (finite_finite @ A8)) => (ordere890947078_space @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_53, axiom, (! [A5:$tType,A8:$tType]: ((((real_V55928688vector @ A5) & (finite_finite @ A8)) => (real_V55928688vector @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Ometric__space_54, axiom, (! [A5:$tType,A8:$tType]: ((((real_V2090557954_space @ A5) & (finite_finite @ A8)) => (real_V2090557954_space @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add__abs_55, axiom, (! [A5:$tType,A8:$tType]: ((((ordere890947078_space @ A5) & (finite_finite @ A8)) => (ordere142940540dd_abs @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__ab__semigroup__add_56, axiom, (! [A5:$tType,A8:$tType]: ((((cancel146912293up_add @ A5) & (finite_finite @ A8)) => (cancel146912293up_add @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Odist__norm_57, axiom, (! [A5:$tType,A8:$tType]: ((((real_V55928688vector @ A5) & (finite_finite @ A8)) => (real_V1639655670t_norm @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add_58, axiom, (! [A5:$tType,A8:$tType]: ((((ordere890947078_space @ A5) & (finite_finite @ A8)) => (ordered_ab_group_add @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Opreorder_59, axiom, (! [A5:$tType,A8:$tType]: ((((order @ A5) & (finite_finite @ A8)) => (preorder @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Olinorder_60, axiom, (! [A5:$tType,A8:$tType]: ((((linorder @ A5) & (cARD_1 @ A8)) => (linorder @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Omonoid__mult_61, axiom, (! [A5:$tType,A8:$tType]: ((((monoid_mult @ A5) & (finite_finite @ A8)) => (monoid_mult @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_62, axiom, (! [A5:$tType,A8:$tType]: ((((finite_finite @ A5) & (finite_finite @ A8)) => (finite_finite @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ogroup__add_63, axiom, (! [A5:$tType,A8:$tType]: ((((group_add @ A5) & (finite_finite @ A8)) => (group_add @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oorder_64, axiom, (! [A5:$tType,A8:$tType]: ((((order @ A5) & (finite_finite @ A8)) => (order @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Nat_Oring__char__0_65, axiom, (! [A5:$tType,A8:$tType]: ((((ring_char_0 @ A5) & (finite_finite @ A8)) => (ring_char_0 @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oord_66, axiom, (! [A5:$tType,A8:$tType]: ((((ord @ A5) & (finite_finite @ A8)) => (ord @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Rings_Oring__1_67, axiom, (! [A5:$tType,A8:$tType]: ((((ring_1 @ A5) & (finite_finite @ A8)) => (ring_1 @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ominus_68, axiom, (! [A5:$tType,A8:$tType]: ((((minus @ A5) & (finite_finite @ A8)) => (minus @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ozero_69, axiom, (! [A5:$tType,A8:$tType]: ((((zero @ A5) & (finite_finite @ A8)) => (zero @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Rings_Oring_70, axiom, (! [A5:$tType,A8:$tType]: ((((ring @ A5) & (finite_finite @ A8)) => (ring @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oone_71, axiom, (! [A5:$tType,A8:$tType]: ((((one @ A5) & (finite_finite @ A8)) => (one @ ((finite_Cartesian_vec @ A5) @ A8)))))).
% 3.74/1.77 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 3.74/1.77 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 3.74/1.77 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 3.74/1.77 thf(tfree_0, hypothesis, (finite_finite @ n)).
% 3.74/1.77 thf(conj_0, conjecture, (((ring_1_of_int @ real) @ ((abs_abs @ int) @ m)) = ((abs_abs @ real) @ ((((finite1433825200ec_nth @ real) @ n) @ (((minus_minus @ ((finite_Cartesian_vec @ real) @ n)) @ x) @ y)) @ i)))).
% 3.74/1.77 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2DTF8750.p
% 3.74/1.77 ------------------------
% 3.97/1.82 ---- Cleaned THF ---
% 3.97/1.83 thf(ty_t_Finite__Cartesian__Product_Ovec,type,
% 3.97/1.83 finite_Cartesian_vec: $tType > $tType > $tType ).
% 3.97/1.83
% 3.97/1.83 thf(ty_t_Numeral__Type_Onum1,type,
% 3.97/1.83 numeral_num1: $tType ).
% 3.97/1.83
% 3.97/1.83 thf(ty_t_Real_Oreal,type,
% 3.97/1.83 real: $tType ).
% 3.97/1.83
% 3.97/1.83 thf(ty_t_Set_Oset,type,
% 3.97/1.83 set: $tType > $tType ).
% 3.97/1.83
% 3.97/1.83 thf(ty_t_Int_Oint,type,
% 3.97/1.83 int: $tType ).
% 3.97/1.83
% 3.97/1.83 thf(ty_tf_n,type,
% 3.97/1.83 n: $tType ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Cardinality_OCARD__1,type,
% 3.97/1.83 cARD_1:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_HOL_Otype,type,
% 3.97/1.83 type:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Groups_Oone,type,
% 3.97/1.83 one:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Rings_Oring,type,
% 3.97/1.83 ring:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Groups_Ozero,type,
% 3.97/1.83 zero:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Fields_Ofield,type,
% 3.97/1.83 field:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Groups_Ominus,type,
% 3.97/1.83 minus:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Rings_Oring__1,type,
% 3.97/1.83 ring_1:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Orderings_Oord,type,
% 3.97/1.83 ord:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Nat_Oring__char__0,type,
% 3.97/1.83 ring_char_0:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Orderings_Oorder,type,
% 3.97/1.83 order:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Groups_Ogroup__add,type,
% 3.97/1.83 group_add:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Orderings_Ono__bot,type,
% 3.97/1.83 no_bot:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Orderings_Ono__top,type,
% 3.97/1.83 no_top:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Finite__Set_Ofinite,type,
% 3.97/1.83 finite_finite:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Groups_Omonoid__mult,type,
% 3.97/1.83 monoid_mult:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Orderings_Olinorder,type,
% 3.97/1.83 linorder:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Orderings_Opreorder,type,
% 3.97/1.83 preorder:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Rings_Oidom__abs__sgn,type,
% 3.97/1.83 idom_abs_sgn:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Orderings_Owellorder,type,
% 3.97/1.83 wellorder:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Orderings_Odense__order,type,
% 3.97/1.83 dense_order:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Rings_Olinordered__idom,type,
% 3.97/1.83 linordered_idom:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Orderings_Odense__linorder,type,
% 3.97/1.83 dense_linorder:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 3.97/1.83 ordered_ab_group_add:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Real__Vector__Spaces_Odist__norm,type,
% 3.97/1.83 real_V1639655670t_norm:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 3.97/1.83 cancel146912293up_add:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Archimedean__Field_Ofloor__ceiling,type,
% 3.97/1.83 archim1727834104eiling:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Groups_Oordered__ab__group__add__abs,type,
% 3.97/1.83 ordere142940540dd_abs:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Real__Vector__Spaces_Ometric__space,type,
% 3.97/1.83 real_V2090557954_space:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 3.97/1.83 linord1659791738miring:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Archimedean__Field_Oarchimedean__field,type,
% 3.97/1.83 archim1804426504_field:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector,type,
% 3.97/1.83 real_V55928688vector:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__algebra__1,type,
% 3.97/1.83 real_V1229719638ebra_1:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Ordered__Euclidean__Space_Oordered__euclidean__space,type,
% 3.97/1.83 ordere890947078_space:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 3.97/1.83 condit1656338222tinuum:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 3.97/1.83 condit1037483654norder:
% 3.97/1.83 !>[A: $tType] : $o ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Archimedean__Field_Oceiling,type,
% 3.97/1.83 archimedean_ceiling:
% 3.97/1.83 !>[A: $tType] : ( A > int ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor,type,
% 3.97/1.83 archim2085082626_floor:
% 3.97/1.83 !>[A: $tType] : ( A > int ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Finite__Cartesian__Product_Oaxis,type,
% 3.97/1.83 finite1218308419n_axis:
% 3.97/1.83 !>[B: $tType,A: $tType] : ( B > A > ( finite_Cartesian_vec @ A @ B ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Finite__Cartesian__Product_Oaxis__index,type,
% 3.97/1.83 finite1115014511_index:
% 3.97/1.83 !>[A: $tType,N: $tType] : ( ( finite_Cartesian_vec @ A @ N ) > N ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Finite__Cartesian__Product_Omap__matrix,type,
% 3.97/1.83 finite1614961371matrix:
% 3.97/1.83 !>[A: $tType,B: $tType,I: $tType,J: $tType] : ( ( A > B ) > ( finite_Cartesian_vec @ ( finite_Cartesian_vec @ A @ I ) @ J ) > ( finite_Cartesian_vec @ ( finite_Cartesian_vec @ B @ I ) @ J ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Finite__Cartesian__Product_Ovec,type,
% 3.97/1.83 finite_Cartesian_vec2:
% 3.97/1.83 !>[A: $tType,B: $tType] : ( A > ( finite_Cartesian_vec @ A @ B ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Finite__Cartesian__Product_Ovec_Ovec__nth,type,
% 3.97/1.83 finite1433825200ec_nth:
% 3.97/1.83 !>[A: $tType,B: $tType] : ( ( finite_Cartesian_vec @ A @ B ) > B > A ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Finite__Cartesian__Product_Ovector__scalar__mult,type,
% 3.97/1.83 finite431509953r_mult:
% 3.97/1.83 !>[A: $tType,N: $tType] : ( A > ( finite_Cartesian_vec @ A @ N ) > ( finite_Cartesian_vec @ A @ N ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Groups_Oabs__class_Oabs,type,
% 3.97/1.83 abs_abs:
% 3.97/1.83 !>[A: $tType] : ( A > A ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 3.97/1.83 minus_minus:
% 3.97/1.83 !>[A: $tType] : ( A > A > A ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Groups_Oone__class_Oone,type,
% 3.97/1.83 one_one:
% 3.97/1.83 !>[A: $tType] : A ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_If,type,
% 3.97/1.83 if:
% 3.97/1.83 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Int_Oring__1__class_OInts,type,
% 3.97/1.83 ring_1_Ints:
% 3.97/1.83 !>[A: $tType] : ( set @ A ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Int_Oring__1__class_Oof__int,type,
% 3.97/1.83 ring_1_of_int:
% 3.97/1.83 !>[A: $tType] : ( int > A ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Minkowskis__Theorem__Mirabelle__jpyvdnlcjd_Oof__int__vec,type,
% 3.97/1.83 minkow1937162798nt_vec:
% 3.97/1.83 !>[B: $tType,A: $tType] : ( ( finite_Cartesian_vec @ int @ B ) > ( finite_Cartesian_vec @ A @ B ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Orderings_Oord__class_Oless,type,
% 3.97/1.83 ord_less:
% 3.97/1.83 !>[A: $tType] : ( A > A > $o ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.97/1.83 ord_less_eq:
% 3.97/1.83 !>[A: $tType] : ( A > A > $o ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist,type,
% 3.97/1.83 real_V2000881966t_dist:
% 3.97/1.83 !>[A: $tType] : ( A > A > real ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm,type,
% 3.97/1.83 real_V1127708846m_norm:
% 3.97/1.83 !>[A: $tType] : ( A > real ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_Set_OCollect,type,
% 3.97/1.83 collect:
% 3.97/1.83 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_c_member,type,
% 3.97/1.83 member:
% 3.97/1.83 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_v_A,type,
% 3.97/1.83 a: set @ ( finite_Cartesian_vec @ real @ n ) ).
% 3.97/1.83
% 3.97/1.83 thf(sy_v_i____,type,
% 3.97/1.83 i: n ).
% 3.97/1.83
% 3.97/1.83 thf(sy_v_m____,type,
% 3.97/1.83 m: int ).
% 3.97/1.83
% 3.97/1.83 thf(sy_v_x____,type,
% 3.97/1.83 x: finite_Cartesian_vec @ real @ n ).
% 3.97/1.83
% 3.97/1.83 thf(sy_v_y____,type,
% 3.97/1.83 y: finite_Cartesian_vec @ real @ n ).
% 3.97/1.83
% 3.97/1.83 thf(fact_0__C1_C_I2_J,axiom,
% 3.97/1.83 member @ ( finite_Cartesian_vec @ real @ n ) @ y @ a ).
% 3.97/1.83
% 3.97/1.83 thf(fact_1__C1_C_I1_J,axiom,
% 3.97/1.83 member @ ( finite_Cartesian_vec @ real @ n ) @ x @ a ).
% 3.97/1.83
% 3.97/1.83 thf(fact_2_m,axiom,
% 3.97/1.83 ( ( ring_1_of_int @ real @ m )
% 3.97/1.83 = ( minus_minus @ real @ ( finite1433825200ec_nth @ real @ n @ x @ i ) @ ( finite1433825200ec_nth @ real @ n @ y @ i ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.97/1.83 ~ ! [M: int] :
% 3.97/1.83 ( ( ring_1_of_int @ real @ M )
% 3.97/1.83 != ( minus_minus @ real @ ( finite1433825200ec_nth @ real @ n @ x @ i ) @ ( finite1433825200ec_nth @ real @ n @ y @ i ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_4_vector__minus__component,axiom,
% 3.97/1.83 ! [A: $tType,B: $tType] :
% 3.97/1.83 ( ( ( finite_finite @ B )
% 3.97/1.83 & ( minus @ A ) )
% 3.97/1.83 => ! [X: finite_Cartesian_vec @ A @ B,Y: finite_Cartesian_vec @ A @ B,I2: B] :
% 3.97/1.83 ( ( finite1433825200ec_nth @ A @ B @ ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ X @ Y ) @ I2 )
% 3.97/1.83 = ( minus_minus @ A @ ( finite1433825200ec_nth @ A @ B @ X @ I2 ) @ ( finite1433825200ec_nth @ A @ B @ Y @ I2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_5_of__int__abs,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linordered_idom @ A )
% 3.97/1.83 => ! [X: int] :
% 3.97/1.83 ( ( ring_1_of_int @ A @ ( abs_abs @ int @ X ) )
% 3.97/1.83 = ( abs_abs @ A @ ( ring_1_of_int @ A @ X ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_6_of__int__diff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ring_1 @ A )
% 3.97/1.83 => ! [W: int,Z: int] :
% 3.97/1.83 ( ( ring_1_of_int @ A @ ( minus_minus @ int @ W @ Z ) )
% 3.97/1.83 = ( minus_minus @ A @ ( ring_1_of_int @ A @ W ) @ ( ring_1_of_int @ A @ Z ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_7__092_060open_062x_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060in_062_A_092_060int_062_092_060close_062,axiom,
% 3.97/1.83 member @ real @ ( minus_minus @ real @ ( finite1433825200ec_nth @ real @ n @ x @ i ) @ ( finite1433825200ec_nth @ real @ n @ y @ i ) ) @ ( ring_1_Ints @ real ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_8_of__int__vec__nth,axiom,
% 3.97/1.83 ! [A: $tType,B: $tType] :
% 3.97/1.83 ( ( ( finite_finite @ B )
% 3.97/1.83 & ( ring_1 @ A ) )
% 3.97/1.83 => ! [V: finite_Cartesian_vec @ int @ B,N2: B] :
% 3.97/1.83 ( ( finite1433825200ec_nth @ A @ B @ ( minkow1937162798nt_vec @ B @ A @ V ) @ N2 )
% 3.97/1.83 = ( ring_1_of_int @ A @ ( finite1433825200ec_nth @ int @ B @ V @ N2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_9_of__int__eq__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ring_char_0 @ A )
% 3.97/1.83 => ! [W: int,Z: int] :
% 3.97/1.83 ( ( ( ring_1_of_int @ A @ W )
% 3.97/1.83 = ( ring_1_of_int @ A @ Z ) )
% 3.97/1.83 = ( W = Z ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_10_abs__abs,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( idom_abs_sgn @ A )
% 3.97/1.83 => ! [A2: A] :
% 3.97/1.83 ( ( abs_abs @ A @ ( abs_abs @ A @ A2 ) )
% 3.97/1.83 = ( abs_abs @ A @ A2 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_11_abs__idempotent,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordere142940540dd_abs @ A )
% 3.97/1.83 => ! [A2: A] :
% 3.97/1.83 ( ( abs_abs @ A @ ( abs_abs @ A @ A2 ) )
% 3.97/1.83 = ( abs_abs @ A @ A2 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_12_minus__apply,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( minus @ B )
% 3.97/1.83 => ( ( minus_minus @ ( A > B ) )
% 3.97/1.83 = ( ^ [A3: A > B,B2: A > B,X2: A] : ( minus_minus @ B @ ( A3 @ X2 ) @ ( B2 @ X2 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_13_abs__minus__commute,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordere142940540dd_abs @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B3 ) )
% 3.97/1.83 = ( abs_abs @ A @ ( minus_minus @ A @ B3 @ A2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_14_lambda__skolem,axiom,
% 3.97/1.83 ! [N: $tType,A: $tType] :
% 3.97/1.83 ( ( finite_finite @ N )
% 3.97/1.83 => ! [P: N > A > $o] :
% 3.97/1.83 ( ( ! [I3: N] :
% 3.97/1.83 ? [X3: A] : ( P @ I3 @ X3 ) )
% 3.97/1.83 = ( ? [X2: finite_Cartesian_vec @ A @ N] :
% 3.97/1.83 ! [I3: N] : ( P @ I3 @ ( finite1433825200ec_nth @ A @ N @ X2 @ I3 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_15_vec__eq__iff,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( finite_finite @ B )
% 3.97/1.83 => ( ( ^ [Y2: finite_Cartesian_vec @ A @ B,Z2: finite_Cartesian_vec @ A @ B] : ( Y2 = Z2 ) )
% 3.97/1.83 = ( ^ [X2: finite_Cartesian_vec @ A @ B,Y3: finite_Cartesian_vec @ A @ B] :
% 3.97/1.83 ! [I3: B] :
% 3.97/1.83 ( ( finite1433825200ec_nth @ A @ B @ X2 @ I3 )
% 3.97/1.83 = ( finite1433825200ec_nth @ A @ B @ Y3 @ I3 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_16_assms,axiom,
% 3.97/1.83 ! [V: finite_Cartesian_vec @ real @ n,I2: n] :
% 3.97/1.83 ( ( member @ ( finite_Cartesian_vec @ real @ n ) @ V @ a )
% 3.97/1.83 => ( member @ real @ ( finite1433825200ec_nth @ real @ n @ V @ I2 ) @ ( ring_1_Ints @ real ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_17_of__int__vec__eq__iff,axiom,
% 3.97/1.83 ! [A: $tType,N: $tType] :
% 3.97/1.83 ( ( ( finite_finite @ N )
% 3.97/1.83 & ( ring_char_0 @ A ) )
% 3.97/1.83 => ! [A2: finite_Cartesian_vec @ int @ N,B3: finite_Cartesian_vec @ int @ N] :
% 3.97/1.83 ( ( ( minkow1937162798nt_vec @ N @ A @ A2 )
% 3.97/1.83 = ( minkow1937162798nt_vec @ N @ A @ B3 ) )
% 3.97/1.83 = ( A2 = B3 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_18_Ints__diff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ring_1 @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( member @ A @ A2 @ ( ring_1_Ints @ A ) )
% 3.97/1.83 => ( ( member @ A @ B3 @ ( ring_1_Ints @ A ) )
% 3.97/1.83 => ( member @ A @ ( minus_minus @ A @ A2 @ B3 ) @ ( ring_1_Ints @ A ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_19_Ints__abs,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linordered_idom @ A )
% 3.97/1.83 => ! [A2: A] :
% 3.97/1.83 ( ( member @ A @ A2 @ ( ring_1_Ints @ A ) )
% 3.97/1.83 => ( member @ A @ ( abs_abs @ A @ A2 ) @ ( ring_1_Ints @ A ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_20_Ints__of__int,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ring_1 @ A )
% 3.97/1.83 => ! [Z: int] : ( member @ A @ ( ring_1_of_int @ A @ Z ) @ ( ring_1_Ints @ A ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_21_Ints__induct,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ring_1 @ A )
% 3.97/1.83 => ! [Q: A,P: A > $o] :
% 3.97/1.83 ( ( member @ A @ Q @ ( ring_1_Ints @ A ) )
% 3.97/1.83 => ( ! [Z3: int] : ( P @ ( ring_1_of_int @ A @ Z3 ) )
% 3.97/1.83 => ( P @ Q ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_22_Ints__cases,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ring_1 @ A )
% 3.97/1.83 => ! [Q: A] :
% 3.97/1.83 ( ( member @ A @ Q @ ( ring_1_Ints @ A ) )
% 3.97/1.83 => ~ ! [Z3: int] :
% 3.97/1.83 ( Q
% 3.97/1.83 != ( ring_1_of_int @ A @ Z3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_23_diff__right__commute,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( cancel146912293up_add @ A )
% 3.97/1.83 => ! [A2: A,C: A,B3: A] :
% 3.97/1.83 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B3 )
% 3.97/1.83 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B3 ) @ C ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_24_diff__eq__diff__eq,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( group_add @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A,D: A] :
% 3.97/1.83 ( ( ( minus_minus @ A @ A2 @ B3 )
% 3.97/1.83 = ( minus_minus @ A @ C @ D ) )
% 3.97/1.83 => ( ( A2 = B3 )
% 3.97/1.83 = ( C = D ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_25_fun__diff__def,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( minus @ B )
% 3.97/1.83 => ( ( minus_minus @ ( A > B ) )
% 3.97/1.83 = ( ^ [A3: A > B,B2: A > B,X2: A] : ( minus_minus @ B @ ( A3 @ X2 ) @ ( B2 @ X2 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_26_vec__nth__inject,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( finite_finite @ B )
% 3.97/1.83 => ! [X: finite_Cartesian_vec @ A @ B,Y: finite_Cartesian_vec @ A @ B] :
% 3.97/1.83 ( ( ( finite1433825200ec_nth @ A @ B @ X )
% 3.97/1.83 = ( finite1433825200ec_nth @ A @ B @ Y ) )
% 3.97/1.83 = ( X = Y ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_27_cond__component,axiom,
% 3.97/1.83 ! [A: $tType,B: $tType] :
% 3.97/1.83 ( ( finite_finite @ B )
% 3.97/1.83 => ! [B3: $o,X: finite_Cartesian_vec @ A @ B,Y: finite_Cartesian_vec @ A @ B,I2: B] :
% 3.97/1.83 ( ( B3
% 3.97/1.83 => ( ( finite1433825200ec_nth @ A @ B @ ( if @ ( finite_Cartesian_vec @ A @ B ) @ B3 @ X @ Y ) @ I2 )
% 3.97/1.83 = ( finite1433825200ec_nth @ A @ B @ X @ I2 ) ) )
% 3.97/1.83 & ( ~ B3
% 3.97/1.83 => ( ( finite1433825200ec_nth @ A @ B @ ( if @ ( finite_Cartesian_vec @ A @ B ) @ B3 @ X @ Y ) @ I2 )
% 3.97/1.83 = ( finite1433825200ec_nth @ A @ B @ Y @ I2 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_28_nth__map__matrix,axiom,
% 3.97/1.83 ! [A: $tType,C2: $tType,D2: $tType,B: $tType] :
% 3.97/1.83 ( ( ( finite_finite @ B )
% 3.97/1.83 & ( finite_finite @ C2 ) )
% 3.97/1.83 => ! [F: D2 > A,X: finite_Cartesian_vec @ ( finite_Cartesian_vec @ D2 @ B ) @ C2,I2: C2,J2: B] :
% 3.97/1.83 ( ( finite1433825200ec_nth @ A @ B @ ( finite1433825200ec_nth @ ( finite_Cartesian_vec @ A @ B ) @ C2 @ ( finite1614961371matrix @ D2 @ A @ B @ C2 @ F @ X ) @ I2 ) @ J2 )
% 3.97/1.83 = ( F @ ( finite1433825200ec_nth @ D2 @ B @ ( finite1433825200ec_nth @ ( finite_Cartesian_vec @ D2 @ B ) @ C2 @ X @ I2 ) @ J2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_29_dist__of__int,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V1229719638ebra_1 @ A )
% 3.97/1.83 => ! [M2: int,N2: int] :
% 3.97/1.83 ( ( real_V2000881966t_dist @ A @ ( ring_1_of_int @ A @ M2 ) @ ( ring_1_of_int @ A @ N2 ) )
% 3.97/1.83 = ( ring_1_of_int @ real @ ( abs_abs @ int @ ( minus_minus @ int @ M2 @ N2 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_30_vec__sub,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( minus @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( finite_Cartesian_vec2 @ A @ B @ ( minus_minus @ A @ X @ Y ) )
% 3.97/1.83 = ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ ( finite_Cartesian_vec2 @ A @ B @ X ) @ ( finite_Cartesian_vec2 @ A @ B @ Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_31_vector__sub__rdistrib,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( ring @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ! [A2: A,B3: A,X: finite_Cartesian_vec @ A @ B] :
% 3.97/1.83 ( ( finite431509953r_mult @ A @ B @ ( minus_minus @ A @ A2 @ B3 ) @ X )
% 3.97/1.83 = ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ ( finite431509953r_mult @ A @ B @ A2 @ X ) @ ( finite431509953r_mult @ A @ B @ B3 @ X ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_32__C1_C_I3_J,axiom,
% 3.97/1.83 ord_less @ real @ ( real_V2000881966t_dist @ ( finite_Cartesian_vec @ real @ n ) @ y @ x ) @ ( one_one @ real ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_33_norm__of__int,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V1229719638ebra_1 @ A )
% 3.97/1.83 => ! [Z: int] :
% 3.97/1.83 ( ( real_V1127708846m_norm @ A @ ( ring_1_of_int @ A @ Z ) )
% 3.97/1.83 = ( abs_abs @ real @ ( ring_1_of_int @ real @ Z ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_34_ceiling__diff__of__int,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A,Z: int] :
% 3.97/1.83 ( ( archimedean_ceiling @ A @ ( minus_minus @ A @ X @ ( ring_1_of_int @ A @ Z ) ) )
% 3.97/1.83 = ( minus_minus @ int @ ( archimedean_ceiling @ A @ X ) @ Z ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_35_axis__nth,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( zero @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ! [I2: B,X: A] :
% 3.97/1.83 ( ( finite1433825200ec_nth @ A @ B @ ( finite1218308419n_axis @ B @ A @ I2 @ X ) @ I2 )
% 3.97/1.83 = X ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_36_vec_Oscale__left__diff__distrib,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( field @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ! [A2: A,B3: A,X: finite_Cartesian_vec @ A @ B] :
% 3.97/1.83 ( ( finite431509953r_mult @ A @ B @ ( minus_minus @ A @ A2 @ B3 ) @ X )
% 3.97/1.83 = ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ ( finite431509953r_mult @ A @ B @ A2 @ X ) @ ( finite431509953r_mult @ A @ B @ B3 @ X ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_37_floor__diff__of__int,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A,Z: int] :
% 3.97/1.83 ( ( archim2085082626_floor @ A @ ( minus_minus @ A @ X @ ( ring_1_of_int @ A @ Z ) ) )
% 3.97/1.83 = ( minus_minus @ int @ ( archim2085082626_floor @ A @ X ) @ Z ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_38_norm__axis__1,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( finite_finite @ A )
% 3.97/1.83 => ! [M2: A] :
% 3.97/1.83 ( ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ real @ A ) @ ( finite1218308419n_axis @ A @ real @ M2 @ ( one_one @ real ) ) )
% 3.97/1.83 = ( one_one @ real ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_39_vec__eq,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( finite_finite @ B )
% 3.97/1.83 => ! [M2: A,N2: A] :
% 3.97/1.83 ( ( ( finite_Cartesian_vec2 @ A @ B @ M2 )
% 3.97/1.83 = ( finite_Cartesian_vec2 @ A @ B @ N2 ) )
% 3.97/1.83 = ( M2 = N2 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_40_vec__inj,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( finite_finite @ B )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ( finite_Cartesian_vec2 @ A @ B @ X )
% 3.97/1.83 = ( finite_Cartesian_vec2 @ A @ B @ Y ) )
% 3.97/1.83 = ( X = Y ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_41_vec_Oscale__one,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( field @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ! [X: finite_Cartesian_vec @ A @ B] :
% 3.97/1.83 ( ( finite431509953r_mult @ A @ B @ ( one_one @ A ) @ X )
% 3.97/1.83 = X ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_42_vector__smult__lid,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( monoid_mult @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ! [X: finite_Cartesian_vec @ A @ B] :
% 3.97/1.83 ( ( finite431509953r_mult @ A @ B @ ( one_one @ A ) @ X )
% 3.97/1.83 = X ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_43_abs__1,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( idom_abs_sgn @ A )
% 3.97/1.83 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 3.97/1.83 = ( one_one @ A ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_44_mem__Collect__eq,axiom,
% 3.97/1.83 ! [A: $tType,A2: A,P: A > $o] :
% 3.97/1.83 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 3.97/1.83 = ( P @ A2 ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_45_Collect__mem__eq,axiom,
% 3.97/1.83 ! [A: $tType,A4: set @ A] :
% 3.97/1.83 ( ( collect @ A
% 3.97/1.83 @ ^ [X2: A] : ( member @ A @ X2 @ A4 ) )
% 3.97/1.83 = A4 ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_46_Collect__cong,axiom,
% 3.97/1.83 ! [A: $tType,P: A > $o,Q2: A > $o] :
% 3.97/1.83 ( ! [X4: A] :
% 3.97/1.83 ( ( P @ X4 )
% 3.97/1.83 = ( Q2 @ X4 ) )
% 3.97/1.83 => ( ( collect @ A @ P )
% 3.97/1.83 = ( collect @ A @ Q2 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_47_ext,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 3.97/1.83 ( ! [X4: A] :
% 3.97/1.83 ( ( F @ X4 )
% 3.97/1.83 = ( G @ X4 ) )
% 3.97/1.83 => ( F = G ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_48_of__int__less__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linordered_idom @ A )
% 3.97/1.83 => ! [W: int,Z: int] :
% 3.97/1.83 ( ( ord_less @ A @ ( ring_1_of_int @ A @ W ) @ ( ring_1_of_int @ A @ Z ) )
% 3.97/1.83 = ( ord_less @ int @ W @ Z ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_49_one__index,axiom,
% 3.97/1.83 ! [N: $tType,A: $tType] :
% 3.97/1.83 ( ( ( one @ A )
% 3.97/1.83 & ( finite_finite @ N ) )
% 3.97/1.83 => ! [I2: N] :
% 3.97/1.83 ( ( finite1433825200ec_nth @ A @ N @ ( one_one @ ( finite_Cartesian_vec @ A @ N ) ) @ I2 )
% 3.97/1.83 = ( one_one @ A ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_50_of__int__eq__1__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ring_char_0 @ A )
% 3.97/1.83 => ! [Z: int] :
% 3.97/1.83 ( ( ( ring_1_of_int @ A @ Z )
% 3.97/1.83 = ( one_one @ A ) )
% 3.97/1.83 = ( Z
% 3.97/1.83 = ( one_one @ int ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_51_of__int__1,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ring_1 @ A )
% 3.97/1.83 => ( ( ring_1_of_int @ A @ ( one_one @ int ) )
% 3.97/1.83 = ( one_one @ A ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_52_abs__norm__cancel,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V55928688vector @ A )
% 3.97/1.83 => ! [A2: A] :
% 3.97/1.83 ( ( abs_abs @ real @ ( real_V1127708846m_norm @ A @ A2 ) )
% 3.97/1.83 = ( real_V1127708846m_norm @ A @ A2 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_53_floor__one,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ( ( archim2085082626_floor @ A @ ( one_one @ A ) )
% 3.97/1.83 = ( one_one @ int ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_54_ceiling__one,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ( ( archimedean_ceiling @ A @ ( one_one @ A ) )
% 3.97/1.83 = ( one_one @ int ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_55_vec__1,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( one @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ( ( finite_Cartesian_vec2 @ A @ B @ ( one_one @ A ) )
% 3.97/1.83 = ( one_one @ ( finite_Cartesian_vec @ A @ B ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_56_floor__of__int,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [Z: int] :
% 3.97/1.83 ( ( archim2085082626_floor @ A @ ( ring_1_of_int @ A @ Z ) )
% 3.97/1.83 = Z ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_57_ceiling__of__int,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [Z: int] :
% 3.97/1.83 ( ( archimedean_ceiling @ A @ ( ring_1_of_int @ A @ Z ) )
% 3.97/1.83 = Z ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_58_vec__component,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( finite_finite @ B )
% 3.97/1.83 => ! [X: A,I2: B] :
% 3.97/1.83 ( ( finite1433825200ec_nth @ A @ B @ ( finite_Cartesian_vec2 @ A @ B @ X ) @ I2 )
% 3.97/1.83 = X ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_59_vector__ssub__ldistrib,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( ring @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ! [C: A,X: finite_Cartesian_vec @ A @ B,Y: finite_Cartesian_vec @ A @ B] :
% 3.97/1.83 ( ( finite431509953r_mult @ A @ B @ C @ ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ X @ Y ) )
% 3.97/1.83 = ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ ( finite431509953r_mult @ A @ B @ C @ X ) @ ( finite431509953r_mult @ A @ B @ C @ Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_60_of__int__1__less__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linordered_idom @ A )
% 3.97/1.83 => ! [Z: int] :
% 3.97/1.83 ( ( ord_less @ A @ ( one_one @ A ) @ ( ring_1_of_int @ A @ Z ) )
% 3.97/1.83 = ( ord_less @ int @ ( one_one @ int ) @ Z ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_61_of__int__less__1__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linordered_idom @ A )
% 3.97/1.83 => ! [Z: int] :
% 3.97/1.83 ( ( ord_less @ A @ ( ring_1_of_int @ A @ Z ) @ ( one_one @ A ) )
% 3.97/1.83 = ( ord_less @ int @ Z @ ( one_one @ int ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_62_norm__one,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V1229719638ebra_1 @ A )
% 3.97/1.83 => ( ( real_V1127708846m_norm @ A @ ( one_one @ A ) )
% 3.97/1.83 = ( one_one @ real ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_63_dist__diff_I2_J,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V55928688vector @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( real_V2000881966t_dist @ A @ ( minus_minus @ A @ A2 @ B3 ) @ A2 )
% 3.97/1.83 = ( real_V1127708846m_norm @ A @ B3 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_64_dist__diff_I1_J,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V55928688vector @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( real_V2000881966t_dist @ A @ A2 @ ( minus_minus @ A @ A2 @ B3 ) )
% 3.97/1.83 = ( real_V1127708846m_norm @ A @ B3 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_65_floor__less__one,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ( ( ord_less @ int @ ( archim2085082626_floor @ A @ X ) @ ( one_one @ int ) )
% 3.97/1.83 = ( ord_less @ A @ X @ ( one_one @ A ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_66_one__less__ceiling,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ( ( ord_less @ int @ ( one_one @ int ) @ ( archimedean_ceiling @ A @ X ) )
% 3.97/1.83 = ( ord_less @ A @ ( one_one @ A ) @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_67_floor__diff__one,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ( ( archim2085082626_floor @ A @ ( minus_minus @ A @ X @ ( one_one @ A ) ) )
% 3.97/1.83 = ( minus_minus @ int @ ( archim2085082626_floor @ A @ X ) @ ( one_one @ int ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_68_ceiling__diff__one,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ( ( archimedean_ceiling @ A @ ( minus_minus @ A @ X @ ( one_one @ A ) ) )
% 3.97/1.83 = ( minus_minus @ int @ ( archimedean_ceiling @ A @ X ) @ ( one_one @ int ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_69_one__reorient,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( one @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ( ( ( one_one @ A )
% 3.97/1.83 = X )
% 3.97/1.83 = ( X
% 3.97/1.83 = ( one_one @ A ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_70_floor__less__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A,Z: int] :
% 3.97/1.83 ( ( ord_less @ int @ ( archim2085082626_floor @ A @ X ) @ Z )
% 3.97/1.83 = ( ord_less @ A @ X @ ( ring_1_of_int @ A @ Z ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_71_less__ceiling__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [Z: int,X: A] :
% 3.97/1.83 ( ( ord_less @ int @ Z @ ( archimedean_ceiling @ A @ X ) )
% 3.97/1.83 = ( ord_less @ A @ ( ring_1_of_int @ A @ Z ) @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_72_vec_Oscale__left__commute,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( field @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ! [A2: A,B3: A,X: finite_Cartesian_vec @ A @ B] :
% 3.97/1.83 ( ( finite431509953r_mult @ A @ B @ A2 @ ( finite431509953r_mult @ A @ B @ B3 @ X ) )
% 3.97/1.83 = ( finite431509953r_mult @ A @ B @ B3 @ ( finite431509953r_mult @ A @ B @ A2 @ X ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_73_dist__norm,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V1639655670t_norm @ A )
% 3.97/1.83 => ( ( real_V2000881966t_dist @ A )
% 3.97/1.83 = ( ^ [X2: A,Y3: A] : ( real_V1127708846m_norm @ A @ ( minus_minus @ A @ X2 @ Y3 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_74_linorder__neqE__linordered__idom,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linordered_idom @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( X != Y )
% 3.97/1.83 => ( ~ ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_75_dist__commute__lessI,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V2090557954_space @ A )
% 3.97/1.83 => ! [Y: A,X: A,E: real] :
% 3.97/1.83 ( ( ord_less @ real @ ( real_V2000881966t_dist @ A @ Y @ X ) @ E )
% 3.97/1.83 => ( ord_less @ real @ ( real_V2000881966t_dist @ A @ X @ Y ) @ E ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_76_dist__commute,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V2090557954_space @ A )
% 3.97/1.83 => ( ( real_V2000881966t_dist @ A )
% 3.97/1.83 = ( ^ [X2: A,Y3: A] : ( real_V2000881966t_dist @ A @ Y3 @ X2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_77_ceiling__less__cancel,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less @ int @ ( archimedean_ceiling @ A @ X ) @ ( archimedean_ceiling @ A @ Y ) )
% 3.97/1.83 => ( ord_less @ A @ X @ Y ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_78_floor__less__cancel,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less @ int @ ( archim2085082626_floor @ A @ X ) @ ( archim2085082626_floor @ A @ Y ) )
% 3.97/1.83 => ( ord_less @ A @ X @ Y ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_79_norm__minus__commute,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V55928688vector @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( real_V1127708846m_norm @ A @ ( minus_minus @ A @ A2 @ B3 ) )
% 3.97/1.83 = ( real_V1127708846m_norm @ A @ ( minus_minus @ A @ B3 @ A2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_80_real__norm__def,axiom,
% 3.97/1.83 ( ( real_V1127708846m_norm @ real )
% 3.97/1.83 = ( abs_abs @ real ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_81_ex__less__of__int,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1804426504_field @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ? [Z3: int] : ( ord_less @ A @ X @ ( ring_1_of_int @ A @ Z3 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_82_ex__of__int__less,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1804426504_field @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ? [Z3: int] : ( ord_less @ A @ ( ring_1_of_int @ A @ Z3 ) @ X ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_83_norm__bound__component__lt__cart,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( finite_finite @ A )
% 3.97/1.83 => ! [X: finite_Cartesian_vec @ real @ A,E: real,I2: A] :
% 3.97/1.83 ( ( ord_less @ real @ ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ real @ A ) @ X ) @ E )
% 3.97/1.83 => ( ord_less @ real @ ( abs_abs @ real @ ( finite1433825200ec_nth @ real @ A @ X @ I2 ) ) @ E ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_84_diff__strict__mono,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordered_ab_group_add @ A )
% 3.97/1.83 => ! [A2: A,B3: A,D: A,C: A] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ord_less @ A @ D @ C )
% 3.97/1.83 => ( ord_less @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_85_diff__eq__diff__less,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordered_ab_group_add @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A,D: A] :
% 3.97/1.83 ( ( ( minus_minus @ A @ A2 @ B3 )
% 3.97/1.83 = ( minus_minus @ A @ C @ D ) )
% 3.97/1.83 => ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 = ( ord_less @ A @ C @ D ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_86_diff__strict__left__mono,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordered_ab_group_add @ A )
% 3.97/1.83 => ! [B3: A,A2: A,C: A] :
% 3.97/1.83 ( ( ord_less @ A @ B3 @ A2 )
% 3.97/1.83 => ( ord_less @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_87_diff__strict__right__mono,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordered_ab_group_add @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ( ord_less @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B3 @ C ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_88_abs__one,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linordered_idom @ A )
% 3.97/1.83 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 3.97/1.83 = ( one_one @ A ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_89_dist__real__def,axiom,
% 3.97/1.83 ( ( real_V2000881966t_dist @ real )
% 3.97/1.83 = ( ^ [X2: real,Y3: real] : ( abs_abs @ real @ ( minus_minus @ real @ X2 @ Y3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_90_Ints__1,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ring_1 @ A )
% 3.97/1.83 => ( member @ A @ ( one_one @ A ) @ ( ring_1_Ints @ A ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_91_vec_Oscale__right__diff__distrib,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( field @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ! [A2: A,X: finite_Cartesian_vec @ A @ B,Y: finite_Cartesian_vec @ A @ B] :
% 3.97/1.83 ( ( finite431509953r_mult @ A @ B @ A2 @ ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ X @ Y ) )
% 3.97/1.83 = ( minus_minus @ ( finite_Cartesian_vec @ A @ B ) @ ( finite431509953r_mult @ A @ B @ A2 @ X ) @ ( finite431509953r_mult @ A @ B @ A2 @ Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_92_Ints__eq__abs__less1,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linordered_idom @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( member @ A @ X @ ( ring_1_Ints @ A ) )
% 3.97/1.83 => ( ( member @ A @ Y @ ( ring_1_Ints @ A ) )
% 3.97/1.83 => ( ( X = Y )
% 3.97/1.83 = ( ord_less @ A @ ( abs_abs @ A @ ( minus_minus @ A @ X @ Y ) ) @ ( one_one @ A ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_93_of__int__ceiling__cancel,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ( ( ( ring_1_of_int @ A @ ( archimedean_ceiling @ A @ X ) )
% 3.97/1.83 = X )
% 3.97/1.83 = ( ? [N3: int] :
% 3.97/1.83 ( X
% 3.97/1.83 = ( ring_1_of_int @ A @ N3 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_94_of__int__floor__cancel,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ( ( ( ring_1_of_int @ A @ ( archim2085082626_floor @ A @ X ) )
% 3.97/1.83 = X )
% 3.97/1.83 = ( ? [N3: int] :
% 3.97/1.83 ( X
% 3.97/1.83 = ( ring_1_of_int @ A @ N3 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_95_real__of__int__floor__gt__diff__one,axiom,
% 3.97/1.83 ! [R: real] : ( ord_less @ real @ ( minus_minus @ real @ R @ ( one_one @ real ) ) @ ( ring_1_of_int @ real @ ( archim2085082626_floor @ real @ R ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_96_real__abs__dist,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V2090557954_space @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( abs_abs @ real @ ( real_V2000881966t_dist @ A @ X @ Y ) )
% 3.97/1.83 = ( real_V2000881966t_dist @ A @ X @ Y ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_97_less__numeral__extra_I4_J,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linord1659791738miring @ A )
% 3.97/1.83 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_98_axis__index__axis,axiom,
% 3.97/1.83 ! [N: $tType] :
% 3.97/1.83 ( ( finite_finite @ N )
% 3.97/1.83 => ! [U: N] :
% 3.97/1.83 ( ( finite1115014511_index @ real @ N @ ( finite1218308419n_axis @ N @ real @ U @ ( one_one @ real ) ) )
% 3.97/1.83 = U ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_99_le__ceiling__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [Z: int,X: A] :
% 3.97/1.83 ( ( ord_less_eq @ int @ Z @ ( archimedean_ceiling @ A @ X ) )
% 3.97/1.83 = ( ord_less @ A @ ( minus_minus @ A @ ( ring_1_of_int @ A @ Z ) @ ( one_one @ A ) ) @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_100_ceiling__split,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [P: int > $o,T: A] :
% 3.97/1.83 ( ( P @ ( archimedean_ceiling @ A @ T ) )
% 3.97/1.83 = ( ! [I3: int] :
% 3.97/1.83 ( ( ( ord_less @ A @ ( minus_minus @ A @ ( ring_1_of_int @ A @ I3 ) @ ( one_one @ A ) ) @ T )
% 3.97/1.83 & ( ord_less_eq @ A @ T @ ( ring_1_of_int @ A @ I3 ) ) )
% 3.97/1.83 => ( P @ I3 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_101_ceiling__eq__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A,A2: int] :
% 3.97/1.83 ( ( ( archimedean_ceiling @ A @ X )
% 3.97/1.83 = A2 )
% 3.97/1.83 = ( ( ord_less @ A @ ( minus_minus @ A @ ( ring_1_of_int @ A @ A2 ) @ ( one_one @ A ) ) @ X )
% 3.97/1.83 & ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ A2 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_102_of__int__le__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linordered_idom @ A )
% 3.97/1.83 => ! [W: int,Z: int] :
% 3.97/1.83 ( ( ord_less_eq @ A @ ( ring_1_of_int @ A @ W ) @ ( ring_1_of_int @ A @ Z ) )
% 3.97/1.83 = ( ord_less_eq @ int @ W @ Z ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_103_zle__diff1__eq,axiom,
% 3.97/1.83 ! [W: int,Z: int] :
% 3.97/1.83 ( ( ord_less_eq @ int @ W @ ( minus_minus @ int @ Z @ ( one_one @ int ) ) )
% 3.97/1.83 = ( ord_less @ int @ W @ Z ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_104_of__int__le__1__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linordered_idom @ A )
% 3.97/1.83 => ! [Z: int] :
% 3.97/1.83 ( ( ord_less_eq @ A @ ( ring_1_of_int @ A @ Z ) @ ( one_one @ A ) )
% 3.97/1.83 = ( ord_less_eq @ int @ Z @ ( one_one @ int ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_105_of__int__1__le__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linordered_idom @ A )
% 3.97/1.83 => ! [Z: int] :
% 3.97/1.83 ( ( ord_less_eq @ A @ ( one_one @ A ) @ ( ring_1_of_int @ A @ Z ) )
% 3.97/1.83 = ( ord_less_eq @ int @ ( one_one @ int ) @ Z ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_106_one__le__floor,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ( ( ord_less_eq @ int @ ( one_one @ int ) @ ( archim2085082626_floor @ A @ X ) )
% 3.97/1.83 = ( ord_less_eq @ A @ ( one_one @ A ) @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_107_ceiling__le__one,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ( ( ord_less_eq @ int @ ( archimedean_ceiling @ A @ X ) @ ( one_one @ int ) )
% 3.97/1.83 = ( ord_less_eq @ A @ X @ ( one_one @ A ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_108_ceiling__mono,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [Y: A,X: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ Y @ X )
% 3.97/1.83 => ( ord_less_eq @ int @ ( archimedean_ceiling @ A @ Y ) @ ( archimedean_ceiling @ A @ X ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_109_floor__mono,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X @ Y )
% 3.97/1.83 => ( ord_less_eq @ int @ ( archim2085082626_floor @ A @ X ) @ ( archim2085082626_floor @ A @ Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_110_less__eq__real__def,axiom,
% 3.97/1.83 ( ( ord_less_eq @ real )
% 3.97/1.83 = ( ^ [X2: real,Y3: real] :
% 3.97/1.83 ( ( ord_less @ real @ X2 @ Y3 )
% 3.97/1.83 | ( X2 = Y3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_111_le__numeral__extra_I4_J,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linord1659791738miring @ A )
% 3.97/1.83 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_112_less__eq__vec__def,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( ord @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ( ( ord_less_eq @ ( finite_Cartesian_vec @ A @ B ) )
% 3.97/1.83 = ( ^ [X2: finite_Cartesian_vec @ A @ B,Y3: finite_Cartesian_vec @ A @ B] :
% 3.97/1.83 ! [I3: B] : ( ord_less_eq @ A @ ( finite1433825200ec_nth @ A @ B @ X2 @ I3 ) @ ( finite1433825200ec_nth @ A @ B @ Y3 @ I3 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_113_int__less__induct,axiom,
% 3.97/1.83 ! [I2: int,K: int,P: int > $o] :
% 3.97/1.83 ( ( ord_less @ int @ I2 @ K )
% 3.97/1.83 => ( ( P @ ( minus_minus @ int @ K @ ( one_one @ int ) ) )
% 3.97/1.83 => ( ! [I4: int] :
% 3.97/1.83 ( ( ord_less @ int @ I4 @ K )
% 3.97/1.83 => ( ( P @ I4 )
% 3.97/1.83 => ( P @ ( minus_minus @ int @ I4 @ ( one_one @ int ) ) ) ) )
% 3.97/1.83 => ( P @ I2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_114_int__le__induct,axiom,
% 3.97/1.83 ! [I2: int,K: int,P: int > $o] :
% 3.97/1.83 ( ( ord_less_eq @ int @ I2 @ K )
% 3.97/1.83 => ( ( P @ K )
% 3.97/1.83 => ( ! [I4: int] :
% 3.97/1.83 ( ( ord_less_eq @ int @ I4 @ K )
% 3.97/1.83 => ( ( P @ I4 )
% 3.97/1.83 => ( P @ ( minus_minus @ int @ I4 @ ( one_one @ int ) ) ) ) )
% 3.97/1.83 => ( P @ I2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_115_ceiling__le,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A,A2: int] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ A2 ) )
% 3.97/1.83 => ( ord_less_eq @ int @ ( archimedean_ceiling @ A @ X ) @ A2 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_116_le__floor__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [Z: int,X: A] :
% 3.97/1.83 ( ( ord_less_eq @ int @ Z @ ( archim2085082626_floor @ A @ X ) )
% 3.97/1.83 = ( ord_less_eq @ A @ ( ring_1_of_int @ A @ Z ) @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_117_ceiling__le__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A,Z: int] :
% 3.97/1.83 ( ( ord_less_eq @ int @ ( archimedean_ceiling @ A @ X ) @ Z )
% 3.97/1.83 = ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ Z ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_118_diff__eq__diff__less__eq,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordered_ab_group_add @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A,D: A] :
% 3.97/1.83 ( ( ( minus_minus @ A @ A2 @ B3 )
% 3.97/1.83 = ( minus_minus @ A @ C @ D ) )
% 3.97/1.83 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_119_diff__right__mono,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordered_ab_group_add @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B3 @ C ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_120_diff__left__mono,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordered_ab_group_add @ A )
% 3.97/1.83 => ! [B3: A,A2: A,C: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ B3 @ A2 )
% 3.97/1.83 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_121_diff__mono,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordered_ab_group_add @ A )
% 3.97/1.83 => ! [A2: A,B3: A,D: A,C: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ord_less_eq @ A @ D @ C )
% 3.97/1.83 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_122_abs__ge__self,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordere142940540dd_abs @ A )
% 3.97/1.83 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ ( abs_abs @ A @ A2 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_123_abs__le__D1,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordere142940540dd_abs @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ ( abs_abs @ A @ A2 ) @ B3 )
% 3.97/1.83 => ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_124_norm__vector__1,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V55928688vector @ A )
% 3.97/1.83 => ( ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ A @ numeral_num1 ) )
% 3.97/1.83 = ( ^ [X2: finite_Cartesian_vec @ A @ numeral_num1] : ( real_V1127708846m_norm @ A @ ( finite1433825200ec_nth @ A @ numeral_num1 @ X2 @ ( one_one @ numeral_num1 ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_125_ex__le__of__int,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1804426504_field @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ? [Z3: int] : ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ Z3 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_126_dist__vector__1,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V55928688vector @ A )
% 3.97/1.83 => ( ( real_V2000881966t_dist @ ( finite_Cartesian_vec @ A @ numeral_num1 ) )
% 3.97/1.83 = ( ^ [X2: finite_Cartesian_vec @ A @ numeral_num1,Y3: finite_Cartesian_vec @ A @ numeral_num1] : ( real_V2000881966t_dist @ A @ ( finite1433825200ec_nth @ A @ numeral_num1 @ X2 @ ( one_one @ numeral_num1 ) ) @ ( finite1433825200ec_nth @ A @ numeral_num1 @ Y3 @ ( one_one @ numeral_num1 ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_127_norm__real,axiom,
% 3.97/1.83 ( ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ real @ numeral_num1 ) )
% 3.97/1.83 = ( ^ [X2: finite_Cartesian_vec @ real @ numeral_num1] : ( abs_abs @ real @ ( finite1433825200ec_nth @ real @ numeral_num1 @ X2 @ ( one_one @ numeral_num1 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_128_ceiling__diff__floor__le__1,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] : ( ord_less_eq @ int @ ( minus_minus @ int @ ( archimedean_ceiling @ A @ X ) @ ( archim2085082626_floor @ A @ X ) ) @ ( one_one @ int ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_129_ceiling__less__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A,Z: int] :
% 3.97/1.83 ( ( ord_less @ int @ ( archimedean_ceiling @ A @ X ) @ Z )
% 3.97/1.83 = ( ord_less_eq @ A @ X @ ( minus_minus @ A @ ( ring_1_of_int @ A @ Z ) @ ( one_one @ A ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_130_abs__triangle__ineq2__sym,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordere142940540dd_abs @ A )
% 3.97/1.83 => ! [A2: A,B3: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B3 ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ B3 @ A2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_131_abs__triangle__ineq3,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordere142940540dd_abs @ A )
% 3.97/1.83 => ! [A2: A,B3: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B3 ) ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_132_abs__triangle__ineq2,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordere142940540dd_abs @ A )
% 3.97/1.83 => ! [A2: A,B3: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B3 ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_133_norm__le__componentwise__cart,axiom,
% 3.97/1.83 ! [A: $tType,N: $tType,B: $tType] :
% 3.97/1.83 ( ( ( real_V55928688vector @ B )
% 3.97/1.83 & ( finite_finite @ N )
% 3.97/1.83 & ( real_V55928688vector @ A ) )
% 3.97/1.83 => ! [X: finite_Cartesian_vec @ A @ N,Y: finite_Cartesian_vec @ B @ N] :
% 3.97/1.83 ( ! [I4: N] : ( ord_less_eq @ real @ ( real_V1127708846m_norm @ A @ ( finite1433825200ec_nth @ A @ N @ X @ I4 ) ) @ ( real_V1127708846m_norm @ B @ ( finite1433825200ec_nth @ B @ N @ Y @ I4 ) ) )
% 3.97/1.83 => ( ord_less_eq @ real @ ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ A @ N ) @ X ) @ ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ B @ N ) @ Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_134_Finite__Cartesian__Product_Onorm__nth__le,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( real_V55928688vector @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ! [X: finite_Cartesian_vec @ A @ B,I2: B] : ( ord_less_eq @ real @ ( real_V1127708846m_norm @ A @ ( finite1433825200ec_nth @ A @ B @ X @ I2 ) ) @ ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ A @ B ) @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_135_real__of__int__floor__ge__diff__one,axiom,
% 3.97/1.83 ! [R: real] : ( ord_less_eq @ real @ ( minus_minus @ real @ R @ ( one_one @ real ) ) @ ( ring_1_of_int @ real @ ( archim2085082626_floor @ real @ R ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_136_of__int__floor__le,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] : ( ord_less_eq @ A @ ( ring_1_of_int @ A @ ( archim2085082626_floor @ A @ X ) ) @ X ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_137_le__of__int__ceiling,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] : ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ ( archimedean_ceiling @ A @ X ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_138_norm__bound__component__le__cart,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( finite_finite @ A )
% 3.97/1.83 => ! [X: finite_Cartesian_vec @ real @ A,E: real,I2: A] :
% 3.97/1.83 ( ( ord_less_eq @ real @ ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ real @ A ) @ X ) @ E )
% 3.97/1.83 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( finite1433825200ec_nth @ real @ A @ X @ I2 ) ) @ E ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_139_component__le__norm__cart,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( finite_finite @ A )
% 3.97/1.83 => ! [X: finite_Cartesian_vec @ real @ A,I2: A] : ( ord_less_eq @ real @ ( abs_abs @ real @ ( finite1433825200ec_nth @ real @ A @ X @ I2 ) ) @ ( real_V1127708846m_norm @ ( finite_Cartesian_vec @ real @ A ) @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_140_dist__real,axiom,
% 3.97/1.83 ( ( real_V2000881966t_dist @ ( finite_Cartesian_vec @ real @ numeral_num1 ) )
% 3.97/1.83 = ( ^ [X2: finite_Cartesian_vec @ real @ numeral_num1,Y3: finite_Cartesian_vec @ real @ numeral_num1] : ( abs_abs @ real @ ( minus_minus @ real @ ( finite1433825200ec_nth @ real @ numeral_num1 @ X2 @ ( one_one @ numeral_num1 ) ) @ ( finite1433825200ec_nth @ real @ numeral_num1 @ Y3 @ ( one_one @ numeral_num1 ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_141_floor__le__ceiling,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] : ( ord_less_eq @ int @ ( archim2085082626_floor @ A @ X ) @ ( archimedean_ceiling @ A @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_142_of__int__ceiling__diff__one__le,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [R: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( ring_1_of_int @ A @ ( archimedean_ceiling @ A @ R ) ) @ ( one_one @ A ) ) @ R ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_143_norm__triangle__ineq2,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V55928688vector @ A )
% 3.97/1.83 => ! [A2: A,B3: A] : ( ord_less_eq @ real @ ( minus_minus @ real @ ( real_V1127708846m_norm @ A @ A2 ) @ ( real_V1127708846m_norm @ A @ B3 ) ) @ ( real_V1127708846m_norm @ A @ ( minus_minus @ A @ A2 @ B3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_144_abs__dist__diff__le,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V2090557954_space @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A] : ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( real_V2000881966t_dist @ A @ A2 @ B3 ) @ ( real_V2000881966t_dist @ A @ B3 @ C ) ) ) @ ( real_V2000881966t_dist @ A @ A2 @ C ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_145_metric__eq__thm,axiom,
% 3.97/1.83 ! [A5: $tType] :
% 3.97/1.83 ( ( real_V2090557954_space @ A5 )
% 3.97/1.83 => ! [X5: A5,S: set @ A5,Y4: A5] :
% 3.97/1.83 ( ( member @ A5 @ X5 @ S )
% 3.97/1.83 => ( ( member @ A5 @ Y4 @ S )
% 3.97/1.83 => ( ( X5 = Y4 )
% 3.97/1.83 = ( ! [X2: A5] :
% 3.97/1.83 ( ( member @ A5 @ X2 @ S )
% 3.97/1.83 => ( ( real_V2000881966t_dist @ A5 @ X5 @ X2 )
% 3.97/1.83 = ( real_V2000881966t_dist @ A5 @ Y4 @ X2 ) ) ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_146_dist__vec__nth__le,axiom,
% 3.97/1.83 ! [D2: $tType,C2: $tType] :
% 3.97/1.83 ( ( ( real_V2090557954_space @ C2 )
% 3.97/1.83 & ( finite_finite @ D2 ) )
% 3.97/1.83 => ! [X: finite_Cartesian_vec @ C2 @ D2,I2: D2,Y: finite_Cartesian_vec @ C2 @ D2] : ( ord_less_eq @ real @ ( real_V2000881966t_dist @ C2 @ ( finite1433825200ec_nth @ C2 @ D2 @ X @ I2 ) @ ( finite1433825200ec_nth @ C2 @ D2 @ Y @ I2 ) ) @ ( real_V2000881966t_dist @ ( finite_Cartesian_vec @ C2 @ D2 ) @ X @ Y ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_147_norm__triangle__ineq3,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( real_V55928688vector @ A )
% 3.97/1.83 => ! [A2: A,B3: A] : ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( real_V1127708846m_norm @ A @ A2 ) @ ( real_V1127708846m_norm @ A @ B3 ) ) ) @ ( real_V1127708846m_norm @ A @ ( minus_minus @ A @ A2 @ B3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_148_ceiling__correct,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ( ( ord_less @ A @ ( minus_minus @ A @ ( ring_1_of_int @ A @ ( archimedean_ceiling @ A @ X ) ) @ ( one_one @ A ) ) @ X )
% 3.97/1.83 & ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ ( archimedean_ceiling @ A @ X ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_149_ceiling__unique,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( archim1727834104eiling @ A )
% 3.97/1.83 => ! [Z: int,X: A] :
% 3.97/1.83 ( ( ord_less @ A @ ( minus_minus @ A @ ( ring_1_of_int @ A @ Z ) @ ( one_one @ A ) ) @ X )
% 3.97/1.83 => ( ( ord_less_eq @ A @ X @ ( ring_1_of_int @ A @ Z ) )
% 3.97/1.83 => ( ( archimedean_ceiling @ A @ X )
% 3.97/1.83 = Z ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_150_order__refl,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_151_complete__interval,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( condit1037483654norder @ A )
% 3.97/1.83 => ! [A2: A,B3: A,P: A > $o] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( P @ A2 )
% 3.97/1.83 => ( ~ ( P @ B3 )
% 3.97/1.83 => ? [C3: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ C3 )
% 3.97/1.83 & ( ord_less_eq @ A @ C3 @ B3 )
% 3.97/1.83 & ! [X6: A] :
% 3.97/1.83 ( ( ( ord_less_eq @ A @ A2 @ X6 )
% 3.97/1.83 & ( ord_less @ A @ X6 @ C3 ) )
% 3.97/1.83 => ( P @ X6 ) )
% 3.97/1.83 & ! [D3: A] :
% 3.97/1.83 ( ! [X4: A] :
% 3.97/1.83 ( ( ( ord_less_eq @ A @ A2 @ X4 )
% 3.97/1.83 & ( ord_less @ A @ X4 @ D3 ) )
% 3.97/1.83 => ( P @ X4 ) )
% 3.97/1.83 => ( ord_less_eq @ A @ D3 @ C3 ) ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_152_eucl__less__le__not__le,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ordere890947078_space @ A )
% 3.97/1.83 => ( ( ord_less @ A )
% 3.97/1.83 = ( ^ [X2: A,Y3: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 3.97/1.83 & ~ ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_153_order_Onot__eq__order__implies__strict,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( A2 != B3 )
% 3.97/1.83 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 => ( ord_less @ A @ A2 @ B3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_154_dual__order_Ostrict__implies__order,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [B3: A,A2: A] :
% 3.97/1.83 ( ( ord_less @ A @ B3 @ A2 )
% 3.97/1.83 => ( ord_less_eq @ A @ B3 @ A2 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_155_vector__one__nth,axiom,
% 3.97/1.83 ! [A: $tType,X: finite_Cartesian_vec @ A @ numeral_num1] :
% 3.97/1.83 ( ( finite_Cartesian_vec2 @ A @ numeral_num1 @ ( finite1433825200ec_nth @ A @ numeral_num1 @ X @ ( one_one @ numeral_num1 ) ) )
% 3.97/1.83 = X ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_156_less__vec__def,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ( ord @ A )
% 3.97/1.83 & ( finite_finite @ B ) )
% 3.97/1.83 => ( ( ord_less @ ( finite_Cartesian_vec @ A @ B ) )
% 3.97/1.83 = ( ^ [X2: finite_Cartesian_vec @ A @ B,Y3: finite_Cartesian_vec @ A @ B] :
% 3.97/1.83 ( ( ord_less_eq @ ( finite_Cartesian_vec @ A @ B ) @ X2 @ Y3 )
% 3.97/1.83 & ~ ( ord_less_eq @ ( finite_Cartesian_vec @ A @ B ) @ Y3 @ X2 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_157_complete__real,axiom,
% 3.97/1.83 ! [S2: set @ real] :
% 3.97/1.83 ( ? [X6: real] : ( member @ real @ X6 @ S2 )
% 3.97/1.83 => ( ? [Z4: real] :
% 3.97/1.83 ! [X4: real] :
% 3.97/1.83 ( ( member @ real @ X4 @ S2 )
% 3.97/1.83 => ( ord_less_eq @ real @ X4 @ Z4 ) )
% 3.97/1.83 => ? [Y5: real] :
% 3.97/1.83 ( ! [X6: real] :
% 3.97/1.83 ( ( member @ real @ X6 @ S2 )
% 3.97/1.83 => ( ord_less_eq @ real @ X6 @ Y5 ) )
% 3.97/1.83 & ! [Z4: real] :
% 3.97/1.83 ( ! [X4: real] :
% 3.97/1.83 ( ( member @ real @ X4 @ S2 )
% 3.97/1.83 => ( ord_less_eq @ real @ X4 @ Z4 ) )
% 3.97/1.83 => ( ord_less_eq @ real @ Y5 @ Z4 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_158_dual__order_Oantisym,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [B3: A,A2: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ B3 @ A2 )
% 3.97/1.83 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 => ( A2 = B3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_159_dual__order_Oeq__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 3.97/1.83 = ( ^ [A6: A,B4: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ B4 @ A6 )
% 3.97/1.83 & ( ord_less_eq @ A @ A6 @ B4 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_160_dual__order_Otrans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [B3: A,A2: A,C: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ B3 @ A2 )
% 3.97/1.83 => ( ( ord_less_eq @ A @ C @ B3 )
% 3.97/1.83 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_161_linorder__wlog,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [P: A > A > $o,A2: A,B3: A] :
% 3.97/1.83 ( ! [A7: A,B5: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A7 @ B5 )
% 3.97/1.83 => ( P @ A7 @ B5 ) )
% 3.97/1.83 => ( ! [A7: A,B5: A] :
% 3.97/1.83 ( ( P @ B5 @ A7 )
% 3.97/1.83 => ( P @ A7 @ B5 ) )
% 3.97/1.83 => ( P @ A2 @ B3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_162_dual__order_Orefl,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_163_order__trans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [X: A,Y: A,Z: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X @ Y )
% 3.97/1.83 => ( ( ord_less_eq @ A @ Y @ Z )
% 3.97/1.83 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_164_order__class_Oorder_Oantisym,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ord_less_eq @ A @ B3 @ A2 )
% 3.97/1.83 => ( A2 = B3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_165_ord__le__eq__trans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ord @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( B3 = C )
% 3.97/1.83 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_166_ord__eq__le__trans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ord @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A] :
% 3.97/1.83 ( ( A2 = B3 )
% 3.97/1.83 => ( ( ord_less_eq @ A @ B3 @ C )
% 3.97/1.83 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_167_order__class_Oorder_Oeq__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 3.97/1.83 = ( ^ [A6: A,B4: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A6 @ B4 )
% 3.97/1.83 & ( ord_less_eq @ A @ B4 @ A6 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_168_antisym__conv,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [Y: A,X: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ Y @ X )
% 3.97/1.83 => ( ( ord_less_eq @ A @ X @ Y )
% 3.97/1.83 = ( X = Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_169_le__cases3,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A,Z: A] :
% 3.97/1.83 ( ( ( ord_less_eq @ A @ X @ Y )
% 3.97/1.83 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 3.97/1.83 => ( ( ( ord_less_eq @ A @ Y @ X )
% 3.97/1.83 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 3.97/1.83 => ( ( ( ord_less_eq @ A @ X @ Z )
% 3.97/1.83 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 3.97/1.83 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 3.97/1.83 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 3.97/1.83 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 3.97/1.83 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 3.97/1.83 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 3.97/1.83 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_170_order_Otrans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ord_less_eq @ A @ B3 @ C )
% 3.97/1.83 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_171_le__cases,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ~ ( ord_less_eq @ A @ X @ Y )
% 3.97/1.83 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_172_eq__refl,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( X = Y )
% 3.97/1.83 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_173_linear,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X @ Y )
% 3.97/1.83 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_174_antisym,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X @ Y )
% 3.97/1.83 => ( ( ord_less_eq @ A @ Y @ X )
% 3.97/1.83 => ( X = Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_175_eq__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 3.97/1.83 = ( ^ [X2: A,Y3: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 3.97/1.83 & ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_176_ord__le__eq__subst,axiom,
% 3.97/1.83 ! [A: $tType,B: $tType] :
% 3.97/1.83 ( ( ( ord @ B )
% 3.97/1.83 & ( ord @ A ) )
% 3.97/1.83 => ! [A2: A,B3: A,F: A > B,C: B] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ( F @ B3 )
% 3.97/1.83 = C )
% 3.97/1.83 => ( ! [X4: A,Y5: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 3.97/1.83 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 3.97/1.83 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_177_ord__eq__le__subst,axiom,
% 3.97/1.83 ! [A: $tType,B: $tType] :
% 3.97/1.83 ( ( ( ord @ B )
% 3.97/1.83 & ( ord @ A ) )
% 3.97/1.83 => ! [A2: A,F: B > A,B3: B,C: B] :
% 3.97/1.83 ( ( A2
% 3.97/1.83 = ( F @ B3 ) )
% 3.97/1.83 => ( ( ord_less_eq @ B @ B3 @ C )
% 3.97/1.83 => ( ! [X4: B,Y5: B] :
% 3.97/1.83 ( ( ord_less_eq @ B @ X4 @ Y5 )
% 3.97/1.83 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 3.97/1.83 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_178_order__subst2,axiom,
% 3.97/1.83 ! [A: $tType,C2: $tType] :
% 3.97/1.83 ( ( ( order @ C2 )
% 3.97/1.83 & ( order @ A ) )
% 3.97/1.83 => ! [A2: A,B3: A,F: A > C2,C: C2] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ord_less_eq @ C2 @ ( F @ B3 ) @ C )
% 3.97/1.83 => ( ! [X4: A,Y5: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 3.97/1.83 => ( ord_less_eq @ C2 @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 3.97/1.83 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_179_order__subst1,axiom,
% 3.97/1.83 ! [A: $tType,B: $tType] :
% 3.97/1.83 ( ( ( order @ B )
% 3.97/1.83 & ( order @ A ) )
% 3.97/1.83 => ! [A2: A,F: B > A,B3: B,C: B] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 3.97/1.83 => ( ( ord_less_eq @ B @ B3 @ C )
% 3.97/1.83 => ( ! [X4: B,Y5: B] :
% 3.97/1.83 ( ( ord_less_eq @ B @ X4 @ Y5 )
% 3.97/1.83 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 3.97/1.83 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_180_le__fun__def,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ord @ B )
% 3.97/1.83 => ( ( ord_less_eq @ ( A > B ) )
% 3.97/1.83 = ( ^ [F2: A > B,G2: A > B] :
% 3.97/1.83 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_181_le__funI,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ord @ B )
% 3.97/1.83 => ! [F: A > B,G: A > B] :
% 3.97/1.83 ( ! [X4: A] : ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) )
% 3.97/1.83 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_182_le__funE,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ord @ B )
% 3.97/1.83 => ! [F: A > B,G: A > B,X: A] :
% 3.97/1.83 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 3.97/1.83 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_183_le__funD,axiom,
% 3.97/1.83 ! [B: $tType,A: $tType] :
% 3.97/1.83 ( ( ord @ B )
% 3.97/1.83 => ! [F: A > B,G: A > B,X: A] :
% 3.97/1.83 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 3.97/1.83 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_184_ex__gt__or__lt,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( condit1656338222tinuum @ A )
% 3.97/1.83 => ! [A2: A] :
% 3.97/1.83 ? [B5: A] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B5 )
% 3.97/1.83 | ( ord_less @ A @ B5 @ A2 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_185_dual__order_Ostrict__implies__not__eq,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [B3: A,A2: A] :
% 3.97/1.83 ( ( ord_less @ A @ B3 @ A2 )
% 3.97/1.83 => ( A2 != B3 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_186_order_Ostrict__implies__not__eq,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ( A2 != B3 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_187_not__less__iff__gr__or__eq,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 3.97/1.83 = ( ( ord_less @ A @ Y @ X )
% 3.97/1.83 | ( X = Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_188_dual__order_Ostrict__trans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [B3: A,A2: A,C: A] :
% 3.97/1.83 ( ( ord_less @ A @ B3 @ A2 )
% 3.97/1.83 => ( ( ord_less @ A @ C @ B3 )
% 3.97/1.83 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_189_linorder__less__wlog,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [P: A > A > $o,A2: A,B3: A] :
% 3.97/1.83 ( ! [A7: A,B5: A] :
% 3.97/1.83 ( ( ord_less @ A @ A7 @ B5 )
% 3.97/1.83 => ( P @ A7 @ B5 ) )
% 3.97/1.83 => ( ! [A7: A] : ( P @ A7 @ A7 )
% 3.97/1.83 => ( ! [A7: A,B5: A] :
% 3.97/1.83 ( ( P @ B5 @ A7 )
% 3.97/1.83 => ( P @ A7 @ B5 ) )
% 3.97/1.83 => ( P @ A2 @ B3 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_190_exists__least__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( wellorder @ A )
% 3.97/1.83 => ( ( ^ [P2: A > $o] :
% 3.97/1.83 ? [X3: A] : ( P2 @ X3 ) )
% 3.97/1.83 = ( ^ [P3: A > $o] :
% 3.97/1.83 ? [N3: A] :
% 3.97/1.83 ( ( P3 @ N3 )
% 3.97/1.83 & ! [M3: A] :
% 3.97/1.83 ( ( ord_less @ A @ M3 @ N3 )
% 3.97/1.83 => ~ ( P3 @ M3 ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_191_less__imp__not__less,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_192_order_Ostrict__trans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ord_less @ A @ B3 @ C )
% 3.97/1.83 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_193_dual__order_Oirrefl,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [A2: A] :
% 3.97/1.83 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_194_linorder__cases,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ~ ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( ( X != Y )
% 3.97/1.83 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_195_less__imp__triv,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [X: A,Y: A,P: $o] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( ( ord_less @ A @ Y @ X )
% 3.97/1.83 => P ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_196_less__imp__not__eq2,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( Y != X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_197_antisym__conv3,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [Y: A,X: A] :
% 3.97/1.83 ( ~ ( ord_less @ A @ Y @ X )
% 3.97/1.83 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 3.97/1.83 = ( X = Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_198_less__induct,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( wellorder @ A )
% 3.97/1.83 => ! [P: A > $o,A2: A] :
% 3.97/1.83 ( ! [X4: A] :
% 3.97/1.83 ( ! [Y6: A] :
% 3.97/1.83 ( ( ord_less @ A @ Y6 @ X4 )
% 3.97/1.83 => ( P @ Y6 ) )
% 3.97/1.83 => ( P @ X4 ) )
% 3.97/1.83 => ( P @ A2 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_199_less__not__sym,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_200_less__imp__not__eq,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( X != Y ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_201_dual__order_Oasym,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [B3: A,A2: A] :
% 3.97/1.83 ( ( ord_less @ A @ B3 @ A2 )
% 3.97/1.83 => ~ ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_202_ord__less__eq__trans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ord @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( B3 = C )
% 3.97/1.83 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_203_ord__eq__less__trans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( ord @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A] :
% 3.97/1.83 ( ( A2 = B3 )
% 3.97/1.83 => ( ( ord_less @ A @ B3 @ C )
% 3.97/1.83 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_204_less__irrefl,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ~ ( ord_less @ A @ X @ X ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_205_less__linear,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 | ( X = Y )
% 3.97/1.83 | ( ord_less @ A @ Y @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_206_less__trans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [X: A,Y: A,Z: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( ( ord_less @ A @ Y @ Z )
% 3.97/1.83 => ( ord_less @ A @ X @ Z ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_207_less__asym_H,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_208_less__asym,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_209_less__imp__neq,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( X != Y ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_210_dense,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( dense_order @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ? [Z3: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Z3 )
% 3.97/1.83 & ( ord_less @ A @ Z3 @ Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_211_order_Oasym,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_212_neq__iff,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( X != Y )
% 3.97/1.83 = ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_213_neqE,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( X != Y )
% 3.97/1.83 => ( ~ ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_214_gt__ex,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( no_top @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ? [X_1: A] : ( ord_less @ A @ X @ X_1 ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_215_lt__ex,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( no_bot @ A )
% 3.97/1.83 => ! [X: A] :
% 3.97/1.83 ? [Y5: A] : ( ord_less @ A @ Y5 @ X ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_216_order__less__subst2,axiom,
% 3.97/1.83 ! [A: $tType,C2: $tType] :
% 3.97/1.83 ( ( ( order @ C2 )
% 3.97/1.83 & ( order @ A ) )
% 3.97/1.83 => ! [A2: A,B3: A,F: A > C2,C: C2] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ord_less @ C2 @ ( F @ B3 ) @ C )
% 3.97/1.83 => ( ! [X4: A,Y5: A] :
% 3.97/1.83 ( ( ord_less @ A @ X4 @ Y5 )
% 3.97/1.83 => ( ord_less @ C2 @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 3.97/1.83 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_217_order__less__subst1,axiom,
% 3.97/1.83 ! [A: $tType,B: $tType] :
% 3.97/1.83 ( ( ( order @ B )
% 3.97/1.83 & ( order @ A ) )
% 3.97/1.83 => ! [A2: A,F: B > A,B3: B,C: B] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ ( F @ B3 ) )
% 3.97/1.83 => ( ( ord_less @ B @ B3 @ C )
% 3.97/1.83 => ( ! [X4: B,Y5: B] :
% 3.97/1.83 ( ( ord_less @ B @ X4 @ Y5 )
% 3.97/1.83 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 3.97/1.83 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_218_ord__less__eq__subst,axiom,
% 3.97/1.83 ! [A: $tType,B: $tType] :
% 3.97/1.83 ( ( ( ord @ B )
% 3.97/1.83 & ( ord @ A ) )
% 3.97/1.83 => ! [A2: A,B3: A,F: A > B,C: B] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ( F @ B3 )
% 3.97/1.83 = C )
% 3.97/1.83 => ( ! [X4: A,Y5: A] :
% 3.97/1.83 ( ( ord_less @ A @ X4 @ Y5 )
% 3.97/1.83 => ( ord_less @ B @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 3.97/1.83 => ( ord_less @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_219_ord__eq__less__subst,axiom,
% 3.97/1.83 ! [A: $tType,B: $tType] :
% 3.97/1.83 ( ( ( ord @ B )
% 3.97/1.83 & ( ord @ A ) )
% 3.97/1.83 => ! [A2: A,F: B > A,B3: B,C: B] :
% 3.97/1.83 ( ( A2
% 3.97/1.83 = ( F @ B3 ) )
% 3.97/1.83 => ( ( ord_less @ B @ B3 @ C )
% 3.97/1.83 => ( ! [X4: B,Y5: B] :
% 3.97/1.83 ( ( ord_less @ B @ X4 @ Y5 )
% 3.97/1.83 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 3.97/1.83 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_220_leD,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [Y: A,X: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ Y @ X )
% 3.97/1.83 => ~ ( ord_less @ A @ X @ Y ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_221_leI,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ~ ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_222_le__less,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ( ( ord_less_eq @ A )
% 3.97/1.83 = ( ^ [X2: A,Y3: A] :
% 3.97/1.83 ( ( ord_less @ A @ X2 @ Y3 )
% 3.97/1.83 | ( X2 = Y3 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_223_less__le,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ( ( ord_less @ A )
% 3.97/1.83 = ( ^ [X2: A,Y3: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 3.97/1.83 & ( X2 != Y3 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_224_order__le__less__subst1,axiom,
% 3.97/1.83 ! [A: $tType,B: $tType] :
% 3.97/1.83 ( ( ( order @ B )
% 3.97/1.83 & ( order @ A ) )
% 3.97/1.83 => ! [A2: A,F: B > A,B3: B,C: B] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 3.97/1.83 => ( ( ord_less @ B @ B3 @ C )
% 3.97/1.83 => ( ! [X4: B,Y5: B] :
% 3.97/1.83 ( ( ord_less @ B @ X4 @ Y5 )
% 3.97/1.83 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 3.97/1.83 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_225_order__le__less__subst2,axiom,
% 3.97/1.83 ! [A: $tType,C2: $tType] :
% 3.97/1.83 ( ( ( order @ C2 )
% 3.97/1.83 & ( order @ A ) )
% 3.97/1.83 => ! [A2: A,B3: A,F: A > C2,C: C2] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ord_less @ C2 @ ( F @ B3 ) @ C )
% 3.97/1.83 => ( ! [X4: A,Y5: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 3.97/1.83 => ( ord_less_eq @ C2 @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 3.97/1.83 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_226_order__less__le__subst1,axiom,
% 3.97/1.83 ! [A: $tType,B: $tType] :
% 3.97/1.83 ( ( ( order @ B )
% 3.97/1.83 & ( order @ A ) )
% 3.97/1.83 => ! [A2: A,F: B > A,B3: B,C: B] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ ( F @ B3 ) )
% 3.97/1.83 => ( ( ord_less_eq @ B @ B3 @ C )
% 3.97/1.83 => ( ! [X4: B,Y5: B] :
% 3.97/1.83 ( ( ord_less_eq @ B @ X4 @ Y5 )
% 3.97/1.83 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 3.97/1.83 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_227_order__less__le__subst2,axiom,
% 3.97/1.83 ! [A: $tType,C2: $tType] :
% 3.97/1.83 ( ( ( order @ C2 )
% 3.97/1.83 & ( order @ A ) )
% 3.97/1.83 => ! [A2: A,B3: A,F: A > C2,C: C2] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ord_less_eq @ C2 @ ( F @ B3 ) @ C )
% 3.97/1.83 => ( ! [X4: A,Y5: A] :
% 3.97/1.83 ( ( ord_less @ A @ X4 @ Y5 )
% 3.97/1.83 => ( ord_less @ C2 @ ( F @ X4 ) @ ( F @ Y5 ) ) )
% 3.97/1.83 => ( ord_less @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_228_not__le,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ~ ( ord_less_eq @ A @ X @ Y ) )
% 3.97/1.83 = ( ord_less @ A @ Y @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_229_not__less,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 3.97/1.83 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_230_le__neq__trans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( A2 != B3 )
% 3.97/1.83 => ( ord_less @ A @ A2 @ B3 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_231_antisym__conv1,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ~ ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( ( ord_less_eq @ A @ X @ Y )
% 3.97/1.83 = ( X = Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_232_antisym__conv2,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X @ Y )
% 3.97/1.83 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 3.97/1.83 = ( X = Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_233_less__imp__le,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_234_le__less__trans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [X: A,Y: A,Z: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X @ Y )
% 3.97/1.83 => ( ( ord_less @ A @ Y @ Z )
% 3.97/1.83 => ( ord_less @ A @ X @ Z ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_235_less__le__trans,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ! [X: A,Y: A,Z: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( ( ord_less_eq @ A @ Y @ Z )
% 3.97/1.83 => ( ord_less @ A @ X @ Z ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_236_dense__ge,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( dense_linorder @ A )
% 3.97/1.83 => ! [Z: A,Y: A] :
% 3.97/1.83 ( ! [X4: A] :
% 3.97/1.83 ( ( ord_less @ A @ Z @ X4 )
% 3.97/1.83 => ( ord_less_eq @ A @ Y @ X4 ) )
% 3.97/1.83 => ( ord_less_eq @ A @ Y @ Z ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_237_dense__le,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( dense_linorder @ A )
% 3.97/1.83 => ! [Y: A,Z: A] :
% 3.97/1.83 ( ! [X4: A] :
% 3.97/1.83 ( ( ord_less @ A @ X4 @ Y )
% 3.97/1.83 => ( ord_less_eq @ A @ X4 @ Z ) )
% 3.97/1.83 => ( ord_less_eq @ A @ Y @ Z ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_238_le__less__linear,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X @ Y )
% 3.97/1.83 | ( ord_less @ A @ Y @ X ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_239_le__imp__less__or__eq,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [X: A,Y: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X @ Y )
% 3.97/1.83 => ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 | ( X = Y ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_240_less__le__not__le,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( preorder @ A )
% 3.97/1.83 => ( ( ord_less @ A )
% 3.97/1.83 = ( ^ [X2: A,Y3: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 3.97/1.83 & ~ ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_241_not__le__imp__less,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( linorder @ A )
% 3.97/1.83 => ! [Y: A,X: A] :
% 3.97/1.83 ( ~ ( ord_less_eq @ A @ Y @ X )
% 3.97/1.83 => ( ord_less @ A @ X @ Y ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_242_order_Ostrict__trans1,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ord_less @ A @ B3 @ C )
% 3.97/1.83 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_243_order_Ostrict__trans2,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [A2: A,B3: A,C: A] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ( ( ord_less_eq @ A @ B3 @ C )
% 3.97/1.83 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_244_order_Oorder__iff__strict,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ( ( ord_less_eq @ A )
% 3.97/1.83 = ( ^ [A6: A,B4: A] :
% 3.97/1.83 ( ( ord_less @ A @ A6 @ B4 )
% 3.97/1.83 | ( A6 = B4 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_245_order_Ostrict__iff__order,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ( ( ord_less @ A )
% 3.97/1.83 = ( ^ [A6: A,B4: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ A6 @ B4 )
% 3.97/1.83 & ( A6 != B4 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_246_dual__order_Ostrict__trans1,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [B3: A,A2: A,C: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ B3 @ A2 )
% 3.97/1.83 => ( ( ord_less @ A @ C @ B3 )
% 3.97/1.83 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_247_dual__order_Ostrict__trans2,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [B3: A,A2: A,C: A] :
% 3.97/1.83 ( ( ord_less @ A @ B3 @ A2 )
% 3.97/1.83 => ( ( ord_less_eq @ A @ C @ B3 )
% 3.97/1.83 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_248_dense__ge__bounded,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( dense_linorder @ A )
% 3.97/1.83 => ! [Z: A,X: A,Y: A] :
% 3.97/1.83 ( ( ord_less @ A @ Z @ X )
% 3.97/1.83 => ( ! [W2: A] :
% 3.97/1.83 ( ( ord_less @ A @ Z @ W2 )
% 3.97/1.83 => ( ( ord_less @ A @ W2 @ X )
% 3.97/1.83 => ( ord_less_eq @ A @ Y @ W2 ) ) )
% 3.97/1.83 => ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_249_dense__le__bounded,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( dense_linorder @ A )
% 3.97/1.83 => ! [X: A,Y: A,Z: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ Y )
% 3.97/1.83 => ( ! [W2: A] :
% 3.97/1.83 ( ( ord_less @ A @ X @ W2 )
% 3.97/1.83 => ( ( ord_less @ A @ W2 @ Y )
% 3.97/1.83 => ( ord_less_eq @ A @ W2 @ Z ) ) )
% 3.97/1.83 => ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_250_order_Ostrict__implies__order,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ! [A2: A,B3: A] :
% 3.97/1.83 ( ( ord_less @ A @ A2 @ B3 )
% 3.97/1.83 => ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_251_dual__order_Oorder__iff__strict,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ( ( ord_less_eq @ A )
% 3.97/1.83 = ( ^ [B4: A,A6: A] :
% 3.97/1.83 ( ( ord_less @ A @ B4 @ A6 )
% 3.97/1.83 | ( A6 = B4 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_252_dual__order_Ostrict__iff__order,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( order @ A )
% 3.97/1.83 => ( ( ord_less @ A )
% 3.97/1.83 = ( ^ [B4: A,A6: A] :
% 3.97/1.83 ( ( ord_less_eq @ A @ B4 @ A6 )
% 3.97/1.83 & ( A6 != B4 ) ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_253_forall__1,axiom,
% 3.97/1.83 ( ( ^ [P2: numeral_num1 > $o] :
% 3.97/1.83 ! [X3: numeral_num1] : ( P2 @ X3 ) )
% 3.97/1.83 = ( ^ [P3: numeral_num1 > $o] : ( P3 @ ( one_one @ numeral_num1 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(fact_254_ex__1,axiom,
% 3.97/1.83 ( ( ^ [P2: numeral_num1 > $o] :
% 3.97/1.83 ? [X3: numeral_num1] : ( P2 @ X3 ) )
% 3.97/1.83 = ( ^ [P3: numeral_num1 > $o] : ( P3 @ ( one_one @ numeral_num1 ) ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(subcl_Finite__Set_Ofinite___HOL_Otype,axiom,
% 3.97/1.83 ! [A: $tType] :
% 3.97/1.83 ( ( finite_finite @ A )
% 3.97/1.83 => ( type @ A ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Cardinality_OCARD__1,axiom,
% 3.97/1.83 cARD_1 @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( preorder @ A8 )
% 3.97/1.83 => ( preorder @ ( A5 > A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( finite_finite @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( finite_finite @ ( A5 > A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( order @ A8 )
% 3.97/1.83 => ( order @ ( A5 > A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_fun___Orderings_Oord,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ord @ A8 )
% 3.97/1.83 => ( ord @ ( A5 > A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_fun___Groups_Ominus,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( minus @ A8 )
% 3.97/1.83 => ( minus @ ( A5 > A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 3.97/1.83 condit1037483654norder @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Rings_Olinordered__nonzero__semiring,axiom,
% 3.97/1.83 linord1659791738miring @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add__abs,axiom,
% 3.97/1.83 ordere142940540dd_abs @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add,axiom,
% 3.97/1.83 cancel146912293up_add @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add,axiom,
% 3.97/1.83 ordered_ab_group_add @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Rings_Olinordered__idom,axiom,
% 3.97/1.83 linordered_idom @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Rings_Oidom__abs__sgn,axiom,
% 3.97/1.83 idom_abs_sgn @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Orderings_Opreorder_1,axiom,
% 3.97/1.83 preorder @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Orderings_Olinorder,axiom,
% 3.97/1.83 linorder @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Groups_Omonoid__mult,axiom,
% 3.97/1.83 monoid_mult @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Orderings_Ono__top,axiom,
% 3.97/1.83 no_top @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Orderings_Ono__bot,axiom,
% 3.97/1.83 no_bot @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Groups_Ogroup__add,axiom,
% 3.97/1.83 group_add @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Orderings_Oorder_2,axiom,
% 3.97/1.83 order @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Nat_Oring__char__0,axiom,
% 3.97/1.83 ring_char_0 @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Orderings_Oord_3,axiom,
% 3.97/1.83 ord @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Rings_Oring__1,axiom,
% 3.97/1.83 ring_1 @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Groups_Ominus_4,axiom,
% 3.97/1.83 minus @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Groups_Ozero,axiom,
% 3.97/1.83 zero @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Rings_Oring,axiom,
% 3.97/1.83 ring @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Int_Oint___Groups_Oone,axiom,
% 3.97/1.83 one @ int ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 3.97/1.83 ! [A5: $tType] : ( preorder @ ( set @ A5 ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Set_Oset___Groups_Omonoid__mult_6,axiom,
% 3.97/1.83 ! [A5: $tType] :
% 3.97/1.83 ( ( monoid_mult @ A5 )
% 3.97/1.83 => ( monoid_mult @ ( set @ A5 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Set_Oset___Finite__Set_Ofinite_7,axiom,
% 3.97/1.83 ! [A5: $tType] :
% 3.97/1.83 ( ( finite_finite @ A5 )
% 3.97/1.83 => ( finite_finite @ ( set @ A5 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Set_Oset___Orderings_Oorder_8,axiom,
% 3.97/1.83 ! [A5: $tType] : ( order @ ( set @ A5 ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Set_Oset___Orderings_Oord_9,axiom,
% 3.97/1.83 ! [A5: $tType] : ( ord @ ( set @ A5 ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Set_Oset___Groups_Ominus_10,axiom,
% 3.97/1.83 ! [A5: $tType] : ( minus @ ( set @ A5 ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Set_Oset___Groups_Ozero_11,axiom,
% 3.97/1.83 ! [A5: $tType] :
% 3.97/1.83 ( ( zero @ A5 )
% 3.97/1.83 => ( zero @ ( set @ A5 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Set_Oset___Groups_Oone_12,axiom,
% 3.97/1.83 ! [A5: $tType] :
% 3.97/1.83 ( ( one @ A5 )
% 3.97/1.83 => ( one @ ( set @ A5 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_HOL_Obool___Orderings_Opreorder_13,axiom,
% 3.97/1.83 preorder @ $o ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_HOL_Obool___Orderings_Olinorder_14,axiom,
% 3.97/1.83 linorder @ $o ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_HOL_Obool___Finite__Set_Ofinite_15,axiom,
% 3.97/1.83 finite_finite @ $o ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_HOL_Obool___Orderings_Oorder_16,axiom,
% 3.97/1.83 order @ $o ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_HOL_Obool___Orderings_Oord_17,axiom,
% 3.97/1.83 ord @ $o ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_HOL_Obool___Groups_Ominus_18,axiom,
% 3.97/1.83 minus @ $o ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_19,axiom,
% 3.97/1.83 condit1037483654norder @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Olinear__continuum,axiom,
% 3.97/1.83 condit1656338222tinuum @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space,axiom,
% 3.97/1.83 ordere890947078_space @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__algebra__1,axiom,
% 3.97/1.83 real_V1229719638ebra_1 @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector,axiom,
% 3.97/1.83 real_V55928688vector @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Archimedean__Field_Oarchimedean__field,axiom,
% 3.97/1.83 archim1804426504_field @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_20,axiom,
% 3.97/1.83 linord1659791738miring @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space,axiom,
% 3.97/1.83 real_V2090557954_space @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs_21,axiom,
% 3.97/1.83 ordere142940540dd_abs @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Archimedean__Field_Ofloor__ceiling,axiom,
% 3.97/1.83 archim1727834104eiling @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_22,axiom,
% 3.97/1.83 cancel146912293up_add @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Real__Vector__Spaces_Odist__norm,axiom,
% 3.97/1.83 real_V1639655670t_norm @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add_23,axiom,
% 3.97/1.83 ordered_ab_group_add @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Orderings_Odense__linorder,axiom,
% 3.97/1.83 dense_linorder @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Rings_Olinordered__idom_24,axiom,
% 3.97/1.83 linordered_idom @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Orderings_Odense__order,axiom,
% 3.97/1.83 dense_order @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Rings_Oidom__abs__sgn_25,axiom,
% 3.97/1.83 idom_abs_sgn @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Orderings_Opreorder_26,axiom,
% 3.97/1.83 preorder @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Orderings_Olinorder_27,axiom,
% 3.97/1.83 linorder @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Groups_Omonoid__mult_28,axiom,
% 3.97/1.83 monoid_mult @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Orderings_Ono__top_29,axiom,
% 3.97/1.83 no_top @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Orderings_Ono__bot_30,axiom,
% 3.97/1.83 no_bot @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Groups_Ogroup__add_31,axiom,
% 3.97/1.83 group_add @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Orderings_Oorder_32,axiom,
% 3.97/1.83 order @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Nat_Oring__char__0_33,axiom,
% 3.97/1.83 ring_char_0 @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Orderings_Oord_34,axiom,
% 3.97/1.83 ord @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Rings_Oring__1_35,axiom,
% 3.97/1.83 ring_1 @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Groups_Ominus_36,axiom,
% 3.97/1.83 minus @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Fields_Ofield,axiom,
% 3.97/1.83 field @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Groups_Ozero_37,axiom,
% 3.97/1.83 zero @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Rings_Oring_38,axiom,
% 3.97/1.83 ring @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Real_Oreal___Groups_Oone_39,axiom,
% 3.97/1.83 one @ real ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Groups_Ocancel__ab__semigroup__add_40,axiom,
% 3.97/1.83 cancel146912293up_add @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Orderings_Owellorder,axiom,
% 3.97/1.83 wellorder @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Orderings_Opreorder_41,axiom,
% 3.97/1.83 preorder @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Orderings_Olinorder_42,axiom,
% 3.97/1.83 linorder @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Groups_Omonoid__mult_43,axiom,
% 3.97/1.83 monoid_mult @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Finite__Set_Ofinite_44,axiom,
% 3.97/1.83 finite_finite @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Groups_Ogroup__add_45,axiom,
% 3.97/1.83 group_add @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Orderings_Oorder_46,axiom,
% 3.97/1.83 order @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Orderings_Oord_47,axiom,
% 3.97/1.83 ord @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Groups_Ominus_48,axiom,
% 3.97/1.83 minus @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Groups_Ozero_49,axiom,
% 3.97/1.83 zero @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Rings_Oring_50,axiom,
% 3.97/1.83 ring @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Numeral__Type_Onum1___Groups_Oone_51,axiom,
% 3.97/1.83 one @ numeral_num1 ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space_52,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( ordere890947078_space @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( ordere890947078_space @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_53,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( real_V55928688vector @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( real_V55928688vector @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Ometric__space_54,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( real_V2090557954_space @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( real_V2090557954_space @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add__abs_55,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( ordere890947078_space @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( ordere142940540dd_abs @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__ab__semigroup__add_56,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( cancel146912293up_add @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( cancel146912293up_add @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Odist__norm_57,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( real_V55928688vector @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( real_V1639655670t_norm @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add_58,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( ordere890947078_space @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( ordered_ab_group_add @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Opreorder_59,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( order @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( preorder @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Olinorder_60,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( linorder @ A5 )
% 3.97/1.83 & ( cARD_1 @ A8 ) )
% 3.97/1.83 => ( linorder @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Omonoid__mult_61,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( monoid_mult @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( monoid_mult @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_62,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( finite_finite @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( finite_finite @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ogroup__add_63,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( group_add @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( group_add @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oorder_64,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( order @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( order @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Nat_Oring__char__0_65,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( ring_char_0 @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( ring_char_0 @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Orderings_Oord_66,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( ord @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( ord @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Rings_Oring__1_67,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( ring_1 @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( ring_1 @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ominus_68,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( minus @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( minus @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ozero_69,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( zero @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( zero @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Rings_Oring_70,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( ring @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( ring @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oone_71,axiom,
% 3.97/1.83 ! [A5: $tType,A8: $tType] :
% 3.97/1.83 ( ( ( one @ A5 )
% 3.97/1.83 & ( finite_finite @ A8 ) )
% 3.97/1.83 => ( one @ ( finite_Cartesian_vec @ A5 @ A8 ) ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(help_If_3_1_T,axiom,
% 3.97/1.83 ! [P: $o] :
% 3.97/1.83 ( ( P = $true )
% 3.97/1.83 | ( P = $false ) ) ).
% 3.97/1.83
% 3.97/1.83 thf(help_If_2_1_T,axiom,
% 3.97/1.83 ! [A: $tType,X: A,Y: A] :
% 3.97/1.83 ( ( if @ A @ $false @ X @ Y )
% 3.97/1.83 = Y ) ).
% 3.97/1.83
% 3.97/1.83 thf(help_If_1_1_T,axiom,
% 3.97/1.83 ! [A: $tType,X: A,Y: A] :
% 3.97/1.83 ( ( if @ A @ $true @ X @ Y )
% 3.97/1.83 = X ) ).
% 3.97/1.83
% 3.97/1.83 thf(tfree_0,hypothesis,
% 3.97/1.83 finite_finite @ n ).
% 3.97/1.83
% 3.97/1.83 thf(conj_0,conjecture,
% 3.97/1.83 ( ( ring_1_of_int @ real @ ( abs_abs @ int @ m ) )
% 3.97/1.83 = ( abs_abs @ real @ ( finite1433825200ec_nth @ real @ n @ ( minus_minus @ ( finite_Cartesian_vec @ real @ n ) @ x @ y ) @ i ) ) ) ).
% 3.97/1.83 ------------------------
% 3.97/1.87 % (8924)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8750 for (2999ds/183Mi)
% 3.97/1.87 % (8927)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8750 for (2999ds/2Mi)
% 3.97/1.87 % (8929)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_8750 for (2999ds/275Mi)
% 3.97/1.87 % (8925)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_8750 for (2999ds/4Mi)
% 3.97/1.87 % (8926)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_8750 for (2999ds/27Mi)
% 3.97/1.87 % (8928)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_8750 for (2999ds/2Mi)
% 3.97/1.87 % (8930)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8750 for (2999ds/18Mi)
% 3.97/1.87 % (8927)Instruction limit reached!
% 3.97/1.87 % (8927)------------------------------
% 3.97/1.87 % (8927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.97/1.87 % (8927)Termination reason: Unknown
% 3.97/1.87 % (8928)Instruction limit reached!
% 3.97/1.87 % (8928)------------------------------
% 3.97/1.87 % (8928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.97/1.87 % (8927)Termination phase: shuffling
% 3.97/1.87
% 3.97/1.87 % (8927)Memory used [KB]: 1407
% 3.97/1.87 % (8927)Time elapsed: 0.004 s
% 3.97/1.87 % (8927)Instructions burned: 2 (million)
% 3.97/1.87 % (8927)------------------------------
% 3.97/1.87 % (8927)------------------------------
% 3.97/1.87 % (8928)Termination reason: Unknown
% 3.97/1.87 % (8928)Termination phase: shuffling
% 3.97/1.87
% 3.97/1.87 % (8928)Memory used [KB]: 1407
% 3.97/1.87 % (8928)Time elapsed: 0.004 s
% 3.97/1.87 % (8928)Instructions burned: 3 (million)
% 3.97/1.87 % (8928)------------------------------
% 3.97/1.87 % (8928)------------------------------
% 3.97/1.87 % (8925)Instruction limit reached!
% 3.97/1.87 % (8925)------------------------------
% 3.97/1.87 % (8925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.97/1.87 % (8925)Termination reason: Unknown
% 3.97/1.87 % (8925)Termination phase: shuffling
% 3.97/1.87
% 3.97/1.87 % (8925)Memory used [KB]: 1407
% 3.97/1.87 % (8925)Time elapsed: 0.004 s
% 3.97/1.87 % (8925)Instructions burned: 4 (million)
% 3.97/1.87 % (8925)------------------------------
% 3.97/1.87 % (8925)------------------------------
% 3.97/1.88 % (8930)Instruction limit reached!
% 3.97/1.88 % (8930)------------------------------
% 3.97/1.88 % (8930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.97/1.88 % (8930)Termination reason: Unknown
% 3.97/1.88 % (8930)Termination phase: shuffling
% 3.97/1.88
% 3.97/1.88 % (8930)Memory used [KB]: 1918
% 3.97/1.88 % (8930)Time elapsed: 0.013 s
% 3.97/1.88 % (8930)Instructions burned: 19 (million)
% 3.97/1.88 % (8930)------------------------------
% 3.97/1.88 % (8930)------------------------------
% 3.97/1.89 % (8926)Instruction limit reached!
% 3.97/1.89 % (8926)------------------------------
% 3.97/1.89 % (8926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.97/1.89 % (8926)Termination reason: Unknown
% 3.97/1.89 % (8926)Termination phase: Property scanning
% 3.97/1.89
% 3.97/1.89 % (8926)Memory used [KB]: 1918
% 3.97/1.89 % (8926)Time elapsed: 0.017 s
% 3.97/1.89 % (8926)Instructions burned: 28 (million)
% 3.97/1.89 % (8926)------------------------------
% 3.97/1.89 % (8926)------------------------------
% 3.97/1.89 % (8933)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_8750 for (2999ds/15Mi)
% 3.97/1.89 % (8931)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8750 for (2999ds/3Mi)
% 3.97/1.89 % (8932)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_8750 for (2999ds/37Mi)
% 3.97/1.89 % (8931)Instruction limit reached!
% 3.97/1.89 % (8931)------------------------------
% 3.97/1.89 % (8931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.97/1.89 % (8931)Termination reason: Unknown
% 3.97/1.89 % (8931)Termination phase: shuffling
% 3.97/1.89
% 3.97/1.89 % (8931)Memory used [KB]: 1407
% 3.97/1.89 % (8931)Time elapsed: 0.004 s
% 3.97/1.89 % (8931)Instructions burned: 3 (million)
% 3.97/1.89 % (8931)------------------------------
% 3.97/1.89 % (8931)------------------------------
% 3.97/1.90 % (8929)Refutation not found, incomplete strategy
% 3.97/1.90 % (8929)------------------------------
% 3.97/1.90 % (8929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.97/1.90 % (8929)Termination reason: Refutation not found, incomplete strategy
% 3.97/1.90
% 3.97/1.90
% 3.97/1.90 % (8929)Memory used [KB]: 6524
% 3.97/1.90 % (8929)Time elapsed: 0.027 s
% 3.97/1.90 % (8929)Instructions burned: 43 (million)
% 3.97/1.90 % (8929)------------------------------
% 3.97/1.90 % (8929)------------------------------
% 4.02/1.90 % (8933)Instruction limit reached!
% 4.02/1.90 % (8933)------------------------------
% 4.02/1.90 % (8933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.90 % (8933)Termination reason: Unknown
% 4.02/1.90 % (8933)Termination phase: shuffling
% 4.02/1.90
% 4.02/1.90 % (8933)Memory used [KB]: 1791
% 4.02/1.90 % (8933)Time elapsed: 0.011 s
% 4.02/1.90 % (8933)Instructions burned: 16 (million)
% 4.02/1.90 % (8933)------------------------------
% 4.02/1.90 % (8933)------------------------------
% 4.02/1.90 % (8934)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_8750 for (2999ds/3Mi)
% 4.02/1.90 % (8934)Instruction limit reached!
% 4.02/1.90 % (8934)------------------------------
% 4.02/1.90 % (8934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.90 % (8934)Termination reason: Unknown
% 4.02/1.90 % (8934)Termination phase: shuffling
% 4.02/1.90
% 4.02/1.90 % (8934)Memory used [KB]: 1535
% 4.02/1.90 % (8934)Time elapsed: 0.004 s
% 4.02/1.90 % (8934)Instructions burned: 4 (million)
% 4.02/1.90 % (8934)------------------------------
% 4.02/1.90 % (8934)------------------------------
% 4.02/1.91 % (8935)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_8750 for (2999ds/1041Mi)
% 4.02/1.91 % (8932)Instruction limit reached!
% 4.02/1.91 % (8932)------------------------------
% 4.02/1.91 % (8932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.91 % (8932)Termination reason: Unknown
% 4.02/1.91 % (8932)Termination phase: Property scanning
% 4.02/1.91
% 4.02/1.91 % (8932)Memory used [KB]: 2174
% 4.02/1.91 % (8932)Time elapsed: 0.022 s
% 4.02/1.91 % (8932)Instructions burned: 37 (million)
% 4.02/1.91 % (8932)------------------------------
% 4.02/1.91 % (8932)------------------------------
% 4.02/1.91 % (8936)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8750 for (2999ds/7Mi)
% 4.02/1.92 % (8937)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8750 for (2999ds/16Mi)
% 4.02/1.92 % (8936)Instruction limit reached!
% 4.02/1.92 % (8936)------------------------------
% 4.02/1.92 % (8936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.92 % (8936)Termination reason: Unknown
% 4.02/1.92 % (8936)Termination phase: shuffling
% 4.02/1.92
% 4.02/1.92 % (8936)Memory used [KB]: 1535
% 4.02/1.92 % (8936)Time elapsed: 0.006 s
% 4.02/1.92 % (8936)Instructions burned: 7 (million)
% 4.02/1.92 % (8936)------------------------------
% 4.02/1.92 % (8936)------------------------------
% 4.02/1.92 % (8938)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_8750 for (2999ds/3Mi)
% 4.02/1.92 % (8938)Instruction limit reached!
% 4.02/1.92 % (8938)------------------------------
% 4.02/1.92 % (8938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.92 % (8938)Termination reason: Unknown
% 4.02/1.92 % (8938)Termination phase: shuffling
% 4.02/1.92
% 4.02/1.92 % (8938)Memory used [KB]: 1407
% 4.02/1.92 % (8938)Time elapsed: 0.003 s
% 4.02/1.92 % (8938)Instructions burned: 3 (million)
% 4.02/1.92 % (8938)------------------------------
% 4.02/1.92 % (8938)------------------------------
% 4.02/1.92 % (8939)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_8750 for (2999ds/3Mi)
% 4.02/1.92 % (8939)Instruction limit reached!
% 4.02/1.92 % (8939)------------------------------
% 4.02/1.92 % (8939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.92 % (8939)Termination reason: Unknown
% 4.02/1.92 % (8939)Termination phase: shuffling
% 4.02/1.92
% 4.02/1.92 % (8939)Memory used [KB]: 1407
% 4.02/1.92 % (8939)Time elapsed: 0.004 s
% 4.02/1.92 % (8939)Instructions burned: 3 (million)
% 4.02/1.92 % (8939)------------------------------
% 4.02/1.92 % (8939)------------------------------
% 4.02/1.92 % (8937)Instruction limit reached!
% 4.02/1.92 % (8937)------------------------------
% 4.02/1.92 % (8937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.92 % (8937)Termination reason: Unknown
% 4.02/1.93 % (8937)Termination phase: shuffling
% 4.02/1.93
% 4.02/1.93 % (8937)Memory used [KB]: 1918
% 4.02/1.93 % (8937)Time elapsed: 0.012 s
% 4.02/1.93 % (8937)Instructions burned: 17 (million)
% 4.02/1.93 % (8937)------------------------------
% 4.02/1.93 % (8937)------------------------------
% 4.02/1.93 % (8940)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8750 for (2999ds/7Mi)
% 4.02/1.93 % (8940)Instruction limit reached!
% 4.02/1.93 % (8940)------------------------------
% 4.02/1.93 % (8940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.93 % (8940)Termination reason: Unknown
% 4.02/1.93 % (8940)Termination phase: shuffling
% 4.02/1.93
% 4.02/1.93 % (8940)Memory used [KB]: 1535
% 4.02/1.93 % (8940)Time elapsed: 0.007 s
% 4.02/1.93 % (8940)Instructions burned: 8 (million)
% 4.02/1.93 % (8940)------------------------------
% 4.02/1.93 % (8940)------------------------------
% 4.02/1.94 % (8941)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_8750 for (2999ds/3Mi)
% 4.02/1.94 % (8941)Instruction limit reached!
% 4.02/1.94 % (8941)------------------------------
% 4.02/1.94 % (8941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.94 % (8941)Termination reason: Unknown
% 4.02/1.94 % (8941)Termination phase: shuffling
% 4.02/1.94
% 4.02/1.94 % (8941)Memory used [KB]: 1407
% 4.02/1.94 % (8941)Time elapsed: 0.004 s
% 4.02/1.94 % (8941)Instructions burned: 4 (million)
% 4.02/1.94 % (8941)------------------------------
% 4.02/1.94 % (8941)------------------------------
% 4.02/1.94 % (8942)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_8750 for (2999ds/4Mi)
% 4.02/1.94 % (8942)Instruction limit reached!
% 4.02/1.94 % (8942)------------------------------
% 4.02/1.94 % (8942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.94 % (8942)Termination reason: Unknown
% 4.02/1.94 % (8942)Termination phase: shuffling
% 4.02/1.94
% 4.02/1.94 % (8943)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_8750 for (2999ds/18Mi)
% 4.02/1.94 % (8942)Memory used [KB]: 1535
% 4.02/1.94 % (8942)Time elapsed: 0.005 s
% 4.02/1.94 % (8942)Instructions burned: 4 (million)
% 4.02/1.94 % (8942)------------------------------
% 4.02/1.94 % (8942)------------------------------
% 4.02/1.94 % (8944)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_8750 for (2999ds/710Mi)
% 4.02/1.95 % (8943)Instruction limit reached!
% 4.02/1.95 % (8943)------------------------------
% 4.02/1.95 % (8943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.95 % (8943)Termination reason: Unknown
% 4.02/1.95 % (8943)Termination phase: shuffling
% 4.02/1.95
% 4.02/1.95 % (8943)Memory used [KB]: 1918
% 4.02/1.95 % (8943)Time elapsed: 0.013 s
% 4.02/1.95 % (8943)Instructions burned: 18 (million)
% 4.02/1.95 % (8943)------------------------------
% 4.02/1.95 % (8943)------------------------------
% 4.02/1.96 % (8945)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8750 for (2999ds/6Mi)
% 4.02/1.96 % (8946)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_8750 for (2999ds/902Mi)
% 4.02/1.96 % (8945)Instruction limit reached!
% 4.02/1.96 % (8945)------------------------------
% 4.02/1.96 % (8945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.96 % (8945)Termination reason: Unknown
% 4.02/1.96 % (8945)Termination phase: shuffling
% 4.02/1.96
% 4.02/1.96 % (8945)Memory used [KB]: 1535
% 4.02/1.96 % (8945)Time elapsed: 0.006 s
% 4.02/1.96 % (8945)Instructions burned: 6 (million)
% 4.02/1.96 % (8945)------------------------------
% 4.02/1.96 % (8945)------------------------------
% 4.02/1.96 % (8947)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_8750 for (2998ds/21Mi)
% 4.02/1.97 % (8924)Instruction limit reached!
% 4.02/1.97 % (8924)------------------------------
% 4.02/1.97 % (8924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.97 % (8924)Termination reason: Unknown
% 4.02/1.97 % (8924)Termination phase: Saturation
% 4.02/1.97
% 4.02/1.97 % (8924)Memory used [KB]: 7291
% 4.02/1.97 % (8924)Time elapsed: 0.105 s
% 4.02/1.97 % (8924)Instructions burned: 184 (million)
% 4.02/1.97 % (8924)------------------------------
% 4.02/1.97 % (8924)------------------------------
% 4.02/1.97 % (8948)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_8750 for (2998ds/5Mi)
% 4.02/1.97 % (8947)Instruction limit reached!
% 4.02/1.97 % (8947)------------------------------
% 4.02/1.97 % (8947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.97 % (8947)Termination reason: Unknown
% 4.02/1.97 % (8947)Termination phase: shuffling
% 4.02/1.97
% 4.02/1.97 % (8947)Memory used [KB]: 1918
% 4.02/1.97 % (8947)Time elapsed: 0.014 s
% 4.02/1.97 % (8947)Instructions burned: 21 (million)
% 4.02/1.97 % (8947)------------------------------
% 4.02/1.97 % (8947)------------------------------
% 4.02/1.98 % (8948)Instruction limit reached!
% 4.02/1.98 % (8948)------------------------------
% 4.02/1.98 % (8948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.98 % (8948)Termination reason: Unknown
% 4.02/1.98 % (8948)Termination phase: shuffling
% 4.02/1.98
% 4.02/1.98 % (8948)Memory used [KB]: 1407
% 4.02/1.98 % (8948)Time elapsed: 0.005 s
% 4.02/1.98 % (8948)Instructions burned: 5 (million)
% 4.02/1.98 % (8948)------------------------------
% 4.02/1.98 % (8948)------------------------------
% 4.02/1.98 % (8949)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_8750 for (2998ds/6Mi)
% 4.02/1.98 % (8949)Instruction limit reached!
% 4.02/1.98 % (8949)------------------------------
% 4.02/1.98 % (8949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/1.98 % (8949)Termination reason: Unknown
% 4.02/1.98 % (8949)Termination phase: shuffling
% 4.02/1.98
% 4.02/1.98 % (8949)Memory used [KB]: 1535
% 4.02/1.98 % (8949)Time elapsed: 0.005 s
% 4.02/1.98 % (8949)Instructions burned: 6 (million)
% 4.02/1.98 % (8949)------------------------------
% 4.02/1.98 % (8949)------------------------------
% 4.02/1.99 % (8950)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_8750 for (2998ds/377Mi)
% 4.02/1.99 % (8951)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_8750 for (2998ds/779Mi)
% 4.02/2.00 % (8952)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_8750 for (2998ds/19Mi)
% 4.02/2.00 % (8953)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_8750 for (2998ds/879Mi)
% 4.02/2.01 % (8952)Instruction limit reached!
% 4.02/2.01 % (8952)------------------------------
% 4.02/2.01 % (8952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/2.01 % (8952)Termination reason: Unknown
% 4.02/2.01 % (8952)Termination phase: shuffling
% 4.02/2.01
% 4.02/2.01 % (8952)Memory used [KB]: 1791
% 4.02/2.01 % (8952)Time elapsed: 0.012 s
% 4.02/2.01 % (8952)Instructions burned: 20 (million)
% 4.02/2.01 % (8952)------------------------------
% 4.02/2.01 % (8952)------------------------------
% 4.02/2.02 % (8946)Refutation not found, incomplete strategy
% 4.02/2.02 % (8946)------------------------------
% 4.02/2.02 % (8946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/2.02 % (8946)Termination reason: Refutation not found, incomplete strategy
% 4.02/2.02
% 4.02/2.02
% 4.02/2.02 % (8946)Memory used [KB]: 7164
% 4.02/2.02 % (8946)Time elapsed: 0.060 s
% 4.02/2.02 % (8946)Instructions burned: 103 (million)
% 4.02/2.02 % (8946)------------------------------
% 4.02/2.02 % (8946)------------------------------
% 5.16/2.03 % (8954)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_8750 for (2998ds/17Mi)
% 5.16/2.04 % (8954)Instruction limit reached!
% 5.16/2.04 % (8954)------------------------------
% 5.16/2.04 % (8954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.16/2.04 % (8954)Termination reason: Unknown
% 5.16/2.04 % (8954)Termination phase: shuffling
% 5.16/2.04
% 5.16/2.04 % (8954)Memory used [KB]: 1918
% 5.16/2.04 % (8954)Time elapsed: 0.012 s
% 5.16/2.04 % (8954)Instructions burned: 17 (million)
% 5.16/2.04 % (8954)------------------------------
% 5.16/2.04 % (8954)------------------------------
% 5.16/2.04 % (8955)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_8750 for (2998ds/3Mi)
% 5.16/2.04 % (8955)Instruction limit reached!
% 5.16/2.04 % (8955)------------------------------
% 5.16/2.04 % (8955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.16/2.04 % (8955)Termination reason: Unknown
% 5.16/2.04 % (8955)Termination phase: shuffling
% 5.16/2.04
% 5.16/2.04 % (8955)Memory used [KB]: 1407
% 5.16/2.04 % (8955)Time elapsed: 0.004 s
% 5.16/2.04 % (8955)Instructions burned: 4 (million)
% 5.16/2.04 % (8955)------------------------------
% 5.16/2.04 % (8955)------------------------------
% 5.16/2.06 % (8956)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_8750 for (2997ds/30Mi)
% 5.16/2.06 % (8957)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_8750 for (2997ds/127Mi)
% 5.16/2.08 % (8956)Instruction limit reached!
% 5.16/2.08 % (8956)------------------------------
% 5.16/2.08 % (8956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.16/2.08 % (8956)Termination reason: Unknown
% 5.16/2.08 % (8956)Termination phase: Property scanning
% 5.16/2.08
% 5.16/2.08 % (8956)Memory used [KB]: 1918
% 5.16/2.08 % (8956)Time elapsed: 0.019 s
% 5.16/2.08 % (8956)Instructions burned: 31 (million)
% 5.16/2.08 % (8956)------------------------------
% 5.16/2.08 % (8956)------------------------------
% 5.16/2.10 % (8958)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_8750 for (2997ds/100Mi)
% 5.78/2.13 % (8957)Instruction limit reached!
% 5.78/2.13 % (8957)------------------------------
% 5.78/2.13 % (8957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.13 % (8957)Termination reason: Unknown
% 5.78/2.13 % (8957)Termination phase: Saturation
% 5.78/2.13
% 5.78/2.13 % (8957)Memory used [KB]: 7036
% 5.78/2.13 % (8957)Time elapsed: 0.073 s
% 5.78/2.13 % (8957)Instructions burned: 127 (million)
% 5.78/2.13 % (8957)------------------------------
% 5.78/2.13 % (8957)------------------------------
% 5.78/2.15 % (8958)Instruction limit reached!
% 5.78/2.15 % (8958)------------------------------
% 5.78/2.15 % (8958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.15 % (8958)Termination reason: Unknown
% 5.78/2.15 % (8958)Termination phase: Saturation
% 5.78/2.15
% 5.78/2.15 % (8958)Memory used [KB]: 6908
% 5.78/2.15 % (8958)Time elapsed: 0.054 s
% 5.78/2.15 % (8958)Instructions burned: 100 (million)
% 5.78/2.15 % (8958)------------------------------
% 5.78/2.15 % (8958)------------------------------
% 5.78/2.15 % (8959)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_8750 for (2996ds/3Mi)
% 5.78/2.16 % (8959)Instruction limit reached!
% 5.78/2.16 % (8959)------------------------------
% 5.78/2.16 % (8959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.16 % (8959)Termination reason: Unknown
% 5.78/2.16 % (8959)Termination phase: shuffling
% 5.78/2.16
% 5.78/2.16 % (8959)Memory used [KB]: 1407
% 5.78/2.16 % (8959)Time elapsed: 0.004 s
% 5.78/2.16 % (8959)Instructions burned: 4 (million)
% 5.78/2.16 % (8959)------------------------------
% 5.78/2.16 % (8959)------------------------------
% 5.78/2.17 % (8960)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_8750 for (2996ds/20Mi)
% 5.78/2.18 % (8961)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_8750 for (2996ds/86Mi)
% 5.78/2.18 % (8960)Instruction limit reached!
% 5.78/2.18 % (8960)------------------------------
% 5.78/2.18 % (8960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.18 % (8960)Termination reason: Unknown
% 5.78/2.18 % (8960)Termination phase: shuffling
% 5.78/2.18
% 5.78/2.18 % (8960)Memory used [KB]: 1918
% 5.78/2.18 % (8960)Time elapsed: 0.014 s
% 5.78/2.18 % (8960)Instructions burned: 20 (million)
% 5.78/2.18 % (8960)------------------------------
% 5.78/2.18 % (8960)------------------------------
% 6.34/2.20 % (8962)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_8750 for (2996ds/107Mi)
% 6.34/2.22 % (8950)Instruction limit reached!
% 6.34/2.22 % (8950)------------------------------
% 6.34/2.22 % (8950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.22 % (8950)Termination reason: Unknown
% 6.34/2.22 % (8950)Termination phase: Saturation
% 6.34/2.22
% 6.34/2.22 % (8950)Memory used [KB]: 7931
% 6.34/2.22 % (8950)Time elapsed: 0.228 s
% 6.34/2.22 % (8950)Instructions burned: 378 (million)
% 6.34/2.22 % (8950)------------------------------
% 6.34/2.22 % (8950)------------------------------
% 6.34/2.23 % (8961)Instruction limit reached!
% 6.34/2.23 % (8961)------------------------------
% 6.34/2.23 % (8961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.23 % (8961)Termination reason: Unknown
% 6.34/2.23 % (8961)Termination phase: Saturation
% 6.34/2.23
% 6.34/2.23 % (8961)Memory used [KB]: 6908
% 6.34/2.23 % (8961)Time elapsed: 0.050 s
% 6.34/2.23 % (8961)Instructions burned: 86 (million)
% 6.34/2.23 % (8961)------------------------------
% 6.34/2.23 % (8961)------------------------------
% 6.34/2.24 % (8963)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_8750 for (2996ds/39Mi)
% 6.34/2.25 % (8964)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_8750 for (2996ds/448Mi)
% 6.34/2.26 % (8963)Instruction limit reached!
% 6.34/2.26 % (8963)------------------------------
% 6.34/2.26 % (8963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.26 % (8963)Termination reason: Unknown
% 6.34/2.26 % (8963)Termination phase: Property scanning
% 6.34/2.26
% 6.34/2.26 % (8963)Memory used [KB]: 2174
% 6.34/2.26 % (8963)Time elapsed: 0.023 s
% 6.34/2.26 % (8963)Instructions burned: 39 (million)
% 6.34/2.26 % (8963)------------------------------
% 6.34/2.26 % (8963)------------------------------
% 6.34/2.26 % (8962)Instruction limit reached!
% 6.34/2.26 % (8962)------------------------------
% 6.34/2.26 % (8962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.26 % (8962)Termination reason: Unknown
% 6.34/2.26 % (8962)Termination phase: Saturation
% 6.34/2.26
% 6.34/2.26 % (8962)Memory used [KB]: 7036
% 6.34/2.26 % (8962)Time elapsed: 0.063 s
% 6.34/2.26 % (8962)Instructions burned: 108 (million)
% 6.34/2.26 % (8962)------------------------------
% 6.34/2.26 % (8962)------------------------------
% 6.34/2.28 % (8965)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_8750 for (2995ds/46Mi)
% 6.34/2.29 % (8966)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_8750 for (2995ds/98Mi)
% 6.98/2.31 % (8965)Instruction limit reached!
% 6.98/2.31 % (8965)------------------------------
% 6.98/2.31 % (8965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.31 % (8965)Termination reason: Unknown
% 6.98/2.31 % (8965)Termination phase: Preprocessing 3
% 6.98/2.31
% 6.98/2.31 % (8965)Memory used [KB]: 2174
% 6.98/2.31 % (8965)Time elapsed: 0.029 s
% 6.98/2.31 % (8965)Instructions burned: 47 (million)
% 6.98/2.31 % (8965)------------------------------
% 6.98/2.31 % (8965)------------------------------
% 6.98/2.33 % (8967)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_8750 for (2995ds/507Mi)
% 6.98/2.34 % (8966)Instruction limit reached!
% 6.98/2.34 % (8966)------------------------------
% 6.98/2.34 % (8966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.34 % (8966)Termination reason: Unknown
% 6.98/2.34 % (8966)Termination phase: Saturation
% 6.98/2.34
% 6.98/2.34 % (8966)Memory used [KB]: 2430
% 6.98/2.34 % (8966)Time elapsed: 0.052 s
% 6.98/2.34 % (8966)Instructions burned: 98 (million)
% 6.98/2.34 % (8966)------------------------------
% 6.98/2.34 % (8966)------------------------------
% 6.98/2.34 % (8944)Instruction limit reached!
% 6.98/2.34 % (8944)------------------------------
% 6.98/2.34 % (8944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.34 % (8944)Termination reason: Unknown
% 6.98/2.34 % (8944)Termination phase: Saturation
% 6.98/2.34
% 6.98/2.34 % (8944)Memory used [KB]: 9083
% 6.98/2.34 % (8944)Time elapsed: 0.395 s
% 6.98/2.34 % (8944)Instructions burned: 710 (million)
% 6.98/2.34 % (8944)------------------------------
% 6.98/2.34 % (8944)------------------------------
% 6.98/2.36 % (8969)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_8750 for (2994ds/39Mi)
% 6.98/2.36 % (8968)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_8750 for (2995ds/149Mi)
% 6.98/2.38 % (8969)Instruction limit reached!
% 6.98/2.38 % (8969)------------------------------
% 6.98/2.38 % (8969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.38 % (8969)Termination reason: Unknown
% 6.98/2.38 % (8969)Termination phase: Preprocessing 3
% 6.98/2.38
% 6.98/2.38 % (8969)Memory used [KB]: 2174
% 6.98/2.38 % (8969)Time elapsed: 0.024 s
% 6.98/2.38 % (8969)Instructions burned: 39 (million)
% 6.98/2.38 % (8969)------------------------------
% 6.98/2.38 % (8969)------------------------------
% 6.98/2.39 % (8967)Refutation not found, incomplete strategy
% 6.98/2.39 % (8967)------------------------------
% 6.98/2.39 % (8967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.39 % (8967)Termination reason: Refutation not found, incomplete strategy
% 6.98/2.39
% 6.98/2.39
% 6.98/2.39 % (8967)Memory used [KB]: 7419
% 6.98/2.39 % (8967)Time elapsed: 0.065 s
% 6.98/2.39 % (8967)Instructions burned: 110 (million)
% 6.98/2.39 % (8967)------------------------------
% 6.98/2.39 % (8967)------------------------------
% 7.57/2.40 % (8970)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_8750 for (2994ds/6Mi)
% 7.57/2.40 % (8970)Instruction limit reached!
% 7.57/2.40 % (8970)------------------------------
% 7.57/2.40 % (8970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.57/2.40 % (8970)Termination reason: Unknown
% 7.57/2.40 % (8970)Termination phase: shuffling
% 7.57/2.40
% 7.57/2.40 % (8970)Memory used [KB]: 1535
% 7.57/2.40 % (8970)Time elapsed: 0.006 s
% 7.57/2.40 % (8970)Instructions burned: 6 (million)
% 7.57/2.40 % (8970)------------------------------
% 7.57/2.40 % (8970)------------------------------
% 7.57/2.42 % (8971)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_8750 for (2994ds/1087Mi)
% 7.57/2.43 % (8972)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_8750 for (2994ds/47Mi)
% 7.57/2.44 % (8968)Instruction limit reached!
% 7.57/2.44 % (8968)------------------------------
% 7.57/2.44 % (8968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.57/2.44 % (8968)Termination reason: Unknown
% 7.57/2.44 % (8968)Termination phase: Saturation
% 7.57/2.44
% 7.57/2.44 % (8968)Memory used [KB]: 7164
% 7.57/2.44 % (8968)Time elapsed: 0.088 s
% 7.57/2.44 % (8968)Instructions burned: 150 (million)
% 7.57/2.44 % (8968)------------------------------
% 7.57/2.44 % (8968)------------------------------
% 7.57/2.44 % (8951)Instruction limit reached!
% 7.57/2.44 % (8951)------------------------------
% 7.57/2.44 % (8951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.57/2.44 % (8951)Termination reason: Unknown
% 7.57/2.44 % (8951)Termination phase: Saturation
% 7.57/2.44
% 7.57/2.44 % (8951)Memory used [KB]: 8443
% 7.57/2.44 % (8951)Time elapsed: 0.451 s
% 7.57/2.44 % (8951)Instructions burned: 780 (million)
% 7.57/2.44 % (8951)------------------------------
% 7.57/2.44 % (8951)------------------------------
% 7.57/2.45 % (8972)Instruction limit reached!
% 7.57/2.45 % (8972)------------------------------
% 7.57/2.45 % (8972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.57/2.45 % (8972)Termination reason: Unknown
% 7.57/2.45 % (8972)Termination phase: Property scanning
% 7.57/2.45
% 7.57/2.45 % (8972)Memory used [KB]: 2302
% 7.57/2.45 % (8972)Time elapsed: 0.029 s
% 7.57/2.45 % (8972)Instructions burned: 48 (million)
% 7.57/2.45 % (8972)------------------------------
% 7.57/2.45 % (8972)------------------------------
% 7.57/2.46 % (8973)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_8750 for (2993ds/44Mi)
% 7.57/2.46 % (8974)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_8750 for (2993ds/432Mi)
% 7.57/2.48 % (8975)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_8750 for (2993ds/62Mi)
% 7.57/2.48 % (8953)Refutation not found, non-redundant clauses discarded% (8953)------------------------------
% 7.57/2.48 % (8953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.57/2.48 % (8953)Termination reason: Refutation not found, non-redundant clauses discarded
% 7.57/2.48
% 7.57/2.48 % (8953)Memory used [KB]: 8187
% 7.57/2.48 % (8953)Time elapsed: 0.499 s
% 7.57/2.48 % (8953)Instructions burned: 830 (million)
% 7.57/2.48 % (8953)------------------------------
% 7.57/2.48 % (8953)------------------------------
% 7.57/2.48 % (8964)Instruction limit reached!
% 7.57/2.48 % (8964)------------------------------
% 7.57/2.48 % (8964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.57/2.48 % (8964)Termination reason: Unknown
% 7.57/2.48 % (8964)Termination phase: Saturation
% 7.57/2.48
% 7.57/2.48 % (8964)Memory used [KB]: 8059
% 7.57/2.48 % (8964)Time elapsed: 0.239 s
% 7.57/2.48 % (8964)Instructions burned: 448 (million)
% 7.57/2.48 % (8964)------------------------------
% 7.57/2.48 % (8964)------------------------------
% 7.57/2.49 % (8973)Instruction limit reached!
% 7.57/2.49 % (8973)------------------------------
% 7.57/2.49 % (8973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.57/2.49 % (8973)Termination reason: Unknown
% 7.57/2.49 % (8973)Termination phase: Property scanning
% 7.57/2.49
% 7.57/2.49 % (8973)Memory used [KB]: 2174
% 7.57/2.49 % (8973)Time elapsed: 0.026 s
% 7.57/2.49 % (8973)Instructions burned: 45 (million)
% 7.57/2.49 % (8973)------------------------------
% 7.57/2.49 % (8973)------------------------------
% 8.29/2.50 % (8976)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_8750 for (2993ds/31Mi)
% 8.29/2.51 % (8977)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_8750 for (2993ds/96Mi)
% 8.29/2.51 % (8978)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_8750 for (2993ds/453Mi)
% 8.29/2.51 % (8935)Instruction limit reached!
% 8.29/2.51 % (8935)------------------------------
% 8.29/2.51 % (8935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.51 % (8935)Termination reason: Unknown
% 8.29/2.51 % (8935)Termination phase: Saturation
% 8.29/2.51
% 8.29/2.51 % (8935)Memory used [KB]: 9594
% 8.29/2.51 % (8935)Time elapsed: 0.603 s
% 8.29/2.51 % (8935)Instructions burned: 1041 (million)
% 8.29/2.51 % (8935)------------------------------
% 8.29/2.51 % (8935)------------------------------
% 8.29/2.51 % (8975)Instruction limit reached!
% 8.29/2.51 % (8975)------------------------------
% 8.29/2.51 % (8975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.51 % (8975)Termination reason: Unknown
% 8.29/2.51 % (8975)Termination phase: Preprocessing 1
% 8.29/2.51
% 8.29/2.51 % (8975)Memory used [KB]: 2174
% 8.29/2.51 % (8975)Time elapsed: 0.035 s
% 8.29/2.51 % (8975)Instructions burned: 62 (million)
% 8.29/2.51 % (8975)------------------------------
% 8.29/2.51 % (8975)------------------------------
% 8.29/2.52 % (8976)Instruction limit reached!
% 8.29/2.52 % (8976)------------------------------
% 8.29/2.52 % (8976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.52 % (8976)Termination reason: Unknown
% 8.29/2.52 % (8976)Termination phase: Property scanning
% 8.29/2.52
% 8.29/2.52 % (8976)Memory used [KB]: 1918
% 8.29/2.52 % (8976)Time elapsed: 0.019 s
% 8.29/2.52 % (8976)Instructions burned: 31 (million)
% 8.29/2.52 % (8976)------------------------------
% 8.29/2.52 % (8976)------------------------------
% 8.29/2.53 % (8979)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_8750 for (2993ds/71Mi)
% 8.29/2.53 % (8980)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_8750 for (2993ds/83Mi)
% 8.29/2.54 % (8981)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_8750 for (2993ds/11Mi)
% 8.29/2.55 % (8981)Instruction limit reached!
% 8.29/2.55 % (8981)------------------------------
% 8.29/2.55 % (8981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.55 % (8981)Termination reason: Unknown
% 8.29/2.55 % (8981)Termination phase: shuffling
% 8.29/2.55
% 8.29/2.55 % (8981)Memory used [KB]: 1663
% 8.29/2.55 % (8981)Time elapsed: 0.008 s
% 8.29/2.55 % (8981)Instructions burned: 12 (million)
% 8.29/2.55 % (8981)------------------------------
% 8.29/2.55 % (8981)------------------------------
% 8.29/2.56 % (8977)Instruction limit reached!
% 8.29/2.56 % (8977)------------------------------
% 8.29/2.56 % (8977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.56 % (8977)Termination reason: Unknown
% 8.29/2.56 % (8977)Termination phase: Saturation
% 8.29/2.56
% 8.29/2.56 % (8977)Memory used [KB]: 6908
% 8.29/2.56 % (8977)Time elapsed: 0.055 s
% 8.29/2.56 % (8977)Instructions burned: 96 (million)
% 8.29/2.56 % (8977)------------------------------
% 8.29/2.56 % (8977)------------------------------
% 8.29/2.57 % (8979)Instruction limit reached!
% 8.29/2.57 % (8979)------------------------------
% 8.29/2.57 % (8979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.57 % (8979)Termination reason: Unknown
% 8.29/2.57 % (8979)Termination phase: Property scanning
% 8.29/2.57
% 8.29/2.57 % (8979)Memory used [KB]: 2302
% 8.29/2.57 % (8979)Time elapsed: 0.040 s
% 8.29/2.57 % (8979)Instructions burned: 71 (million)
% 8.29/2.57 % (8979)------------------------------
% 8.29/2.57 % (8979)------------------------------
% 8.29/2.57 % (8982)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_8750 for (2992ds/41Mi)
% 8.29/2.58 % (8980)Instruction limit reached!
% 8.29/2.58 % (8980)------------------------------
% 8.29/2.58 % (8980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.58 % (8980)Termination reason: Unknown
% 8.29/2.58 % (8980)Termination phase: Saturation
% 8.29/2.58
% 8.29/2.58 % (8980)Memory used [KB]: 6780
% 8.29/2.58 % (8980)Time elapsed: 0.050 s
% 8.29/2.58 % (8980)Instructions burned: 83 (million)
% 8.29/2.58 % (8980)------------------------------
% 8.29/2.58 % (8980)------------------------------
% 8.29/2.58 % (8983)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8750 for (2992ds/6Mi)
% 8.29/2.58 % (8983)Instruction limit reached!
% 8.29/2.58 % (8983)------------------------------
% 8.29/2.58 % (8983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.58 % (8983)Termination reason: Unknown
% 8.29/2.58 % (8983)Termination phase: shuffling
% 8.29/2.58
% 8.29/2.58 % (8983)Memory used [KB]: 1535
% 8.29/2.58 % (8983)Time elapsed: 0.006 s
% 8.29/2.58 % (8983)Instructions burned: 6 (million)
% 8.29/2.58 % (8983)------------------------------
% 8.29/2.58 % (8983)------------------------------
% 8.29/2.59 % (8984)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_8750 for (2992ds/150Mi)
% 8.29/2.59 % (8982)Instruction limit reached!
% 8.29/2.59 % (8982)------------------------------
% 8.29/2.59 % (8982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.59 % (8982)Termination reason: Unknown
% 8.29/2.59 % (8982)Termination phase: Property scanning
% 8.29/2.59
% 8.29/2.59 % (8982)Memory used [KB]: 2174
% 8.29/2.59 % (8982)Time elapsed: 0.024 s
% 8.29/2.59 % (8982)Instructions burned: 42 (million)
% 8.29/2.59 % (8982)------------------------------
% 8.29/2.59 % (8982)------------------------------
% 8.70/2.60 % (8985)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_8750 for (2992ds/343Mi)
% 8.70/2.60 % (8986)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_8750 for (2992ds/109Mi)
% 8.70/2.61 % (8987)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_8750 for (2992ds/253Mi)
% 8.70/2.67 % (8986)Instruction limit reached!
% 8.70/2.67 % (8986)------------------------------
% 8.70/2.67 % (8986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.67 % (8986)Termination reason: Unknown
% 8.70/2.67 % (8986)Termination phase: Saturation
% 8.70/2.67
% 8.70/2.67 % (8986)Memory used [KB]: 7036
% 8.70/2.67 % (8986)Time elapsed: 0.064 s
% 8.70/2.67 % (8986)Instructions burned: 110 (million)
% 8.70/2.67 % (8986)------------------------------
% 8.70/2.67 % (8986)------------------------------
% 8.70/2.67 % (8984)Instruction limit reached!
% 8.70/2.67 % (8984)------------------------------
% 8.70/2.67 % (8984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.67 % (8984)Termination reason: Unknown
% 8.70/2.67 % (8984)Termination phase: Saturation
% 8.70/2.67
% 8.70/2.67 % (8984)Memory used [KB]: 7164
% 8.70/2.67 % (8984)Time elapsed: 0.113 s
% 8.70/2.67 % (8984)Instructions burned: 151 (million)
% 8.70/2.67 % (8984)------------------------------
% 8.70/2.67 % (8984)------------------------------
% 8.70/2.69 % (8988)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_8750 for (2991ds/140Mi)
% 8.89/2.70 % (8989)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_8750 for (2991ds/614Mi)
% 8.89/2.72 % (8974)Instruction limit reached!
% 8.89/2.72 % (8974)------------------------------
% 8.89/2.72 % (8974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.72 % (8974)Termination reason: Unknown
% 8.89/2.72 % (8974)Termination phase: Saturation
% 8.89/2.72
% 8.89/2.72 % (8974)Memory used [KB]: 4733
% 8.89/2.72 % (8974)Time elapsed: 0.255 s
% 8.89/2.72 % (8974)Instructions burned: 432 (million)
% 8.89/2.72 % (8974)------------------------------
% 8.89/2.72 % (8974)------------------------------
% 8.89/2.74 % (8990)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_8750 for (2991ds/202Mi)
% 8.89/2.76 % (8987)Instruction limit reached!
% 8.89/2.76 % (8987)------------------------------
% 8.89/2.76 % (8987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.76 % (8987)Termination reason: Unknown
% 8.89/2.76 % (8987)Termination phase: Saturation
% 8.89/2.76
% 8.89/2.76 % (8987)Memory used [KB]: 7675
% 8.89/2.76 % (8987)Time elapsed: 0.146 s
% 8.89/2.76 % (8987)Instructions burned: 253 (million)
% 8.89/2.76 % (8987)------------------------------
% 8.89/2.76 % (8987)------------------------------
% 8.89/2.76 % (8978)Instruction limit reached!
% 8.89/2.76 % (8978)------------------------------
% 8.89/2.76 % (8978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.76 % (8978)Termination reason: Unknown
% 8.89/2.76 % (8978)Termination phase: Saturation
% 8.89/2.76
% 8.89/2.76 % (8978)Memory used [KB]: 7931
% 8.89/2.76 % (8978)Time elapsed: 0.258 s
% 8.89/2.76 % (8978)Instructions burned: 453 (million)
% 8.89/2.76 % (8978)------------------------------
% 8.89/2.76 % (8978)------------------------------
% 8.89/2.76 % (8990)Refutation not found, incomplete strategy
% 8.89/2.76 % (8990)------------------------------
% 8.89/2.76 % (8990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.77 % (8990)Termination reason: Refutation not found, incomplete strategy
% 8.89/2.77
% 8.89/2.77
% 8.89/2.77 % (8990)Memory used [KB]: 6652
% 8.89/2.77 % (8990)Time elapsed: 0.028 s
% 8.89/2.77 % (8990)Instructions burned: 44 (million)
% 8.89/2.77 % (8990)------------------------------
% 8.89/2.77 % (8990)------------------------------
% 8.89/2.77 % (8988)Instruction limit reached!
% 8.89/2.77 % (8988)------------------------------
% 8.89/2.77 % (8988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.77 % (8988)Termination reason: Unknown
% 8.89/2.77 % (8988)Termination phase: Saturation
% 8.89/2.77
% 8.89/2.77 % (8988)Memory used [KB]: 7291
% 8.89/2.77 % (8988)Time elapsed: 0.084 s
% 8.89/2.77 % (8988)Instructions burned: 141 (million)
% 8.89/2.77 % (8988)------------------------------
% 8.89/2.77 % (8988)------------------------------
% 8.89/2.78 % (8991)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_8750 for (2990ds/339Mi)
% 8.89/2.78 % (8992)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_8750 for (2990ds/283Mi)
% 8.89/2.79 % (8993)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_8750 for (2990ds/134Mi)
% 8.89/2.79 % (8994)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_8750 for (2990ds/298Mi)
% 9.75/2.80 % (8985)Instruction limit reached!
% 9.75/2.80 % (8985)------------------------------
% 9.75/2.80 % (8985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.80 % (8985)Termination reason: Unknown
% 9.75/2.80 % (8985)Termination phase: Saturation
% 9.75/2.80
% 9.75/2.80 % (8985)Memory used [KB]: 7803
% 9.75/2.80 % (8985)Time elapsed: 0.203 s
% 9.75/2.80 % (8985)Instructions burned: 343 (million)
% 9.75/2.80 % (8985)------------------------------
% 9.75/2.80 % (8985)------------------------------
% 9.75/2.82 % (8995)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_8750 for (2990ds/192Mi)
% 9.75/2.86 % (8993)Instruction limit reached!
% 9.75/2.86 % (8993)------------------------------
% 9.75/2.86 % (8993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.86 % (8993)Termination reason: Unknown
% 9.75/2.86 % (8993)Termination phase: Saturation
% 9.75/2.86
% 9.75/2.86 % (8993)Memory used [KB]: 7164
% 9.75/2.86 % (8993)Time elapsed: 0.079 s
% 9.75/2.86 % (8993)Instructions burned: 134 (million)
% 9.75/2.86 % (8993)------------------------------
% 9.75/2.86 % (8993)------------------------------
% 9.75/2.89 % (8996)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_8750 for (2989ds/258Mi)
% 10.08/2.93 % (8995)Instruction limit reached!
% 10.08/2.93 % (8995)------------------------------
% 10.08/2.93 % (8995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.08/2.93 % (8995)Termination reason: Unknown
% 10.08/2.93 % (8995)Termination phase: Saturation
% 10.08/2.93
% 10.08/2.93 % (8995)Memory used [KB]: 7931
% 10.08/2.93 % (8995)Time elapsed: 0.113 s
% 10.08/2.93 % (8995)Instructions burned: 192 (million)
% 10.08/2.93 % (8995)------------------------------
% 10.08/2.93 % (8995)------------------------------
% 10.08/2.95 % (8992)Instruction limit reached!
% 10.08/2.95 % (8992)------------------------------
% 10.08/2.95 % (8992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.08/2.95 % (8992)Termination reason: Unknown
% 10.08/2.95 % (8992)Termination phase: Saturation
% 10.08/2.95
% 10.08/2.95 % (8992)Memory used [KB]: 7931
% 10.08/2.95 % (8992)Time elapsed: 0.166 s
% 10.08/2.95 % (8992)Instructions burned: 283 (million)
% 10.08/2.95 % (8992)------------------------------
% 10.08/2.95 % (8992)------------------------------
% 10.08/2.95 % (8997)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_8750 for (2989ds/90Mi)
% 10.08/2.96 % (8994)Instruction limit reached!
% 10.08/2.96 % (8994)------------------------------
% 10.08/2.96 % (8994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.08/2.96 % (8994)Termination reason: Unknown
% 10.08/2.96 % (8994)Termination phase: Saturation
% 10.08/2.96
% 10.08/2.96 % (8994)Memory used [KB]: 8059
% 10.08/2.96 % (8994)Time elapsed: 0.171 s
% 10.08/2.96 % (8994)Instructions burned: 299 (million)
% 10.08/2.96 % (8994)------------------------------
% 10.08/2.96 % (8994)------------------------------
% 10.08/2.97 % (8998)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_8750 for (2988ds/231Mi)
% 10.08/2.98 % (8991)Instruction limit reached!
% 10.08/2.98 % (8991)------------------------------
% 10.08/2.98 % (8991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.08/2.98 % (8991)Termination reason: Unknown
% 10.08/2.98 % (8991)Termination phase: Saturation
% 10.08/2.98
% 10.08/2.98 % (8991)Memory used [KB]: 7675
% 10.08/2.98 % (8991)Time elapsed: 0.202 s
% 10.08/2.98 % (8991)Instructions burned: 339 (million)
% 10.08/2.98 % (8991)------------------------------
% 10.08/2.98 % (8991)------------------------------
% 10.08/2.98 % (8999)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_8750 for (2988ds/458Mi)
% 10.08/3.00 % (9000)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_8750 for (2988ds/31Mi)
% 10.08/3.00 % (8997)Instruction limit reached!
% 10.08/3.00 % (8997)------------------------------
% 10.08/3.00 % (8997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.08/3.00 % (8997)Termination reason: Unknown
% 10.08/3.00 % (8997)Termination phase: Saturation
% 10.08/3.00
% 10.08/3.00 % (8997)Memory used [KB]: 6908
% 10.08/3.00 % (8997)Time elapsed: 0.052 s
% 10.08/3.00 % (8997)Instructions burned: 90 (million)
% 10.08/3.00 % (8997)------------------------------
% 10.08/3.00 % (8997)------------------------------
% 10.08/3.02 % (9000)Instruction limit reached!
% 10.08/3.02 % (9000)------------------------------
% 10.08/3.02 % (9000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.08/3.02 % (9000)Termination reason: Unknown
% 10.08/3.02 % (9000)Termination phase: Property scanning
% 10.08/3.02
% 10.08/3.02 % (9000)Memory used [KB]: 1918
% 10.08/3.02 % (9000)Time elapsed: 0.019 s
% 10.08/3.02 % (9000)Instructions burned: 31 (million)
% 10.08/3.02 % (9000)------------------------------
% 10.08/3.02 % (9000)------------------------------
% 10.08/3.03 % (9001)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_8750 for (2988ds/297Mi)
% 12.14/3.04 % (8996)Instruction limit reached!
% 12.14/3.04 % (8996)------------------------------
% 12.14/3.04 % (8996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.14/3.04 % (8996)Termination reason: Unknown
% 12.14/3.04 % (8996)Termination phase: Saturation
% 12.14/3.04
% 12.14/3.04 % (8996)Memory used [KB]: 7675
% 12.14/3.04 % (8996)Time elapsed: 0.152 s
% 12.14/3.04 % (8996)Instructions burned: 258 (million)
% 12.14/3.04 % (8996)------------------------------
% 12.14/3.04 % (8996)------------------------------
% 12.14/3.04 % (9002)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_8750 for (2988ds/987Mi)
% 12.14/3.05 % (8989)Instruction limit reached!
% 12.14/3.05 % (8989)------------------------------
% 12.14/3.05 % (8989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.14/3.05 % (8989)Termination reason: Unknown
% 12.14/3.05 % (8989)Termination phase: Saturation
% 12.14/3.05
% 12.14/3.05 % (8989)Memory used [KB]: 8699
% 12.14/3.05 % (8989)Time elapsed: 0.356 s
% 12.14/3.05 % (8989)Instructions burned: 614 (million)
% 12.14/3.05 % (8989)------------------------------
% 12.14/3.05 % (8989)------------------------------
% 12.14/3.06 % (9003)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_8750 for (2988ds/182Mi)
% 12.14/3.07 % (8971)Instruction limit reached!
% 12.14/3.07 % (8971)------------------------------
% 12.14/3.07 % (8971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.14/3.07 % (8971)Termination reason: Unknown
% 12.14/3.07 % (8971)Termination phase: Saturation
% 12.14/3.07
% 12.14/3.07 % (8971)Memory used [KB]: 8699
% 12.14/3.07 % (8971)Time elapsed: 0.643 s
% 12.14/3.07 % (8971)Instructions burned: 1087 (million)
% 12.14/3.07 % (8971)------------------------------
% 12.14/3.07 % (8971)------------------------------
% 12.14/3.07 % (9004)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_8750 for (2987ds/182Mi)
% 12.14/3.09 % (8998)Instruction limit reached!
% 12.14/3.09 % (8998)------------------------------
% 12.14/3.09 % (8998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.14/3.09 % (8998)Termination reason: Unknown
% 12.14/3.09 % (8998)Termination phase: Saturation
% 12.14/3.09
% 12.14/3.09 % (8998)Memory used [KB]: 7164
% 12.14/3.09 % (8998)Time elapsed: 0.121 s
% 12.14/3.09 % (8998)Instructions burned: 231 (million)
% 12.14/3.09 % (8998)------------------------------
% 12.14/3.09 % (8998)------------------------------
% 12.14/3.09 % (9005)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_8750 for (2987ds/154Mi)
% 12.14/3.11 % (9006)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_8750 for (2987ds/79Mi)
% 12.44/3.15 % (9006)Instruction limit reached!
% 12.44/3.15 % (9006)------------------------------
% 12.44/3.15 % (9006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.44/3.15 % (9006)Termination reason: Unknown
% 12.44/3.15 % (9006)Termination phase: Saturation
% 12.44/3.15
% 12.44/3.15 % (9006)Memory used [KB]: 6780
% 12.44/3.15 % (9006)Time elapsed: 0.046 s
% 12.44/3.15 % (9006)Instructions burned: 79 (million)
% 12.44/3.15 % (9006)------------------------------
% 12.44/3.15 % (9006)------------------------------
% 12.44/3.16 % (9003)Instruction limit reached!
% 12.44/3.16 % (9003)------------------------------
% 12.44/3.16 % (9003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.44/3.16 % (9003)Termination reason: Unknown
% 12.44/3.16 % (9003)Termination phase: Saturation
% 12.44/3.16
% 12.44/3.16 % (9003)Memory used [KB]: 7291
% 12.44/3.16 % (9003)Time elapsed: 0.106 s
% 12.44/3.16 % (9003)Instructions burned: 182 (million)
% 12.44/3.16 % (9003)------------------------------
% 12.44/3.16 % (9003)------------------------------
% 12.44/3.17 % (9005)Instruction limit reached!
% 12.44/3.17 % (9005)------------------------------
% 12.44/3.17 % (9005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.44/3.17 % (9005)Termination reason: Unknown
% 12.44/3.17 % (9005)Termination phase: Saturation
% 12.44/3.17
% 12.44/3.17 % (9005)Memory used [KB]: 3070
% 12.44/3.17 % (9005)Time elapsed: 0.087 s
% 12.44/3.17 % (9005)Instructions burned: 155 (million)
% 12.44/3.17 % (9005)------------------------------
% 12.44/3.17 % (9005)------------------------------
% 12.44/3.18 % (9007)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_8750 for (2986ds/216Mi)
% 12.44/3.18 % (9004)Instruction limit reached!
% 12.44/3.18 % (9004)------------------------------
% 12.44/3.18 % (9004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.44/3.18 % (9004)Termination reason: Unknown
% 12.44/3.18 % (9004)Termination phase: Saturation
% 12.44/3.18
% 12.44/3.18 % (9004)Memory used [KB]: 7419
% 12.44/3.18 % (9004)Time elapsed: 0.111 s
% 12.44/3.18 % (9004)Instructions burned: 182 (million)
% 12.44/3.18 % (9004)------------------------------
% 12.44/3.18 % (9004)------------------------------
% 12.44/3.18 % (9008)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_8750 for (2986ds/114Mi)
% 12.44/3.19 % (9009)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_8750 for (2986ds/922Mi)
% 12.94/3.20 % (9001)Instruction limit reached!
% 12.94/3.20 % (9001)------------------------------
% 12.94/3.20 % (9001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.94/3.20 % (9001)Termination reason: Unknown
% 12.94/3.20 % (9001)Termination phase: Saturation
% 12.94/3.20
% 12.94/3.20 % (9001)Memory used [KB]: 7675
% 12.94/3.20 % (9001)Time elapsed: 0.173 s
% 12.94/3.20 % (9001)Instructions burned: 297 (million)
% 12.94/3.20 % (9001)------------------------------
% 12.94/3.20 % (9001)------------------------------
% 12.94/3.20 % (9010)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_8750 for (2986ds/182Mi)
% 12.94/3.22 % (9011)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_8750 for (2986ds/164Mi)
% 12.94/3.24 % (8999)Refutation not found, non-redundant clauses discarded% (8999)------------------------------
% 12.94/3.24 % (8999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.94/3.24 % (8999)Termination reason: Refutation not found, non-redundant clauses discarded
% 12.94/3.24
% 12.94/3.24 % (8999)Memory used [KB]: 7931
% 12.94/3.24 % (8999)Time elapsed: 0.264 s
% 12.94/3.24 % (8999)Instructions burned: 446 (million)
% 12.94/3.24 % (8999)------------------------------
% 12.94/3.24 % (8999)------------------------------
% 12.94/3.25 % (9008)Instruction limit reached!
% 12.94/3.25 % (9008)------------------------------
% 12.94/3.25 % (9008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.94/3.25 % (9008)Termination reason: Unknown
% 12.94/3.25 % (9008)Termination phase: Saturation
% 12.94/3.25
% 12.94/3.25 % (9008)Memory used [KB]: 7036
% 12.94/3.25 % (9008)Time elapsed: 0.066 s
% 12.94/3.25 % (9008)Instructions burned: 115 (million)
% 12.94/3.25 % (9008)------------------------------
% 12.94/3.25 % (9008)------------------------------
% 12.94/3.27 % (9012)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_8750 for (2985ds/50Mi)
% 12.94/3.27 % (9013)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_8750 for (2985ds/368Mi)
% 12.94/3.29 % (9012)Instruction limit reached!
% 12.94/3.29 % (9012)------------------------------
% 12.94/3.29 % (9012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.94/3.29 % (9012)Termination reason: Unknown
% 12.94/3.29 % (9012)Termination phase: Property scanning
% 12.94/3.29
% 12.94/3.29 % (9012)Memory used [KB]: 2174
% 12.94/3.29 % (9012)Time elapsed: 0.029 s
% 12.94/3.29 % (9012)Instructions burned: 51 (million)
% 12.94/3.29 % (9012)------------------------------
% 12.94/3.29 % (9012)------------------------------
% 12.94/3.30 % (9007)Instruction limit reached!
% 12.94/3.30 % (9007)------------------------------
% 12.94/3.30 % (9007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.94/3.30 % (9007)Termination reason: Unknown
% 12.94/3.30 % (9007)Termination phase: Saturation
% 12.94/3.30
% 12.94/3.30 % (9007)Memory used [KB]: 7419
% 12.94/3.30 % (9007)Time elapsed: 0.123 s
% 12.94/3.30 % (9007)Instructions burned: 216 (million)
% 12.94/3.30 % (9007)------------------------------
% 12.94/3.30 % (9007)------------------------------
% 13.32/3.30 % (9010)Instruction limit reached!
% 13.32/3.30 % (9010)------------------------------
% 13.32/3.30 % (9010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/3.30 % (9010)Termination reason: Unknown
% 13.32/3.30 % (9010)Termination phase: Saturation
% 13.32/3.30
% 13.32/3.30 % (9010)Memory used [KB]: 7291
% 13.32/3.30 % (9010)Time elapsed: 0.100 s
% 13.32/3.30 % (9010)Instructions burned: 183 (million)
% 13.32/3.30 % (9010)------------------------------
% 13.32/3.30 % (9010)------------------------------
% 13.32/3.31 % (9011)Instruction limit reached!
% 13.32/3.31 % (9011)------------------------------
% 13.32/3.31 % (9011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/3.31 % (9011)Termination reason: Unknown
% 13.32/3.31 % (9011)Termination phase: Saturation
% 13.32/3.31
% 13.32/3.31 % (9011)Memory used [KB]: 2430
% 13.32/3.31 % (9011)Time elapsed: 0.089 s
% 13.32/3.31 % (9011)Instructions burned: 164 (million)
% 13.32/3.31 % (9011)------------------------------
% 13.32/3.31 % (9011)------------------------------
% 13.32/3.31 % (9014)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_8750 for (2985ds/1021Mi)
% 13.32/3.32 % (9015)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_8750 for (2985ds/267Mi)
% 13.32/3.32 % (9016)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_8750 for (2985ds/204Mi)
% 13.32/3.33 % (9017)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_8750 for (2985ds/26Mi)
% 13.32/3.34 % (9017)Instruction limit reached!
% 13.32/3.34 % (9017)------------------------------
% 13.32/3.34 % (9017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/3.34 % (9017)Termination reason: Unknown
% 13.32/3.34 % (9017)Termination phase: shuffling
% 13.32/3.34
% 13.32/3.34 % (9017)Memory used [KB]: 2046
% 13.32/3.34 % (9017)Time elapsed: 0.016 s
% 13.32/3.34 % (9017)Instructions burned: 26 (million)
% 13.32/3.34 % (9017)------------------------------
% 13.32/3.34 % (9017)------------------------------
% 13.32/3.37 % (9018)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_8750 for (2984ds/53Mi)
% 13.32/3.38 % (9018)Instruction limit reached!
% 13.32/3.38 % (9018)------------------------------
% 13.32/3.38 % (9018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/3.38 % (9018)Termination reason: Unknown
% 13.32/3.38 % (9018)Termination phase: Property scanning
% 13.32/3.38
% 13.32/3.38 % (9018)Memory used [KB]: 2174
% 13.32/3.38 % (9018)Time elapsed: 0.016 s
% 13.32/3.38 % (9018)Instructions burned: 53 (million)
% 13.32/3.38 % (9018)------------------------------
% 13.32/3.38 % (9018)------------------------------
% 13.32/3.39 % (9019)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_8750 for (2984ds/4436Mi)
% 13.76/3.44 % (9016)Instruction limit reached!
% 13.76/3.44 % (9016)------------------------------
% 13.76/3.44 % (9016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/3.44 % (9016)Termination reason: Unknown
% 13.76/3.44 % (9016)Termination phase: Saturation
% 13.76/3.44
% 13.76/3.44 % (9016)Memory used [KB]: 7419
% 13.76/3.44 % (9016)Time elapsed: 0.142 s
% 13.76/3.44 % (9016)Instructions burned: 204 (million)
% 13.76/3.44 % (9016)------------------------------
% 13.76/3.44 % (9016)------------------------------
% 13.76/3.47 % (9020)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_8750 for (2983ds/1539Mi)
% 13.76/3.47 % (9015)Instruction limit reached!
% 13.76/3.47 % (9015)------------------------------
% 13.76/3.47 % (9015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/3.47 % (9015)Termination reason: Unknown
% 13.76/3.47 % (9015)Termination phase: Saturation
% 13.76/3.47
% 13.76/3.47 % (9015)Memory used [KB]: 7803
% 13.76/3.47 % (9015)Time elapsed: 0.176 s
% 13.76/3.47 % (9015)Instructions burned: 267 (million)
% 13.76/3.47 % (9015)------------------------------
% 13.76/3.47 % (9015)------------------------------
% 13.76/3.49 % (9013)Instruction limit reached!
% 13.76/3.49 % (9013)------------------------------
% 13.76/3.49 % (9013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/3.49 % (9013)Termination reason: Unknown
% 13.76/3.49 % (9013)Termination phase: Saturation
% 13.76/3.49
% 13.76/3.49 % (9013)Memory used [KB]: 8443
% 13.76/3.49 % (9013)Time elapsed: 0.223 s
% 13.76/3.49 % (9013)Instructions burned: 369 (million)
% 13.76/3.49 % (9013)------------------------------
% 13.76/3.49 % (9013)------------------------------
% 13.76/3.49 % (9021)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_8750 for (2983ds/408Mi)
% 14.31/3.51 % (9022)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_8750 for (2983ds/5205Mi)
% 14.31/3.63 % (9002)Instruction limit reached!
% 14.31/3.63 % (9002)------------------------------
% 14.31/3.63 % (9002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.31/3.63 % (9002)Termination reason: Unknown
% 14.31/3.63 % (9002)Termination phase: Saturation
% 14.31/3.63
% 14.31/3.63 % (9002)Memory used [KB]: 9978
% 14.31/3.63 % (9002)Time elapsed: 0.589 s
% 14.31/3.63 % (9002)Instructions burned: 988 (million)
% 14.31/3.63 % (9002)------------------------------
% 14.31/3.63 % (9002)------------------------------
% 14.31/3.65 % (9023)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_8750 for (2982ds/1913Mi)
% 14.93/3.72 % (9009)Instruction limit reached!
% 14.93/3.72 % (9009)------------------------------
% 14.93/3.72 % (9009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.93/3.72 % (9009)Termination reason: Unknown
% 14.93/3.72 % (9009)Termination phase: Saturation
% 14.93/3.72
% 14.93/3.72 % (9009)Memory used [KB]: 8059
% 14.93/3.72 % (9009)Time elapsed: 0.526 s
% 14.93/3.72 % (9009)Instructions burned: 922 (million)
% 14.93/3.72 % (9009)------------------------------
% 14.93/3.72 % (9009)------------------------------
% 14.93/3.73 % (9021)Instruction limit reached!
% 14.93/3.73 % (9021)------------------------------
% 14.93/3.73 % (9021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.93/3.73 % (9021)Termination reason: Unknown
% 14.93/3.73 % (9021)Termination phase: Saturation
% 14.93/3.73
% 14.93/3.73 % (9021)Memory used [KB]: 8315
% 14.93/3.73 % (9021)Time elapsed: 0.235 s
% 14.93/3.73 % (9021)Instructions burned: 408 (million)
% 14.93/3.73 % (9021)------------------------------
% 14.93/3.73 % (9021)------------------------------
% 14.93/3.74 % (9024)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_8750 for (2981ds/4350Mi)
% 14.93/3.75 % (9025)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_8750 for (2981ds/68Mi)
% 14.93/3.79 % (9025)Instruction limit reached!
% 14.93/3.79 % (9025)------------------------------
% 14.93/3.79 % (9025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.93/3.79 % (9025)Termination reason: Unknown
% 14.93/3.79 % (9025)Termination phase: Property scanning
% 14.93/3.79
% 14.93/3.79 % (9025)Memory used [KB]: 2302
% 14.93/3.79 % (9025)Time elapsed: 0.041 s
% 14.93/3.79 % (9025)Instructions burned: 69 (million)
% 14.93/3.79 % (9025)------------------------------
% 14.93/3.79 % (9025)------------------------------
% 15.78/3.81 % (9026)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_8750 for (2980ds/358Mi)
% 15.78/3.89 % (9014)Instruction limit reached!
% 15.78/3.89 % (9014)------------------------------
% 15.78/3.89 % (9014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.78/3.89 % (9014)Termination reason: Unknown
% 15.78/3.89 % (9014)Termination phase: Saturation
% 15.78/3.89
% 15.78/3.89 % (9014)Memory used [KB]: 9978
% 15.78/3.89 % (9014)Time elapsed: 0.578 s
% 15.78/3.89 % (9014)Instructions burned: 1021 (million)
% 15.78/3.89 % (9014)------------------------------
% 15.78/3.89 % (9014)------------------------------
% 16.38/3.91 % (9027)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_8750 for (2979ds/31Mi)
% 16.38/3.93 % (9027)Instruction limit reached!
% 16.38/3.93 % (9027)------------------------------
% 16.38/3.93 % (9027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.38/3.93 % (9027)Termination reason: Unknown
% 16.38/3.93 % (9027)Termination phase: Property scanning
% 16.38/3.93
% 16.38/3.93 % (9027)Memory used [KB]: 1918
% 16.38/3.93 % (9027)Time elapsed: 0.020 s
% 16.38/3.93 % (9027)Instructions burned: 31 (million)
% 16.38/3.93 % (9027)------------------------------
% 16.38/3.93 % (9027)------------------------------
% 16.38/3.95 % (9028)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_8750 for (2979ds/279Mi)
% 16.38/4.02 % (9026)Instruction limit reached!
% 16.38/4.02 % (9026)------------------------------
% 16.38/4.02 % (9026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.38/4.02 % (9026)Termination reason: Unknown
% 16.38/4.02 % (9026)Termination phase: Saturation
% 16.38/4.02
% 16.38/4.02 % (9026)Memory used [KB]: 7803
% 16.38/4.02 % (9026)Time elapsed: 0.214 s
% 16.38/4.02 % (9026)Instructions burned: 359 (million)
% 16.38/4.02 % (9026)------------------------------
% 16.38/4.02 % (9026)------------------------------
% 19.11/4.04 % (9029)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_8750 for (2978ds/258Mi)
% 19.11/4.11 % (9028)Instruction limit reached!
% 19.11/4.11 % (9028)------------------------------
% 19.11/4.11 % (9028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.11/4.11 % (9028)Termination reason: Unknown
% 19.11/4.11 % (9028)Termination phase: Saturation
% 19.11/4.11
% 19.11/4.11 % (9028)Memory used [KB]: 7675
% 19.11/4.11 % (9028)Time elapsed: 0.154 s
% 19.11/4.11 % (9028)Instructions burned: 279 (million)
% 19.11/4.11 % (9028)------------------------------
% 19.11/4.11 % (9028)------------------------------
% 19.74/4.13 % (9030)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_8750 for (2977ds/26Mi)
% 19.74/4.14 % (9030)Instruction limit reached!
% 19.74/4.14 % (9030)------------------------------
% 19.74/4.14 % (9030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.74/4.14 % (9030)Termination reason: Unknown
% 19.74/4.14 % (9030)Termination phase: shuffling
% 19.74/4.14
% 19.74/4.14 % (9030)Memory used [KB]: 2046
% 19.74/4.14 % (9030)Time elapsed: 0.016 s
% 19.74/4.14 % (9030)Instructions burned: 27 (million)
% 19.74/4.14 % (9030)------------------------------
% 19.74/4.14 % (9030)------------------------------
% 19.74/4.17 % (9031)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_8750 for (2976ds/995Mi)
% 19.74/4.20 % (9029)Instruction limit reached!
% 19.74/4.20 % (9029)------------------------------
% 19.74/4.20 % (9029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.74/4.20 % (9029)Termination reason: Unknown
% 19.74/4.20 % (9029)Termination phase: Saturation
% 19.74/4.20
% 19.74/4.20 % (9029)Memory used [KB]: 7675
% 19.74/4.20 % (9029)Time elapsed: 0.153 s
% 19.74/4.20 % (9029)Instructions burned: 259 (million)
% 19.74/4.20 % (9029)------------------------------
% 19.74/4.20 % (9029)------------------------------
% 20.30/4.22 % (9032)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_8750 for (2976ds/373Mi)
% 20.81/4.37 % (9020)Instruction limit reached!
% 20.81/4.37 % (9020)------------------------------
% 20.81/4.37 % (9020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.81/4.37 % (9020)Termination reason: Unknown
% 20.81/4.37 % (9020)Termination phase: Saturation
% 20.81/4.37
% 20.81/4.37 % (9020)Memory used [KB]: 11257
% 20.81/4.37 % (9020)Time elapsed: 0.910 s
% 20.81/4.37 % (9020)Instructions burned: 1540 (million)
% 20.81/4.37 % (9020)------------------------------
% 20.81/4.37 % (9020)------------------------------
% 21.30/4.40 % (9033)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_8750 for (2974ds/253Mi)
% 21.30/4.44 % (9032)Instruction limit reached!
% 21.30/4.44 % (9032)------------------------------
% 21.30/4.44 % (9032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.30/4.44 % (9032)Termination reason: Unknown
% 21.30/4.44 % (9032)Termination phase: Saturation
% 21.30/4.44
% 21.30/4.44 % (9032)Memory used [KB]: 8827
% 21.30/4.44 % (9032)Time elapsed: 0.223 s
% 21.30/4.44 % (9032)Instructions burned: 374 (million)
% 21.30/4.44 % (9032)------------------------------
% 21.30/4.44 % (9032)------------------------------
% 21.30/4.46 % (9034)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_8750 for (2973ds/832Mi)
% 21.94/4.53 % (9034)Refutation not found, incomplete strategy
% 21.94/4.53 % (9034)------------------------------
% 21.94/4.53 % (9034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.94/4.53 % (9034)Termination reason: Refutation not found, incomplete strategy
% 21.94/4.53
% 21.94/4.53
% 21.94/4.53 % (9034)Memory used [KB]: 7547
% 21.94/4.53 % (9034)Time elapsed: 0.069 s
% 21.94/4.53 % (9034)Instructions burned: 114 (million)
% 21.94/4.53 % (9034)------------------------------
% 21.94/4.53 % (9034)------------------------------
% 21.94/4.54 % (9033)Instruction limit reached!
% 21.94/4.54 % (9033)------------------------------
% 21.94/4.54 % (9033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.94/4.54 % (9033)Termination reason: Unknown
% 21.94/4.54 % (9033)Termination phase: Saturation
% 21.94/4.54
% 21.94/4.54 % (9033)Memory used [KB]: 7675
% 21.94/4.54 % (9033)Time elapsed: 0.142 s
% 21.94/4.54 % (9033)Instructions burned: 254 (million)
% 21.94/4.54 % (9033)------------------------------
% 21.94/4.54 % (9033)------------------------------
% 21.94/4.55 % (9035)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_8750 for (2973ds/668Mi)
% 21.94/4.56 % (9036)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_8750 for (2972ds/40Mi)
% 21.94/4.58 % (9036)Instruction limit reached!
% 21.94/4.58 % (9036)------------------------------
% 21.94/4.58 % (9036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.94/4.58 % (9036)Termination reason: Unknown
% 21.94/4.58 % (9036)Termination phase: Property scanning
% 21.94/4.58
% 21.94/4.58 % (9036)Memory used [KB]: 2174
% 21.94/4.58 % (9036)Time elapsed: 0.024 s
% 21.94/4.58 % (9036)Instructions burned: 41 (million)
% 21.94/4.58 % (9036)------------------------------
% 21.94/4.58 % (9036)------------------------------
% 22.64/4.60 % (9037)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_8750 for (2972ds/294Mi)
% 23.04/4.73 % (9031)Instruction limit reached!
% 23.04/4.73 % (9031)------------------------------
% 23.04/4.73 % (9031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.04/4.73 % (9031)Termination reason: Unknown
% 23.04/4.73 % (9031)Termination phase: Saturation
% 23.04/4.73
% 23.04/4.73 % (9031)Memory used [KB]: 9466
% 23.04/4.73 % (9031)Time elapsed: 0.563 s
% 23.04/4.73 % (9031)Instructions burned: 995 (million)
% 23.04/4.73 % (9031)------------------------------
% 23.04/4.73 % (9031)------------------------------
% 23.04/4.75 % (9038)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_8750 for (2971ds/187Mi)
% 23.04/4.77 % (9037)Instruction limit reached!
% 23.04/4.77 % (9037)------------------------------
% 23.04/4.77 % (9037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.04/4.77 % (9037)Termination reason: Unknown
% 23.04/4.77 % (9037)Termination phase: Saturation
% 23.04/4.77
% 23.04/4.77 % (9037)Memory used [KB]: 8571
% 23.04/4.77 % (9037)Time elapsed: 0.166 s
% 23.04/4.77 % (9037)Instructions burned: 294 (million)
% 23.04/4.77 % (9037)------------------------------
% 23.04/4.77 % (9037)------------------------------
% 23.04/4.79 % (9039)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_8750 for (2970ds/371Mi)
% 24.20/4.82 % (9023)Instruction limit reached!
% 24.20/4.82 % (9023)------------------------------
% 24.20/4.82 % (9023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.20/4.82 % (9023)Termination reason: Unknown
% 24.20/4.82 % (9023)Termination phase: Saturation
% 24.20/4.82
% 24.20/4.82 % (9023)Memory used [KB]: 10490
% 24.20/4.82 % (9023)Time elapsed: 1.172 s
% 24.20/4.82 % (9023)Instructions burned: 1914 (million)
% 24.20/4.82 % (9023)------------------------------
% 24.20/4.82 % (9023)------------------------------
% 24.20/4.84 % (9040)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_8750 for (2970ds/1827Mi)
% 24.20/4.86 % (9038)Instruction limit reached!
% 24.20/4.86 % (9038)------------------------------
% 24.20/4.86 % (9038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.20/4.86 % (9038)Termination reason: Unknown
% 24.20/4.86 % (9038)Termination phase: Saturation
% 24.20/4.86
% 24.20/4.86 % (9038)Memory used [KB]: 7547
% 24.20/4.86 % (9038)Time elapsed: 0.115 s
% 24.20/4.86 % (9038)Instructions burned: 188 (million)
% 24.20/4.86 % (9038)------------------------------
% 24.20/4.86 % (9038)------------------------------
% 24.20/4.89 % (9041)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_8750 for (2969ds/70Mi)
% 24.67/4.92 % (9041)Instruction limit reached!
% 24.67/4.92 % (9041)------------------------------
% 24.67/4.92 % (9041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.67/4.92 % (9041)Termination reason: Unknown
% 24.67/4.92 % (9041)Termination phase: Preprocessing 3
% 24.67/4.92
% 24.67/4.92 % (9041)Memory used [KB]: 2302
% 24.67/4.92 % (9041)Time elapsed: 0.040 s
% 24.67/4.92 % (9041)Instructions burned: 71 (million)
% 24.67/4.92 % (9041)------------------------------
% 24.67/4.92 % (9041)------------------------------
% 24.67/4.93 % (9035)Instruction limit reached!
% 24.67/4.93 % (9035)------------------------------
% 24.67/4.93 % (9035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.67/4.93 % (9035)Termination reason: Unknown
% 24.67/4.93 % (9035)Termination phase: Saturation
% 24.67/4.93
% 24.67/4.93 % (9035)Memory used [KB]: 13688
% 24.67/4.93 % (9035)Time elapsed: 0.379 s
% 24.67/4.93 % (9035)Instructions burned: 669 (million)
% 24.67/4.93 % (9035)------------------------------
% 24.67/4.93 % (9035)------------------------------
% 24.67/4.95 % (9042)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_8750 for (2969ds/316Mi)
% 24.67/4.95 % (9043)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_8750 for (2969ds/932Mi)
% 24.67/5.01 % (9039)Refutation not found, non-redundant clauses discarded% (9039)------------------------------
% 24.67/5.01 % (9039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.67/5.01 % (9039)Termination reason: Refutation not found, non-redundant clauses discarded
% 24.67/5.01
% 24.67/5.01 % (9039)Memory used [KB]: 8187
% 24.67/5.01 % (9039)Time elapsed: 0.216 s
% 24.67/5.01 % (9039)Instructions burned: 349 (million)
% 24.67/5.01 % (9039)------------------------------
% 24.67/5.01 % (9039)------------------------------
% 26.10/5.03 % (9044)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_8750 for (2968ds/4714Mi)
% 26.10/5.12 % (9042)Instruction limit reached!
% 26.10/5.12 % (9042)------------------------------
% 26.10/5.12 % (9042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.10/5.12 % (9042)Termination reason: Unknown
% 26.10/5.12 % (9042)Termination phase: Saturation
% 26.10/5.12
% 26.10/5.12 % (9042)Memory used [KB]: 8187
% 26.10/5.12 % (9042)Time elapsed: 0.177 s
% 26.10/5.12 % (9042)Instructions burned: 317 (million)
% 26.10/5.12 % (9042)------------------------------
% 26.10/5.12 % (9042)------------------------------
% 26.74/5.14 % (9045)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_8750 for (2967ds/8250Mi)
% 28.57/5.52 % (9043)Instruction limit reached!
% 28.57/5.52 % (9043)------------------------------
% 28.57/5.52 % (9043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.57/5.52 % (9043)Termination reason: Unknown
% 28.57/5.52 % (9043)Termination phase: Saturation
% 28.57/5.52
% 28.57/5.52 % (9043)Memory used [KB]: 10618
% 28.57/5.52 % (9043)Time elapsed: 0.588 s
% 28.57/5.52 % (9043)Instructions burned: 933 (million)
% 28.57/5.52 % (9043)------------------------------
% 28.57/5.52 % (9043)------------------------------
% 28.57/5.54 % (9046)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_8750 for (2963ds/770Mi)
% 28.57/5.57 % (9046)Refutation not found, incomplete strategy
% 28.57/5.57 % (9046)------------------------------
% 28.57/5.57 % (9046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.57/5.57 % (9046)Termination reason: Refutation not found, incomplete strategy
% 28.57/5.57
% 28.57/5.57
% 28.57/5.57 % (9046)Memory used [KB]: 6524
% 28.57/5.57 % (9046)Time elapsed: 0.025 s
% 28.57/5.57 % (9046)Instructions burned: 37 (million)
% 28.57/5.57 % (9046)------------------------------
% 28.57/5.57 % (9046)------------------------------
% 28.57/5.59 % (9047)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_8750 for (2962ds/794Mi)
% 30.26/5.93 % (9040)Instruction limit reached!
% 30.26/5.93 % (9040)------------------------------
% 30.26/5.93 % (9040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.26/5.93 % (9040)Termination reason: Unknown
% 30.26/5.93 % (9040)Termination phase: Saturation
% 30.26/5.93
% 30.26/5.93 % (9040)Memory used [KB]: 12792
% 30.26/5.93 % (9040)Time elapsed: 1.088 s
% 30.26/5.93 % (9040)Instructions burned: 1827 (million)
% 30.26/5.93 % (9040)------------------------------
% 30.26/5.93 % (9040)------------------------------
% 30.26/5.95 % (9019)Instruction limit reached!
% 30.26/5.95 % (9019)------------------------------
% 30.26/5.95 % (9019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.26/5.95 % (9019)Termination reason: Unknown
% 30.26/5.95 % (9019)Termination phase: Saturation
% 30.26/5.95
% 30.26/5.95 % (9019)Memory used [KB]: 14072
% 30.26/5.95 % (9019)Time elapsed: 2.557 s
% 30.26/5.95 % (9019)Instructions burned: 4436 (million)
% 30.26/5.95 % (9019)------------------------------
% 30.26/5.95 % (9019)------------------------------
% 30.26/5.95 % (9048)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_8750 for (2959ds/464Mi)
% 30.26/5.97 % (9049)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_8750 for (2958ds/1376Mi)
% 33.11/6.07 % (9047)Instruction limit reached!
% 33.11/6.07 % (9047)------------------------------
% 33.11/6.07 % (9047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.11/6.07 % (9047)Termination reason: Unknown
% 33.11/6.07 % (9047)Termination phase: Saturation
% 33.11/6.07
% 33.11/6.07 % (9047)Memory used [KB]: 5756
% 33.11/6.07 % (9047)Time elapsed: 0.507 s
% 33.11/6.07 % (9047)Instructions burned: 794 (million)
% 33.11/6.07 % (9047)------------------------------
% 33.11/6.07 % (9047)------------------------------
% 33.11/6.10 % (9050)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_8750 for (2957ds/906Mi)
% 34.21/6.22 % (9048)Instruction limit reached!
% 34.21/6.22 % (9048)------------------------------
% 34.21/6.22 % (9048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.21/6.22 % (9048)Termination reason: Unknown
% 34.21/6.22 % (9048)Termination phase: Saturation
% 34.21/6.22
% 34.21/6.22 % (9048)Memory used [KB]: 7675
% 34.21/6.22 % (9048)Time elapsed: 0.293 s
% 34.21/6.22 % (9048)Instructions burned: 464 (million)
% 34.21/6.22 % (9048)------------------------------
% 34.21/6.22 % (9048)------------------------------
% 34.21/6.24 % (9051)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_8750 for (2956ds/434Mi)
% 34.21/6.28 % (9024)Instruction limit reached!
% 34.21/6.28 % (9024)------------------------------
% 34.21/6.28 % (9024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.21/6.28 % (9024)Termination reason: Unknown
% 34.21/6.28 % (9024)Termination phase: Saturation
% 34.21/6.28
% 34.21/6.28 % (9024)Memory used [KB]: 18421
% 34.21/6.28 % (9024)Time elapsed: 2.546 s
% 34.21/6.28 % (9024)Instructions burned: 4350 (million)
% 34.21/6.28 % (9024)------------------------------
% 34.21/6.28 % (9024)------------------------------
% 34.74/6.31 % (9052)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_8750 for (2955ds/865Mi)
% 35.14/6.49 % (9051)Instruction limit reached!
% 35.14/6.49 % (9051)------------------------------
% 35.14/6.49 % (9051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.14/6.49 % (9051)Termination reason: Unknown
% 35.14/6.49 % (9051)Termination phase: Saturation
% 35.14/6.49
% 35.14/6.49 % (9051)Memory used [KB]: 7803
% 35.14/6.49 % (9051)Time elapsed: 0.243 s
% 35.14/6.49 % (9051)Instructions burned: 434 (million)
% 35.14/6.49 % (9051)------------------------------
% 35.14/6.49 % (9051)------------------------------
% 35.80/6.51 % (9053)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_8750 for (2953ds/593Mi)
% 36.20/6.68 % (9050)Instruction limit reached!
% 36.20/6.68 % (9050)------------------------------
% 36.20/6.68 % (9050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.20/6.68 % (9050)Termination reason: Unknown
% 36.20/6.68 % (9050)Termination phase: Saturation
% 36.20/6.68
% 36.20/6.68 % (9050)Memory used [KB]: 10874
% 36.20/6.68 % (9050)Time elapsed: 0.583 s
% 36.20/6.68 % (9050)Instructions burned: 906 (million)
% 36.20/6.68 % (9050)------------------------------
% 36.20/6.68 % (9050)------------------------------
% 37.22/6.70 % (9054)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_8750 for (2951ds/443Mi)
% 37.22/6.70 % (9022)Instruction limit reached!
% 37.22/6.70 % (9022)------------------------------
% 37.22/6.70 % (9022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.22/6.70 % (9022)Termination reason: Unknown
% 37.22/6.70 % (9022)Termination phase: Saturation
% 37.22/6.70
% 37.22/6.70 % (9022)Memory used [KB]: 18805
% 37.22/6.70 % (9022)Time elapsed: 3.191 s
% 37.22/6.70 % (9022)Instructions burned: 5205 (million)
% 37.22/6.70 % (9022)------------------------------
% 37.22/6.70 % (9022)------------------------------
% 37.22/6.73 % (9055)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_8750 for (2951ds/594Mi)
% 37.54/6.80 % (9052)Instruction limit reached!
% 37.54/6.80 % (9052)------------------------------
% 37.54/6.80 % (9052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.54/6.80 % (9052)Termination reason: Unknown
% 37.54/6.80 % (9052)Termination phase: Saturation
% 37.54/6.80
% 37.54/6.80 % (9052)Memory used [KB]: 8571
% 37.54/6.80 % (9052)Time elapsed: 0.492 s
% 37.54/6.80 % (9052)Instructions burned: 865 (million)
% 37.54/6.80 % (9052)------------------------------
% 37.54/6.80 % (9052)------------------------------
% 37.54/6.82 % (9049)Instruction limit reached!
% 37.54/6.82 % (9049)------------------------------
% 37.54/6.82 % (9049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.54/6.82 % (9049)Termination reason: Unknown
% 37.54/6.82 % (9049)Termination phase: Saturation
% 37.54/6.82
% 37.54/6.82 % (9049)Memory used [KB]: 14711
% 37.54/6.82 % (9049)Time elapsed: 0.869 s
% 37.54/6.82 % (9049)Instructions burned: 1377 (million)
% 37.54/6.82 % (9049)------------------------------
% 37.54/6.82 % (9049)------------------------------
% 37.54/6.82 % (9056)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_8750 for (2950ds/327Mi)
% 37.54/6.84 % (9057)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_8750 for (2950ds/5411Mi)
% 37.54/6.85 % (9053)Instruction limit reached!
% 37.54/6.85 % (9053)------------------------------
% 37.54/6.85 % (9053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.54/6.85 % (9053)Termination reason: Unknown
% 37.54/6.85 % (9053)Termination phase: Saturation
% 37.54/6.85
% 37.54/6.85 % (9053)Memory used [KB]: 8571
% 37.54/6.85 % (9053)Time elapsed: 0.343 s
% 37.54/6.85 % (9053)Instructions burned: 594 (million)
% 37.54/6.85 % (9053)------------------------------
% 37.54/6.85 % (9053)------------------------------
% 37.54/6.86 % (9057)Refutation not found, incomplete strategy
% 37.54/6.86 % (9057)------------------------------
% 37.54/6.86 % (9057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.54/6.86 % (9057)Termination reason: Refutation not found, incomplete strategy
% 37.54/6.86
% 37.54/6.86
% 37.54/6.86 % (9057)Memory used [KB]: 6652
% 37.54/6.86 % (9057)Time elapsed: 0.015 s
% 37.54/6.86 % (9057)Instructions burned: 41 (million)
% 37.54/6.86 % (9057)------------------------------
% 37.54/6.86 % (9057)------------------------------
% 37.54/6.87 % (9058)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_8750 for (2949ds/1762Mi)
% 37.54/6.88 % (9059)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_8750 for (2949ds/96Mi)
% 38.67/6.93 % (9059)Instruction limit reached!
% 38.67/6.93 % (9059)------------------------------
% 38.67/6.93 % (9059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.67/6.93 % (9059)Termination reason: Unknown
% 38.67/6.93 % (9059)Termination phase: Saturation
% 38.67/6.93
% 38.67/6.93 % (9059)Memory used [KB]: 6908
% 38.67/6.93 % (9059)Time elapsed: 0.053 s
% 38.67/6.93 % (9059)Instructions burned: 97 (million)
% 38.67/6.93 % (9059)------------------------------
% 38.67/6.93 % (9059)------------------------------
% 38.67/6.95 % (9060)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_8750 for (2949ds/503Mi)
% 38.67/6.97 % (9054)Instruction limit reached!
% 38.67/6.97 % (9054)------------------------------
% 38.67/6.97 % (9054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.67/6.97 % (9054)Termination reason: Unknown
% 38.67/6.97 % (9054)Termination phase: Saturation
% 38.67/6.97
% 38.67/6.97 % (9054)Memory used [KB]: 8699
% 38.67/6.97 % (9054)Time elapsed: 0.271 s
% 38.67/6.97 % (9054)Instructions burned: 443 (million)
% 38.67/6.97 % (9054)------------------------------
% 38.67/6.97 % (9054)------------------------------
% 38.67/6.99 % (9061)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_8750 for (2948ds/90Mi)
% 38.67/7.01 % (9056)Instruction limit reached!
% 38.67/7.01 % (9056)------------------------------
% 38.67/7.01 % (9056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.67/7.01 % (9056)Termination reason: Unknown
% 38.67/7.01 % (9056)Termination phase: Saturation
% 38.67/7.01
% 38.67/7.01 % (9056)Memory used [KB]: 8059
% 38.67/7.01 % (9056)Time elapsed: 0.187 s
% 38.67/7.01 % (9056)Instructions burned: 327 (million)
% 38.67/7.01 % (9056)------------------------------
% 38.67/7.01 % (9056)------------------------------
% 39.95/7.03 % (9062)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_8750 for (2948ds/593Mi)
% 39.95/7.04 % (9061)Instruction limit reached!
% 39.95/7.04 % (9061)------------------------------
% 39.95/7.04 % (9061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.95/7.04 % (9061)Termination reason: Unknown
% 39.95/7.04 % (9061)Termination phase: Saturation
% 39.95/7.04
% 39.95/7.04 % (9061)Memory used [KB]: 6908
% 39.95/7.04 % (9061)Time elapsed: 0.053 s
% 39.95/7.05 % (9061)Instructions burned: 91 (million)
% 39.95/7.05 % (9061)------------------------------
% 39.95/7.05 % (9061)------------------------------
% 39.95/7.07 % (9063)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_8750 for (2947ds/1512Mi)
% 39.95/7.07 % (9055)Instruction limit reached!
% 39.95/7.07 % (9055)------------------------------
% 39.95/7.07 % (9055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.95/7.07 % (9055)Termination reason: Unknown
% 39.95/7.07 % (9055)Termination phase: Saturation
% 39.95/7.07
% 39.95/7.07 % (9055)Memory used [KB]: 9466
% 39.95/7.07 % (9055)Time elapsed: 0.345 s
% 39.95/7.07 % (9055)Instructions burned: 594 (million)
% 39.95/7.07 % (9055)------------------------------
% 39.95/7.07 % (9055)------------------------------
% 39.95/7.09 % (9064)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_8750 for (2947ds/569Mi)
% 40.45/7.14 % (9063)Refutation not found, incomplete strategy
% 40.45/7.14 % (9063)------------------------------
% 40.45/7.14 % (9063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.45/7.14 % (9063)Termination reason: Refutation not found, incomplete strategy
% 40.45/7.14
% 40.45/7.14
% 40.45/7.14 % (9063)Memory used [KB]: 7547
% 40.45/7.14 % (9063)Time elapsed: 0.071 s
% 40.45/7.14 % (9063)Instructions burned: 117 (million)
% 40.45/7.14 % (9063)------------------------------
% 40.45/7.14 % (9063)------------------------------
% 40.45/7.16 % (9065)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_8750 for (2946ds/501Mi)
% 40.86/7.25 % (9060)Instruction limit reached!
% 40.86/7.25 % (9060)------------------------------
% 40.86/7.25 % (9060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.86/7.25 % (9060)Termination reason: Unknown
% 40.86/7.25 % (9060)Termination phase: Saturation
% 40.86/7.25
% 40.86/7.25 % (9060)Memory used [KB]: 7803
% 40.86/7.25 % (9060)Time elapsed: 0.316 s
% 40.86/7.25 % (9060)Instructions burned: 503 (million)
% 40.86/7.25 % (9060)------------------------------
% 40.86/7.25 % (9060)------------------------------
% 40.86/7.27 % (9066)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_8750 for (2945ds/562Mi)
% 41.22/7.39 % (9062)Instruction limit reached!
% 41.22/7.39 % (9062)------------------------------
% 41.22/7.39 % (9062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.22/7.39 % (9062)Termination reason: Unknown
% 41.22/7.39 % (9062)Termination phase: Saturation
% 41.22/7.39
% 41.22/7.39 % (9062)Memory used [KB]: 8699
% 41.22/7.39 % (9062)Time elapsed: 0.360 s
% 41.22/7.39 % (9062)Instructions burned: 594 (million)
% 41.22/7.39 % (9062)------------------------------
% 41.22/7.39 % (9062)------------------------------
% 41.93/7.41 % (9067)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_8750 for (2944ds/406Mi)
% 41.93/7.41 % (9064)Instruction limit reached!
% 41.93/7.41 % (9064)------------------------------
% 41.93/7.41 % (9064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.93/7.41 % (9064)Termination reason: Unknown
% 41.93/7.41 % (9064)Termination phase: Saturation
% 41.93/7.41
% 41.93/7.41 % (9064)Memory used [KB]: 8187
% 41.93/7.41 % (9064)Time elapsed: 0.321 s
% 41.93/7.41 % (9064)Instructions burned: 570 (million)
% 41.93/7.41 % (9064)------------------------------
% 41.93/7.41 % (9064)------------------------------
% 41.93/7.43 % (9065)Instruction limit reached!
% 41.93/7.43 % (9065)------------------------------
% 41.93/7.43 % (9065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.93/7.43 % (9065)Termination reason: Unknown
% 41.93/7.43 % (9065)Termination phase: Saturation
% 41.93/7.43
% 41.93/7.43 % (9065)Memory used [KB]: 8443
% 41.93/7.43 % (9065)Time elapsed: 0.274 s
% 41.93/7.43 % (9065)Instructions burned: 501 (million)
% 41.93/7.43 % (9065)------------------------------
% 41.93/7.43 % (9065)------------------------------
% 41.93/7.44 % (9068)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_8750 for (2944ds/582Mi)
% 41.93/7.46 % (9069)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_8750 for (2944ds/456Mi)
% 42.86/7.59 % (9066)Instruction limit reached!
% 42.86/7.59 % (9066)------------------------------
% 42.86/7.59 % (9066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.86/7.59 % (9066)Termination reason: Unknown
% 42.86/7.59 % (9066)Termination phase: Saturation
% 42.86/7.59
% 42.86/7.59 % (9066)Memory used [KB]: 7803
% 42.86/7.59 % (9066)Time elapsed: 0.321 s
% 42.86/7.59 % (9066)Instructions burned: 562 (million)
% 42.86/7.59 % (9066)------------------------------
% 42.86/7.59 % (9066)------------------------------
% 43.50/7.61 % (9067)Refutation not found, non-redundant clauses discarded% (9067)------------------------------
% 43.50/7.61 % (9067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.50/7.61 % (9067)Termination reason: Refutation not found, non-redundant clauses discarded
% 43.50/7.61
% 43.50/7.61 % (9067)Memory used [KB]: 7803
% 43.50/7.61 % (9067)Time elapsed: 0.203 s
% 43.50/7.61 % (9067)Instructions burned: 340 (million)
% 43.50/7.61 % (9067)------------------------------
% 43.50/7.61 % (9067)------------------------------
% 43.50/7.62 % (9070)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_8750 for (2942ds/393Mi)
% 43.50/7.64 % (9071)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_8750 for (2942ds/1335Mi)
% 44.03/7.73 % (9069)Instruction limit reached!
% 44.03/7.73 % (9069)------------------------------
% 44.03/7.73 % (9069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.03/7.73 % (9069)Termination reason: Unknown
% 44.03/7.73 % (9069)Termination phase: Saturation
% 44.03/7.73
% 44.03/7.73 % (9069)Memory used [KB]: 9338
% 44.03/7.73 % (9069)Time elapsed: 0.273 s
% 44.03/7.73 % (9069)Instructions burned: 457 (million)
% 44.03/7.73 % (9069)------------------------------
% 44.03/7.73 % (9069)------------------------------
% 44.03/7.75 % (9072)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_8750 for (2941ds/3373Mi)
% 44.03/7.79 % (9068)Instruction limit reached!
% 44.03/7.79 % (9068)------------------------------
% 44.03/7.79 % (9068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.03/7.79 % (9068)Termination reason: Unknown
% 44.03/7.79 % (9068)Termination phase: Saturation
% 44.03/7.79
% 44.03/7.79 % (9068)Memory used [KB]: 9466
% 44.03/7.79 % (9068)Time elapsed: 0.358 s
% 44.03/7.79 % (9068)Instructions burned: 582 (million)
% 44.03/7.79 % (9068)------------------------------
% 44.03/7.79 % (9068)------------------------------
% 45.00/7.80 % (9044)Instruction limit reached!
% 45.00/7.80 % (9044)------------------------------
% 45.00/7.80 % (9044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.00/7.80 % (9044)Termination reason: Unknown
% 45.00/7.80 % (9044)Termination phase: Saturation
% 45.00/7.80
% 45.00/7.80 % (9044)Memory used [KB]: 18677
% 45.00/7.80 % (9044)Time elapsed: 2.770 s
% 45.00/7.80 % (9044)Instructions burned: 4714 (million)
% 45.00/7.80 % (9044)------------------------------
% 45.00/7.80 % (9044)------------------------------
% 45.00/7.81 % (9073)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_8750 for (2940ds/474Mi)
% 45.00/7.82 % (9074)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_8750 for (2940ds/157Mi)
% 45.00/7.83 % (9070)Instruction limit reached!
% 45.00/7.83 % (9070)------------------------------
% 45.00/7.83 % (9070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.00/7.83 % (9070)Termination reason: Unknown
% 45.00/7.83 % (9070)Termination phase: Saturation
% 45.00/7.83
% 45.00/7.83 % (9070)Memory used [KB]: 7675
% 45.00/7.83 % (9070)Time elapsed: 0.221 s
% 45.00/7.83 % (9070)Instructions burned: 393 (million)
% 45.00/7.83 % (9070)------------------------------
% 45.00/7.83 % (9070)------------------------------
% 45.00/7.86 % (9075)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_8750 for (2940ds/590Mi)
% 45.00/7.87 % (9058)Instruction limit reached!
% 45.00/7.87 % (9058)------------------------------
% 45.00/7.87 % (9058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.00/7.87 % (9058)Termination reason: Unknown
% 45.00/7.87 % (9058)Termination phase: Saturation
% 45.00/7.87
% 45.00/7.87 % (9058)Memory used [KB]: 12025
% 45.00/7.87 % (9058)Time elapsed: 1.0000 s
% 45.00/7.87 % (9058)Instructions burned: 1763 (million)
% 45.00/7.87 % (9058)------------------------------
% 45.00/7.87 % (9058)------------------------------
% 45.00/7.89 % (9076)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_8750 for (2939ds/104Mi)
% 45.43/7.90 % (9074)Instruction limit reached!
% 45.43/7.90 % (9074)------------------------------
% 45.43/7.90 % (9074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.43/7.90 % (9074)Termination reason: Unknown
% 45.43/7.90 % (9074)Termination phase: Saturation
% 45.43/7.90
% 45.43/7.90 % (9074)Memory used [KB]: 7036
% 45.43/7.90 % (9074)Time elapsed: 0.086 s
% 45.43/7.90 % (9074)Instructions burned: 158 (million)
% 45.43/7.90 % (9074)------------------------------
% 45.43/7.90 % (9074)------------------------------
% 45.43/7.93 % (9077)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_8750 for (2939ds/414Mi)
% 45.43/7.95 % (9076)Instruction limit reached!
% 45.43/7.95 % (9076)------------------------------
% 45.43/7.95 % (9076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.43/7.95 % (9076)Termination reason: Unknown
% 45.43/7.95 % (9076)Termination phase: Saturation
% 45.43/7.95
% 45.43/7.95 % (9076)Memory used [KB]: 2814
% 45.43/7.95 % (9076)Time elapsed: 0.062 s
% 45.43/7.95 % (9076)Instructions burned: 104 (million)
% 45.43/7.95 % (9076)------------------------------
% 45.43/7.95 % (9076)------------------------------
% 45.43/7.98 % (9078)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_8750 for (2938ds/715Mi)
% 46.98/8.10 % (9073)Instruction limit reached!
% 46.98/8.10 % (9073)------------------------------
% 46.98/8.10 % (9073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.98/8.10 % (9073)Termination reason: Unknown
% 46.98/8.10 % (9073)Termination phase: Saturation
% 46.98/8.10
% 46.98/8.10 % (9073)Memory used [KB]: 8443
% 46.98/8.10 % (9073)Time elapsed: 0.287 s
% 46.98/8.10 % (9073)Instructions burned: 475 (million)
% 46.98/8.10 % (9073)------------------------------
% 46.98/8.10 % (9073)------------------------------
% 46.98/8.12 % (9079)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_8750 for (2937ds/961Mi)
% 47.70/8.16 % (9077)Instruction limit reached!
% 47.70/8.16 % (9077)------------------------------
% 47.70/8.16 % (9077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.70/8.16 % (9077)Termination reason: Unknown
% 47.70/8.16 % (9077)Termination phase: Saturation
% 47.70/8.16
% 47.70/8.16 % (9077)Memory used [KB]: 7803
% 47.70/8.16 % (9077)Time elapsed: 0.255 s
% 47.70/8.16 % (9077)Instructions burned: 415 (million)
% 47.70/8.16 % (9077)------------------------------
% 47.70/8.16 % (9077)------------------------------
% 47.70/8.18 % (9075)Instruction limit reached!
% 47.70/8.18 % (9075)------------------------------
% 47.70/8.18 % (9075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.70/8.18 % (9075)Termination reason: Unknown
% 47.70/8.18 % (9075)Termination phase: Saturation
% 47.70/8.18
% 47.70/8.18 % (9075)Memory used [KB]: 7931
% 47.70/8.18 % (9075)Time elapsed: 0.325 s
% 47.70/8.18 % (9075)Instructions burned: 590 (million)
% 47.70/8.18 % (9075)------------------------------
% 47.70/8.18 % (9075)------------------------------
% 47.70/8.18 % (9080)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_8750 for (2936ds/1213Mi)
% 48.09/8.20 % (9081)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_8750 for (2936ds/1979Mi)
% 48.87/8.41 % (9071)Instruction limit reached!
% 48.87/8.41 % (9071)------------------------------
% 48.87/8.41 % (9071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.87/8.41 % (9071)Termination reason: Unknown
% 48.87/8.41 % (9071)Termination phase: Saturation
% 48.87/8.41
% 48.87/8.41 % (9071)Memory used [KB]: 8571
% 48.87/8.41 % (9071)Time elapsed: 0.771 s
% 48.87/8.41 % (9071)Instructions burned: 1336 (million)
% 48.87/8.41 % (9071)------------------------------
% 48.87/8.41 % (9071)------------------------------
% 48.87/8.42 % (9078)Instruction limit reached!
% 48.87/8.42 % (9078)------------------------------
% 48.87/8.42 % (9078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.87/8.42 % (9078)Termination reason: Unknown
% 48.87/8.42 % (9078)Termination phase: Saturation
% 48.87/8.42
% 48.87/8.42 % (9078)Memory used [KB]: 4733
% 48.87/8.42 % (9078)Time elapsed: 0.466 s
% 48.87/8.42 % (9078)Instructions burned: 715 (million)
% 48.87/8.42 % (9078)------------------------------
% 48.87/8.42 % (9078)------------------------------
% 48.87/8.43 % (9082)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_8750 for (2934ds/481Mi)
% 48.87/8.44 % (9083)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_8750 for (2934ds/783Mi)
% 49.33/8.69 % (9079)Instruction limit reached!
% 49.33/8.69 % (9079)------------------------------
% 49.33/8.69 % (9079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.33/8.69 % (9079)Termination reason: Unknown
% 49.33/8.69 % (9079)Termination phase: Saturation
% 49.33/8.69
% 49.33/8.69 % (9079)Memory used [KB]: 8059
% 49.33/8.69 % (9079)Time elapsed: 0.591 s
% 49.33/8.69 % (9079)Instructions burned: 961 (million)
% 49.33/8.69 % (9079)------------------------------
% 49.33/8.69 % (9079)------------------------------
% 50.13/8.71 % (9084)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_8750 for (2931ds/432Mi)
% 50.13/8.71 % (9082)Instruction limit reached!
% 50.13/8.71 % (9082)------------------------------
% 50.13/8.71 % (9082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.13/8.71 % (9082)Termination reason: Unknown
% 50.13/8.71 % (9082)Termination phase: Saturation
% 50.13/8.71
% 50.13/8.71 % (9082)Memory used [KB]: 8443
% 50.13/8.71 % (9082)Time elapsed: 0.312 s
% 50.13/8.71 % (9082)Instructions burned: 482 (million)
% 50.13/8.71 % (9082)------------------------------
% 50.13/8.71 % (9082)------------------------------
% 50.13/8.74 % (9085)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_8750 for (2931ds/1670Mi)
% 50.64/8.88 % (9083)Instruction limit reached!
% 50.64/8.88 % (9083)------------------------------
% 50.64/8.88 % (9083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.64/8.88 % (9083)Termination reason: Unknown
% 50.64/8.88 % (9083)Termination phase: Saturation
% 50.64/8.88
% 50.64/8.88 % (9083)Memory used [KB]: 8955
% 50.64/8.88 % (9083)Time elapsed: 0.466 s
% 50.64/8.88 % (9083)Instructions burned: 784 (million)
% 50.64/8.88 % (9083)------------------------------
% 50.64/8.88 % (9083)------------------------------
% 51.29/8.91 % (9086)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_8750 for (2929ds/90Mi)
% 51.29/8.92 % (9080)Instruction limit reached!
% 51.29/8.92 % (9080)------------------------------
% 51.29/8.92 % (9080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.29/8.92 % (9080)Termination reason: Unknown
% 51.29/8.92 % (9080)Termination phase: Saturation
% 51.29/8.92
% 51.29/8.92 % (9080)Memory used [KB]: 9466
% 51.29/8.92 % (9080)Time elapsed: 0.768 s
% 51.29/8.92 % (9080)Instructions burned: 1214 (million)
% 51.29/8.92 % (9080)------------------------------
% 51.29/8.92 % (9080)------------------------------
% 51.29/8.95 % (9087)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_8750 for (2929ds/346Mi)
% 51.29/8.96 % (9086)Instruction limit reached!
% 51.29/8.96 % (9086)------------------------------
% 51.29/8.96 % (9086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.29/8.96 % (9086)Termination reason: Unknown
% 51.29/8.96 % (9086)Termination phase: Saturation
% 51.29/8.96
% 51.29/8.96 % (9084)Instruction limit reached!
% 51.29/8.96 % (9084)------------------------------
% 51.29/8.96 % (9084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.29/8.96 % (9084)Termination reason: Unknown
% 51.29/8.96 % (9084)Termination phase: Saturation
% 51.29/8.96
% 51.29/8.96 % (9084)Memory used [KB]: 8059
% 51.29/8.96 % (9084)Time elapsed: 0.273 s
% 51.29/8.96 % (9084)Instructions burned: 432 (million)
% 51.29/8.96 % (9084)------------------------------
% 51.29/8.96 % (9084)------------------------------
% 51.29/8.96 % (9086)Memory used [KB]: 6908
% 51.29/8.96 % (9086)Time elapsed: 0.052 s
% 51.29/8.96 % (9086)Instructions burned: 90 (million)
% 51.29/8.96 % (9086)------------------------------
% 51.29/8.96 % (9086)------------------------------
% 51.29/8.98 % (9089)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_8750 for (2928ds/6454Mi)
% 51.29/8.98 % (9088)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_8750 for (2928ds/401Mi)
% 54.71/9.15 % (9087)Instruction limit reached!
% 54.71/9.15 % (9087)------------------------------
% 54.71/9.15 % (9087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.71/9.15 % (9087)Termination reason: Unknown
% 54.71/9.15 % (9087)Termination phase: Saturation
% 54.71/9.15
% 54.71/9.15 % (9087)Memory used [KB]: 8187
% 54.71/9.15 % (9087)Time elapsed: 0.204 s
% 54.71/9.15 % (9087)Instructions burned: 347 (million)
% 54.71/9.15 % (9087)------------------------------
% 54.71/9.15 % (9087)------------------------------
% 54.71/9.17 % (9090)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_8750 for (2926ds/283Mi)
% 55.16/9.21 % (9088)Instruction limit reached!
% 55.16/9.21 % (9088)------------------------------
% 55.16/9.21 % (9088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.16/9.21 % (9088)Termination reason: Unknown
% 55.16/9.21 % (9088)Termination phase: Saturation
% 55.16/9.21
% 55.16/9.21 % (9088)Memory used [KB]: 8187
% 55.16/9.21 % (9088)Time elapsed: 0.233 s
% 55.16/9.21 % (9088)Instructions burned: 402 (million)
% 55.16/9.21 % (9088)------------------------------
% 55.16/9.21 % (9088)------------------------------
% 55.16/9.23 % (9091)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_8750 for (2926ds/865Mi)
% 55.69/9.33 % (9081)Instruction limit reached!
% 55.69/9.33 % (9081)------------------------------
% 55.69/9.33 % (9081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.69/9.33 % (9081)Termination reason: Unknown
% 55.69/9.33 % (9081)Termination phase: Saturation
% 55.69/9.33
% 55.69/9.33 % (9081)Memory used [KB]: 8571
% 55.69/9.33 % (9081)Time elapsed: 1.148 s
% 55.69/9.33 % (9081)Instructions burned: 1980 (million)
% 55.69/9.33 % (9081)------------------------------
% 55.69/9.33 % (9081)------------------------------
% 55.69/9.34 % (9090)Instruction limit reached!
% 55.69/9.34 % (9090)------------------------------
% 55.69/9.34 % (9090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.69/9.34 % (9090)Termination reason: Unknown
% 55.69/9.34 % (9090)Termination phase: Saturation
% 55.69/9.34
% 55.69/9.34 % (9090)Memory used [KB]: 7931
% 55.69/9.34 % (9090)Time elapsed: 0.169 s
% 55.69/9.34 % (9090)Instructions burned: 283 (million)
% 55.69/9.34 % (9090)------------------------------
% 55.69/9.34 % (9090)------------------------------
% 55.69/9.35 % (9092)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_8750 for (2925ds/4528Mi)
% 55.69/9.35 % (9093)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_8750 for (2924ds/1001Mi)
% 55.69/9.37 % (9092)Refutation not found, incomplete strategy
% 55.69/9.37 % (9092)------------------------------
% 55.69/9.37 % (9092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.69/9.37 % (9092)Termination reason: Refutation not found, incomplete strategy
% 55.69/9.37
% 55.69/9.37
% 55.69/9.37 % (9092)Memory used [KB]: 2046
% 55.69/9.37 % (9092)Time elapsed: 0.025 s
% 55.69/9.37 % (9092)Instructions burned: 38 (million)
% 55.69/9.37 % (9092)------------------------------
% 55.69/9.37 % (9092)------------------------------
% 55.69/9.39 % (9094)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_8750 for (2924ds/102Mi)
% 56.34/9.45 % (9094)Instruction limit reached!
% 56.34/9.45 % (9094)------------------------------
% 56.34/9.45 % (9094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.34/9.45 % (9094)Termination reason: Unknown
% 56.34/9.45 % (9094)Termination phase: Saturation
% 56.34/9.45
% 56.34/9.45 % (9094)Memory used [KB]: 6908
% 56.34/9.45 % (9094)Time elapsed: 0.055 s
% 56.34/9.45 % (9094)Instructions burned: 102 (million)
% 56.34/9.45 % (9094)------------------------------
% 56.34/9.45 % (9094)------------------------------
% 56.34/9.47 % (9095)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_8750 for (2923ds/952Mi)
% 57.23/9.68 % (9072)Instruction limit reached!
% 57.23/9.68 % (9072)------------------------------
% 57.23/9.68 % (9072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.23/9.68 % (9072)Termination reason: Unknown
% 57.23/9.68 % (9072)Termination phase: Saturation
% 57.23/9.68
% 57.23/9.68 % (9072)Memory used [KB]: 12281
% 57.23/9.68 % (9072)Time elapsed: 1.928 s
% 57.23/9.68 % (9072)Instructions burned: 3374 (million)
% 57.23/9.68 % (9072)------------------------------
% 57.23/9.68 % (9072)------------------------------
% 57.61/9.70 % (9096)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_8750 for (2921ds/578Mi)
% 57.61/9.70 % (9085)Instruction limit reached!
% 57.61/9.70 % (9085)------------------------------
% 57.61/9.70 % (9085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.61/9.70 % (9085)Termination reason: Unknown
% 57.61/9.70 % (9085)Termination phase: Saturation
% 57.61/9.70
% 57.61/9.70 % (9085)Memory used [KB]: 9722
% 57.61/9.70 % (9085)Time elapsed: 0.969 s
% 57.61/9.70 % (9085)Instructions burned: 1670 (million)
% 57.61/9.70 % (9085)------------------------------
% 57.61/9.70 % (9085)------------------------------
% 57.61/9.73 % (9097)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_8750 for (2921ds/643Mi)
% 57.61/9.74 % (9091)Instruction limit reached!
% 57.61/9.74 % (9091)------------------------------
% 57.61/9.74 % (9091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.61/9.74 % (9091)Termination reason: Unknown
% 57.61/9.74 % (9091)Termination phase: Saturation
% 57.61/9.74
% 57.61/9.74 % (9091)Memory used [KB]: 9978
% 57.61/9.74 % (9091)Time elapsed: 0.508 s
% 57.61/9.74 % (9091)Instructions burned: 865 (million)
% 57.61/9.74 % (9091)------------------------------
% 57.61/9.74 % (9091)------------------------------
% 57.61/9.76 % (9098)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_8750 for (2920ds/865Mi)
% 58.57/9.94 % (9093)Instruction limit reached!
% 58.57/9.94 % (9093)------------------------------
% 58.57/9.94 % (9093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.57/9.94 % (9093)Termination reason: Unknown
% 58.57/9.94 % (9093)Termination phase: Saturation
% 58.57/9.94
% 58.57/9.94 % (9093)Memory used [KB]: 8443
% 58.57/9.94 % (9093)Time elapsed: 0.587 s
% 58.57/9.94 % (9093)Instructions burned: 1001 (million)
% 58.57/9.94 % (9093)------------------------------
% 58.57/9.94 % (9093)------------------------------
% 58.57/9.96 % (9099)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_8750 for (2918ds/1174Mi)
% 60.97/10.03 % (9096)Instruction limit reached!
% 60.97/10.03 % (9096)------------------------------
% 60.97/10.03 % (9096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.97/10.03 % (9096)Termination reason: Unknown
% 60.97/10.03 % (9096)Termination phase: Saturation
% 60.97/10.03
% 60.97/10.03 % (9096)Memory used [KB]: 8699
% 60.97/10.03 % (9096)Time elapsed: 0.333 s
% 60.97/10.03 % (9096)Instructions burned: 579 (million)
% 60.97/10.03 % (9096)------------------------------
% 60.97/10.03 % (9096)------------------------------
% 60.97/10.04 % (9095)Instruction limit reached!
% 60.97/10.04 % (9095)------------------------------
% 60.97/10.04 % (9095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.97/10.04 % (9095)Termination reason: Unknown
% 60.97/10.04 % (9095)Termination phase: Saturation
% 60.97/10.04
% 60.97/10.04 % (9095)Memory used [KB]: 10234
% 60.97/10.04 % (9095)Time elapsed: 0.575 s
% 60.97/10.04 % (9095)Instructions burned: 952 (million)
% 60.97/10.04 % (9095)------------------------------
% 60.97/10.04 % (9095)------------------------------
% 60.97/10.05 % (9045)Instruction limit reached!
% 60.97/10.05 % (9045)------------------------------
% 60.97/10.05 % (9045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.97/10.05 % (9045)Termination reason: Unknown
% 60.97/10.05 % (9045)Termination phase: Saturation
% 60.97/10.05
% 60.97/10.05 % (9045)Memory used [KB]: 25458
% 60.97/10.05 % (9045)Time elapsed: 4.910 s
% 60.97/10.05 % (9045)Instructions burned: 8250 (million)
% 60.97/10.05 % (9045)------------------------------
% 60.97/10.05 % (9045)------------------------------
% 60.97/10.05 % (9100)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_8750 for (2918ds/644Mi)
% 60.97/10.06 % (9101)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_8750 for (2917ds/1201Mi)
% 60.97/10.08 % (9102)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_8750 for (2917ds/1046Mi)
% 60.97/10.09 % (9097)Instruction limit reached!
% 60.97/10.09 % (9097)------------------------------
% 60.97/10.09 % (9097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.97/10.09 % (9097)Termination reason: Unknown
% 60.97/10.09 % (9097)Termination phase: Saturation
% 60.97/10.09
% 60.97/10.09 % (9097)Memory used [KB]: 9083
% 60.97/10.09 % (9097)Time elapsed: 0.368 s
% 60.97/10.09 % (9097)Instructions burned: 644 (million)
% 60.97/10.09 % (9097)------------------------------
% 60.97/10.09 % (9097)------------------------------
% 60.97/10.12 % (9103)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_8750 for (2917ds/222Mi)
% 61.68/10.24 % (9103)Instruction limit reached!
% 61.68/10.24 % (9103)------------------------------
% 61.68/10.24 % (9103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.68/10.24 % (9103)Termination reason: Unknown
% 61.68/10.24 % (9103)Termination phase: Saturation
% 61.68/10.24
% 61.68/10.24 % (9103)Memory used [KB]: 7419
% 61.68/10.24 % (9103)Time elapsed: 0.124 s
% 61.68/10.24 % (9103)Instructions burned: 223 (million)
% 61.68/10.24 % (9103)------------------------------
% 61.68/10.24 % (9103)------------------------------
% 61.68/10.26 % (9104)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_8750 for (2915ds/68Mi)
% 61.68/10.27 % (9098)Instruction limit reached!
% 61.68/10.27 % (9098)------------------------------
% 61.68/10.27 % (9098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.68/10.27 % (9098)Termination reason: Unknown
% 61.68/10.27 % (9098)Termination phase: Saturation
% 61.68/10.27
% 61.68/10.27 % (9098)Memory used [KB]: 9594
% 61.68/10.27 % (9098)Time elapsed: 0.513 s
% 61.68/10.27 % (9098)Instructions burned: 865 (million)
% 61.68/10.27 % (9098)------------------------------
% 61.68/10.27 % (9098)------------------------------
% 61.68/10.29 % (9105)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_8750 for (2915ds/454Mi)
% 62.11/10.30 % (9104)Instruction limit reached!
% 62.11/10.30 % (9104)------------------------------
% 62.11/10.30 % (9104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.11/10.30 % (9104)Termination reason: Unknown
% 62.11/10.30 % (9104)Termination phase: Property scanning
% 62.11/10.30
% 62.11/10.30 % (9104)Memory used [KB]: 2302
% 62.11/10.30 % (9104)Time elapsed: 0.041 s
% 62.11/10.30 % (9104)Instructions burned: 68 (million)
% 62.11/10.30 % (9104)------------------------------
% 62.11/10.30 % (9104)------------------------------
% 62.11/10.32 % (9106)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_8750 for (2915ds/360Mi)
% 62.38/10.45 % (9100)Instruction limit reached!
% 62.38/10.45 % (9100)------------------------------
% 62.38/10.45 % (9100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.38/10.45 % (9100)Termination reason: Unknown
% 62.38/10.45 % (9100)Termination phase: Saturation
% 62.38/10.45
% 62.38/10.45 % (9100)Memory used [KB]: 11897
% 62.38/10.45 % (9100)Time elapsed: 0.398 s
% 62.38/10.45 % (9100)Instructions burned: 645 (million)
% 62.38/10.45 % (9100)------------------------------
% 62.38/10.45 % (9100)------------------------------
% 62.38/10.47 % (9107)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_8750 for (2913ds/157Mi)
% 62.99/10.53 % (9106)Instruction limit reached!
% 62.99/10.53 % (9106)------------------------------
% 62.99/10.53 % (9106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.99/10.53 % (9106)Termination reason: Unknown
% 62.99/10.53 % (9106)Termination phase: Saturation
% 62.99/10.53
% 62.99/10.53 % (9106)Memory used [KB]: 8059
% 62.99/10.53 % (9106)Time elapsed: 0.206 s
% 62.99/10.53 % (9106)Instructions burned: 360 (million)
% 62.99/10.53 % (9106)------------------------------
% 62.99/10.53 % (9106)------------------------------
% 62.99/10.55 % (9105)Instruction limit reached!
% 62.99/10.55 % (9105)------------------------------
% 62.99/10.55 % (9105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.99/10.55 % (9105)Termination reason: Unknown
% 62.99/10.55 % (9105)Termination phase: Saturation
% 62.99/10.55
% 62.99/10.55 % (9105)Memory used [KB]: 12665
% 62.99/10.55 % (9105)Time elapsed: 0.255 s
% 62.99/10.55 % (9105)Instructions burned: 454 (million)
% 62.99/10.55 % (9105)------------------------------
% 62.99/10.55 % (9105)------------------------------
% 62.99/10.55 % (9108)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_8750 for (2913ds/5061Mi)
% 62.99/10.56 % (9107)Instruction limit reached!
% 62.99/10.56 % (9107)------------------------------
% 62.99/10.56 % (9107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.99/10.56 % (9107)Termination reason: Unknown
% 62.99/10.56 % (9107)Termination phase: Saturation
% 62.99/10.56
% 62.99/10.56 % (9107)Memory used [KB]: 7036
% 62.99/10.56 % (9107)Time elapsed: 0.089 s
% 62.99/10.56 % (9107)Instructions burned: 158 (million)
% 62.99/10.56 % (9107)------------------------------
% 62.99/10.56 % (9107)------------------------------
% 62.99/10.57 % (9109)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_8750 for (2912ds/2401Mi)
% 62.99/10.58 % (9110)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_8750 for (2912ds/5798Mi)
% 63.80/10.66 % (9102)Instruction limit reached!
% 63.80/10.66 % (9102)------------------------------
% 63.80/10.66 % (9102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.80/10.66 % (9102)Termination reason: Unknown
% 63.80/10.66 % (9102)Termination phase: Saturation
% 63.80/10.66
% 63.80/10.66 % (9102)Memory used [KB]: 9338
% 63.80/10.66 % (9102)Time elapsed: 0.583 s
% 63.80/10.66 % (9102)Instructions burned: 1046 (million)
% 63.80/10.66 % (9102)------------------------------
% 63.80/10.66 % (9102)------------------------------
% 63.80/10.66 % (9099)Instruction limit reached!
% 63.80/10.66 % (9099)------------------------------
% 63.80/10.66 % (9099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.80/10.66 % (9099)Termination reason: Unknown
% 63.80/10.66 % (9099)Termination phase: Saturation
% 63.80/10.66
% 63.80/10.66 % (9099)Memory used [KB]: 11385
% 63.80/10.66 % (9099)Time elapsed: 0.698 s
% 63.80/10.66 % (9099)Instructions burned: 1174 (million)
% 63.80/10.66 % (9099)------------------------------
% 63.80/10.66 % (9099)------------------------------
% 63.80/10.68 % (9111)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_8750 for (2911ds/346Mi)
% 63.80/10.68 % (9112)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_8750 for (2911ds/1321Mi)
% 64.67/10.80 % (9101)Instruction limit reached!
% 64.67/10.80 % (9101)------------------------------
% 64.67/10.80 % (9101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.67/10.80 % (9101)Termination reason: Unknown
% 64.67/10.80 % (9101)Termination phase: Saturation
% 64.67/10.80
% 64.67/10.80 % (9101)Memory used [KB]: 10362
% 64.67/10.80 % (9101)Time elapsed: 0.735 s
% 64.67/10.80 % (9101)Instructions burned: 1202 (million)
% 64.67/10.80 % (9101)------------------------------
% 64.67/10.80 % (9101)------------------------------
% 64.67/10.82 % (9113)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_8750 for (2910ds/1312Mi)
% 64.67/10.88 % (9111)Instruction limit reached!
% 64.67/10.88 % (9111)------------------------------
% 64.67/10.88 % (9111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.67/10.88 % (9111)Termination reason: Unknown
% 64.67/10.88 % (9111)Termination phase: Saturation
% 64.67/10.88
% 64.67/10.88 % (9111)Memory used [KB]: 8187
% 64.67/10.88 % (9111)Time elapsed: 0.205 s
% 64.67/10.88 % (9111)Instructions burned: 347 (million)
% 64.67/10.88 % (9111)------------------------------
% 64.67/10.88 % (9111)------------------------------
% 65.75/10.91 % (9114)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_8750 for (2909ds/672Mi)
% 69.88/11.30 % (9114)Instruction limit reached!
% 69.88/11.30 % (9114)------------------------------
% 69.88/11.30 % (9114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.88/11.30 % (9114)Termination reason: Unknown
% 69.88/11.30 % (9114)Termination phase: Saturation
% 69.88/11.30
% 69.88/11.30 % (9114)Memory used [KB]: 8059
% 69.88/11.30 % (9114)Time elapsed: 0.400 s
% 69.88/11.30 % (9114)Instructions burned: 673 (million)
% 69.88/11.30 % (9114)------------------------------
% 69.88/11.30 % (9114)------------------------------
% 69.88/11.33 % (9115)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_8750 for (2905ds/1897Mi)
% 70.48/11.42 % (9112)Instruction limit reached!
% 70.48/11.42 % (9112)------------------------------
% 70.48/11.42 % (9112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.48/11.42 % (9112)Termination reason: Unknown
% 70.48/11.42 % (9112)Termination phase: Saturation
% 70.48/11.42
% 70.48/11.42 % (9112)Memory used [KB]: 5245
% 70.48/11.42 % (9112)Time elapsed: 0.739 s
% 70.48/11.42 % (9112)Instructions burned: 1322 (million)
% 70.48/11.42 % (9112)------------------------------
% 70.48/11.42 % (9112)------------------------------
% 70.48/11.44 % (9116)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_8750 for (2904ds/1202Mi)
% 71.02/11.60 % (9113)Instruction limit reached!
% 71.02/11.60 % (9113)------------------------------
% 71.02/11.60 % (9113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.02/11.60 % (9113)Termination reason: Unknown
% 71.02/11.60 % (9113)Termination phase: Saturation
% 71.02/11.60
% 71.02/11.60 % (9113)Memory used [KB]: 9850
% 71.02/11.60 % (9113)Time elapsed: 0.779 s
% 71.02/11.60 % (9113)Instructions burned: 1312 (million)
% 71.02/11.60 % (9113)------------------------------
% 71.02/11.60 % (9113)------------------------------
% 71.52/11.62 % (9117)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_8750 for (2902ds/1493Mi)
% 71.94/11.76 % (9089)Refutation not found, non-redundant clauses discarded% (9089)------------------------------
% 71.94/11.76 % (9089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.94/11.76 % (9089)Termination reason: Refutation not found, non-redundant clauses discarded
% 71.94/11.76
% 71.94/11.76 % (9089)Memory used [KB]: 9594
% 71.94/11.76 % (9089)Time elapsed: 2.780 s
% 71.94/11.76 % (9089)Instructions burned: 5063 (million)
% 71.94/11.76 % (9089)------------------------------
% 71.94/11.76 % (9089)------------------------------
% 71.94/11.78 % (9118)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_8750 for (2900ds/7679Mi)
% 72.63/12.01 % (9109)Instruction limit reached!
% 72.63/12.01 % (9109)------------------------------
% 72.63/12.01 % (9109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.63/12.01 % (9109)Termination reason: Unknown
% 72.63/12.01 % (9109)Termination phase: Saturation
% 72.63/12.01
% 72.63/12.01 % (9109)Memory used [KB]: 10106
% 72.63/12.01 % (9109)Time elapsed: 1.442 s
% 72.63/12.01 % (9109)Instructions burned: 2401 (million)
% 72.63/12.01 % (9109)------------------------------
% 72.63/12.01 % (9109)------------------------------
% 74.87/12.03 % (9119)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_8750 for (2898ds/340Mi)
% 75.49/12.13 % (9116)Instruction limit reached!
% 75.49/12.13 % (9116)------------------------------
% 75.49/12.13 % (9116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.49/12.13 % (9116)Termination reason: Unknown
% 75.49/12.13 % (9116)Termination phase: Saturation
% 75.49/12.13
% 75.49/12.13 % (9116)Memory used [KB]: 4733
% 75.49/12.13 % (9116)Time elapsed: 0.693 s
% 75.49/12.13 % (9116)Instructions burned: 1203 (million)
% 75.49/12.13 % (9116)------------------------------
% 75.49/12.13 % (9116)------------------------------
% 75.49/12.15 % (9120)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_8750 for (2897ds/3672Mi)
% 75.94/12.24 % (9119)Instruction limit reached!
% 75.94/12.24 % (9119)------------------------------
% 75.94/12.24 % (9119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.94/12.24 % (9119)Termination reason: Unknown
% 75.94/12.24 % (9119)Termination phase: Saturation
% 75.94/12.24
% 75.94/12.24 % (9119)Memory used [KB]: 8827
% 75.94/12.24 % (9119)Time elapsed: 0.206 s
% 75.94/12.24 % (9119)Instructions burned: 340 (million)
% 75.94/12.24 % (9119)------------------------------
% 75.94/12.24 % (9119)------------------------------
% 75.94/12.26 % (9121)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_8750 for (2896ds/1535Mi)
% 77.16/12.42 % (9115)Instruction limit reached!
% 77.16/12.42 % (9115)------------------------------
% 77.16/12.42 % (9115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.16/12.42 % (9115)Termination reason: Unknown
% 77.16/12.42 % (9115)Termination phase: Saturation
% 77.16/12.42
% 77.16/12.42 % (9115)Memory used [KB]: 12025
% 77.16/12.42 % (9115)Time elapsed: 1.098 s
% 77.16/12.42 % (9115)Instructions burned: 1898 (million)
% 77.16/12.42 % (9115)------------------------------
% 77.16/12.42 % (9115)------------------------------
% 77.16/12.43 % (9117)Instruction limit reached!
% 77.16/12.43 % (9117)------------------------------
% 77.16/12.43 % (9117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.16/12.43 % (9117)Termination reason: Unknown
% 77.16/12.43 % (9117)Termination phase: Saturation
% 77.16/12.43
% 77.16/12.43 % (9117)Memory used [KB]: 12025
% 77.16/12.43 % (9117)Time elapsed: 0.817 s
% 77.16/12.43 % (9117)Instructions burned: 1493 (million)
% 77.16/12.43 % (9117)------------------------------
% 77.16/12.43 % (9117)------------------------------
% 77.16/12.44 % (9122)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_8750 for (2894ds/4637Mi)
% 77.16/12.46 % (9123)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_8750 for (2893ds/3174Mi)
% 81.94/13.10 % (9121)Instruction limit reached!
% 81.94/13.10 % (9121)------------------------------
% 81.94/13.10 % (9121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.94/13.10 % (9121)Termination reason: Unknown
% 81.94/13.10 % (9121)Termination phase: Saturation
% 81.94/13.10
% 81.94/13.10 % (9121)Memory used [KB]: 12153
% 81.94/13.10 % (9121)Time elapsed: 0.868 s
% 81.94/13.10 % (9121)Instructions burned: 1535 (million)
% 81.94/13.10 % (9121)------------------------------
% 81.94/13.10 % (9121)------------------------------
% 81.94/13.13 % (9124)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_8750 for (2887ds/307Mi)
% 83.66/13.30 % (9124)Instruction limit reached!
% 83.66/13.30 % (9124)------------------------------
% 83.66/13.30 % (9124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.66/13.30 % (9124)Termination reason: Unknown
% 83.66/13.30 % (9124)Termination phase: Saturation
% 83.66/13.30
% 83.66/13.30 % (9124)Memory used [KB]: 7547
% 83.66/13.30 % (9124)Time elapsed: 0.171 s
% 83.66/13.30 % (9124)Instructions burned: 307 (million)
% 83.66/13.30 % (9124)------------------------------
% 83.66/13.30 % (9124)------------------------------
% 83.66/13.32 % (9125)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_8750 for (2885ds/3619Mi)
% 83.66/13.38 % (9125)Refutation not found, incomplete strategy
% 83.66/13.38 % (9125)------------------------------
% 83.66/13.38 % (9125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.66/13.38 % (9125)Termination reason: Refutation not found, incomplete strategy
% 83.66/13.38
% 83.66/13.38
% 83.66/13.38 % (9125)Memory used [KB]: 7164
% 83.66/13.38 % (9125)Time elapsed: 0.062 s
% 83.66/13.38 % (9125)Instructions burned: 105 (million)
% 83.66/13.38 % (9125)------------------------------
% 83.66/13.38 % (9125)------------------------------
% 84.55/13.40 % (9126)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_8750 for (2884ds/2325Mi)
% 85.76/13.63 % (9108)Instruction limit reached!
% 85.76/13.63 % (9108)------------------------------
% 85.76/13.63 % (9108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.76/13.63 % (9108)Termination reason: Unknown
% 85.76/13.63 % (9108)Termination phase: Saturation
% 85.76/13.63
% 85.76/13.63 % (9108)Memory used [KB]: 21875
% 85.76/13.63 % (9108)Time elapsed: 3.078 s
% 85.76/13.63 % (9108)Instructions burned: 5061 (million)
% 85.76/13.63 % (9108)------------------------------
% 85.76/13.63 % (9108)------------------------------
% 85.76/13.65 % (9127)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_8750 for (2881ds/2341Mi)
% 86.31/13.76 % (9110)Instruction limit reached!
% 86.31/13.76 % (9110)------------------------------
% 86.31/13.76 % (9110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.31/13.76 % (9110)Termination reason: Unknown
% 86.31/13.76 % (9110)Termination phase: Saturation
% 86.31/13.76
% 86.31/13.76 % (9110)Memory used [KB]: 13688
% 86.31/13.76 % (9110)Time elapsed: 3.197 s
% 86.31/13.76 % (9110)Instructions burned: 5798 (million)
% 86.31/13.76 % (9110)------------------------------
% 86.31/13.76 % (9110)------------------------------
% 86.31/13.79 % (9128)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_8750 for (2880ds/7257Mi)
% 90.87/14.32 % (9120)Instruction limit reached!
% 90.87/14.32 % (9120)------------------------------
% 90.87/14.32 % (9120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.87/14.32 % (9120)Termination reason: Unknown
% 90.87/14.32 % (9120)Termination phase: Saturation
% 90.87/14.32
% 90.87/14.32 % (9120)Memory used [KB]: 12665
% 90.87/14.32 % (9120)Time elapsed: 2.164 s
% 90.87/14.32 % (9120)Instructions burned: 3672 (million)
% 90.87/14.32 % (9120)------------------------------
% 90.87/14.32 % (9120)------------------------------
% 90.87/14.34 % (9129)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_8750 for (2875ds/3710Mi)
% 90.87/14.35 % (9123)Instruction limit reached!
% 90.87/14.35 % (9123)------------------------------
% 90.87/14.35 % (9123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.87/14.35 % (9123)Termination reason: Unknown
% 90.87/14.35 % (9123)Termination phase: Saturation
% 90.87/14.35
% 90.87/14.35 % (9123)Memory used [KB]: 13432
% 90.87/14.35 % (9123)Time elapsed: 1.891 s
% 90.87/14.35 % (9123)Instructions burned: 3174 (million)
% 90.87/14.35 % (9123)------------------------------
% 90.87/14.35 % (9123)------------------------------
% 90.87/14.37 % (9130)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_8750 for (2874ds/326Mi)
% 91.94/14.56 % (9130)Instruction limit reached!
% 91.94/14.56 % (9130)------------------------------
% 91.94/14.56 % (9130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.94/14.56 % (9130)Termination reason: Unknown
% 91.94/14.56 % (9130)Termination phase: Saturation
% 91.94/14.56
% 91.94/14.56 % (9130)Memory used [KB]: 7803
% 91.94/14.56 % (9130)Time elapsed: 0.191 s
% 91.94/14.56 % (9130)Instructions burned: 327 (million)
% 91.94/14.56 % (9130)------------------------------
% 91.94/14.56 % (9130)------------------------------
% 91.94/14.58 % (9131)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_8750 for (2872ds/1100Mi)
% 93.16/14.78 % (9126)Instruction limit reached!
% 93.16/14.78 % (9126)------------------------------
% 93.16/14.78 % (9126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.16/14.78 % (9126)Termination reason: Unknown
% 93.16/14.78 % (9126)Termination phase: Saturation
% 93.16/14.78
% 93.16/14.78 % (9126)Memory used [KB]: 11257
% 93.16/14.78 % (9126)Time elapsed: 1.377 s
% 93.16/14.78 % (9126)Instructions burned: 2326 (million)
% 93.16/14.78 % (9126)------------------------------
% 93.16/14.78 % (9126)------------------------------
% 93.64/14.80 % (9132)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_8750 for (2870ds/406Mi)
% 94.04/15.00 % (9127)Instruction limit reached!
% 94.04/15.00 % (9127)------------------------------
% 94.04/15.00 % (9127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.04/15.00 % (9127)Termination reason: Unknown
% 94.04/15.00 % (9127)Termination phase: Saturation
% 94.04/15.00
% 94.04/15.00 % (9127)Memory used [KB]: 9850
% 94.04/15.00 % (9127)Time elapsed: 1.353 s
% 94.04/15.00 % (9127)Instructions burned: 2341 (million)
% 94.04/15.00 % (9127)------------------------------
% 94.04/15.00 % (9127)------------------------------
% 94.04/15.01 % (9132)Refutation not found, non-redundant clauses discarded% (9132)------------------------------
% 94.04/15.01 % (9132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.04/15.01 % (9132)Termination reason: Refutation not found, non-redundant clauses discarded
% 94.04/15.01
% 94.04/15.01 % (9132)Memory used [KB]: 7803
% 94.04/15.01 % (9132)Time elapsed: 0.204 s
% 94.04/15.01 % (9132)Instructions burned: 336 (million)
% 94.04/15.01 % (9132)------------------------------
% 94.04/15.01 % (9132)------------------------------
% 94.04/15.02 % (9133)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_8750 for (2868ds/1871Mi)
% 95.91/15.03 % (9134)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_8750 for (2868ds/1194Mi)
% 96.43/15.18 % (9122)Instruction limit reached!
% 96.43/15.18 % (9122)------------------------------
% 96.43/15.18 % (9122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.43/15.18 % (9122)Termination reason: Unknown
% 96.43/15.18 % (9122)Termination phase: Saturation
% 96.43/15.18
% 96.43/15.18 % (9122)Memory used [KB]: 14583
% 96.43/15.18 % (9122)Time elapsed: 2.764 s
% 96.43/15.18 % (9122)Instructions burned: 4637 (million)
% 96.43/15.18 % (9122)------------------------------
% 96.43/15.18 % (9122)------------------------------
% 96.78/15.21 % (9135)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_8750 for (2866ds/474Mi)
% 96.78/15.25 % (9131)Instruction limit reached!
% 96.78/15.25 % (9131)------------------------------
% 96.78/15.25 % (9131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.78/15.25 % (9131)Termination reason: Unknown
% 96.78/15.25 % (9131)Termination phase: Saturation
% 96.78/15.25
% 96.78/15.25 % (9131)Memory used [KB]: 10490
% 96.78/15.25 % (9131)Time elapsed: 0.671 s
% 96.78/15.25 % (9131)Instructions burned: 1100 (million)
% 96.78/15.25 % (9131)------------------------------
% 96.78/15.25 % (9131)------------------------------
% 96.78/15.27 % (9137)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_8750 for (2865ds/3115Mi)
% 97.45/15.49 % (9135)Instruction limit reached!
% 97.45/15.49 % (9135)------------------------------
% 97.45/15.49 % (9135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.45/15.49 % (9135)Termination reason: Unknown
% 97.45/15.49 % (9135)Termination phase: Saturation
% 97.45/15.49
% 97.45/15.49 % (9135)Memory used [KB]: 8443
% 97.45/15.49 % (9135)Time elapsed: 0.283 s
% 97.45/15.49 % (9135)Instructions burned: 475 (million)
% 97.45/15.49 % (9135)------------------------------
% 97.45/15.49 % (9135)------------------------------
% 98.07/15.51 % (9138)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_8750 for (2863ds/831Mi)
% 98.67/15.73 % (9134)Instruction limit reached!
% 98.67/15.73 % (9134)------------------------------
% 98.67/15.73 % (9134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.67/15.73 % (9134)Termination reason: Unknown
% 98.67/15.73 % (9134)Termination phase: Saturation
% 98.67/15.73
% 98.67/15.73 % (9134)Memory used [KB]: 10106
% 98.67/15.73 % (9134)Time elapsed: 0.708 s
% 98.67/15.73 % (9134)Instructions burned: 1195 (million)
% 98.67/15.73 % (9134)------------------------------
% 98.67/15.73 % (9134)------------------------------
% 98.67/15.76 % (9139)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_8750 for (2860ds/1188Mi)
% 99.97/15.99 % (9138)Instruction limit reached!
% 99.97/15.99 % (9138)------------------------------
% 99.97/15.99 % (9138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.97/15.99 % (9138)Termination reason: Unknown
% 99.97/15.99 % (9138)Termination phase: Saturation
% 99.97/15.99
% 99.97/15.99 % (9138)Memory used [KB]: 8571
% 99.97/15.99 % (9138)Time elapsed: 0.481 s
% 99.97/15.99 % (9138)Instructions burned: 832 (million)
% 99.97/15.99 % (9138)------------------------------
% 99.97/15.99 % (9138)------------------------------
% 99.97/16.02 % (9140)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_8750 for (2858ds/2868Mi)
% 102.91/16.07 % (9118)Instruction limit reached!
% 102.91/16.07 % (9118)------------------------------
% 102.91/16.07 % (9118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.91/16.07 % (9118)Termination reason: Unknown
% 102.91/16.07 % (9118)Termination phase: Saturation
% 102.91/16.07
% 102.91/16.07 % (9118)Memory used [KB]: 14839
% 102.91/16.07 % (9118)Time elapsed: 4.309 s
% 102.91/16.07 % (9118)Instructions burned: 7679 (million)
% 102.91/16.07 % (9118)------------------------------
% 102.91/16.07 % (9118)------------------------------
% 102.91/16.10 % (9141)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_8750 for (2857ds/1516Mi)
% 102.91/16.12 % (9133)Instruction limit reached!
% 102.91/16.12 % (9133)------------------------------
% 102.91/16.12 % (9133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.91/16.12 % (9133)Termination reason: Unknown
% 102.91/16.12 % (9133)Termination phase: Saturation
% 102.91/16.12
% 102.91/16.12 % (9133)Memory used [KB]: 14072
% 102.91/16.12 % (9133)Time elapsed: 1.094 s
% 102.91/16.12 % (9133)Instructions burned: 1872 (million)
% 102.91/16.12 % (9133)------------------------------
% 102.91/16.12 % (9133)------------------------------
% 103.62/16.14 % (9142)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_8750 for (2857ds/2321Mi)
% 104.96/16.47 % (9139)Instruction limit reached!
% 104.96/16.47 % (9139)------------------------------
% 104.96/16.47 % (9139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.96/16.47 % (9139)Termination reason: Unknown
% 104.96/16.47 % (9139)Termination phase: Saturation
% 104.96/16.47
% 104.96/16.47 % (9139)Memory used [KB]: 9978
% 104.96/16.47 % (9139)Time elapsed: 0.716 s
% 104.96/16.47 % (9139)Instructions burned: 1188 (million)
% 104.96/16.47 % (9139)------------------------------
% 104.96/16.47 % (9139)------------------------------
% 104.96/16.49 % (9143)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_8750 for (2853ds/2812Mi)
% 106.24/16.76 % (9129)Instruction limit reached!
% 106.24/16.76 % (9129)------------------------------
% 106.24/16.76 % (9129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.24/16.76 % (9129)Termination reason: Unknown
% 106.24/16.76 % (9129)Termination phase: Saturation
% 106.24/16.76
% 106.24/16.76 % (9129)Memory used [KB]: 21236
% 106.24/16.76 % (9129)Time elapsed: 2.427 s
% 106.24/16.76 % (9129)Instructions burned: 3710 (million)
% 106.24/16.76 % (9129)------------------------------
% 106.24/16.76 % (9129)------------------------------
% 106.24/16.79 % (9144)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_8750 for (2850ds/4604Mi)
% 106.94/16.95 % (9141)Instruction limit reached!
% 106.94/16.95 % (9141)------------------------------
% 106.94/16.95 % (9141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.94/16.95 % (9141)Termination reason: Unknown
% 106.94/16.95 % (9141)Termination phase: Saturation
% 106.94/16.95
% 106.94/16.95 % (9141)Memory used [KB]: 12025
% 106.94/16.95 % (9141)Time elapsed: 0.858 s
% 106.94/16.95 % (9141)Instructions burned: 1516 (million)
% 106.94/16.95 % (9141)------------------------------
% 106.94/16.95 % (9141)------------------------------
% 106.94/16.98 % (9145)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_8750 for (2848ds/2678Mi)
% 109.92/17.07 % (9137)Instruction limit reached!
% 109.92/17.07 % (9137)------------------------------
% 109.92/17.07 % (9137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 109.92/17.07 % (9137)Termination reason: Unknown
% 109.92/17.07 % (9137)Termination phase: Saturation
% 109.92/17.07
% 109.92/17.07 % (9137)Memory used [KB]: 16758
% 109.92/17.07 % (9137)Time elapsed: 1.805 s
% 109.92/17.08 % (9137)Instructions burned: 3116 (million)
% 109.92/17.08 % (9137)------------------------------
% 109.92/17.08 % (9137)------------------------------
% 109.92/17.10 % (9146)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_8750 for (2847ds/643Mi)
% 112.21/17.45 % (9146)Instruction limit reached!
% 112.21/17.45 % (9146)------------------------------
% 112.21/17.45 % (9146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 112.21/17.45 % (9146)Termination reason: Unknown
% 112.21/17.45 % (9146)Termination phase: Saturation
% 112.21/17.45
% 112.21/17.45 % (9146)Memory used [KB]: 9083
% 112.21/17.45 % (9146)Time elapsed: 0.356 s
% 112.21/17.45 % (9146)Instructions burned: 644 (million)
% 112.21/17.45 % (9146)------------------------------
% 112.21/17.45 % (9146)------------------------------
% 112.21/17.48 % (9147)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_8750 for (2843ds/458Mi)
% 112.21/17.48 % (9142)Instruction limit reached!
% 112.21/17.48 % (9142)------------------------------
% 112.21/17.48 % (9142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 112.21/17.48 % (9142)Termination reason: Unknown
% 112.21/17.48 % (9142)Termination phase: Saturation
% 112.21/17.48
% 112.21/17.48 % (9142)Memory used [KB]: 13176
% 112.21/17.48 % (9142)Time elapsed: 1.344 s
% 112.21/17.48 % (9142)Instructions burned: 2321 (million)
% 112.21/17.48 % (9142)------------------------------
% 112.21/17.48 % (9142)------------------------------
% 113.20/17.51 % (9148)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_8750 for (2843ds/2546Mi)
% 113.71/17.68 % (9140)Instruction limit reached!
% 113.71/17.68 % (9140)------------------------------
% 113.71/17.68 % (9140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 113.71/17.68 % (9140)Termination reason: Unknown
% 113.71/17.68 % (9140)Termination phase: Saturation
% 113.71/17.68
% 113.71/17.68 % (9140)Memory used [KB]: 18166
% 113.71/17.68 % (9140)Time elapsed: 1.669 s
% 113.71/17.68 % (9140)Instructions burned: 2869 (million)
% 113.71/17.68 % (9140)------------------------------
% 113.71/17.68 % (9140)------------------------------
% 114.20/17.71 % (9149)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_8750 for (2841ds/1432Mi)
% 114.20/17.73 % (9147)Instruction limit reached!
% 114.20/17.73 % (9147)------------------------------
% 114.20/17.73 % (9147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.20/17.73 % (9147)Termination reason: Unknown
% 114.20/17.73 % (9147)Termination phase: Saturation
% 114.20/17.73
% 114.20/17.73 % (9147)Memory used [KB]: 7931
% 114.20/17.73 % (9147)Time elapsed: 0.258 s
% 114.20/17.73 % (9147)Instructions burned: 458 (million)
% 114.20/17.73 % (9147)------------------------------
% 114.20/17.73 % (9147)------------------------------
% 114.20/17.76 % (9150)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_8750 for (2840ds/386Mi)
% 114.88/17.87 % (9128)Instruction limit reached!
% 114.88/17.87 % (9128)------------------------------
% 114.88/17.87 % (9128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.88/17.87 % (9128)Termination reason: Unknown
% 114.88/17.87 % (9128)Termination phase: Saturation
% 114.88/17.87
% 114.88/17.87 % (9128)Memory used [KB]: 14583
% 114.88/17.87 % (9128)Time elapsed: 4.082 s
% 114.88/17.87 % (9128)Instructions burned: 7258 (million)
% 114.88/17.87 % (9128)------------------------------
% 114.88/17.87 % (9128)------------------------------
% 114.88/17.89 % (9151)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_8750 for (2839ds/360Mi)
% 115.26/17.97 % (9150)Instruction limit reached!
% 115.26/17.97 % (9150)------------------------------
% 115.26/17.97 % (9150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.26/17.97 % (9150)Termination reason: Unknown
% 115.26/17.97 % (9150)Termination phase: Saturation
% 115.26/17.97
% 115.26/17.97 % (9150)Memory used [KB]: 8187
% 115.26/17.98 % (9150)Time elapsed: 0.221 s
% 115.26/17.98 % (9150)Instructions burned: 386 (million)
% 115.26/17.98 % (9150)------------------------------
% 115.26/17.98 % (9150)------------------------------
% 115.26/18.00 % (9152)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_8750 for (2838ds/5446Mi)
% 116.91/18.10 % (9151)Instruction limit reached!
% 116.91/18.10 % (9151)------------------------------
% 116.91/18.10 % (9151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 116.91/18.10 % (9151)Termination reason: Unknown
% 116.91/18.10 % (9151)Termination phase: Saturation
% 116.91/18.10
% 116.91/18.10 % (9151)Memory used [KB]: 8059
% 116.91/18.10 % (9151)Time elapsed: 0.208 s
% 116.91/18.10 % (9151)Instructions burned: 360 (million)
% 116.91/18.10 % (9151)------------------------------
% 116.91/18.10 % (9151)------------------------------
% 116.91/18.12 % (9153)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_8750 for (2837ds/2573Mi)
% 117.62/18.18 % (9143)Instruction limit reached!
% 117.62/18.18 % (9143)------------------------------
% 117.62/18.18 % (9143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 117.62/18.18 % (9143)Termination reason: Unknown
% 117.62/18.18 % (9143)Termination phase: Saturation
% 117.62/18.18
% 117.62/18.18 % (9143)Memory used [KB]: 14328
% 117.62/18.18 % (9143)Time elapsed: 1.693 s
% 117.62/18.18 % (9143)Instructions burned: 2813 (million)
% 117.62/18.18 % (9143)------------------------------
% 117.62/18.18 % (9143)------------------------------
% 118.04/18.21 % (9154)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_8750 for (2836ds/2655Mi)
% 119.55/18.51 % (9145)Instruction limit reached!
% 119.55/18.51 % (9145)------------------------------
% 119.55/18.51 % (9145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.55/18.51 % (9145)Termination reason: Unknown
% 119.55/18.51 % (9145)Termination phase: Saturation
% 119.55/18.51
% 119.55/18.51 % (9145)Memory used [KB]: 10746
% 119.55/18.51 % (9145)Time elapsed: 1.533 s
% 119.55/18.51 % (9145)Instructions burned: 2679 (million)
% 119.55/18.51 % (9145)------------------------------
% 119.55/18.51 % (9145)------------------------------
% 119.55/18.53 % (9155)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_8750 for (2833ds/2781Mi)
% 119.55/18.54 % (9149)Instruction limit reached!
% 119.55/18.54 % (9149)------------------------------
% 119.55/18.54 % (9149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.55/18.54 % (9149)Termination reason: Unknown
% 119.55/18.54 % (9149)Termination phase: Saturation
% 119.55/18.54
% 119.55/18.54 % (9149)Memory used [KB]: 12025
% 119.55/18.54 % (9149)Time elapsed: 0.838 s
% 119.55/18.54 % (9149)Instructions burned: 1432 (million)
% 119.55/18.54 % (9149)------------------------------
% 119.55/18.54 % (9149)------------------------------
% 119.55/18.57 % (9156)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_8750 for (2832ds/307Mi)
% 120.24/18.73 % (9156)Instruction limit reached!
% 120.24/18.73 % (9156)------------------------------
% 120.24/18.73 % (9156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 120.24/18.73 % (9156)Termination reason: Unknown
% 120.24/18.73 % (9156)Termination phase: Saturation
% 120.24/18.73
% 120.24/18.73 % (9156)Memory used [KB]: 7419
% 120.24/18.73 % (9156)Time elapsed: 0.169 s
% 120.24/18.73 % (9156)Instructions burned: 307 (million)
% 120.24/18.73 % (9156)------------------------------
% 120.24/18.73 % (9156)------------------------------
% 120.24/18.76 % (9157)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_8750 for (2831ds/1548Mi)
% 123.91/19.08 % (9148)Instruction limit reached!
% 123.91/19.08 % (9148)------------------------------
% 123.91/19.08 % (9148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 123.91/19.08 % (9148)Termination reason: Unknown
% 123.91/19.08 % (9148)Termination phase: Saturation
% 123.91/19.08
% 123.91/19.08 % (9148)Memory used [KB]: 12153
% 123.91/19.08 % (9148)Time elapsed: 1.563 s
% 123.91/19.08 % (9148)Instructions burned: 2546 (million)
% 123.91/19.08 % (9148)------------------------------
% 123.91/19.08 % (9148)------------------------------
% 123.91/19.10 % (9158)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_8750 for (2827ds/5214Mi)
% 125.01/19.28 % (9144)Instruction limit reached!
% 125.01/19.28 % (9144)------------------------------
% 125.01/19.28 % (9144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.01/19.28 % (9144)Termination reason: Unknown
% 125.01/19.28 % (9144)Termination phase: Saturation
% 125.01/19.28
% 125.01/19.28 % (9144)Memory used [KB]: 12409
% 125.01/19.28 % (9144)Time elapsed: 2.497 s
% 125.01/19.28 % (9144)Instructions burned: 4605 (million)
% 125.01/19.28 % (9144)------------------------------
% 125.01/19.28 % (9144)------------------------------
% 125.62/19.31 % (9159)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_8750 for (2825ds/3201Mi)
% 127.13/19.60 % (9153)Instruction limit reached!
% 127.13/19.60 % (9153)------------------------------
% 127.13/19.60 % (9153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.13/19.60 % (9153)Termination reason: Unknown
% 127.13/19.60 % (9153)Termination phase: Saturation
% 127.13/19.60
% 127.13/19.60 % (9153)Memory used [KB]: 17014
% 127.13/19.60 % (9153)Time elapsed: 1.482 s
% 127.13/19.60 % (9153)Instructions burned: 2573 (million)
% 127.13/19.60 % (9153)------------------------------
% 127.13/19.60 % (9153)------------------------------
% 127.13/19.63 % (9160)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_8750 for (2822ds/454Mi)
% 127.13/19.64 % (9157)Instruction limit reached!
% 127.13/19.64 % (9157)------------------------------
% 127.13/19.64 % (9157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.13/19.64 % (9157)Termination reason: Unknown
% 127.13/19.64 % (9157)Termination phase: Saturation
% 127.13/19.64
% 127.13/19.64 % (9157)Memory used [KB]: 10874
% 127.13/19.64 % (9157)Time elapsed: 0.890 s
% 127.13/19.64 % (9157)Instructions burned: 1549 (million)
% 127.13/19.64 % (9157)------------------------------
% 127.13/19.64 % (9157)------------------------------
% 127.13/19.67 % (9161)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_8750 for (2821ds/3049Mi)
% 127.49/19.79 % (9154)Instruction limit reached!
% 127.49/19.79 % (9154)------------------------------
% 127.49/19.79 % (9154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.49/19.79 % (9154)Termination reason: Unknown
% 127.49/19.79 % (9154)Termination phase: Saturation
% 127.49/19.79
% 127.49/19.79 % (9154)Memory used [KB]: 15607
% 127.49/19.79 % (9154)Time elapsed: 1.586 s
% 127.49/19.79 % (9154)Instructions burned: 2655 (million)
% 127.49/19.79 % (9154)------------------------------
% 127.49/19.79 % (9154)------------------------------
% 127.80/19.82 % (9162)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_8750 for (2820ds/7311Mi)
% 127.80/19.88 % (9160)Instruction limit reached!
% 127.80/19.88 % (9160)------------------------------
% 127.80/19.88 % (9160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.80/19.88 % (9160)Termination reason: Unknown
% 127.80/19.88 % (9160)Termination phase: Saturation
% 127.80/19.88
% 127.80/19.88 % (9160)Memory used [KB]: 12920
% 127.80/19.88 % (9160)Time elapsed: 0.255 s
% 127.80/19.88 % (9160)Instructions burned: 454 (million)
% 127.80/19.88 % (9160)------------------------------
% 127.80/19.88 % (9160)------------------------------
% 128.27/19.90 % (9163)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_8750 for (2819ds/6804Mi)
% 128.27/19.97 % (9163)Refutation not found, incomplete strategy
% 128.27/19.97 % (9163)------------------------------
% 128.27/19.97 % (9163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 128.27/19.97 % (9163)Termination reason: Refutation not found, incomplete strategy
% 128.27/19.97
% 128.27/19.97
% 128.27/19.97 % (9163)Memory used [KB]: 7547
% 128.27/19.97 % (9163)Time elapsed: 0.068 s
% 128.27/19.97 % (9163)Instructions burned: 115 (million)
% 128.27/19.97 % (9163)------------------------------
% 128.27/19.97 % (9163)------------------------------
% 128.27/19.99 % (9164)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_8750 for (2818ds/1683Mi)
% 131.61/20.17 % (9155)Instruction limit reached!
% 131.61/20.17 % (9155)------------------------------
% 131.61/20.17 % (9155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 131.61/20.17 % (9155)Termination reason: Unknown
% 131.61/20.17 % (9155)Termination phase: Saturation
% 131.61/20.17
% 131.61/20.17 % (9155)Memory used [KB]: 5245
% 131.61/20.17 % (9155)Time elapsed: 1.638 s
% 131.61/20.17 % (9155)Instructions burned: 2781 (million)
% 131.61/20.17 % (9155)------------------------------
% 131.61/20.17 % (9155)------------------------------
% 131.61/20.19 % (9165)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_8750 for (2816ds/4688Mi)
% 136.28/20.99 % (9164)Instruction limit reached!
% 136.28/20.99 % (9164)------------------------------
% 136.28/20.99 % (9164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 136.28/20.99 % (9164)Termination reason: Unknown
% 136.28/20.99 % (9164)Termination phase: Saturation
% 136.28/20.99
% 136.28/20.99 % (9164)Memory used [KB]: 11513
% 136.28/20.99 % (9164)Time elapsed: 1.0000 s
% 136.28/20.99 % (9164)Instructions burned: 1683 (million)
% 136.28/20.99 % (9164)------------------------------
% 136.28/20.99 % (9164)------------------------------
% 136.28/21.01 % (9166)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_8750 for (2808ds/2207Mi)
% 137.88/21.05 % (9162)Refutation not found, non-redundant clauses discarded% (9162)------------------------------
% 137.88/21.05 % (9162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 137.88/21.05 % (9162)Termination reason: Refutation not found, non-redundant clauses discarded
% 137.88/21.05
% 137.88/21.05 % (9162)Memory used [KB]: 13432
% 137.88/21.05 % (9162)Time elapsed: 1.234 s
% 137.88/21.05 % (9162)Instructions burned: 2108 (million)
% 137.88/21.05 % (9162)------------------------------
% 137.88/21.05 % (9162)------------------------------
% 137.88/21.07 % (9167)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_8750 for (2807ds/8216Mi)
% 138.52/21.17 % (9159)Instruction limit reached!
% 138.52/21.17 % (9159)------------------------------
% 138.52/21.17 % (9159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 138.52/21.17 % (9159)Termination reason: Unknown
% 138.52/21.17 % (9159)Termination phase: Saturation
% 138.52/21.17
% 138.52/21.17 % (9159)Memory used [KB]: 13176
% 138.52/21.17 % (9159)Time elapsed: 1.863 s
% 138.52/21.17 % (9159)Instructions burned: 3201 (million)
% 138.52/21.17 % (9159)------------------------------
% 138.52/21.17 % (9159)------------------------------
% 138.52/21.19 % (9168)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_8750 for (2806ds/430Mi)
% 138.93/21.28 % (9152)Instruction limit reached!
% 138.93/21.28 % (9152)------------------------------
% 138.93/21.28 % (9152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 138.93/21.28 % (9152)Termination reason: Unknown
% 138.93/21.28 % (9152)Termination phase: Saturation
% 138.93/21.28
% 138.93/21.28 % (9152)Memory used [KB]: 24306
% 138.93/21.28 % (9152)Time elapsed: 3.289 s
% 138.93/21.28 % (9152)Instructions burned: 5446 (million)
% 138.93/21.28 % (9152)------------------------------
% 138.93/21.28 % (9152)------------------------------
% 139.42/21.31 % (9169)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_8750 for (2805ds/2012Mi)
% 139.81/21.40 % (9161)Instruction limit reached!
% 139.81/21.40 % (9161)------------------------------
% 139.81/21.40 % (9161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 139.81/21.40 % (9161)Termination reason: Unknown
% 139.81/21.40 % (9161)Termination phase: Saturation
% 139.81/21.40
% 139.81/21.40 % (9161)Memory used [KB]: 9466
% 139.81/21.40 % (9161)Time elapsed: 1.750 s
% 139.81/21.40 % (9161)Instructions burned: 3049 (million)
% 139.81/21.40 % (9161)------------------------------
% 139.81/21.40 % (9161)------------------------------
% 139.81/21.42 % (9168)Instruction limit reached!
% 139.81/21.42 % (9168)------------------------------
% 139.81/21.42 % (9168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 139.81/21.42 % (9168)Termination reason: Unknown
% 139.81/21.42 % (9168)Termination phase: Saturation
% 139.81/21.42
% 139.81/21.42 % (9168)Memory used [KB]: 7675
% 139.81/21.42 % (9168)Time elapsed: 0.234 s
% 139.81/21.42 % (9168)Instructions burned: 430 (million)
% 139.81/21.42 % (9168)------------------------------
% 139.81/21.42 % (9168)------------------------------
% 139.81/21.42 % (9170)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_8750 for (2804ds/631Mi)
% 139.81/21.45 % (9171)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_8750 for (2804ds/8785Mi)
% 141.30/21.81 % (9170)Instruction limit reached!
% 141.30/21.81 % (9170)------------------------------
% 141.30/21.81 % (9170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 141.30/21.81 % (9170)Termination reason: Unknown
% 141.30/21.81 % (9170)Termination phase: Saturation
% 141.30/21.81
% 141.30/21.81 % (9170)Memory used [KB]: 11769
% 141.30/21.81 % (9170)Time elapsed: 0.388 s
% 141.30/21.81 % (9170)Instructions burned: 631 (million)
% 141.30/21.81 % (9170)------------------------------
% 141.30/21.81 % (9170)------------------------------
% 141.30/21.84 % (9172)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_8750 for (2800ds/739Mi)
% 142.01/22.00 % (9158)Instruction limit reached!
% 142.01/22.00 % (9158)------------------------------
% 142.01/22.00 % (9158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 142.01/22.00 % (9158)Termination reason: Unknown
% 142.01/22.00 % (9158)Termination phase: Saturation
% 142.01/22.00
% 142.01/22.00 % (9158)Memory used [KB]: 15095
% 142.01/22.00 % (9158)Time elapsed: 2.905 s
% 142.01/22.00 % (9158)Instructions burned: 5215 (million)
% 142.01/22.00 % (9158)------------------------------
% 142.01/22.00 % (9158)------------------------------
% 144.76/22.03 % (9173)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_8750 for (2798ds/5473Mi)
% 145.89/22.29 % (9172)Instruction limit reached!
% 145.89/22.29 % (9172)------------------------------
% 145.89/22.29 % (9172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 145.89/22.29 % (9172)Termination reason: Unknown
% 145.89/22.29 % (9172)Termination phase: Saturation
% 145.89/22.29
% 145.89/22.29 % (9172)Memory used [KB]: 8827
% 145.89/22.29 % (9172)Time elapsed: 0.455 s
% 145.89/22.29 % (9172)Instructions burned: 740 (million)
% 145.89/22.29 % (9172)------------------------------
% 145.89/22.29 % (9172)------------------------------
% 146.49/22.31 % (9174)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_8750 for (2795ds/43570Mi)
% 146.49/22.32 % (9166)Instruction limit reached!
% 146.49/22.32 % (9166)------------------------------
% 146.49/22.32 % (9166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 146.49/22.32 % (9166)Termination reason: Unknown
% 146.49/22.32 % (9166)Termination phase: Saturation
% 146.49/22.32
% 146.49/22.32 % (9166)Memory used [KB]: 14072
% 146.49/22.32 % (9166)Time elapsed: 1.335 s
% 146.49/22.32 % (9166)Instructions burned: 2208 (million)
% 146.49/22.32 % (9166)------------------------------
% 146.49/22.32 % (9166)------------------------------
% 146.49/22.34 % (9174)Refutation not found, incomplete strategy
% 146.49/22.34 % (9174)------------------------------
% 146.49/22.34 % (9174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 146.49/22.34 % (9174)Termination reason: Refutation not found, incomplete strategy
% 146.49/22.34
% 146.49/22.34
% 146.49/22.34 % (9174)Memory used [KB]: 6524
% 146.49/22.34 % (9174)Time elapsed: 0.027 s
% 146.49/22.34 % (9174)Instructions burned: 43 (million)
% 146.49/22.34 % (9174)------------------------------
% 146.49/22.34 % (9174)------------------------------
% 146.49/22.35 % (9175)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_8750 for (2795ds/8382Mi)
% 146.49/22.36 % (9176)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_8750 for (2794ds/407Mi)
% 147.38/22.54 % (9169)Instruction limit reached!
% 147.38/22.54 % (9169)------------------------------
% 147.38/22.54 % (9169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.38/22.54 % (9169)Termination reason: Unknown
% 147.38/22.54 % (9169)Termination phase: Saturation
% 147.38/22.54
% 147.38/22.54 % (9169)Memory used [KB]: 19701
% 147.38/22.54 % (9169)Time elapsed: 1.228 s
% 147.38/22.54 % (9169)Instructions burned: 2013 (million)
% 147.38/22.54 % (9169)------------------------------
% 147.38/22.54 % (9169)------------------------------
% 147.38/22.54 % (9165)Instruction limit reached!
% 147.38/22.54 % (9165)------------------------------
% 147.38/22.54 % (9165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.38/22.54 % (9165)Termination reason: Unknown
% 147.38/22.54 % (9165)Termination phase: Saturation
% 147.38/22.54
% 147.38/22.54 % (9165)Memory used [KB]: 10874
% 147.38/22.54 % (9165)Time elapsed: 2.364 s
% 147.38/22.54 % (9165)Instructions burned: 4689 (million)
% 147.38/22.54 % (9165)------------------------------
% 147.38/22.54 % (9165)------------------------------
% 147.38/22.55 % (9176)Instruction limit reached!
% 147.38/22.55 % (9176)------------------------------
% 147.38/22.55 % (9176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.38/22.55 % (9176)Termination reason: Unknown
% 147.38/22.55 % (9176)Termination phase: Saturation
% 147.38/22.55
% 147.38/22.55 % (9176)Memory used [KB]: 8443
% 147.38/22.55 % (9176)Time elapsed: 0.189 s
% 147.38/22.55 % (9176)Instructions burned: 408 (million)
% 147.38/22.55 % (9176)------------------------------
% 147.38/22.55 % (9176)------------------------------
% 147.38/22.55 % (9177)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_8750 for (2792ds/2971Mi)
% 147.38/22.56 % (9178)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_8750 for (2792ds/9822Mi)
% 147.38/22.56 % (9179)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_8750 for (2792ds/8425Mi)
% 154.48/23.49 % (9177)Instruction limit reached!
% 154.48/23.49 % (9177)------------------------------
% 154.48/23.49 % (9177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 154.48/23.49 % (9177)Termination reason: Unknown
% 154.48/23.49 % (9177)Termination phase: Saturation
% 154.48/23.49
% 154.48/23.49 % (9177)Memory used [KB]: 17398
% 154.48/23.49 % (9177)Time elapsed: 0.939 s
% 154.48/23.49 % (9177)Instructions burned: 2972 (million)
% 154.48/23.49 % (9177)------------------------------
% 154.48/23.49 % (9177)------------------------------
% 154.48/23.50 % (9409)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_8750 for (2783ds/3107Mi)
% 156.99/23.84 % (9173)Instruction limit reached!
% 156.99/23.84 % (9173)------------------------------
% 156.99/23.84 % (9173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 156.99/23.84 % (9173)Termination reason: Unknown
% 156.99/23.84 % (9173)Termination phase: Saturation
% 156.99/23.84
% 156.99/23.84 % (9173)Memory used [KB]: 8699
% 156.99/23.84 % (9173)Time elapsed: 1.812 s
% 156.99/23.84 % (9173)Instructions burned: 5476 (million)
% 156.99/23.84 % (9173)------------------------------
% 156.99/23.84 % (9173)------------------------------
% 156.99/23.85 % (9410)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_8750 for (2779ds/7967Mi)
% 160.80/24.32 % (9167)Instruction limit reached!
% 160.80/24.32 % (9167)------------------------------
% 160.80/24.32 % (9167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 160.80/24.32 % (9167)Termination reason: Unknown
% 160.80/24.32 % (9167)Termination phase: Saturation
% 160.80/24.32
% 160.80/24.32 % (9167)Memory used [KB]: 16886
% 160.80/24.32 % (9167)Time elapsed: 3.270 s
% 160.80/24.32 % (9167)Instructions burned: 8218 (million)
% 160.80/24.32 % (9167)------------------------------
% 160.80/24.32 % (9167)------------------------------
% 160.80/24.33 % (9411)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_8750 for (2775ds/3629Mi)
% 161.43/24.47 % (9409)Refutation not found, non-redundant clauses discarded% (9409)------------------------------
% 161.43/24.47 % (9409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 161.43/24.47 % (9409)Termination reason: Refutation not found, non-redundant clauses discarded
% 161.43/24.47
% 161.43/24.47 % (9409)Memory used [KB]: 11513
% 161.43/24.47 % (9409)Time elapsed: 0.976 s
% 161.43/24.47 % (9409)Instructions burned: 3051 (million)
% 161.43/24.47 % (9409)------------------------------
% 161.43/24.47 % (9409)------------------------------
% 161.43/24.48 % (9412)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_8750 for (2773ds/939Mi)
% 162.53/24.61 % (9171)Instruction limit reached!
% 162.53/24.61 % (9171)------------------------------
% 162.53/24.61 % (9171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 162.53/24.61 % (9171)Termination reason: Unknown
% 162.53/24.61 % (9171)Termination phase: Saturation
% 162.53/24.61
% 162.53/24.61 % (9171)Memory used [KB]: 20980
% 162.53/24.61 % (9171)Time elapsed: 3.166 s
% 162.53/24.61 % (9171)Instructions burned: 8786 (million)
% 162.53/24.61 % (9171)------------------------------
% 162.53/24.61 % (9171)------------------------------
% 162.53/24.62 % (9413)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_8750 for (2772ds/1188Mi)
% 162.95/24.78 % (9412)Instruction limit reached!
% 162.95/24.78 % (9412)------------------------------
% 162.95/24.78 % (9412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 162.95/24.78 % (9412)Termination reason: Unknown
% 162.95/24.78 % (9412)Termination phase: Saturation
% 162.95/24.78
% 162.95/24.78 % (9412)Memory used [KB]: 10490
% 162.95/24.78 % (9412)Time elapsed: 0.316 s
% 162.95/24.78 % (9412)Instructions burned: 940 (million)
% 162.95/24.78 % (9412)------------------------------
% 162.95/24.78 % (9412)------------------------------
% 162.95/24.79 % (9414)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_8750 for (2770ds/3205Mi)
% 164.07/25.00 % (9413)Instruction limit reached!
% 164.07/25.00 % (9413)------------------------------
% 164.07/25.00 % (9413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 164.07/25.00 % (9413)Termination reason: Unknown
% 164.07/25.00 % (9413)Termination phase: Saturation
% 164.07/25.00
% 164.07/25.00 % (9413)Memory used [KB]: 9978
% 164.07/25.00 % (9413)Time elapsed: 0.404 s
% 164.07/25.00 % (9413)Instructions burned: 1188 (million)
% 164.07/25.00 % (9413)------------------------------
% 164.07/25.00 % (9413)------------------------------
% 164.07/25.01 % (9415)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_8750 for (2768ds/865Mi)
% 165.88/25.06 % (9175)Instruction limit reached!
% 165.88/25.06 % (9175)------------------------------
% 165.88/25.06 % (9175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 165.88/25.06 % (9175)Termination reason: Unknown
% 165.88/25.06 % (9175)Termination phase: Saturation
% 165.88/25.06
% 165.88/25.06 % (9175)Memory used [KB]: 19573
% 165.88/25.06 % (9175)Time elapsed: 2.720 s
% 165.88/25.06 % (9175)Instructions burned: 8383 (million)
% 165.88/25.06 % (9175)------------------------------
% 165.88/25.06 % (9175)------------------------------
% 165.88/25.08 % (9416)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_8750 for (2767ds/7469Mi)
% 166.43/25.18 % (9179)Instruction limit reached!
% 166.43/25.18 % (9179)------------------------------
% 166.43/25.18 % (9179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 166.43/25.18 % (9179)Termination reason: Unknown
% 166.43/25.18 % (9179)Termination phase: Saturation
% 166.43/25.18
% 166.43/25.18 % (9179)Memory used [KB]: 14456
% 166.43/25.18 % (9179)Time elapsed: 2.624 s
% 166.43/25.18 % (9179)Instructions burned: 8427 (million)
% 166.43/25.18 % (9179)------------------------------
% 166.43/25.18 % (9179)------------------------------
% 166.43/25.19 % (9417)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_8750 for (2766ds/4165Mi)
% 166.81/25.28 % (9415)Instruction limit reached!
% 166.81/25.28 % (9415)------------------------------
% 166.81/25.28 % (9415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 166.81/25.28 % (9415)Termination reason: Unknown
% 166.81/25.28 % (9415)Termination phase: Saturation
% 166.81/25.28
% 166.81/25.28 % (9415)Memory used [KB]: 9594
% 166.81/25.28 % (9415)Time elapsed: 0.274 s
% 166.81/25.28 % (9415)Instructions burned: 866 (million)
% 166.81/25.28 % (9415)------------------------------
% 166.81/25.28 % (9415)------------------------------
% 166.81/25.29 % (9418)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_8750 for (2765ds/13468Mi)
% 167.89/25.48 % (9411)Instruction limit reached!
% 167.89/25.48 % (9411)------------------------------
% 167.89/25.48 % (9411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 167.89/25.48 % (9411)Termination reason: Unknown
% 167.89/25.48 % (9411)Termination phase: Saturation
% 167.89/25.48
% 167.89/25.48 % (9411)Memory used [KB]: 15735
% 167.89/25.48 % (9411)Time elapsed: 1.171 s
% 167.89/25.48 % (9411)Instructions burned: 3631 (million)
% 167.89/25.48 % (9411)------------------------------
% 167.89/25.48 % (9411)------------------------------
% 167.89/25.49 % (9419)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_8750 for (2763ds/2635Mi)
% 168.58/25.61 % (9178)Instruction limit reached!
% 168.58/25.61 % (9178)------------------------------
% 168.58/25.61 % (9178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 168.58/25.61 % (9178)Termination reason: Unknown
% 168.58/25.61 % (9178)Termination phase: Saturation
% 168.58/25.61
% 168.58/25.61 % (9178)Memory used [KB]: 15351
% 168.58/25.61 % (9178)Time elapsed: 3.058 s
% 168.58/25.61 % (9178)Instructions burned: 9822 (million)
% 168.58/25.61 % (9178)------------------------------
% 168.58/25.61 % (9178)------------------------------
% 168.58/25.62 % (9420)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_8750 for (2762ds/631Mi)
% 169.01/25.81 % (9414)Instruction limit reached!
% 169.01/25.81 % (9414)------------------------------
% 169.01/25.81 % (9414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 169.01/25.81 % (9414)Termination reason: Unknown
% 169.01/25.81 % (9414)Termination phase: Saturation
% 169.01/25.81
% 169.01/25.81 % (9414)Memory used [KB]: 13432
% 169.01/25.81 % (9414)Time elapsed: 1.023 s
% 169.01/25.81 % (9414)Instructions burned: 3207 (million)
% 169.01/25.81 % (9414)------------------------------
% 169.01/25.81 % (9414)------------------------------
% 169.01/25.81 % (9420)Instruction limit reached!
% 169.01/25.81 % (9420)------------------------------
% 169.01/25.81 % (9420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 169.01/25.81 % (9420)Termination reason: Unknown
% 169.01/25.81 % (9420)Termination phase: Saturation
% 169.01/25.81
% 169.01/25.81 % (9420)Memory used [KB]: 9083
% 169.01/25.81 % (9420)Time elapsed: 0.192 s
% 169.01/25.81 % (9420)Instructions burned: 631 (million)
% 169.01/25.81 % (9420)------------------------------
% 169.01/25.81 % (9420)------------------------------
% 169.01/25.82 % (9421)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_8750 for (2760ds/15557Mi)
% 169.01/25.82 % (9422)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_8750 for (2760ds/2142Mi)
% 174.82/26.32 % (9410)Instruction limit reached!
% 174.82/26.32 % (9410)------------------------------
% 174.82/26.32 % (9410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 174.82/26.32 % (9410)Termination reason: Unknown
% 174.82/26.32 % (9410)Termination phase: Saturation
% 174.82/26.32
% 174.82/26.32 % (9410)Memory used [KB]: 19573
% 174.82/26.32 % (9410)Time elapsed: 2.475 s
% 174.82/26.32 % (9410)Instructions burned: 7970 (million)
% 174.82/26.32 % (9410)------------------------------
% 174.82/26.32 % (9410)------------------------------
% 174.82/26.33 % (9419)Instruction limit reached!
% 174.82/26.33 % (9419)------------------------------
% 174.82/26.33 % (9419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 174.82/26.33 % (9419)Termination reason: Unknown
% 174.82/26.33 % (9419)Termination phase: Saturation
% 174.82/26.33
% 174.82/26.33 % (9419)Memory used [KB]: 12025
% 174.82/26.33 % (9419)Time elapsed: 0.839 s
% 174.82/26.33 % (9419)Instructions burned: 2635 (million)
% 174.82/26.33 % (9419)------------------------------
% 174.82/26.33 % (9419)------------------------------
% 174.82/26.33 % (9423)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_8750 for (2755ds/5624Mi)
% 174.82/26.34 % (9424)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_8750 for (2755ds/1665Mi)
% 175.92/26.51 % (9422)Instruction limit reached!
% 175.92/26.51 % (9422)------------------------------
% 175.92/26.51 % (9422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 175.92/26.51 % (9422)Termination reason: Unknown
% 175.92/26.51 % (9422)Termination phase: Saturation
% 175.92/26.51
% 175.92/26.51 % (9422)Memory used [KB]: 9850
% 175.92/26.51 % (9422)Time elapsed: 0.683 s
% 175.92/26.51 % (9422)Instructions burned: 2142 (million)
% 175.92/26.51 % (9422)------------------------------
% 175.92/26.51 % (9422)------------------------------
% 175.92/26.52 % (9425)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_8750 for (2753ds/64912Mi)
% 175.92/26.53 % (9425)Refutation not found, incomplete strategy
% 175.92/26.53 % (9425)------------------------------
% 175.92/26.53 % (9425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 175.92/26.53 % (9425)Termination reason: Refutation not found, incomplete strategy
% 175.92/26.53
% 175.92/26.53
% 175.92/26.53 % (9425)Memory used [KB]: 2046
% 175.92/26.53 % (9425)Time elapsed: 0.013 s
% 175.92/26.53 % (9425)Instructions burned: 36 (million)
% 175.92/26.53 % (9425)------------------------------
% 175.92/26.53 % (9425)------------------------------
% 175.92/26.54 % (9426)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_8750 for (2752ds/7801Mi)
% 175.92/26.55 % (9417)Instruction limit reached!
% 175.92/26.55 % (9417)------------------------------
% 175.92/26.55 % (9417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 175.92/26.55 % (9417)Termination reason: Unknown
% 175.92/26.55 % (9417)Termination phase: Saturation
% 175.92/26.55
% 175.92/26.55 % (9417)Memory used [KB]: 26097
% 175.92/26.55 % (9417)Time elapsed: 1.362 s
% 175.92/26.55 % (9417)Instructions burned: 4167 (million)
% 175.92/26.55 % (9417)------------------------------
% 175.92/26.55 % (9417)------------------------------
% 175.92/26.56 % (9427)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_8750 for (2752ds/15194Mi)
% 176.93/26.85 % (9424)Instruction limit reached!
% 176.93/26.85 % (9424)------------------------------
% 176.93/26.85 % (9424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 176.93/26.85 % (9424)Termination reason: Unknown
% 176.93/26.85 % (9424)Termination phase: Saturation
% 176.93/26.85
% 176.93/26.85 % (9424)Memory used [KB]: 10106
% 176.93/26.85 % (9424)Time elapsed: 0.520 s
% 176.93/26.85 % (9424)Instructions burned: 1665 (million)
% 176.93/26.85 % (9424)------------------------------
% 176.93/26.85 % (9424)------------------------------
% 176.93/26.87 % (9428)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_8750 for (2749ds/6753Mi)
% 177.77/26.90 % (9428)Refutation not found, incomplete strategy
% 177.77/26.90 % (9428)------------------------------
% 177.77/26.90 % (9428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 177.77/26.90 % (9428)Termination reason: Refutation not found, incomplete strategy
% 177.77/26.90
% 177.77/26.90
% 177.77/26.90 % (9428)Memory used [KB]: 7547
% 177.77/26.90 % (9428)Time elapsed: 0.038 s
% 177.77/26.90 % (9428)Instructions burned: 114 (million)
% 177.77/26.90 % (9428)------------------------------
% 177.77/26.90 % (9428)------------------------------
% 177.77/26.91 % (9429)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_8750 for (2749ds/1003Mi)
% 181.17/27.23 % (9429)Instruction limit reached!
% 181.17/27.23 % (9429)------------------------------
% 181.17/27.23 % (9429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 181.17/27.23 % (9429)Termination reason: Unknown
% 181.17/27.23 % (9429)Termination phase: Saturation
% 181.17/27.23
% 181.17/27.23 % (9429)Memory used [KB]: 9083
% 181.17/27.23 % (9429)Time elapsed: 0.316 s
% 181.17/27.23 % (9429)Instructions burned: 1004 (million)
% 181.17/27.23 % (9429)------------------------------
% 181.17/27.23 % (9429)------------------------------
% 181.17/27.24 % (9430)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_8750 for (2746ds/13018Mi)
% 183.01/27.50 % (9416)Instruction limit reached!
% 183.01/27.50 % (9416)------------------------------
% 183.01/27.50 % (9416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 183.01/27.50 % (9416)Termination reason: Unknown
% 183.01/27.50 % (9416)Termination phase: Saturation
% 183.01/27.50
% 183.01/27.50 % (9416)Memory used [KB]: 17014
% 183.01/27.50 % (9416)Time elapsed: 2.429 s
% 183.01/27.50 % (9416)Instructions burned: 7470 (million)
% 183.01/27.50 % (9416)------------------------------
% 183.01/27.50 % (9416)------------------------------
% 183.01/27.51 % (9431)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_8750 for (2743ds/1267Mi)
% 184.53/27.90 % (9431)Instruction limit reached!
% 184.53/27.90 % (9431)------------------------------
% 184.53/27.90 % (9431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 184.53/27.90 % (9431)Termination reason: Unknown
% 184.53/27.90 % (9431)Termination phase: Saturation
% 184.53/27.90
% 184.53/27.90 % (9431)Memory used [KB]: 10618
% 184.53/27.90 % (9431)Time elapsed: 0.384 s
% 184.53/27.90 % (9431)Instructions burned: 1269 (million)
% 184.53/27.90 % (9431)------------------------------
% 184.53/27.90 % (9431)------------------------------
% 185.03/27.91 % (9432)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_8750 for (2739ds/2570Mi)
% 186.93/28.12 % (9423)Instruction limit reached!
% 186.93/28.12 % (9423)------------------------------
% 186.93/28.12 % (9423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 186.93/28.12 % (9423)Termination reason: Unknown
% 186.93/28.12 % (9423)Termination phase: Saturation
% 186.93/28.12
% 186.93/28.12 % (9423)Memory used [KB]: 13304
% 186.93/28.12 % (9423)Time elapsed: 1.813 s
% 186.93/28.12 % (9423)Instructions burned: 5624 (million)
% 186.93/28.12 % (9423)------------------------------
% 186.93/28.12 % (9423)------------------------------
% 187.68/28.13 % (9433)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_8750 for (2737ds/13163Mi)
% 191.13/28.70 % (9432)Instruction limit reached!
% 191.13/28.70 % (9432)------------------------------
% 191.13/28.70 % (9432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 191.13/28.70 % (9432)Termination reason: Unknown
% 191.13/28.70 % (9432)Termination phase: Saturation
% 191.13/28.70
% 191.13/28.70 % (9432)Memory used [KB]: 15351
% 191.13/28.70 % (9432)Time elapsed: 0.797 s
% 191.13/28.70 % (9432)Instructions burned: 2572 (million)
% 191.13/28.70 % (9432)------------------------------
% 191.13/28.70 % (9432)------------------------------
% 191.13/28.71 % (9434)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_8750 for (2731ds/5087Mi)
% 193.98/29.05 % (9426)Instruction limit reached!
% 193.98/29.05 % (9426)------------------------------
% 193.98/29.05 % (9426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 193.98/29.05 % (9426)Termination reason: Unknown
% 193.98/29.05 % (9426)Termination phase: Saturation
% 193.98/29.05
% 193.98/29.05 % (9426)Memory used [KB]: 31470
% 193.98/29.05 % (9426)Time elapsed: 2.514 s
% 193.98/29.05 % (9426)Instructions burned: 7802 (million)
% 193.98/29.05 % (9426)------------------------------
% 193.98/29.05 % (9426)------------------------------
% 193.98/29.06 % (9435)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_8750 for (2727ds/10380Mi)
% 197.46/29.66 % (9418)Instruction limit reached!
% 197.46/29.66 % (9418)------------------------------
% 197.46/29.66 % (9418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 197.46/29.66 % (9418)Termination reason: Unknown
% 197.46/29.66 % (9418)Termination phase: Saturation
% 197.46/29.66
% 197.46/29.66 % (9418)Memory used [KB]: 22259
% 197.46/29.66 % (9418)Time elapsed: 4.371 s
% 197.46/29.66 % (9418)Instructions burned: 13469 (million)
% 197.46/29.66 % (9418)------------------------------
% 197.46/29.66 % (9418)------------------------------
% 197.46/29.68 % (9627)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_8750 for (2721ds/4218Mi)
% 202.93/30.33 % (9434)Refutation not found, non-redundant clauses discarded% (9434)------------------------------
% 202.93/30.33 % (9434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 202.93/30.33 % (9434)Termination reason: Refutation not found, non-redundant clauses discarded
% 202.93/30.33
% 202.93/30.33 % (9434)Memory used [KB]: 12409
% 202.93/30.33 % (9434)Time elapsed: 1.622 s
% 202.93/30.33 % (9434)Instructions burned: 5016 (million)
% 202.93/30.33 % (9434)------------------------------
% 202.93/30.33 % (9434)------------------------------
% 202.93/30.35 % (9929)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_8750 for (2714ds/3971Mi)
% 203.58/30.44 % (9421)Instruction limit reached!
% 203.58/30.44 % (9421)------------------------------
% 203.58/30.44 % (9421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 203.58/30.44 % (9421)Termination reason: Unknown
% 203.58/30.44 % (9421)Termination phase: Saturation
% 203.58/30.44
% 203.58/30.44 % (9421)Memory used [KB]: 25458
% 203.58/30.44 % (9421)Time elapsed: 4.623 s
% 203.58/30.44 % (9421)Instructions burned: 15558 (million)
% 203.58/30.44 % (9421)------------------------------
% 203.58/30.44 % (9421)------------------------------
% 203.58/30.45 % (9974)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_8750 for (2713ds/14014Mi)
% 206.14/30.95 % (9627)Instruction limit reached!
% 206.14/30.95 % (9627)------------------------------
% 206.14/30.95 % (9627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 206.14/30.95 % (9627)Termination reason: Unknown
% 206.14/30.95 % (9627)Termination phase: Saturation
% 206.14/30.95
% 206.14/30.95 % (9627)Memory used [KB]: 18166
% 206.14/30.95 % (9627)Time elapsed: 1.298 s
% 206.14/30.95 % (9627)Instructions burned: 4219 (million)
% 206.14/30.95 % (9627)------------------------------
% 206.14/30.95 % (9627)------------------------------
% 206.14/30.96 % (10037)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_8750 for (2708ds/8517Mi)
% 209.95/31.32 % (9435)Instruction limit reached!
% 209.95/31.32 % (9435)------------------------------
% 209.95/31.32 % (9435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 209.95/31.32 % (9435)Termination reason: Unknown
% 209.95/31.32 % (9435)Termination phase: Saturation
% 209.95/31.32
% 209.95/31.32 % (9435)Memory used [KB]: 7547
% 209.95/31.32 % (9435)Time elapsed: 2.277 s
% 209.95/31.32 % (9435)Instructions burned: 10381 (million)
% 209.95/31.32 % (9435)------------------------------
% 209.95/31.32 % (9435)------------------------------
% 209.95/31.33 % (10038)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_8750 for (2705ds/10148Mi)
% 210.59/31.40 % (9430)Instruction limit reached!
% 210.59/31.40 % (9430)------------------------------
% 210.59/31.40 % (9430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 210.59/31.40 % (9430)Termination reason: Unknown
% 210.59/31.40 % (9430)Termination phase: Saturation
% 210.59/31.40
% 210.59/31.40 % (9430)Memory used [KB]: 31598
% 210.59/31.40 % (9430)Time elapsed: 4.163 s
% 210.59/31.40 % (9430)Instructions burned: 13018 (million)
% 210.59/31.40 % (9430)------------------------------
% 210.59/31.40 % (9430)------------------------------
% 210.59/31.41 % (10039)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_8750 for (2704ds/9078Mi)
% 210.59/31.42 % (9427)Instruction limit reached!
% 210.59/31.42 % (9427)------------------------------
% 210.59/31.42 % (9427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 210.59/31.42 % (9427)Termination reason: Unknown
% 210.59/31.42 % (9427)Termination phase: Saturation
% 210.59/31.42
% 210.59/31.42 % (9427)Memory used [KB]: 20468
% 210.59/31.42 % (9427)Time elapsed: 4.859 s
% 210.59/31.42 % (9427)Instructions burned: 15194 (million)
% 210.59/31.42 % (9427)------------------------------
% 210.59/31.42 % (9427)------------------------------
% 210.59/31.43 % (10040)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_8750 for (2704ds/16164Mi)
% 211.05/31.52 % (9929)Instruction limit reached!
% 211.05/31.52 % (9929)------------------------------
% 211.05/31.52 % (9929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 211.05/31.52 % (9929)Termination reason: Unknown
% 211.05/31.52 % (9929)Termination phase: Saturation
% 211.05/31.52
% 211.05/31.52 % (9929)Memory used [KB]: 11001
% 211.05/31.52 % (9929)Time elapsed: 1.175 s
% 211.05/31.52 % (9929)Instructions burned: 3971 (million)
% 211.05/31.52 % (9929)------------------------------
% 211.05/31.52 % (9929)------------------------------
% 211.05/31.53 % (10041)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_8750 for (2703ds/6102Mi)
% 215.74/32.18 % (9433)Instruction limit reached!
% 215.74/32.18 % (9433)------------------------------
% 215.74/32.18 % (9433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 215.74/32.18 % (9433)Termination reason: Unknown
% 215.74/32.18 % (9433)Termination phase: Saturation
% 215.74/32.18
% 215.74/32.18 % (9433)Memory used [KB]: 63197
% 215.74/32.18 % (9433)Time elapsed: 4.050 s
% 215.74/32.18 % (9433)Instructions burned: 13163 (million)
% 215.74/32.18 % (9433)------------------------------
% 215.74/32.18 % (9433)------------------------------
% 215.74/32.20 % (10042)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_8750 for (2696ds/10308Mi)
% 223.96/33.39 % (10041)Refutation not found, non-redundant clauses discarded% (10041)------------------------------
% 223.96/33.39 % (10041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 223.96/33.39 % (10041)Termination reason: Refutation not found, non-redundant clauses discarded
% 223.96/33.39
% 223.96/33.39 % (10041)Memory used [KB]: 13560
% 223.96/33.39 % (10041)Time elapsed: 1.865 s
% 223.96/33.39 % (10041)Instructions burned: 5992 (million)
% 223.96/33.39 % (10041)------------------------------
% 223.96/33.39 % (10041)------------------------------
% 224.68/33.40 % (10043)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_8750 for (2684ds/4041Mi)
% 224.68/33.49 % (10037)Refutation not found, non-redundant clauses discarded% (10037)------------------------------
% 224.68/33.49 % (10037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 224.68/33.49 % (10037)Termination reason: Refutation not found, non-redundant clauses discarded
% 224.68/33.49
% 224.68/33.49 % (10037)Memory used [KB]: 17398
% 224.68/33.49 % (10037)Time elapsed: 2.531 s
% 224.68/33.49 % (10037)Instructions burned: 8081 (million)
% 224.68/33.49 % (10037)------------------------------
% 224.68/33.49 % (10037)------------------------------
% 225.30/33.50 % (10044)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_8750 for (2683ds/6901Mi)
% 230.31/34.27 % (10039)Instruction limit reached!
% 230.31/34.27 % (10039)------------------------------
% 230.31/34.27 % (10039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 230.31/34.27 % (10039)Termination reason: Unknown
% 230.31/34.27 % (10039)Termination phase: Saturation
% 230.31/34.27
% 230.31/34.27 % (10039)Memory used [KB]: 21364
% 230.31/34.27 % (10039)Time elapsed: 2.861 s
% 230.31/34.27 % (10039)Instructions burned: 9078 (million)
% 230.31/34.27 % (10039)------------------------------
% 230.31/34.27 % (10039)------------------------------
% 230.31/34.28 % (10045)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on DTF2THF_8750 for (2675ds/5576Mi)
% 231.60/34.43 % (10038)Instruction limit reached!
% 231.60/34.43 % (10038)------------------------------
% 231.60/34.43 % (10038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 231.60/34.43 % (10038)Termination reason: Unknown
% 231.60/34.43 % (10038)Termination phase: Saturation
% 231.60/34.43
% 231.60/34.43 % (10038)Memory used [KB]: 17654
% 231.60/34.43 % (10038)Time elapsed: 3.105 s
% 231.60/34.43 % (10038)Instructions burned: 10149 (million)
% 231.60/34.43 % (10038)------------------------------
% 231.60/34.43 % (10038)------------------------------
% 231.60/34.44 % (10046)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=2014:si=on:rtra=on_0 on DTF2THF_8750 for (2674ds/2014Mi)
% 232.64/34.64 % (10043)Instruction limit reached!
% 232.64/34.64 % (10043)------------------------------
% 232.64/34.64 % (10043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 232.64/34.64 % (10043)Termination reason: Unknown
% 232.64/34.64 % (10043)Termination phase: Saturation
% 232.64/34.64
% 232.64/34.64 % (10043)Memory used [KB]: 14072
% 232.64/34.64 % (10043)Time elapsed: 1.233 s
% 232.64/34.64 % (10043)Instructions burned: 4043 (million)
% 232.64/34.64 % (10043)------------------------------
% 232.64/34.64 % (10043)------------------------------
% 232.64/34.65 % (10047)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_8750 for (2671ds/5115Mi)
% 233.52/34.89 % (10044)First to succeed.
% 232.52/34.90 % (10044)Refutation found. Thanks to Tanya!
% 232.52/34.90 % SZS status Theorem for DTF2THF_8750
% 232.52/34.90 % SZS output start Proof for DTF2THF_8750
% 232.52/34.90 thf(type_def_5, type, int: $tType).
% 232.52/34.90 thf(type_def_7, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 232.52/34.90 thf(type_def_8, type, set: ($tType) > $tType).
% 232.52/34.90 thf(type_def_9, type, real: $tType).
% 232.52/34.90 thf(type_def_10, type, n: $tType).
% 232.52/34.90 thf(type_def_11, type, numeral_num1: $tType).
% 232.52/34.90 thf(func_def_0, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 232.52/34.90 thf(func_def_1, type, numeral_num1: $tType).
% 232.52/34.90 thf(func_def_2, type, real: $tType).
% 232.52/34.90 thf(func_def_3, type, set: ($tType) > $tType).
% 232.52/34.90 thf(func_def_4, type, int: $tType).
% 232.52/34.90 thf(func_def_5, type, n: $tType).
% 232.52/34.90 thf(func_def_6, type, cARD_1: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_7, type, type: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_8, type, one: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_9, type, ring: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_10, type, zero: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_11, type, field: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_12, type, minus: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_13, type, ring_1: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_14, type, ord: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_15, type, ring_char_0: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_16, type, order: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_17, type, group_add: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_18, type, no_bot: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_19, type, no_top: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_20, type, finite_finite: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_21, type, monoid_mult: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_22, type, linorder: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_23, type, preorder: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_24, type, idom_abs_sgn: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_25, type, wellorder: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_26, type, dense_order: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_27, type, linordered_idom: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_28, type, dense_linorder: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_29, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_30, type, real_V1639655670t_norm: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_31, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_32, type, archim1727834104eiling: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_33, type, ordere142940540dd_abs: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_34, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_35, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_36, type, archim1804426504_field: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_37, type, real_V55928688vector: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_38, type, real_V1229719638ebra_1: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_39, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_40, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_41, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 232.52/34.90 thf(func_def_42, type, archimedean_ceiling: !>[X0: $tType]:(X0 > int)).
% 232.52/34.90 thf(func_def_43, type, archim2085082626_floor: !>[X0: $tType]:(X0 > int)).
% 232.52/34.90 thf(func_def_44, type, finite1218308419n_axis: !>[X0: $tType, X1: $tType]:(X0 > X1 > finite_Cartesian_vec @ X1 @ X0)).
% 232.52/34.90 thf(func_def_45, type, finite1115014511_index: !>[X0: $tType, X1: $tType]:(finite_Cartesian_vec @ X0 @ X1 > X1)).
% 232.52/34.90 thf(func_def_46, type, finite1614961371matrix: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > finite_Cartesian_vec @ finite_Cartesian_vec @ X0 @ X2 @ X3 > finite_Cartesian_vec @ finite_Cartesian_vec @ X1 @ X2 @ X3)).
% 232.52/34.90 thf(func_def_47, type, finite_Cartesian_vec2: !>[X0: $tType, X1: $tType]:(X0 > finite_Cartesian_vec @ X0 @ X1)).
% 232.52/34.90 thf(func_def_48, type, finite1433825200ec_nth: !>[X0: $tType, X1: $tType]:(finite_Cartesian_vec @ X0 @ X1 > X1 > X0)).
% 232.52/34.90 thf(func_def_49, type, finite431509953r_mult: !>[X0: $tType, X1: $tType]:(X0 > finite_Cartesian_vec @ X0 @ X1 > finite_Cartesian_vec @ X0 @ X1)).
% 232.52/34.90 thf(func_def_50, type, abs_abs: !>[X0: $tType]:(X0 > X0)).
% 232.52/34.90 thf(func_def_51, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 232.52/34.90 thf(func_def_52, type, one_one: !>[X0: $tType]:(X0)).
% 232.52/34.90 thf(func_def_53, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 232.52/34.90 thf(func_def_54, type, ring_1_Ints: !>[X0: $tType]:(set @ X0)).
% 232.52/34.90 thf(func_def_55, type, ring_1_of_int: !>[X0: $tType]:(int > X0)).
% 232.52/34.90 thf(func_def_56, type, minkow1937162798nt_vec: !>[X0: $tType, X1: $tType]:(finite_Cartesian_vec @ int @ X0 > finite_Cartesian_vec @ X1 @ X0)).
% 232.52/34.90 thf(func_def_57, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 232.52/34.90 thf(func_def_58, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 232.52/34.90 thf(func_def_59, type, real_V2000881966t_dist: !>[X0: $tType]:(X0 > X0 > real)).
% 232.52/34.90 thf(func_def_60, type, real_V1127708846m_norm: !>[X0: $tType]:(X0 > real)).
% 232.52/34.90 thf(func_def_61, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 232.52/34.90 thf(func_def_62, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 232.52/34.90 thf(func_def_63, type, a: set @ finite_Cartesian_vec @ real @ n).
% 232.52/34.90 thf(func_def_64, type, i: n).
% 232.52/34.90 thf(func_def_65, type, m: int).
% 232.52/34.90 thf(func_def_66, type, x: finite_Cartesian_vec @ real @ n).
% 232.52/34.90 thf(func_def_67, type, y: finite_Cartesian_vec @ real @ n).
% 232.52/34.90 thf(func_def_82, type, sP0: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 232.52/34.90 thf(func_def_83, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 232.52/34.90 thf(func_def_84, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 232.52/34.90 thf(func_def_85, type, sK3: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 232.52/34.90 thf(func_def_86, type, sK4: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 232.52/34.90 thf(func_def_87, type, sK5: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 232.52/34.90 thf(func_def_88, type, sK6: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 232.52/34.90 thf(func_def_89, type, sK7: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 232.52/34.90 thf(func_def_90, type, sK8: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 232.52/34.90 thf(func_def_91, type, sK9: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_92, type, sK10: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_93, type, sK11: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_94, type, sK12: !>[X0: $tType]:((X0 > $o) > int)).
% 232.52/34.90 thf(func_def_95, type, sK13: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_96, type, sK14: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_97, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:(finite_Cartesian_vec @ X2 @ X1 > finite_Cartesian_vec @ X0 @ X1 > X1)).
% 232.52/34.90 thf(func_def_98, type, sK16: !>[X0: $tType]:(X0 > int)).
% 232.52/34.90 thf(func_def_99, type, sK17: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 232.52/34.90 thf(func_def_100, type, sK18: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 232.52/34.90 thf(func_def_101, type, sK19: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 232.52/34.90 thf(func_def_102, type, sK20: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 232.52/34.90 thf(func_def_103, type, sK21: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 232.52/34.90 thf(func_def_104, type, sK22: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 232.52/34.90 thf(func_def_105, type, sK23: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 232.52/34.90 thf(func_def_106, type, sK24: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 232.52/34.90 thf(func_def_107, type, sK25: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 232.52/34.90 thf(func_def_108, type, sK26: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_109, type, sK27: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_110, type, sK28: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_111, type, sK29: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 232.52/34.90 thf(func_def_112, type, sK30: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 232.52/34.90 thf(func_def_113, type, sK31: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 232.52/34.90 thf(func_def_114, type, sK32: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 232.52/34.90 thf(func_def_115, type, sK33: real > set @ real > real).
% 232.52/34.90 thf(func_def_116, type, sK34: set @ real > real).
% 232.52/34.90 thf(func_def_117, type, sK35: real > set @ real > real).
% 232.52/34.90 thf(func_def_118, type, sK36: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_119, type, sK37: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_120, type, sK38: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_121, type, sK39: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_122, type, sK40: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 232.52/34.90 thf(func_def_123, type, sK41: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 232.52/34.90 thf(func_def_124, type, sK42: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_125, type, sK43: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 232.52/34.90 thf(func_def_126, type, sK44: (int > $o) > int > int).
% 232.52/34.90 thf(func_def_127, type, sK45: int).
% 232.52/34.90 thf(func_def_128, type, sK46: (int > $o) > int > int).
% 232.52/34.90 thf(func_def_129, type, sK47: !>[X0: $tType]:((X0 > $o) > X0)).
% 232.52/34.90 thf(func_def_131, type, sK49: !>[X0: $tType]:(X0 > int)).
% 232.52/34.90 thf(func_def_132, type, sK50: !>[X0: $tType]:(X0 > int)).
% 232.52/34.90 thf(func_def_133, type, sK51: !>[X0: $tType]:((int > $o) > X0 > int)).
% 232.52/34.90 thf(func_def_134, type, sK52: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > finite_Cartesian_vec @ X1 @ X0)).
% 232.52/34.90 thf(func_def_135, type, sK53: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 232.52/34.90 thf(func_def_136, type, sK54: !>[X0: $tType, X1: $tType]:(X0 > (X0 > X1 > $o) > X1)).
% 232.52/34.90 thf(func_def_137, type, sK55: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > finite_Cartesian_vec @ X1 @ X0 > X0)).
% 232.52/34.90 thf(func_def_138, type, sK56: !>[X0: $tType]:(X0 > set @ X0 > X0 > X0)).
% 232.52/34.90 thf(func_def_139, type, ph57: !>[X0: $tType]:(X0)).
% 232.52/34.90 thf(func_def_140, type, sK58: (numeral_num1 > $o) > numeral_num1).
% 232.52/34.90 thf(func_def_141, type, sK59: (numeral_num1 > $o) > numeral_num1).
% 232.52/34.90 thf(func_def_142, type, sK60: (numeral_num1 > $o) > numeral_num1).
% 232.52/34.90 thf(f10303,plain,(
% 232.52/34.90 $false),
% 232.52/34.90 inference(avatar_sat_refutation,[status(thm)],[f2036,f2067,f2082,f2107,f2112,f2137,f2229,f2239,f2244,f2313,f2319,f2320,f2330,f2349,f2900,f2901,f3519,f3529,f10299,f10302])).
% 232.52/34.90 thf(f10302,plain,(
% 232.52/34.90 (m != (sK16 @ real @ (ring_1_of_int @ real @ m))) | ((ring_1_of_int @ real @ m) != (finite1433825200ec_nth @ real @ n @ (minus_minus @ finite_Cartesian_vec @ real @ n @ x @ y) @ i)) | ((abs_abs @ real @ (ring_1_of_int @ real @ m)) != (ring_1_of_int @ real @ (abs_abs @ int @ (sK16 @ real @ (ring_1_of_int @ real @ m))))) | ((ring_1_of_int @ real @ (abs_abs @ int @ m)) = (abs_abs @ real @ (finite1433825200ec_nth @ real @ n @ (minus_minus @ finite_Cartesian_vec @ real @ n @ x @ y) @ i)))),
% 232.52/34.90 introduced(definition,[],[theory_tautology_sat_conflict])).
% 232.52/34.90 thf(f10299,plain,(
% 232.52/34.90 spl48_321 | ~spl48_16 | ~spl48_25 | ~spl48_51),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f10298,f2241,f2109,f2064,f10293])).
% 232.52/34.90 thf(f10293,definition,(
% 232.52/34.90 spl48_321 <=> ((ring_1_of_int @ real @ m) = (finite1433825200ec_nth @ real @ n @ (minus_minus @ finite_Cartesian_vec @ real @ n @ x @ y) @ i))),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_321])],[avatar_definition])).
% 232.52/34.90 thf(f2064,definition,(
% 232.52/34.90 spl48_16 <=> (minus @ real = $true)),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_16])],[avatar_definition])).
% 232.52/34.90 thf(f2109,definition,(
% 232.52/34.90 spl48_25 <=> (finite_finite @ n = $true)),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_25])],[avatar_definition])).
% 232.52/34.90 thf(f2241,definition,(
% 232.52/34.90 spl48_51 <=> ((ring_1_of_int @ real @ m) = (minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)))),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_51])],[avatar_definition])).
% 232.52/34.90 thf(f10298,plain,(
% 232.52/34.90 ((ring_1_of_int @ real @ m) = (finite1433825200ec_nth @ real @ n @ (minus_minus @ finite_Cartesian_vec @ real @ n @ x @ y) @ i)) | (~spl48_16 | ~spl48_25 | ~spl48_51)),
% 232.52/34.90 inference(subsumption_resolution,[status(thm)],[f10297,f2111])).
% 232.52/34.90 thf(f2111,plain,(
% 232.52/34.90 (finite_finite @ n = $true) | ~spl48_25),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2109])).
% 232.52/34.90 thf(f10297,plain,(
% 232.52/34.90 (finite_finite @ n != $true) | ((ring_1_of_int @ real @ m) = (finite1433825200ec_nth @ real @ n @ (minus_minus @ finite_Cartesian_vec @ real @ n @ x @ y) @ i)) | (~spl48_16 | ~spl48_51)),
% 232.52/34.90 inference(subsumption_resolution,[status(thm)],[f10234,f2066])).
% 232.52/34.90 thf(f2066,plain,(
% 232.52/34.90 (minus @ real = $true) | ~spl48_16),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2064])).
% 232.52/34.90 thf(f10234,plain,(
% 232.52/34.90 ((ring_1_of_int @ real @ m) = (finite1433825200ec_nth @ real @ n @ (minus_minus @ finite_Cartesian_vec @ real @ n @ x @ y) @ i)) | (minus @ real != $true) | (finite_finite @ n != $true) | ~spl48_51),
% 232.52/34.90 inference(superposition,[status(thm)],[f2243,f1756])).
% 232.52/34.90 thf(f1756,plain,(
% 232.52/34.90 ( ! [X1 : $tType,X0 : $tType,X2 : finite_Cartesian_vec @ X0 @ X1,X3 : finite_Cartesian_vec @ X0 @ X1,X4 : X1] : (((minus_minus @ X0 @ (finite1433825200ec_nth @ X0 @ X1 @ X2 @ X4) @ (finite1433825200ec_nth @ X0 @ X1 @ X3 @ X4)) = (finite1433825200ec_nth @ X0 @ X1 @ (minus_minus @ finite_Cartesian_vec @ X0 @ X1 @ X2 @ X3) @ X4)) | (finite_finite @ X1 != $true) | (minus @ X0 != $true)) )),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f1283])).
% 232.52/34.90 thf(f1283,plain,(
% 232.52/34.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : finite_Cartesian_vec @ X0 @ X1,X3 : finite_Cartesian_vec @ X0 @ X1,X4 : X1] : ((minus_minus @ X0 @ (finite1433825200ec_nth @ X0 @ X1 @ X2 @ X4) @ (finite1433825200ec_nth @ X0 @ X1 @ X3 @ X4)) = (finite1433825200ec_nth @ X0 @ X1 @ (minus_minus @ finite_Cartesian_vec @ X0 @ X1 @ X2 @ X3) @ X4)) | (finite_finite @ X1 != $true) | (minus @ X0 != $true))),
% 232.52/34.90 inference(flattening,[status(thm)],[f1282])).
% 232.52/34.90 thf(f1282,plain,(
% 232.52/34.90 ! [X0 : $tType,X1 : $tType] : (! [X2 : finite_Cartesian_vec @ X0 @ X1,X3 : finite_Cartesian_vec @ X0 @ X1,X4 : X1] : ((minus_minus @ X0 @ (finite1433825200ec_nth @ X0 @ X1 @ X2 @ X4) @ (finite1433825200ec_nth @ X0 @ X1 @ X3 @ X4)) = (finite1433825200ec_nth @ X0 @ X1 @ (minus_minus @ finite_Cartesian_vec @ X0 @ X1 @ X2 @ X3) @ X4)) | ((minus @ X0 != $true) | (finite_finite @ X1 != $true)))),
% 232.52/34.90 inference(ennf_transformation,[status(thm)],[f409])).
% 232.52/34.90 thf(f409,plain,(
% 232.52/34.90 ! [X0 : $tType,X1 : $tType] : (((minus @ X0 = $true) & (finite_finite @ X1 = $true)) => ! [X2 : finite_Cartesian_vec @ X0 @ X1,X3 : finite_Cartesian_vec @ X0 @ X1,X4 : X1] : ((minus_minus @ X0 @ (finite1433825200ec_nth @ X0 @ X1 @ X2 @ X4) @ (finite1433825200ec_nth @ X0 @ X1 @ X3 @ X4)) = (finite1433825200ec_nth @ X0 @ X1 @ (minus_minus @ finite_Cartesian_vec @ X0 @ X1 @ X2 @ X3) @ X4)))),
% 232.52/34.90 inference(fool_elimination,[status(thm)],[f408])).
% 232.52/34.90 thf(f408,plain,(
% 232.52/34.90 ! [X0 : $tType,X1 : $tType] : ((minus @ X0 & finite_finite @ X1) => ! [X2 : finite_Cartesian_vec @ X0 @ X1,X3 : finite_Cartesian_vec @ X0 @ X1,X4 : X1] : ((minus_minus @ X0 @ (finite1433825200ec_nth @ X0 @ X1 @ X2 @ X4) @ (finite1433825200ec_nth @ X0 @ X1 @ X3 @ X4)) = (finite1433825200ec_nth @ X0 @ X1 @ (minus_minus @ finite_Cartesian_vec @ X0 @ X1 @ X2 @ X3) @ X4)))),
% 232.52/34.90 inference(rectify,[status(thm)],[f5])).
% 232.52/34.90 thf(f5,axiom,(
% 232.52/34.90 ! [X0 : $tType,X1 : $tType] : ((minus @ X0 & finite_finite @ X1) => ! [X6 : finite_Cartesian_vec @ X0 @ X1,X7 : finite_Cartesian_vec @ X0 @ X1,X8 : X1] : ((finite1433825200ec_nth @ X0 @ X1 @ (minus_minus @ finite_Cartesian_vec @ X0 @ X1 @ X6 @ X7) @ X8) = (minus_minus @ X0 @ (finite1433825200ec_nth @ X0 @ X1 @ X6 @ X8) @ (finite1433825200ec_nth @ X0 @ X1 @ X7 @ X8))))),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',fact_4_vector__minus__component)).
% 232.52/34.90 thf(f2243,plain,(
% 232.52/34.90 ((ring_1_of_int @ real @ m) = (minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i))) | ~spl48_51),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2241])).
% 232.52/34.90 thf(f3529,plain,(
% 232.52/34.90 spl48_146 | ~spl48_30 | ~spl48_66 | ~spl48_106),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f3528,f2897,f2336,f2134,f3523])).
% 232.52/34.90 thf(f3523,definition,(
% 232.52/34.90 spl48_146 <=> (m = (sK16 @ real @ (ring_1_of_int @ real @ m)))),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_146])],[avatar_definition])).
% 232.52/34.90 thf(f2134,definition,(
% 232.52/34.90 spl48_30 <=> (archim1727834104eiling @ real = $true)),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_30])],[avatar_definition])).
% 232.52/34.90 thf(f2336,definition,(
% 232.52/34.90 spl48_66 <=> (m = (archim2085082626_floor @ real @ (ring_1_of_int @ real @ m)))),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_66])],[avatar_definition])).
% 232.52/34.90 thf(f2897,definition,(
% 232.52/34.90 spl48_106 <=> ((ring_1_of_int @ real @ m) = (ring_1_of_int @ real @ (sK16 @ real @ (ring_1_of_int @ real @ m))))),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_106])],[avatar_definition])).
% 232.52/34.90 thf(f3528,plain,(
% 232.52/34.90 (m = (sK16 @ real @ (ring_1_of_int @ real @ m))) | (~spl48_30 | ~spl48_66 | ~spl48_106)),
% 232.52/34.90 inference(forward_demodulation,[status(thm)],[f3527,f2338])).
% 232.52/34.90 thf(f2338,plain,(
% 232.52/34.90 (m = (archim2085082626_floor @ real @ (ring_1_of_int @ real @ m))) | ~spl48_66),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2336])).
% 232.52/34.90 thf(f3527,plain,(
% 232.52/34.90 ((sK16 @ real @ (ring_1_of_int @ real @ m)) = (archim2085082626_floor @ real @ (ring_1_of_int @ real @ m))) | (~spl48_30 | ~spl48_106)),
% 232.52/34.90 inference(subsumption_resolution,[status(thm)],[f3512,f2136])).
% 232.52/34.90 thf(f2136,plain,(
% 232.52/34.90 (archim1727834104eiling @ real = $true) | ~spl48_30),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2134])).
% 232.52/34.90 thf(f3512,plain,(
% 232.52/34.90 ((sK16 @ real @ (ring_1_of_int @ real @ m)) = (archim2085082626_floor @ real @ (ring_1_of_int @ real @ m))) | (archim1727834104eiling @ real != $true) | ~spl48_106),
% 232.52/34.90 inference(superposition,[status(thm)],[f1555,f2899])).
% 232.52/34.90 thf(f2899,plain,(
% 232.52/34.90 ((ring_1_of_int @ real @ m) = (ring_1_of_int @ real @ (sK16 @ real @ (ring_1_of_int @ real @ m)))) | ~spl48_106),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2897])).
% 232.52/34.90 thf(f1555,plain,(
% 232.52/34.90 ( ! [X0 : $tType,X1 : int] : (((archim2085082626_floor @ X0 @ (ring_1_of_int @ X0 @ X1)) = X1) | (archim1727834104eiling @ X0 != $true)) )),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f1182])).
% 232.52/34.90 thf(f1182,plain,(
% 232.52/34.90 ! [X0 : $tType] : (! [X1 : int] : ((archim2085082626_floor @ X0 @ (ring_1_of_int @ X0 @ X1)) = X1) | (archim1727834104eiling @ X0 != $true))),
% 232.52/34.90 inference(ennf_transformation,[status(thm)],[f707])).
% 232.52/34.90 thf(f707,plain,(
% 232.52/34.90 ! [X0 : $tType] : ((archim1727834104eiling @ X0 = $true) => ! [X1 : int] : ((archim2085082626_floor @ X0 @ (ring_1_of_int @ X0 @ X1)) = X1))),
% 232.52/34.90 inference(fool_elimination,[status(thm)],[f706])).
% 232.52/34.90 thf(f706,plain,(
% 232.52/34.90 ! [X0 : $tType] : (archim1727834104eiling @ X0 => ! [X1 : int] : ((archim2085082626_floor @ X0 @ (ring_1_of_int @ X0 @ X1)) = X1))),
% 232.52/34.90 inference(rectify,[status(thm)],[f57])).
% 232.52/34.90 thf(f57,axiom,(
% 232.52/34.90 ! [X0 : $tType] : (archim1727834104eiling @ X0 => ! [X10 : int] : ((archim2085082626_floor @ X0 @ (ring_1_of_int @ X0 @ X10)) = X10))),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',fact_56_floor__of__int)).
% 232.52/34.90 thf(f3519,plain,(
% 232.52/34.90 spl48_145 | ~spl48_24 | ~spl48_106),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f3514,f2897,f2104,f3516])).
% 232.52/34.90 thf(f3516,definition,(
% 232.52/34.90 spl48_145 <=> ((abs_abs @ real @ (ring_1_of_int @ real @ m)) = (ring_1_of_int @ real @ (abs_abs @ int @ (sK16 @ real @ (ring_1_of_int @ real @ m)))))),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_145])],[avatar_definition])).
% 232.52/34.90 thf(f2104,definition,(
% 232.52/34.90 spl48_24 <=> (linordered_idom @ real = $true)),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_24])],[avatar_definition])).
% 232.52/34.90 thf(f3514,plain,(
% 232.52/34.90 ((abs_abs @ real @ (ring_1_of_int @ real @ m)) = (ring_1_of_int @ real @ (abs_abs @ int @ (sK16 @ real @ (ring_1_of_int @ real @ m))))) | (~spl48_24 | ~spl48_106)),
% 232.52/34.90 inference(subsumption_resolution,[status(thm)],[f3510,f2106])).
% 232.52/34.90 thf(f2106,plain,(
% 232.52/34.90 (linordered_idom @ real = $true) | ~spl48_24),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2104])).
% 232.52/34.90 thf(f3510,plain,(
% 232.52/34.90 ((abs_abs @ real @ (ring_1_of_int @ real @ m)) = (ring_1_of_int @ real @ (abs_abs @ int @ (sK16 @ real @ (ring_1_of_int @ real @ m))))) | (linordered_idom @ real != $true) | ~spl48_106),
% 232.52/34.90 inference(superposition,[status(thm)],[f1490,f2899])).
% 232.52/34.90 thf(f1490,plain,(
% 232.52/34.90 ( ! [X0 : $tType,X1 : int] : (((ring_1_of_int @ X0 @ (abs_abs @ int @ X1)) = (abs_abs @ X0 @ (ring_1_of_int @ X0 @ X1))) | (linordered_idom @ X0 != $true)) )),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f1381])).
% 232.52/34.90 thf(f1381,plain,(
% 232.52/34.90 ! [X0 : $tType] : ((linordered_idom @ X0 != $true) | ! [X1 : int] : ((ring_1_of_int @ X0 @ (abs_abs @ int @ X1)) = (abs_abs @ X0 @ (ring_1_of_int @ X0 @ X1))))),
% 232.52/34.90 inference(ennf_transformation,[status(thm)],[f795])).
% 232.52/34.90 thf(f795,plain,(
% 232.52/34.90 ! [X0 : $tType] : ((linordered_idom @ X0 = $true) => ! [X1 : int] : ((ring_1_of_int @ X0 @ (abs_abs @ int @ X1)) = (abs_abs @ X0 @ (ring_1_of_int @ X0 @ X1))))),
% 232.52/34.90 inference(fool_elimination,[status(thm)],[f794])).
% 232.52/34.90 thf(f794,plain,(
% 232.52/34.90 ! [X0 : $tType] : (linordered_idom @ X0 => ! [X1 : int] : ((ring_1_of_int @ X0 @ (abs_abs @ int @ X1)) = (abs_abs @ X0 @ (ring_1_of_int @ X0 @ X1))))),
% 232.52/34.90 inference(rectify,[status(thm)],[f6])).
% 232.52/34.90 thf(f6,axiom,(
% 232.52/34.90 ! [X0 : $tType] : (linordered_idom @ X0 => ! [X6 : int] : ((ring_1_of_int @ X0 @ (abs_abs @ int @ X6)) = (abs_abs @ X0 @ (ring_1_of_int @ X0 @ X6))))),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',fact_5_of__int__abs)).
% 232.52/34.90 thf(f2901,plain,(
% 232.52/34.90 ((ring_1_of_int @ real @ m) != (minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i))) | ((member @ real @ (minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) @ ring_1_Ints @ real) != $true) | ((member @ real @ (ring_1_of_int @ real @ m) @ ring_1_Ints @ real) = $true)),
% 232.52/34.90 introduced(definition,[],[theory_tautology_sat_conflict])).
% 232.52/34.90 thf(f2900,plain,(
% 232.52/34.90 spl48_106 | ~spl48_19 | ~spl48_57),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f2895,f2271,f2079,f2897])).
% 232.52/34.90 thf(f2079,definition,(
% 232.52/34.90 spl48_19 <=> (ring_1 @ real = $true)),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_19])],[avatar_definition])).
% 232.52/34.90 thf(f2271,definition,(
% 232.52/34.90 spl48_57 <=> ((member @ real @ (ring_1_of_int @ real @ m) @ ring_1_Ints @ real) = $true)),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_57])],[avatar_definition])).
% 232.52/34.90 thf(f2895,plain,(
% 232.52/34.90 ((ring_1_of_int @ real @ m) = (ring_1_of_int @ real @ (sK16 @ real @ (ring_1_of_int @ real @ m)))) | (~spl48_19 | ~spl48_57)),
% 232.52/34.90 inference(subsumption_resolution,[status(thm)],[f2894,f2081])).
% 232.52/34.90 thf(f2081,plain,(
% 232.52/34.90 (ring_1 @ real = $true) | ~spl48_19),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2079])).
% 232.52/34.90 thf(f2894,plain,(
% 232.52/34.90 ((ring_1_of_int @ real @ m) = (ring_1_of_int @ real @ (sK16 @ real @ (ring_1_of_int @ real @ m)))) | (ring_1 @ real != $true) | ~spl48_57),
% 232.52/34.90 inference(trivial_inequality_removal,[status(thm)],[f2889])).
% 232.52/34.90 thf(f2889,plain,(
% 232.52/34.90 ($true != $true) | (ring_1 @ real != $true) | ((ring_1_of_int @ real @ m) = (ring_1_of_int @ real @ (sK16 @ real @ (ring_1_of_int @ real @ m)))) | ~spl48_57),
% 232.52/34.90 inference(superposition,[status(thm)],[f1556,f2273])).
% 232.52/34.90 thf(f2273,plain,(
% 232.52/34.90 ((member @ real @ (ring_1_of_int @ real @ m) @ ring_1_Ints @ real) = $true) | ~spl48_57),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2271])).
% 232.52/34.90 thf(f1556,plain,(
% 232.52/34.90 ( ! [X0 : $tType,X1 : X0] : (((member @ X0 @ X1 @ ring_1_Ints @ X0) != $true) | (ring_1 @ X0 != $true) | ((ring_1_of_int @ X0 @ (sK16 @ X0 @ X1)) = X1)) )),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f1420])).
% 232.52/34.90 thf(f1420,plain,(
% 232.52/34.90 ! [X0 : $tType] : ((ring_1 @ X0 != $true) | ! [X1 : X0] : (((member @ X0 @ X1 @ ring_1_Ints @ X0) != $true) | ((ring_1_of_int @ X0 @ (sK16 @ X0 @ X1)) = X1)))),
% 232.52/34.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f1278,f1419])).
% 232.52/34.90 thf(f1419,plain,(
% 232.52/34.90 ! [X0 : $tType,X1 : X0] : (? [X2 : int] : ((ring_1_of_int @ X0 @ X2) = X1) => ((ring_1_of_int @ X0 @ (sK16 @ X0 @ X1)) = X1))),
% 232.52/34.90 introduced(definition,[],[choice_axiom])).
% 232.52/34.90 thf(f1278,plain,(
% 232.52/34.90 ! [X0 : $tType] : ((ring_1 @ X0 != $true) | ! [X1 : X0] : (((member @ X0 @ X1 @ ring_1_Ints @ X0) != $true) | ? [X2 : int] : ((ring_1_of_int @ X0 @ X2) = X1)))),
% 232.52/34.90 inference(ennf_transformation,[status(thm)],[f445])).
% 232.52/34.90 thf(f445,plain,(
% 232.52/34.90 ! [X0 : $tType] : ((ring_1 @ X0 = $true) => ! [X1 : X0] : (((member @ X0 @ X1 @ ring_1_Ints @ X0) = $true) => ~! [X2 : int] : ((ring_1_of_int @ X0 @ X2) != X1)))),
% 232.52/34.90 inference(fool_elimination,[status(thm)],[f444])).
% 232.52/34.90 thf(f444,plain,(
% 232.52/34.90 ! [X0 : $tType] : (ring_1 @ X0 => ! [X1 : X0] : ((member @ X0 @ X1 @ ring_1_Ints @ X0) => ~! [X2 : int] : ((ring_1_of_int @ X0 @ X2) != X1)))),
% 232.52/34.90 inference(rectify,[status(thm)],[f23])).
% 232.52/34.90 thf(f23,axiom,(
% 232.52/34.90 ! [X0 : $tType] : (ring_1 @ X0 => ! [X24 : X0] : ((member @ X0 @ X24 @ ring_1_Ints @ X0) => ~! [X25 : int] : ((ring_1_of_int @ X0 @ X25) != X24)))),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',fact_22_Ints__cases)).
% 232.52/34.90 thf(f2349,plain,(
% 232.52/34.90 spl48_66 | ~spl48_63 | ~spl48_64),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f2348,f2325,f2316,f2336])).
% 232.52/34.90 thf(f2316,definition,(
% 232.52/34.90 spl48_63 <=> ((archim2085082626_floor @ real @ (ring_1_of_int @ real @ m)) = sK45)),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_63])],[avatar_definition])).
% 232.52/34.90 thf(f2325,definition,(
% 232.52/34.90 spl48_64 <=> (m = sK45)),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_64])],[avatar_definition])).
% 232.52/34.90 thf(f2348,plain,(
% 232.52/34.90 (m = (archim2085082626_floor @ real @ (ring_1_of_int @ real @ m))) | (~spl48_63 | ~spl48_64)),
% 232.52/34.90 inference(forward_demodulation,[status(thm)],[f2318,f2327])).
% 232.52/34.90 thf(f2327,plain,(
% 232.52/34.90 (m = sK45) | ~spl48_64),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2325])).
% 232.52/34.90 thf(f2318,plain,(
% 232.52/34.90 ((archim2085082626_floor @ real @ (ring_1_of_int @ real @ m)) = sK45) | ~spl48_63),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2316])).
% 232.52/34.90 thf(f2330,plain,(
% 232.52/34.90 spl48_64 | ~spl48_30 | ~spl48_62),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f2329,f2310,f2134,f2325])).
% 232.52/34.90 thf(f2310,definition,(
% 232.52/34.90 spl48_62 <=> ((archimedean_ceiling @ real @ (ring_1_of_int @ real @ m)) = sK45)),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_62])],[avatar_definition])).
% 232.52/34.90 thf(f2329,plain,(
% 232.52/34.90 (m = sK45) | (~spl48_30 | ~spl48_62)),
% 232.52/34.90 inference(subsumption_resolution,[status(thm)],[f2322,f2136])).
% 232.52/34.90 thf(f2322,plain,(
% 232.52/34.90 (archim1727834104eiling @ real != $true) | (m = sK45) | ~spl48_62),
% 232.52/34.90 inference(superposition,[status(thm)],[f1618,f2312])).
% 232.52/34.90 thf(f2312,plain,(
% 232.52/34.90 ((archimedean_ceiling @ real @ (ring_1_of_int @ real @ m)) = sK45) | ~spl48_62),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2310])).
% 232.52/34.90 thf(f1618,plain,(
% 232.52/34.90 ( ! [X0 : $tType,X1 : int] : (((archimedean_ceiling @ X0 @ (ring_1_of_int @ X0 @ X1)) = X1) | (archim1727834104eiling @ X0 != $true)) )),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f1134])).
% 232.52/34.90 thf(f1134,plain,(
% 232.52/34.90 ! [X0 : $tType] : (! [X1 : int] : ((archimedean_ceiling @ X0 @ (ring_1_of_int @ X0 @ X1)) = X1) | (archim1727834104eiling @ X0 != $true))),
% 232.52/34.90 inference(ennf_transformation,[status(thm)],[f453])).
% 232.52/34.90 thf(f453,plain,(
% 232.52/34.90 ! [X0 : $tType] : ((archim1727834104eiling @ X0 = $true) => ! [X1 : int] : ((archimedean_ceiling @ X0 @ (ring_1_of_int @ X0 @ X1)) = X1))),
% 232.52/34.90 inference(fool_elimination,[status(thm)],[f452])).
% 232.52/34.90 thf(f452,plain,(
% 232.52/34.90 ! [X0 : $tType] : (archim1727834104eiling @ X0 => ! [X1 : int] : ((archimedean_ceiling @ X0 @ (ring_1_of_int @ X0 @ X1)) = X1))),
% 232.52/34.90 inference(rectify,[status(thm)],[f58])).
% 232.52/34.90 thf(f58,axiom,(
% 232.52/34.90 ! [X0 : $tType] : (archim1727834104eiling @ X0 => ! [X10 : int] : ((archimedean_ceiling @ X0 @ (ring_1_of_int @ X0 @ X10)) = X10))),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',fact_57_ceiling__of__int)).
% 232.52/34.90 thf(f2320,plain,(
% 232.52/34.90 ((ring_1_of_int @ real @ m) != (minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i))) | ((minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) != (ring_1_of_int @ real @ sK45)) | ((ring_1_of_int @ real @ m) = (ring_1_of_int @ real @ sK45))),
% 232.52/34.90 introduced(definition,[],[theory_tautology_sat_conflict])).
% 232.52/34.90 thf(f2319,plain,(
% 232.52/34.90 spl48_63 | ~spl48_30 | ~spl48_58),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f2314,f2275,f2134,f2316])).
% 232.52/34.90 thf(f2275,definition,(
% 232.52/34.90 spl48_58 <=> ((ring_1_of_int @ real @ m) = (ring_1_of_int @ real @ sK45))),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_58])],[avatar_definition])).
% 232.52/34.90 thf(f2314,plain,(
% 232.52/34.90 ((archim2085082626_floor @ real @ (ring_1_of_int @ real @ m)) = sK45) | (~spl48_30 | ~spl48_58)),
% 232.52/34.90 inference(subsumption_resolution,[status(thm)],[f2306,f2136])).
% 232.52/34.90 thf(f2306,plain,(
% 232.52/34.90 (archim1727834104eiling @ real != $true) | ((archim2085082626_floor @ real @ (ring_1_of_int @ real @ m)) = sK45) | ~spl48_58),
% 232.52/34.90 inference(superposition,[status(thm)],[f1555,f2277])).
% 232.52/34.90 thf(f2277,plain,(
% 232.52/34.90 ((ring_1_of_int @ real @ m) = (ring_1_of_int @ real @ sK45)) | ~spl48_58),
% 232.52/34.90 inference(avatar_component_clause,[status(thm)],[f2275])).
% 232.52/34.90 thf(f2313,plain,(
% 232.52/34.90 spl48_62 | ~spl48_30 | ~spl48_58),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f2308,f2275,f2134,f2310])).
% 232.52/34.90 thf(f2308,plain,(
% 232.52/34.90 ((archimedean_ceiling @ real @ (ring_1_of_int @ real @ m)) = sK45) | (~spl48_30 | ~spl48_58)),
% 232.52/34.90 inference(subsumption_resolution,[status(thm)],[f2307,f2136])).
% 232.52/34.90 thf(f2307,plain,(
% 232.52/34.90 (archim1727834104eiling @ real != $true) | ((archimedean_ceiling @ real @ (ring_1_of_int @ real @ m)) = sK45) | ~spl48_58),
% 232.52/34.90 inference(superposition,[status(thm)],[f1618,f2277])).
% 232.52/34.90 thf(f2244,plain,(
% 232.52/34.90 spl48_51),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f1579,f2241])).
% 232.52/34.90 thf(f1579,plain,(
% 232.52/34.90 ((ring_1_of_int @ real @ m) = (minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)))),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f3])).
% 232.52/34.90 thf(f3,axiom,(
% 232.52/34.90 ((ring_1_of_int @ real @ m) = (minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)))),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',fact_2_m)).
% 232.52/34.90 thf(f2239,plain,(
% 232.52/34.90 spl48_50),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f1771,f2236])).
% 232.52/34.90 thf(f2236,definition,(
% 232.52/34.90 spl48_50 <=> ((member @ real @ (minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) @ ring_1_Ints @ real) = $true)),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_50])],[avatar_definition])).
% 232.52/34.90 thf(f1771,plain,(
% 232.52/34.90 ((member @ real @ (minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) @ ring_1_Ints @ real) = $true)),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f835])).
% 232.52/34.90 thf(f835,plain,(
% 232.52/34.90 ((member @ real @ (minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) @ ring_1_Ints @ real) = $true)),
% 232.52/34.90 inference(fool_elimination,[status(thm)],[f834])).
% 232.52/34.90 thf(f834,plain,(
% 232.52/34.90 (member @ real @ (minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) @ ring_1_Ints @ real)),
% 232.52/34.90 inference(rectify,[status(thm)],[f8])).
% 232.52/34.90 thf(f8,axiom,(
% 232.52/34.90 (member @ real @ (minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) @ ring_1_Ints @ real)),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',fact_7__092_060open_062x_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060in_062_A_092_060int_062_092_060close_062)).
% 232.52/34.90 thf(f2229,plain,(
% 232.52/34.90 ~spl48_48),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f1675,f2226])).
% 232.52/34.90 thf(f2226,definition,(
% 232.52/34.90 spl48_48 <=> ((ring_1_of_int @ real @ (abs_abs @ int @ m)) = (abs_abs @ real @ (finite1433825200ec_nth @ real @ n @ (minus_minus @ finite_Cartesian_vec @ real @ n @ x @ y) @ i)))),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_48])],[avatar_definition])).
% 232.52/34.90 thf(f1675,plain,(
% 232.52/34.90 ((ring_1_of_int @ real @ (abs_abs @ int @ m)) != (abs_abs @ real @ (finite1433825200ec_nth @ real @ n @ (minus_minus @ finite_Cartesian_vec @ real @ n @ x @ y) @ i)))),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f1086])).
% 232.52/34.90 thf(f1086,plain,(
% 232.52/34.90 ((ring_1_of_int @ real @ (abs_abs @ int @ m)) != (abs_abs @ real @ (finite1433825200ec_nth @ real @ n @ (minus_minus @ finite_Cartesian_vec @ real @ n @ x @ y) @ i)))),
% 232.52/34.90 inference(flattening,[status(thm)],[f368])).
% 232.52/34.90 thf(f368,negated_conjecture,(
% 232.52/34.90 ~((ring_1_of_int @ real @ (abs_abs @ int @ m)) = (abs_abs @ real @ (finite1433825200ec_nth @ real @ n @ (minus_minus @ finite_Cartesian_vec @ real @ n @ x @ y) @ i)))),
% 232.52/34.90 inference(negated_conjecture,[status(cth)],[f367])).
% 232.52/34.90 thf(f367,conjecture,(
% 232.52/34.90 ((ring_1_of_int @ real @ (abs_abs @ int @ m)) = (abs_abs @ real @ (finite1433825200ec_nth @ real @ n @ (minus_minus @ finite_Cartesian_vec @ real @ n @ x @ y) @ i)))),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',conj_0)).
% 232.52/34.90 thf(f2137,plain,(
% 232.52/34.90 spl48_30),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f1608,f2134])).
% 232.52/34.90 thf(f1608,plain,(
% 232.52/34.90 (archim1727834104eiling @ real = $true)),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f555])).
% 232.52/34.90 thf(f555,plain,(
% 232.52/34.90 (archim1727834104eiling @ real = $true)),
% 232.52/34.90 inference(fool_elimination,[status(thm)],[f554])).
% 232.52/34.90 thf(f554,plain,(
% 232.52/34.90 archim1727834104eiling @ real),
% 232.52/34.90 inference(rectify,[status(thm)],[f307])).
% 232.52/34.90 thf(f307,axiom,(
% 232.52/34.90 archim1727834104eiling @ real),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',tcon_Real_Oreal___Archimedean__Field_Ofloor__ceiling)).
% 232.52/34.90 thf(f2112,plain,(
% 232.52/34.90 spl48_25),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f1597,f2109])).
% 232.52/34.90 thf(f1597,plain,(
% 232.52/34.90 (finite_finite @ n = $true)),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f535])).
% 232.52/34.90 thf(f535,plain,(
% 232.52/34.90 (finite_finite @ n = $true)),
% 232.52/34.90 inference(fool_elimination,[status(thm)],[f534])).
% 232.52/34.90 thf(f534,plain,(
% 232.52/34.90 finite_finite @ n),
% 232.52/34.90 inference(rectify,[status(thm)],[f366])).
% 232.52/34.90 thf(f366,axiom,(
% 232.52/34.90 finite_finite @ n),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',tfree_0)).
% 232.52/34.90 thf(f2107,plain,(
% 232.52/34.90 spl48_24),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f1581,f2104])).
% 232.52/34.90 thf(f1581,plain,(
% 232.52/34.90 (linordered_idom @ real = $true)),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f551])).
% 232.52/34.90 thf(f551,plain,(
% 232.52/34.90 (linordered_idom @ real = $true)),
% 232.52/34.90 inference(fool_elimination,[status(thm)],[f550])).
% 232.52/34.90 thf(f550,plain,(
% 232.52/34.90 linordered_idom @ real),
% 232.52/34.90 inference(rectify,[status(thm)],[f312])).
% 232.52/34.90 thf(f312,axiom,(
% 232.52/34.90 linordered_idom @ real),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',tcon_Real_Oreal___Rings_Olinordered__idom_24)).
% 232.52/34.90 thf(f2082,plain,(
% 232.52/34.90 spl48_19),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f1526,f2079])).
% 232.52/34.90 thf(f1526,plain,(
% 232.52/34.90 (ring_1 @ real = $true)),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f539])).
% 232.52/34.90 thf(f539,plain,(
% 232.52/34.90 (ring_1 @ real = $true)),
% 232.52/34.90 inference(fool_elimination,[status(thm)],[f538])).
% 232.52/34.90 thf(f538,plain,(
% 232.52/34.90 ring_1 @ real),
% 232.52/34.90 inference(rectify,[status(thm)],[f324])).
% 232.52/34.90 thf(f324,axiom,(
% 232.52/34.90 ring_1 @ real),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',tcon_Real_Oreal___Rings_Oring__1_35)).
% 232.52/34.90 thf(f2067,plain,(
% 232.52/34.90 spl48_16),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f1484,f2064])).
% 232.52/34.90 thf(f1484,plain,(
% 232.52/34.90 (minus @ real = $true)),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f407])).
% 232.52/34.90 thf(f407,plain,(
% 232.52/34.90 (minus @ real = $true)),
% 232.52/34.90 inference(fool_elimination,[status(thm)],[f406])).
% 232.52/34.90 thf(f406,plain,(
% 232.52/34.90 minus @ real),
% 232.52/34.90 inference(rectify,[status(thm)],[f325])).
% 232.52/34.90 thf(f325,axiom,(
% 232.52/34.90 minus @ real),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',tcon_Real_Oreal___Groups_Ominus_36)).
% 232.52/34.90 thf(f2036,plain,(
% 232.52/34.90 spl48_10),
% 232.52/34.90 inference(avatar_split_clause,[status(thm)],[f1730,f2033])).
% 232.52/34.90 thf(f2033,definition,(
% 232.52/34.90 spl48_10 <=> ((minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) = (ring_1_of_int @ real @ sK45))),
% 232.52/34.90 introduced(definition,[new_symbols(naming,[spl48_10])],[avatar_definition])).
% 232.52/34.90 thf(f1730,plain,(
% 232.52/34.90 ((minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) = (ring_1_of_int @ real @ sK45))),
% 232.52/34.90 inference(cnf_transformation,[status(thm)],[f1460])).
% 232.52/34.90 thf(f1460,plain,(
% 232.52/34.90 ((minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) = (ring_1_of_int @ real @ sK45))),
% 232.52/34.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f1380,f1459])).
% 232.52/34.90 thf(f1459,plain,(
% 232.52/34.90 ? [X0 : int] : ((minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) = (ring_1_of_int @ real @ X0)) => ((minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) = (ring_1_of_int @ real @ sK45))),
% 232.52/34.90 introduced(definition,[],[choice_axiom])).
% 232.52/34.90 thf(f1380,plain,(
% 232.52/34.90 ? [X0 : int] : ((minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) = (ring_1_of_int @ real @ X0))),
% 232.52/34.90 inference(ennf_transformation,[status(thm)],[f1088])).
% 232.52/34.90 thf(f1088,plain,(
% 232.52/34.90 ~! [X0 : int] : ((minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) != (ring_1_of_int @ real @ X0))),
% 232.52/34.90 inference(rectify,[status(thm)],[f4])).
% 232.52/34.90 thf(f4,axiom,(
% 232.52/34.90 ~! [X5 : int] : ((minus_minus @ real @ (finite1433825200ec_nth @ real @ n @ x @ i) @ (finite1433825200ec_nth @ real @ n @ y @ i)) != (ring_1_of_int @ real @ X5))),
% 232.52/34.90 file('/export/starexec/sandbox/tmp/tmp.jv9zGgUHgU/DTF2THF_8750.p',fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 232.52/34.90 % SZS output end Proof for DTF2THF_8750
% 232.52/34.90 % (10044)------------------------------
% 232.52/34.90 % (10044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 232.52/34.90 % (10044)Termination reason: Refutation
% 232.52/34.90
% 232.52/34.90 % (10044)Memory used [KB]: 13304
% 232.52/34.90 % (10044)Time elapsed: 1.393 s
% 232.52/34.90 % (10044)Instructions burned: 4419 (million)
% 232.52/34.90 % (10044)------------------------------
% 232.52/34.90 % (10044)------------------------------
% 232.52/34.90 % (8923)Success in time 33.063 s
%------------------------------------------------------------------------------