%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP116^2 : 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 : n017.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 08:55:41 AM UTC 2026
% Result : Theorem 114.12s 17.46s
% Output : Refutation 114.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP116^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n017.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 08:25:11 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : ITP116^2 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.46 % Domain : Interactive Theorem Proving
% 0.29/0.46 % Problem : Sledgehammer Minkowskis_Theorem problem prob_203__6248138_1
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Des21]
% 0.29/0.46 % Names : Minkowskis_Theorem/prob_203__6248138_1 [Des21]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v8.1.0, 0.25 v7.5.0
% 0.29/0.46 % Syntax : Number of formulae : 467 ( 148 unt; 69 typ; 0 def)
% 0.29/0.46 % Number of atoms : 953 ( 268 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 7 ( 2 avg)
% 0.29/0.46 % Number of connectives : 4989 ( 16 ~; 2 |; 95 &;4528 @)
% 0.29/0.46 % ( 0 <=>; 348 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 20 ( 6 avg)
% 0.29/0.46 % Number of types : 5 ( 4 usr)
% 0.29/0.46 % Number of type conns : 273 ( 273 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 68 ( 65 usr; 4 con; 0-5 aty)
% 0.29/0.46 % Number of variables : 1225 ( 122 ^;1037 !; 3 ?;1225 :)
% 0.29/0.46 % ( 63 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.46 % SPC : TH1_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:30:09.913
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % Could-be-implicit typings (7)
% 0.29/0.46 thf(ty_t_Finite__Cartesian__Product_Ovec,type,
% 0.29/0.46 finite_Cartesian_vec: $tType > $tType > $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Sigma__Algebra_Omeasure,type,
% 0.29/0.46 sigma_measure: $tType > $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Real_Oreal,type,
% 0.29/0.46 real: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Set_Oset,type,
% 0.29/0.46 set: $tType > $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Nat_Onat,type,
% 0.29/0.46 nat: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Int_Oint,type,
% 0.29/0.46 int: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_tf_n,type,
% 0.29/0.46 n: $tType ).
% 0.29/0.46
% 0.29/0.46 % Explicit typings (62)
% 0.29/0.46 thf(sy_cl_Real__Vector__Spaces_Ometric__space,type,
% 0.29/0.46 real_V2090557954_space:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Ordered__Euclidean__Space_Oordered__euclidean__space,type,
% 0.29/0.46 ordere890947078_space:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_HOL_Otype,type,
% 0.29/0.46 type:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oplus,type,
% 0.29/0.46 plus:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ozero,type,
% 0.29/0.46 zero:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ominus,type,
% 0.29/0.46 minus:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Nat_Oring__char__0,type,
% 0.29/0.46 ring_char_0:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.29/0.46 group_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Lattices_Olattice,type,
% 0.29/0.46 lattice:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.29/0.46 finite_finite:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Omonoid__add,type,
% 0.29/0.46 monoid_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Countable_Ocountable,type,
% 0.29/0.46 countable:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oab__group__add,type,
% 0.29/0.46 ab_group_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.29/0.46 semigroup_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.29/0.46 comm_monoid_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.29/0.46 ab_semigroup_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 0.29/0.46 comm_monoid_diff:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.29/0.46 semilattice_inf:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.29/0.46 cancel_semigroup_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.29/0.46 ordered_ab_group_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Topological__Spaces_Ot2__space,type,
% 0.29/0.46 topological_t2_space:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.29/0.46 cancel1352612707id_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Limits_Otopological__monoid__add,type,
% 0.29/0.46 topolo1314133330id_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.29/0.46 cancel146912293up_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.29/0.46 linord219039673up_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Real__Vector__Spaces_Oreal__vector,type,
% 0.29/0.46 real_V1076094709vector:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Euclidean__Space_Oeuclidean__space,type,
% 0.29/0.46 euclid925273238_space:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.29/0.46 ordere779506340up_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Topological__Spaces_Olinorder__topology,type,
% 0.29/0.46 topolo2117631714pology:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Topological__Spaces_Otopological__space,type,
% 0.29/0.46 topolo503727757_space:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.29/0.46 canoni770627133id_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector,type,
% 0.29/0.46 real_V55928688vector:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.29/0.46 ordere236663937imp_le:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Elementary__Topology_Osecond__countable__topology,type,
% 0.29/0.46 elemen1026692323pology:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 0.29/0.46 ordere516151231imp_le:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Borel__Space_Ois__borel,type,
% 0.29/0.46 borel_is_borel:
% 0.29/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( sigma_measure @ A ) > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Borel__Space_Otopological__space__class_Oborel,type,
% 0.29/0.46 borel_1404511681_borel:
% 0.29/0.46 !>[A: $tType] : ( sigma_measure @ A ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Complete__Measure_Ocompletion,type,
% 0.29/0.46 complete_completion:
% 0.29/0.46 !>[A: $tType] : ( ( sigma_measure @ A ) > ( sigma_measure @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Complete__Measure_Omain__part,type,
% 0.29/0.46 complete_main_part:
% 0.29/0.46 !>[A: $tType] : ( ( sigma_measure @ A ) > ( set @ A ) > ( set @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.29/0.46 minus_minus:
% 0.29/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.29/0.46 plus_plus:
% 0.29/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.29/0.46 zero_zero:
% 0.29/0.46 !>[A: $tType] : A ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_If,type,
% 0.29/0.46 if:
% 0.29/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.29/0.46 inf_inf:
% 0.29/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Lebesgue__Measure_Olborel,type,
% 0.29/0.46 lebesgue_lborel:
% 0.29/0.46 !>[A: $tType] : ( sigma_measure @ A ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Minkowskis__Theorem__Mirabelle__jpyvdnlcjd_Oof__int__vec,type,
% 0.29/0.46 minkow1937162798nt_vec:
% 0.29/0.46 !>[B: $tType,A: $tType] : ( ( finite_Cartesian_vec @ int @ B ) > ( finite_Cartesian_vec @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_OLeast,type,
% 0.29/0.46 ord_Least:
% 0.29/0.46 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.29/0.46 ord_less_eq:
% 0.29/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect,type,
% 0.29/0.46 collect:
% 0.29/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oimage,type,
% 0.29/0.46 image:
% 0.29/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Ovimage,type,
% 0.29/0.46 vimage:
% 0.29/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Sigma__Algebra_Omeasurable,type,
% 0.29/0.46 sigma_measurable:
% 0.29/0.46 !>[A: $tType,B: $tType] : ( ( sigma_measure @ A ) > ( sigma_measure @ B ) > ( set @ ( A > B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Sigma__Algebra_Orestrict__space,type,
% 0.29/0.46 sigma_restrict_space:
% 0.29/0.46 !>[A: $tType] : ( ( sigma_measure @ A ) > ( set @ A ) > ( sigma_measure @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Sigma__Algebra_Osets,type,
% 0.29/0.46 sigma_sets:
% 0.29/0.46 !>[A: $tType] : ( ( sigma_measure @ A ) > ( set @ ( set @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Sigma__Algebra_Ospace,type,
% 0.29/0.46 sigma_space:
% 0.29/0.46 !>[A: $tType] : ( ( sigma_measure @ A ) > ( set @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Sigma__Algebra_Ovimage__algebra,type,
% 0.29/0.46 sigma_vimage_algebra:
% 0.29/0.46 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( A > B ) > ( sigma_measure @ B ) > ( sigma_measure @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member,type,
% 0.29/0.46 member:
% 0.29/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_R____,type,
% 0.29/0.46 r: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_S,type,
% 0.29/0.46 s: set @ ( finite_Cartesian_vec @ real @ n ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_T_H____,type,
% 0.29/0.46 t: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_T____,type,
% 0.29/0.46 t2: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_a____,type,
% 0.29/0.46 a: finite_Cartesian_vec @ int @ n ).
% 0.29/0.46
% 0.29/0.46 % Relevant facts (255)
% 0.29/0.46 thf(fact_0_assms_I1_J,axiom,
% 0.29/0.46 member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % assms(1)
% 0.29/0.46 thf(fact_1_of__int__vec__eq__iff,axiom,
% 0.29/0.46 ! [A: $tType,N: $tType] :
% 0.29/0.46 ( ( ( finite_finite @ N )
% 0.29/0.46 & ( ring_char_0 @ A ) )
% 0.29/0.46 => ! [A2: finite_Cartesian_vec @ int @ N,B2: finite_Cartesian_vec @ int @ N] :
% 0.29/0.46 ( ( ( minkow1937162798nt_vec @ N @ A @ A2 )
% 0.29/0.46 = ( minkow1937162798nt_vec @ N @ A @ B2 ) )
% 0.29/0.46 = ( A2 = B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % of_int_vec_eq_iff
% 0.29/0.46 thf(fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
% 0.29/0.46 ! [A3: finite_Cartesian_vec @ int @ n] :
% 0.29/0.46 ( ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A3 ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
% 0.29/0.46 => ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
% 0.29/0.46 @ ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
% 0.29/0.46 @ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
% 0.29/0.46 @ ^ [X: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ X @ ( minkow1937162798nt_vec @ n @ real @ A3 ) )
% 0.29/0.46 @ ( t2 @ A3 ) )
% 0.29/0.46 @ ( sigma_space @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
% 0.29/0.46 @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>\<And>a. T a \<in> sets lebesgue \<Longrightarrow> (\<lambda>x. x + of_int_vec a) -` T a \<inter> space lebesgue \<in> sets lebesgue\<close>
% 0.29/0.46 thf(fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
% 0.29/0.46 ! [A2: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A2 ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>\<And>a. T a \<in> sets lebesgue\<close>
% 0.29/0.46 thf(fact_4_T_H__altdef,axiom,
% 0.29/0.46 ! [A2: finite_Cartesian_vec @ int @ n] :
% 0.29/0.46 ( ( t @ A2 )
% 0.29/0.46 = ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
% 0.29/0.46 @ ^ [X: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ X @ ( minkow1937162798nt_vec @ n @ real @ A2 ) )
% 0.29/0.46 @ ( t2 @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % T'_altdef
% 0.29/0.46 thf(fact_5__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
% 0.29/0.46 ! [A2: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( r @ A2 ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>\<And>a. R a \<in> sets lebesgue\<close>
% 0.29/0.46 thf(fact_6_sets__completionI__sets,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,M: sigma_measure @ A] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ A4 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( member @ ( set @ A ) @ A4 @ ( sigma_sets @ A @ ( complete_completion @ A @ M ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets_completionI_sets
% 0.29/0.46 thf(fact_7__092_060open_062_092_060And_062a_O_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_092_060in_062_Alebesgue_A_092_060rightarrow_062_092_060_094sub_062M_Alebesgue_092_060close_062,axiom,
% 0.29/0.46 ! [A2: finite_Cartesian_vec @ int @ n] :
% 0.29/0.46 ( member @ ( ( finite_Cartesian_vec @ real @ n ) > ( finite_Cartesian_vec @ real @ n ) )
% 0.29/0.46 @ ^ [X: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ X @ ( minkow1937162798nt_vec @ n @ real @ A2 ) )
% 0.29/0.46 @ ( sigma_measurable @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>\<And>a. (\<lambda>x. x + of_int_vec a) \<in> lebesgue \<rightarrow>\<^sub>M lebesgue\<close>
% 0.29/0.46 thf(fact_8_vimage__ident,axiom,
% 0.29/0.46 ! [A: $tType,Y: set @ A] :
% 0.29/0.46 ( ( vimage @ A @ A
% 0.29/0.46 @ ^ [X: A] : X
% 0.29/0.46 @ Y )
% 0.29/0.46 = Y ) ).
% 0.29/0.46
% 0.29/0.46 % vimage_ident
% 0.29/0.46 thf(fact_9_vimage__Collect__eq,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,F: A > B,P: B > $o] :
% 0.29/0.46 ( ( vimage @ A @ B @ F @ ( collect @ B @ P ) )
% 0.29/0.46 = ( collect @ A
% 0.29/0.46 @ ^ [Y2: A] : ( P @ ( F @ Y2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vimage_Collect_eq
% 0.29/0.46 thf(fact_10_vimageI,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,F: B > A,A2: B,B2: A,B3: set @ A] :
% 0.29/0.46 ( ( ( F @ A2 )
% 0.29/0.46 = B2 )
% 0.29/0.46 => ( ( member @ A @ B2 @ B3 )
% 0.29/0.46 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ B3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vimageI
% 0.29/0.46 thf(fact_11_vimage__eq,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 0.29/0.46 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 0.29/0.46 = ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % vimage_eq
% 0.29/0.46 thf(fact_12_set__plus__intro,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( plus @ A )
% 0.29/0.46 => ! [A2: A,C: set @ A,B2: A,D: set @ A] :
% 0.29/0.46 ( ( member @ A @ A2 @ C )
% 0.29/0.46 => ( ( member @ A @ B2 @ D )
% 0.29/0.46 => ( member @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( plus_plus @ ( set @ A ) @ C @ D ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % set_plus_intro
% 0.29/0.46 thf(fact_13_add__left__cancel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel_semigroup_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.46 = ( B2 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_left_cancel
% 0.29/0.46 thf(fact_14_add__right__cancel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel_semigroup_add @ A )
% 0.29/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.29/0.46 = ( plus_plus @ A @ C2 @ A2 ) )
% 0.29/0.46 = ( B2 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_right_cancel
% 0.29/0.46 thf(fact_15_vimage__def,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( vimage @ A @ B )
% 0.29/0.46 = ( ^ [F2: A > B,B4: set @ B] :
% 0.29/0.46 ( collect @ A
% 0.29/0.46 @ ^ [X: A] : ( member @ B @ ( F2 @ X ) @ B4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vimage_def
% 0.29/0.46 thf(fact_16_vimageD,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,A2: A,F: A > B,A4: set @ B] :
% 0.29/0.46 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ A4 ) )
% 0.29/0.46 => ( member @ B @ ( F @ A2 ) @ A4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % vimageD
% 0.29/0.46 thf(fact_17_vimageE,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 0.29/0.46 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 0.29/0.46 => ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % vimageE
% 0.29/0.46 thf(fact_18_IntI,axiom,
% 0.29/0.46 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( member @ A @ C2 @ A4 )
% 0.29/0.46 => ( ( member @ A @ C2 @ B3 )
% 0.29/0.46 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % IntI
% 0.29/0.46 thf(fact_19_Int__iff,axiom,
% 0.29/0.46 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 = ( ( member @ A @ C2 @ A4 )
% 0.29/0.46 & ( member @ A @ C2 @ B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Int_iff
% 0.29/0.46 thf(fact_20_space__completion,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A] :
% 0.29/0.46 ( ( sigma_space @ A @ ( complete_completion @ A @ M ) )
% 0.29/0.46 = ( sigma_space @ A @ M ) ) ).
% 0.29/0.46
% 0.29/0.46 % space_completion
% 0.29/0.46 thf(fact_21_vimage__Int,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,F: A > B,A4: set @ B,B3: set @ B] :
% 0.29/0.46 ( ( vimage @ A @ B @ F @ ( inf_inf @ ( set @ B ) @ A4 @ B3 ) )
% 0.29/0.46 = ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ A4 ) @ ( vimage @ A @ B @ F @ B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vimage_Int
% 0.29/0.46 thf(fact_22_T__def,axiom,
% 0.29/0.46 ( t2
% 0.29/0.46 = ( ^ [A5: finite_Cartesian_vec @ int @ n] : ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( r @ A5 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % T_def
% 0.29/0.46 thf(fact_23_IntE,axiom,
% 0.29/0.46 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 => ~ ( ( member @ A @ C2 @ A4 )
% 0.29/0.46 => ~ ( member @ A @ C2 @ B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % IntE
% 0.29/0.46 thf(fact_24_IntD1,axiom,
% 0.29/0.46 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 => ( member @ A @ C2 @ A4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % IntD1
% 0.29/0.46 thf(fact_25_IntD2,axiom,
% 0.29/0.46 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 => ( member @ A @ C2 @ B3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % IntD2
% 0.29/0.46 thf(fact_26_Int__assoc,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,B3: set @ A,C: set @ A] :
% 0.29/0.46 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) @ C )
% 0.29/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ B3 @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Int_assoc
% 0.29/0.46 thf(fact_27_Int__absorb,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A] :
% 0.29/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ A4 )
% 0.29/0.46 = A4 ) ).
% 0.29/0.46
% 0.29/0.46 % Int_absorb
% 0.29/0.46 thf(fact_28_Int__commute,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.29/0.46 = ( ^ [A6: set @ A,B4: set @ A] : ( inf_inf @ ( set @ A ) @ B4 @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Int_commute
% 0.29/0.46 thf(fact_29_Int__left__absorb,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Int_left_absorb
% 0.29/0.46 thf(fact_30_Int__left__commute,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,B3: set @ A,C: set @ A] :
% 0.29/0.46 ( ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ B3 @ C ) )
% 0.29/0.46 = ( inf_inf @ ( set @ A ) @ B3 @ ( inf_inf @ ( set @ A ) @ A4 @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Int_left_commute
% 0.29/0.46 thf(fact_31_Collect__conj__eq,axiom,
% 0.29/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/0.46 ( ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( P @ X )
% 0.29/0.46 & ( Q @ X ) ) )
% 0.29/0.46 = ( inf_inf @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_conj_eq
% 0.29/0.46 thf(fact_32_Int__Collect,axiom,
% 0.29/0.46 ! [A: $tType,X2: A,A4: set @ A,P: A > $o] :
% 0.29/0.46 ( ( member @ A @ X2 @ ( inf_inf @ ( set @ A ) @ A4 @ ( collect @ A @ P ) ) )
% 0.29/0.46 = ( ( member @ A @ X2 @ A4 )
% 0.29/0.46 & ( P @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Int_Collect
% 0.29/0.46 thf(fact_33_Int__def,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.29/0.46 = ( ^ [A6: set @ A,B4: set @ A] :
% 0.29/0.46 ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ A6 )
% 0.29/0.46 & ( member @ A @ X @ B4 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Int_def
% 0.29/0.46 thf(fact_34_measurable__completion,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,F: A > B,M: sigma_measure @ A,N2: sigma_measure @ B] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ N2 ) )
% 0.29/0.46 => ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( complete_completion @ A @ M ) @ N2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_completion
% 0.29/0.46 thf(fact_35_vimage__inter__cong,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,S: set @ A,F: A > B,G: A > B,Y3: set @ B] :
% 0.29/0.46 ( ! [W: A] :
% 0.29/0.46 ( ( member @ A @ W @ S )
% 0.29/0.46 => ( ( F @ W )
% 0.29/0.46 = ( G @ W ) ) )
% 0.29/0.46 => ( ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ Y3 ) @ S )
% 0.29/0.46 = ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ G @ Y3 ) @ S ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vimage_inter_cong
% 0.29/0.46 thf(fact_36_add__right__imp__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel_semigroup_add @ A )
% 0.29/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.29/0.46 = ( plus_plus @ A @ C2 @ A2 ) )
% 0.29/0.46 => ( B2 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_right_imp_eq
% 0.29/0.46 thf(fact_37_add__left__imp__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel_semigroup_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.46 => ( B2 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_left_imp_eq
% 0.29/0.46 thf(fact_38_add_Oleft__commute,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_semigroup_add @ A )
% 0.29/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.left_commute
% 0.29/0.46 thf(fact_39_add_Ocommute,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_semigroup_add @ A )
% 0.29/0.46 => ( ( plus_plus @ A )
% 0.29/0.46 = ( ^ [A5: A,B5: A] : ( plus_plus @ A @ B5 @ A5 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.commute
% 0.29/0.46 thf(fact_40_add_Oright__cancel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.29/0.46 = ( plus_plus @ A @ C2 @ A2 ) )
% 0.29/0.46 = ( B2 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.right_cancel
% 0.29/0.46 thf(fact_41_add_Oleft__cancel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ C2 ) )
% 0.29/0.46 = ( B2 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.left_cancel
% 0.29/0.46 thf(fact_42_add_Oassoc,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semigroup_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.assoc
% 0.29/0.46 thf(fact_43_set__plus__elim,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( plus @ A )
% 0.29/0.46 => ! [X2: A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( member @ A @ X2 @ ( plus_plus @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 => ~ ! [A7: A,B6: A] :
% 0.29/0.46 ( ( X2
% 0.29/0.46 = ( plus_plus @ A @ A7 @ B6 ) )
% 0.29/0.46 => ( ( member @ A @ A7 @ A4 )
% 0.29/0.46 => ~ ( member @ A @ B6 @ B3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % set_plus_elim
% 0.29/0.46 thf(fact_44_group__cancel_Oadd2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( comm_monoid_add @ A )
% 0.29/0.46 => ! [B3: A,K: A,B2: A,A2: A] :
% 0.29/0.46 ( ( B3
% 0.29/0.46 = ( plus_plus @ A @ K @ B2 ) )
% 0.29/0.46 => ( ( plus_plus @ A @ A2 @ B3 )
% 0.29/0.46 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % group_cancel.add2
% 0.29/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.29/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.29/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.29/0.46 = ( P @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % mem_Collect_eq
% 0.29/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A] :
% 0.29/0.46 ( ( collect @ A
% 0.29/0.46 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 0.29/0.46 = A4 ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_mem_eq
% 0.29/0.46 thf(fact_47_Collect__cong,axiom,
% 0.29/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/0.46 ( ! [X3: A] :
% 0.29/0.46 ( ( P @ X3 )
% 0.29/0.46 = ( Q @ X3 ) )
% 0.29/0.46 => ( ( collect @ A @ P )
% 0.29/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_cong
% 0.29/0.46 thf(fact_48_ext,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.29/0.46 ( ! [X3: A] :
% 0.29/0.46 ( ( F @ X3 )
% 0.29/0.46 = ( G @ X3 ) )
% 0.29/0.46 => ( F = G ) ) ).
% 0.29/0.46
% 0.29/0.46 % ext
% 0.29/0.46 thf(fact_49_group__cancel_Oadd1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( comm_monoid_add @ A )
% 0.29/0.46 => ! [A4: A,K: A,A2: A,B2: A] :
% 0.29/0.46 ( ( A4
% 0.29/0.46 = ( plus_plus @ A @ K @ A2 ) )
% 0.29/0.46 => ( ( plus_plus @ A @ A4 @ B2 )
% 0.29/0.46 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % group_cancel.add1
% 0.29/0.46 thf(fact_50_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere779506340up_add @ A )
% 0.29/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.29/0.46 ( ( ( I = J )
% 0.29/0.46 & ( K = L ) )
% 0.29/0.46 => ( ( plus_plus @ A @ I @ K )
% 0.29/0.46 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_mono_thms_linordered_semiring(4)
% 0.29/0.46 thf(fact_51_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_semigroup_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ab_semigroup_add_class.add_ac(1)
% 0.29/0.46 thf(fact_52_vimage__Collect,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,P: B > $o,F: A > B,Q: A > $o] :
% 0.29/0.46 ( ! [X3: A] :
% 0.29/0.46 ( ( P @ ( F @ X3 ) )
% 0.29/0.46 = ( Q @ X3 ) )
% 0.29/0.46 => ( ( vimage @ A @ B @ F @ ( collect @ B @ P ) )
% 0.29/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vimage_Collect
% 0.29/0.46 thf(fact_53_vimageI2,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,F: B > A,A2: B,A4: set @ A] :
% 0.29/0.46 ( ( member @ A @ ( F @ A2 ) @ A4 )
% 0.29/0.46 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vimageI2
% 0.29/0.46 thf(fact_54_sets_OInt__space__eq2,axiom,
% 0.29/0.46 ! [A: $tType,X2: set @ A,M: sigma_measure @ A] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ X2 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( inf_inf @ ( set @ A ) @ X2 @ ( sigma_space @ A @ M ) )
% 0.29/0.46 = X2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets.Int_space_eq2
% 0.29/0.46 thf(fact_55_sets_OInt__space__eq1,axiom,
% 0.29/0.46 ! [A: $tType,X2: set @ A,M: sigma_measure @ A] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ X2 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( inf_inf @ ( set @ A ) @ ( sigma_space @ A @ M ) @ X2 )
% 0.29/0.46 = X2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets.Int_space_eq1
% 0.29/0.46 thf(fact_56_measurable__sets,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,F: A > B,M: sigma_measure @ A,A4: sigma_measure @ B,S: set @ B] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ A4 ) )
% 0.29/0.46 => ( ( member @ ( set @ B ) @ S @ ( sigma_sets @ B @ A4 ) )
% 0.29/0.46 => ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ S ) @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_sets
% 0.29/0.46 thf(fact_57_measurableI,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,M: sigma_measure @ A,F: A > B,N2: sigma_measure @ B] :
% 0.29/0.46 ( ! [X3: A] :
% 0.29/0.46 ( ( member @ A @ X3 @ ( sigma_space @ A @ M ) )
% 0.29/0.46 => ( member @ B @ ( F @ X3 ) @ ( sigma_space @ B @ N2 ) ) )
% 0.29/0.46 => ( ! [A8: set @ B] :
% 0.29/0.46 ( ( member @ ( set @ B ) @ A8 @ ( sigma_sets @ B @ N2 ) )
% 0.29/0.46 => ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ A8 ) @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) ) )
% 0.29/0.46 => ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ N2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurableI
% 0.29/0.46 thf(fact_58_sets_Otop,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A] : ( member @ ( set @ A ) @ ( sigma_space @ A @ M ) @ ( sigma_sets @ A @ M ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets.top
% 0.29/0.46 thf(fact_59_sets_OInt,axiom,
% 0.29/0.46 ! [A: $tType,A2: set @ A,M: sigma_measure @ A,B2: set @ A] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ A2 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( member @ ( set @ A ) @ B2 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ ( sigma_sets @ A @ M ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets.Int
% 0.29/0.46 thf(fact_60_measurable__If__set,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,F: A > B,M: sigma_measure @ A,M2: sigma_measure @ B,G: A > B,A4: set @ A] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ M2 ) )
% 0.29/0.46 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ M2 ) )
% 0.29/0.46 => ( ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( member @ ( A > B )
% 0.29/0.46 @ ^ [X: A] : ( if @ B @ ( member @ A @ X @ A4 ) @ ( F @ X ) @ ( G @ X ) )
% 0.29/0.46 @ ( sigma_measurable @ A @ B @ M @ M2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_If_set
% 0.29/0.46 thf(fact_61_measurable__sets__Collect,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,F: A > B,M: sigma_measure @ A,N2: sigma_measure @ B,P: B > $o] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ N2 ) )
% 0.29/0.46 => ( ( member @ ( set @ B )
% 0.29/0.46 @ ( collect @ B
% 0.29/0.46 @ ^ [X: B] :
% 0.29/0.46 ( ( member @ B @ X @ ( sigma_space @ B @ N2 ) )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ B @ N2 ) )
% 0.29/0.46 => ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( P @ ( F @ X ) ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_sets_Collect
% 0.29/0.46 thf(fact_62_measurable__If,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,F: A > B,M: sigma_measure @ A,M2: sigma_measure @ B,G: A > B,P: A > $o] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ M2 ) )
% 0.29/0.46 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ M2 ) )
% 0.29/0.46 => ( ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( member @ ( A > B )
% 0.29/0.46 @ ^ [X: A] : ( if @ B @ ( P @ X ) @ ( F @ X ) @ ( G @ X ) )
% 0.29/0.46 @ ( sigma_measurable @ A @ B @ M @ M2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_If
% 0.29/0.46 thf(fact_63_inf__apply,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ B )
% 0.29/0.46 => ( ( inf_inf @ ( A > B ) )
% 0.29/0.46 = ( ^ [F2: A > B,G2: A > B,X: A] : ( inf_inf @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_apply
% 0.29/0.46 thf(fact_64_inf__right__idem,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [X2: A,Y3: A] :
% 0.29/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X2 @ Y3 ) @ Y3 )
% 0.29/0.46 = ( inf_inf @ A @ X2 @ Y3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_right_idem
% 0.29/0.46 thf(fact_65_inf_Oright__idem,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 0.29/0.46 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf.right_idem
% 0.29/0.46 thf(fact_66_inf__left__idem,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [X2: A,Y3: A] :
% 0.29/0.46 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ X2 @ Y3 ) )
% 0.29/0.46 = ( inf_inf @ A @ X2 @ Y3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_left_idem
% 0.29/0.46 thf(fact_67_inf_Oleft__idem,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.29/0.46 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf.left_idem
% 0.29/0.46 thf(fact_68_inf__idem,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [X2: A] :
% 0.29/0.46 ( ( inf_inf @ A @ X2 @ X2 )
% 0.29/0.46 = X2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_idem
% 0.29/0.46 thf(fact_69_inf_Oidem,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( inf_inf @ A @ A2 @ A2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf.idem
% 0.29/0.46 thf(fact_70_inf__set__def,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( inf_inf @ ( set @ A ) )
% 0.29/0.46 = ( ^ [A6: set @ A,B4: set @ A] :
% 0.29/0.46 ( collect @ A
% 0.29/0.46 @ ( inf_inf @ ( A > $o )
% 0.29/0.46 @ ^ [X: A] : ( member @ A @ X @ A6 )
% 0.29/0.46 @ ^ [X: A] : ( member @ A @ X @ B4 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_set_def
% 0.29/0.46 thf(fact_71_inf__left__commute,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [X2: A,Y3: A,Z: A] :
% 0.29/0.46 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y3 @ Z ) )
% 0.29/0.46 = ( inf_inf @ A @ Y3 @ ( inf_inf @ A @ X2 @ Z ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_left_commute
% 0.29/0.46 thf(fact_72_inf_Oleft__commute,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.29/0.46 ( ( inf_inf @ A @ B2 @ ( inf_inf @ A @ A2 @ C2 ) )
% 0.29/0.46 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf.left_commute
% 0.29/0.46 thf(fact_73_inf__commute,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ( ( inf_inf @ A )
% 0.29/0.46 = ( ^ [X: A,Y2: A] : ( inf_inf @ A @ Y2 @ X ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_commute
% 0.29/0.46 thf(fact_74_inf_Ocommute,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ( ( inf_inf @ A )
% 0.29/0.46 = ( ^ [A5: A,B5: A] : ( inf_inf @ A @ B5 @ A5 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf.commute
% 0.29/0.46 thf(fact_75_inf__assoc,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [X2: A,Y3: A,Z: A] :
% 0.29/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X2 @ Y3 ) @ Z )
% 0.29/0.46 = ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y3 @ Z ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_assoc
% 0.29/0.46 thf(fact_76_inf_Oassoc,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.46 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf.assoc
% 0.29/0.46 thf(fact_77_boolean__algebra__cancel_Oinf2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [B3: A,K: A,B2: A,A2: A] :
% 0.29/0.46 ( ( B3
% 0.29/0.46 = ( inf_inf @ A @ K @ B2 ) )
% 0.29/0.46 => ( ( inf_inf @ A @ A2 @ B3 )
% 0.29/0.46 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % boolean_algebra_cancel.inf2
% 0.29/0.46 thf(fact_78_boolean__algebra__cancel_Oinf1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [A4: A,K: A,A2: A,B2: A] :
% 0.29/0.46 ( ( A4
% 0.29/0.46 = ( inf_inf @ A @ K @ A2 ) )
% 0.29/0.46 => ( ( inf_inf @ A @ A4 @ B2 )
% 0.29/0.46 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % boolean_algebra_cancel.inf1
% 0.29/0.46 thf(fact_79_inf__fun__def,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ B )
% 0.29/0.46 => ( ( inf_inf @ ( A > B ) )
% 0.29/0.46 = ( ^ [F2: A > B,G2: A > B,X: A] : ( inf_inf @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_fun_def
% 0.29/0.46 thf(fact_80_inf__sup__aci_I1_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( lattice @ A )
% 0.29/0.46 => ( ( inf_inf @ A )
% 0.29/0.46 = ( ^ [X: A,Y2: A] : ( inf_inf @ A @ Y2 @ X ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_sup_aci(1)
% 0.29/0.46 thf(fact_81_inf__sup__aci_I2_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( lattice @ A )
% 0.29/0.46 => ! [X2: A,Y3: A,Z: A] :
% 0.29/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X2 @ Y3 ) @ Z )
% 0.29/0.46 = ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y3 @ Z ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_sup_aci(2)
% 0.29/0.46 thf(fact_82_inf__sup__aci_I3_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( lattice @ A )
% 0.29/0.46 => ! [X2: A,Y3: A,Z: A] :
% 0.29/0.46 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y3 @ Z ) )
% 0.29/0.46 = ( inf_inf @ A @ Y3 @ ( inf_inf @ A @ X2 @ Z ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_sup_aci(3)
% 0.29/0.46 thf(fact_83_inf__sup__aci_I4_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( lattice @ A )
% 0.29/0.46 => ! [X2: A,Y3: A] :
% 0.29/0.46 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ X2 @ Y3 ) )
% 0.29/0.46 = ( inf_inf @ A @ X2 @ Y3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_sup_aci(4)
% 0.29/0.46 thf(fact_84_measurable__compose__rev,axiom,
% 0.29/0.46 ! [A: $tType,C3: $tType,B: $tType,F: A > B,L2: sigma_measure @ A,N2: sigma_measure @ B,G: C3 > A,M: sigma_measure @ C3] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ L2 @ N2 ) )
% 0.29/0.46 => ( ( member @ ( C3 > A ) @ G @ ( sigma_measurable @ C3 @ A @ M @ L2 ) )
% 0.29/0.46 => ( member @ ( C3 > B )
% 0.29/0.46 @ ^ [X: C3] : ( F @ ( G @ X ) )
% 0.29/0.46 @ ( sigma_measurable @ C3 @ B @ M @ N2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_compose_rev
% 0.29/0.46 thf(fact_85_measurable__compose,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,C3: $tType,F: A > B,M: sigma_measure @ A,N2: sigma_measure @ B,G: B > C3,L2: sigma_measure @ C3] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ N2 ) )
% 0.29/0.46 => ( ( member @ ( B > C3 ) @ G @ ( sigma_measurable @ B @ C3 @ N2 @ L2 ) )
% 0.29/0.46 => ( member @ ( A > C3 )
% 0.29/0.46 @ ^ [X: A] : ( G @ ( F @ X ) )
% 0.29/0.46 @ ( sigma_measurable @ A @ C3 @ M @ L2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_compose
% 0.29/0.46 thf(fact_86_measurable__id,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A] :
% 0.29/0.46 ( member @ ( A > A )
% 0.29/0.46 @ ^ [X: A] : X
% 0.29/0.46 @ ( sigma_measurable @ A @ A @ M @ M ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_id
% 0.29/0.46 thf(fact_87_measurable__cong__sets,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,M: sigma_measure @ A,M2: sigma_measure @ A,N2: sigma_measure @ B,N3: sigma_measure @ B] :
% 0.29/0.46 ( ( ( sigma_sets @ A @ M )
% 0.29/0.46 = ( sigma_sets @ A @ M2 ) )
% 0.29/0.46 => ( ( ( sigma_sets @ B @ N2 )
% 0.29/0.46 = ( sigma_sets @ B @ N3 ) )
% 0.29/0.46 => ( ( sigma_measurable @ A @ B @ M @ N2 )
% 0.29/0.46 = ( sigma_measurable @ A @ B @ M2 @ N3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_cong_sets
% 0.29/0.46 thf(fact_88_sets__eq__imp__space__eq,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,M2: sigma_measure @ A] :
% 0.29/0.46 ( ( ( sigma_sets @ A @ M )
% 0.29/0.46 = ( sigma_sets @ A @ M2 ) )
% 0.29/0.46 => ( ( sigma_space @ A @ M )
% 0.29/0.46 = ( sigma_space @ A @ M2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets_eq_imp_space_eq
% 0.29/0.46 thf(fact_89_measurable__cong__simp,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,M: sigma_measure @ A,N2: sigma_measure @ A,M2: sigma_measure @ B,N3: sigma_measure @ B,F: A > B,G: A > B] :
% 0.29/0.46 ( ( M = N2 )
% 0.29/0.46 => ( ( M2 = N3 )
% 0.29/0.46 => ( ! [W: A] :
% 0.29/0.46 ( ( member @ A @ W @ ( sigma_space @ A @ M ) )
% 0.29/0.46 => ( ( F @ W )
% 0.29/0.46 = ( G @ W ) ) )
% 0.29/0.46 => ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ M2 ) )
% 0.29/0.46 = ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ N2 @ N3 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_cong_simp
% 0.29/0.46 thf(fact_90_measurable__space,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,F: A > B,M: sigma_measure @ A,A4: sigma_measure @ B,X2: A] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ A4 ) )
% 0.29/0.46 => ( ( member @ A @ X2 @ ( sigma_space @ A @ M ) )
% 0.29/0.46 => ( member @ B @ ( F @ X2 ) @ ( sigma_space @ B @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_space
% 0.29/0.46 thf(fact_91_measurable__cong,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,M: sigma_measure @ A,F: A > B,G: A > B,M2: sigma_measure @ B] :
% 0.29/0.46 ( ! [W: A] :
% 0.29/0.46 ( ( member @ A @ W @ ( sigma_space @ A @ M ) )
% 0.29/0.46 => ( ( F @ W )
% 0.29/0.46 = ( G @ W ) ) )
% 0.29/0.46 => ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ M2 ) )
% 0.29/0.46 = ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ M2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_cong
% 0.29/0.46 thf(fact_92_measurable__ident__sets,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,M2: sigma_measure @ A] :
% 0.29/0.46 ( ( ( sigma_sets @ A @ M )
% 0.29/0.46 = ( sigma_sets @ A @ M2 ) )
% 0.29/0.46 => ( member @ ( A > A )
% 0.29/0.46 @ ^ [X: A] : X
% 0.29/0.46 @ ( sigma_measurable @ A @ A @ M @ M2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_ident_sets
% 0.29/0.46 thf(fact_93_sets_Osets__Collect_I5_J,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,Pb: $o] :
% 0.29/0.46 ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & Pb ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets.sets_Collect(5)
% 0.29/0.46 thf(fact_94_sets_Osets__Collect__imp,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,P: A > $o,Q: A > $o] :
% 0.29/0.46 ( ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( Q @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( ( Q @ X )
% 0.29/0.46 => ( P @ X ) ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets.sets_Collect_imp
% 0.29/0.46 thf(fact_95_sets_Osets__Collect__neg,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,P: A > $o] :
% 0.29/0.46 ( ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ~ ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets.sets_Collect_neg
% 0.29/0.46 thf(fact_96_sets_Osets__Collect__conj,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,P: A > $o,Q: A > $o] :
% 0.29/0.46 ( ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( Q @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( Q @ X )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets.sets_Collect_conj
% 0.29/0.46 thf(fact_97_sets_Osets__Collect__disj,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,P: A > $o,Q: A > $o] :
% 0.29/0.46 ( ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( Q @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( ( Q @ X )
% 0.29/0.46 | ( P @ X ) ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets.sets_Collect_disj
% 0.29/0.46 thf(fact_98_sets_Osets__Collect__const,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,P: $o] :
% 0.29/0.46 ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & P ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets.sets_Collect_const
% 0.29/0.46 thf(fact_99_measurable__const,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,C2: A,M2: sigma_measure @ A,M: sigma_measure @ B] :
% 0.29/0.46 ( ( member @ A @ C2 @ ( sigma_space @ A @ M2 ) )
% 0.29/0.46 => ( member @ ( B > A )
% 0.29/0.46 @ ^ [X: B] : C2
% 0.29/0.46 @ ( sigma_measurable @ B @ A @ M @ M2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_const
% 0.29/0.46 thf(fact_100_T_H__def,axiom,
% 0.29/0.46 ( t
% 0.29/0.46 = ( ^ [A5: finite_Cartesian_vec @ int @ n] :
% 0.29/0.46 ( image @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
% 0.29/0.46 @ ^ [X: finite_Cartesian_vec @ real @ n] : ( minus_minus @ ( finite_Cartesian_vec @ real @ n ) @ X @ ( minkow1937162798nt_vec @ n @ real @ A5 ) )
% 0.29/0.46 @ ( t2 @ A5 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % T'_def
% 0.29/0.46 thf(fact_101_inf__Int__eq,axiom,
% 0.29/0.46 ! [A: $tType,R: set @ A,S: set @ A] :
% 0.29/0.46 ( ( inf_inf @ ( A > $o )
% 0.29/0.46 @ ^ [X: A] : ( member @ A @ X @ R )
% 0.29/0.46 @ ^ [X: A] : ( member @ A @ X @ S ) )
% 0.29/0.46 = ( ^ [X: A] : ( member @ A @ X @ ( inf_inf @ ( set @ A ) @ R @ S ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_Int_eq
% 0.29/0.46 thf(fact_102_main__part__sets,axiom,
% 0.29/0.46 ! [A: $tType,S: set @ A,M: sigma_measure @ A] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ ( complete_completion @ A @ M ) ) )
% 0.29/0.46 => ( member @ ( set @ A ) @ ( complete_main_part @ A @ M @ S ) @ ( sigma_sets @ A @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % main_part_sets
% 0.29/0.46 thf(fact_103_measurable__restrict__space__iff,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,Omega: set @ A,M: sigma_measure @ A,C2: B,N2: sigma_measure @ B,F: A > B] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ Omega @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( member @ B @ C2 @ ( sigma_space @ B @ N2 ) )
% 0.29/0.46 => ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ M @ Omega ) @ N2 ) )
% 0.29/0.46 = ( member @ ( A > B )
% 0.29/0.46 @ ^ [X: A] : ( if @ B @ ( member @ A @ X @ Omega ) @ ( F @ X ) @ C2 )
% 0.29/0.46 @ ( sigma_measurable @ A @ B @ M @ N2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_restrict_space_iff
% 0.29/0.46 thf(fact_104_sets__Least,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,P: nat > A > $o,A4: set @ nat] :
% 0.29/0.46 ( ! [I2: nat] :
% 0.29/0.46 ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( P @ I2 @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( member @ ( set @ A )
% 0.29/0.46 @ ( inf_inf @ ( set @ A )
% 0.29/0.46 @ ( vimage @ A @ nat
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ord_Least @ nat
% 0.29/0.46 @ ^ [J2: nat] : ( P @ J2 @ X ) )
% 0.29/0.46 @ A4 )
% 0.29/0.46 @ ( sigma_space @ A @ M ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets_Least
% 0.29/0.46 thf(fact_105_in__vimage__algebra,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,A4: set @ A,M: sigma_measure @ A,F: B > A,X4: set @ B] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ A4 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( member @ ( set @ B ) @ ( inf_inf @ ( set @ B ) @ ( vimage @ B @ A @ F @ A4 ) @ X4 ) @ ( sigma_sets @ B @ ( sigma_vimage_algebra @ B @ A @ X4 @ F @ M ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % in_vimage_algebra
% 0.29/0.46 thf(fact_106_in__borel__measurable__borel,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( topolo503727757_space @ B )
% 0.29/0.46 => ! [F: A > B,M: sigma_measure @ A] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 = ( ! [X: set @ B] :
% 0.29/0.46 ( ( member @ ( set @ B ) @ X @ ( sigma_sets @ B @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ X ) @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % in_borel_measurable_borel
% 0.29/0.46 thf(fact_107_image__eqI,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,B2: A,F: B > A,X2: B,A4: set @ B] :
% 0.29/0.46 ( ( B2
% 0.29/0.46 = ( F @ X2 ) )
% 0.29/0.46 => ( ( member @ B @ X2 @ A4 )
% 0.29/0.46 => ( member @ A @ B2 @ ( image @ B @ A @ F @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_eqI
% 0.29/0.46 thf(fact_108_minus__apply,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( minus @ B )
% 0.29/0.46 => ( ( minus_minus @ ( A > B ) )
% 0.29/0.46 = ( ^ [A6: A > B,B4: A > B,X: A] : ( minus_minus @ B @ ( A6 @ X ) @ ( B4 @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % minus_apply
% 0.29/0.46 thf(fact_109_inf1I,axiom,
% 0.29/0.46 ! [A: $tType,A4: A > $o,X2: A,B3: A > $o] :
% 0.29/0.46 ( ( A4 @ X2 )
% 0.29/0.46 => ( ( B3 @ X2 )
% 0.29/0.46 => ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf1I
% 0.29/0.46 thf(fact_110_image__ident,axiom,
% 0.29/0.46 ! [A: $tType,Y: set @ A] :
% 0.29/0.46 ( ( image @ A @ A
% 0.29/0.46 @ ^ [X: A] : X
% 0.29/0.46 @ Y )
% 0.29/0.46 = Y ) ).
% 0.29/0.46
% 0.29/0.46 % image_ident
% 0.29/0.46 thf(fact_111_add__diff__cancel__right_H,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel146912293up_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel_right'
% 0.29/0.46 thf(fact_112_add__diff__cancel__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel146912293up_add @ A )
% 0.29/0.46 => ! [A2: A,C2: A,B2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.29/0.46 = ( minus_minus @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel_right
% 0.29/0.46 thf(fact_113_add__diff__cancel__left_H,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel146912293up_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ A2 )
% 0.29/0.46 = B2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel_left'
% 0.29/0.46 thf(fact_114_add__diff__cancel__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel146912293up_add @ A )
% 0.29/0.46 => ! [C2: A,A2: A,B2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 0.29/0.46 = ( minus_minus @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel_left
% 0.29/0.46 thf(fact_115_diff__add__cancel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B2 ) @ B2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_add_cancel
% 0.29/0.46 thf(fact_116_add__diff__cancel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel
% 0.29/0.46 thf(fact_117_space__vimage__algebra,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,X4: set @ A,F: A > B,M: sigma_measure @ B] :
% 0.29/0.46 ( ( sigma_space @ A @ ( sigma_vimage_algebra @ A @ B @ X4 @ F @ M ) )
% 0.29/0.46 = X4 ) ).
% 0.29/0.46
% 0.29/0.46 % space_vimage_algebra
% 0.29/0.46 thf(fact_118_main__part,axiom,
% 0.29/0.46 ! [A: $tType,S: set @ A,M: sigma_measure @ A] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( complete_main_part @ A @ M @ S )
% 0.29/0.46 = S ) ) ).
% 0.29/0.46
% 0.29/0.46 % main_part
% 0.29/0.46 thf(fact_119_space__restrict__space2,axiom,
% 0.29/0.46 ! [A: $tType,Omega: set @ A,M: sigma_measure @ A] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ Omega @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( sigma_space @ A @ ( sigma_restrict_space @ A @ M @ Omega ) )
% 0.29/0.46 = Omega ) ) ).
% 0.29/0.46
% 0.29/0.46 % space_restrict_space2
% 0.29/0.46 thf(fact_120_inf1E,axiom,
% 0.29/0.46 ! [A: $tType,A4: A > $o,B3: A > $o,X2: A] :
% 0.29/0.46 ( ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X2 )
% 0.29/0.46 => ~ ( ( A4 @ X2 )
% 0.29/0.46 => ~ ( B3 @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf1E
% 0.29/0.46 thf(fact_121_inf1D1,axiom,
% 0.29/0.46 ! [A: $tType,A4: A > $o,B3: A > $o,X2: A] :
% 0.29/0.46 ( ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X2 )
% 0.29/0.46 => ( A4 @ X2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf1D1
% 0.29/0.46 thf(fact_122_inf1D2,axiom,
% 0.29/0.46 ! [A: $tType,A4: A > $o,B3: A > $o,X2: A] :
% 0.29/0.46 ( ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X2 )
% 0.29/0.46 => ( B3 @ X2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf1D2
% 0.29/0.46 thf(fact_123_borel__measurable__diff,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( ( elemen1026692323pology @ B )
% 0.29/0.46 & ( real_V55928688vector @ B ) )
% 0.29/0.46 => ! [F: A > B,M: sigma_measure @ A,G: A > B] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( member @ ( A > B )
% 0.29/0.46 @ ^ [X: A] : ( minus_minus @ B @ ( F @ X ) @ ( G @ X ) )
% 0.29/0.46 @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_diff
% 0.29/0.46 thf(fact_124_fun__diff__def,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( minus @ B )
% 0.29/0.46 => ( ( minus_minus @ ( A > B ) )
% 0.29/0.46 = ( ^ [A6: A > B,B4: A > B,X: A] : ( minus_minus @ B @ ( A6 @ X ) @ ( B4 @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % fun_diff_def
% 0.29/0.46 thf(fact_125_Compr__image__eq,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 0.29/0.46 ( ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( image @ B @ A @ F @ A4 ) )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 = ( image @ B @ A @ F
% 0.29/0.46 @ ( collect @ B
% 0.29/0.46 @ ^ [X: B] :
% 0.29/0.46 ( ( member @ B @ X @ A4 )
% 0.29/0.46 & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compr_image_eq
% 0.29/0.46 thf(fact_126_image__image,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,C3: $tType,F: B > A,G: C3 > B,A4: set @ C3] :
% 0.29/0.46 ( ( image @ B @ A @ F @ ( image @ C3 @ B @ G @ A4 ) )
% 0.29/0.46 = ( image @ C3 @ A
% 0.29/0.46 @ ^ [X: C3] : ( F @ ( G @ X ) )
% 0.29/0.46 @ A4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_image
% 0.29/0.46 thf(fact_127_imageE,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,B2: A,F: B > A,A4: set @ B] :
% 0.29/0.46 ( ( member @ A @ B2 @ ( image @ B @ A @ F @ A4 ) )
% 0.29/0.46 => ~ ! [X3: B] :
% 0.29/0.46 ( ( B2
% 0.29/0.46 = ( F @ X3 ) )
% 0.29/0.46 => ~ ( member @ B @ X3 @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % imageE
% 0.29/0.46 thf(fact_128_diff__right__commute,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel146912293up_add @ A )
% 0.29/0.46 => ! [A2: A,C2: A,B2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C2 ) @ B2 )
% 0.29/0.46 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_right_commute
% 0.29/0.46 thf(fact_129_diff__eq__diff__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A,D2: A] :
% 0.29/0.46 ( ( ( minus_minus @ A @ A2 @ B2 )
% 0.29/0.46 = ( minus_minus @ A @ C2 @ D2 ) )
% 0.29/0.46 => ( ( A2 = B2 )
% 0.29/0.46 = ( C2 = D2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_eq_diff_eq
% 0.29/0.46 thf(fact_130_rev__image__eqI,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,X2: A,A4: set @ A,B2: B,F: A > B] :
% 0.29/0.46 ( ( member @ A @ X2 @ A4 )
% 0.29/0.46 => ( ( B2
% 0.29/0.46 = ( F @ X2 ) )
% 0.29/0.46 => ( member @ B @ B2 @ ( image @ A @ B @ F @ A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % rev_image_eqI
% 0.29/0.46 thf(fact_131_ball__imageD,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 0.29/0.46 ( ! [X3: A] :
% 0.29/0.46 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A4 ) )
% 0.29/0.46 => ( P @ X3 ) )
% 0.29/0.46 => ! [X5: B] :
% 0.29/0.46 ( ( member @ B @ X5 @ A4 )
% 0.29/0.46 => ( P @ ( F @ X5 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ball_imageD
% 0.29/0.46 thf(fact_132_image__cong,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,M: set @ A,N2: set @ A,F: A > B,G: A > B] :
% 0.29/0.46 ( ( M = N2 )
% 0.29/0.46 => ( ! [X3: A] :
% 0.29/0.46 ( ( member @ A @ X3 @ N2 )
% 0.29/0.46 => ( ( F @ X3 )
% 0.29/0.46 = ( G @ X3 ) ) )
% 0.29/0.46 => ( ( image @ A @ B @ F @ M )
% 0.29/0.46 = ( image @ A @ B @ G @ N2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_cong
% 0.29/0.46 thf(fact_133_bex__imageD,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 0.29/0.46 ( ? [X5: A] :
% 0.29/0.46 ( ( member @ A @ X5 @ ( image @ B @ A @ F @ A4 ) )
% 0.29/0.46 & ( P @ X5 ) )
% 0.29/0.46 => ? [X3: B] :
% 0.29/0.46 ( ( member @ B @ X3 @ A4 )
% 0.29/0.46 & ( P @ ( F @ X3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bex_imageD
% 0.29/0.46 thf(fact_134_image__iff,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,Z: A,F: B > A,A4: set @ B] :
% 0.29/0.46 ( ( member @ A @ Z @ ( image @ B @ A @ F @ A4 ) )
% 0.29/0.46 = ( ? [X: B] :
% 0.29/0.46 ( ( member @ B @ X @ A4 )
% 0.29/0.46 & ( Z
% 0.29/0.46 = ( F @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_iff
% 0.29/0.46 thf(fact_135_imageI,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,X2: A,A4: set @ A,F: A > B] :
% 0.29/0.46 ( ( member @ A @ X2 @ A4 )
% 0.29/0.46 => ( member @ B @ ( F @ X2 ) @ ( image @ A @ B @ F @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % imageI
% 0.29/0.46 thf(fact_136_borel__measurable__const,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( topolo503727757_space @ B )
% 0.29/0.46 => ! [C2: B,M: sigma_measure @ A] :
% 0.29/0.46 ( member @ ( A > B )
% 0.29/0.46 @ ^ [X: A] : C2
% 0.29/0.46 @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_const
% 0.29/0.46 thf(fact_137_sets__restrict__space__cong,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,N2: sigma_measure @ A,Omega: set @ A] :
% 0.29/0.46 ( ( ( sigma_sets @ A @ M )
% 0.29/0.46 = ( sigma_sets @ A @ N2 ) )
% 0.29/0.46 => ( ( sigma_sets @ A @ ( sigma_restrict_space @ A @ M @ Omega ) )
% 0.29/0.46 = ( sigma_sets @ A @ ( sigma_restrict_space @ A @ N2 @ Omega ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets_restrict_space_cong
% 0.29/0.46 thf(fact_138_restrict__space__sets__cong,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,B3: set @ A,M: sigma_measure @ A,N2: sigma_measure @ A] :
% 0.29/0.46 ( ( A4 = B3 )
% 0.29/0.46 => ( ( ( sigma_sets @ A @ M )
% 0.29/0.46 = ( sigma_sets @ A @ N2 ) )
% 0.29/0.46 => ( ( sigma_sets @ A @ ( sigma_restrict_space @ A @ M @ A4 ) )
% 0.29/0.46 = ( sigma_sets @ A @ ( sigma_restrict_space @ A @ N2 @ B3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % restrict_space_sets_cong
% 0.29/0.46 thf(fact_139_measurable__restrict__space1,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,F: A > B,M: sigma_measure @ A,N2: sigma_measure @ B,Omega: set @ A] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ N2 ) )
% 0.29/0.46 => ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ M @ Omega ) @ N2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_restrict_space1
% 0.29/0.46 thf(fact_140_add__implies__diff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel1352612707id_add @ A )
% 0.29/0.46 => ! [C2: A,B2: A,A2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ C2 @ B2 )
% 0.29/0.46 = A2 )
% 0.29/0.46 => ( C2
% 0.29/0.46 = ( minus_minus @ A @ A2 @ B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_implies_diff
% 0.29/0.46 thf(fact_141_diff__diff__add,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel146912293up_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.46 = ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_diff_add
% 0.29/0.46 thf(fact_142_diff__add__eq__diff__diff__swap,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.29/0.46 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C2 ) @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_add_eq_diff_diff_swap
% 0.29/0.46 thf(fact_143_diff__add__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_group_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B2 ) @ C2 )
% 0.29/0.46 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_add_eq
% 0.29/0.46 thf(fact_144_diff__diff__eq2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ A2 @ ( minus_minus @ A @ B2 @ C2 ) )
% 0.29/0.46 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_diff_eq2
% 0.29/0.46 thf(fact_145_add__diff__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B2 @ C2 ) )
% 0.29/0.46 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_eq
% 0.29/0.46 thf(fact_146_eq__diff__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A,C2: A,B2: A] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( minus_minus @ A @ C2 @ B2 ) )
% 0.29/0.46 = ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.46 = C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % eq_diff_eq
% 0.29/0.46 thf(fact_147_diff__eq__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ( minus_minus @ A @ A2 @ B2 )
% 0.29/0.46 = C2 )
% 0.29/0.46 = ( A2
% 0.29/0.46 = ( plus_plus @ A @ C2 @ B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_eq_eq
% 0.29/0.46 thf(fact_148_group__cancel_Osub1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_group_add @ A )
% 0.29/0.46 => ! [A4: A,K: A,A2: A,B2: A] :
% 0.29/0.46 ( ( A4
% 0.29/0.46 = ( plus_plus @ A @ K @ A2 ) )
% 0.29/0.46 => ( ( minus_minus @ A @ A4 @ B2 )
% 0.29/0.46 = ( plus_plus @ A @ K @ ( minus_minus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % group_cancel.sub1
% 0.29/0.46 thf(fact_149_sets__vimage__algebra__cong,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,M: sigma_measure @ A,N2: sigma_measure @ A,X4: set @ B,F: B > A] :
% 0.29/0.46 ( ( ( sigma_sets @ A @ M )
% 0.29/0.46 = ( sigma_sets @ A @ N2 ) )
% 0.29/0.46 => ( ( sigma_sets @ B @ ( sigma_vimage_algebra @ B @ A @ X4 @ F @ M ) )
% 0.29/0.46 = ( sigma_sets @ B @ ( sigma_vimage_algebra @ B @ A @ X4 @ F @ N2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets_vimage_algebra_cong
% 0.29/0.46 thf(fact_150_vimage__algebra__cong,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,X4: set @ A,Y: set @ A,F: A > B,G: A > B,M: sigma_measure @ B,N2: sigma_measure @ B] :
% 0.29/0.46 ( ( X4 = Y )
% 0.29/0.46 => ( ! [X3: A] :
% 0.29/0.46 ( ( member @ A @ X3 @ Y )
% 0.29/0.46 => ( ( F @ X3 )
% 0.29/0.46 = ( G @ X3 ) ) )
% 0.29/0.46 => ( ( ( sigma_sets @ B @ M )
% 0.29/0.46 = ( sigma_sets @ B @ N2 ) )
% 0.29/0.46 => ( ( sigma_vimage_algebra @ A @ B @ X4 @ F @ M )
% 0.29/0.46 = ( sigma_vimage_algebra @ A @ B @ Y @ G @ N2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vimage_algebra_cong
% 0.29/0.46 thf(fact_151_borel__measurable__const__add,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( real_V55928688vector @ A )
% 0.29/0.46 => ! [F: B > A,M: sigma_measure @ B,A2: A] :
% 0.29/0.46 ( ( member @ ( B > A ) @ F @ ( sigma_measurable @ B @ A @ M @ ( borel_1404511681_borel @ A ) ) )
% 0.29/0.46 => ( member @ ( B > A )
% 0.29/0.46 @ ^ [X: B] : ( plus_plus @ A @ A2 @ ( F @ X ) )
% 0.29/0.46 @ ( sigma_measurable @ B @ A @ M @ ( borel_1404511681_borel @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_const_add
% 0.29/0.46 thf(fact_152_borel__measurable__add,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( ( elemen1026692323pology @ B )
% 0.29/0.46 & ( topolo1314133330id_add @ B ) )
% 0.29/0.46 => ! [F: A > B,M: sigma_measure @ A,G: A > B] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( member @ ( A > B )
% 0.29/0.46 @ ^ [X: A] : ( plus_plus @ B @ ( F @ X ) @ ( G @ X ) )
% 0.29/0.46 @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_add
% 0.29/0.46 thf(fact_153_borel__measurable__inf,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( ( elemen1026692323pology @ B )
% 0.29/0.46 & ( lattice @ B )
% 0.29/0.46 & ( topolo2117631714pology @ B ) )
% 0.29/0.46 => ! [F: A > B,M: sigma_measure @ A,G: A > B] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( member @ ( A > B )
% 0.29/0.46 @ ^ [X: A] : ( inf_inf @ B @ ( G @ X ) @ ( F @ X ) )
% 0.29/0.46 @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_inf
% 0.29/0.46 thf(fact_154_sets__restrict__restrict__space,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( sigma_sets @ A @ ( sigma_restrict_space @ A @ ( sigma_restrict_space @ A @ M @ A4 ) @ B3 ) )
% 0.29/0.46 = ( sigma_sets @ A @ ( sigma_restrict_space @ A @ M @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets_restrict_restrict_space
% 0.29/0.46 thf(fact_155_space__restrict__space,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,Omega: set @ A] :
% 0.29/0.46 ( ( sigma_space @ A @ ( sigma_restrict_space @ A @ M @ Omega ) )
% 0.29/0.46 = ( inf_inf @ ( set @ A ) @ Omega @ ( sigma_space @ A @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % space_restrict_space
% 0.29/0.46 thf(fact_156_measurable__sets__borel,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( topolo503727757_space @ A )
% 0.29/0.46 => ! [F: A > B,M: sigma_measure @ B,A4: set @ B] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( borel_1404511681_borel @ A ) @ M ) )
% 0.29/0.46 => ( ( member @ ( set @ B ) @ A4 @ ( sigma_sets @ B @ M ) )
% 0.29/0.46 => ( member @ ( set @ A ) @ ( vimage @ A @ B @ F @ A4 ) @ ( sigma_sets @ A @ ( borel_1404511681_borel @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_sets_borel
% 0.29/0.46 thf(fact_157_sets__Collect__restrict__space__iff,axiom,
% 0.29/0.46 ! [A: $tType,S: set @ A,M: sigma_measure @ A,P: A > $o] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ ( sigma_restrict_space @ A @ M @ S ) ) )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ ( sigma_restrict_space @ A @ M @ S ) ) )
% 0.29/0.46 = ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( member @ A @ X @ S )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets_Collect_restrict_space_iff
% 0.29/0.46 thf(fact_158_borel__measurable__eq,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( elemen1026692323pology @ B )
% 0.29/0.46 & ( topolo2117631714pology @ B ) )
% 0.29/0.46 => ! [F: A > B,M: sigma_measure @ A,G: A > B] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [W2: A] :
% 0.29/0.46 ( ( member @ A @ W2 @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( ( F @ W2 )
% 0.29/0.46 = ( G @ W2 ) ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_eq
% 0.29/0.46 thf(fact_159_borel__measurable__neq,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( elemen1026692323pology @ B )
% 0.29/0.46 & ( topolo2117631714pology @ B ) )
% 0.29/0.46 => ! [F: A > B,M: sigma_measure @ A,G: A > B] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [W2: A] :
% 0.29/0.46 ( ( member @ A @ W2 @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( ( F @ W2 )
% 0.29/0.46 != ( G @ W2 ) ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_neq
% 0.29/0.46 thf(fact_160_measurable__equality__set,axiom,
% 0.29/0.46 ! [A: $tType,D3: $tType] :
% 0.29/0.46 ( ( ( elemen1026692323pology @ A )
% 0.29/0.46 & ( topological_t2_space @ A ) )
% 0.29/0.46 => ! [F: D3 > A,M: sigma_measure @ D3,G: D3 > A] :
% 0.29/0.46 ( ( member @ ( D3 > A ) @ F @ ( sigma_measurable @ D3 @ A @ M @ ( borel_1404511681_borel @ A ) ) )
% 0.29/0.46 => ( ( member @ ( D3 > A ) @ G @ ( sigma_measurable @ D3 @ A @ M @ ( borel_1404511681_borel @ A ) ) )
% 0.29/0.46 => ( member @ ( set @ D3 )
% 0.29/0.46 @ ( collect @ D3
% 0.29/0.46 @ ^ [X: D3] :
% 0.29/0.46 ( ( member @ D3 @ X @ ( sigma_space @ D3 @ M ) )
% 0.29/0.46 & ( ( F @ X )
% 0.29/0.46 = ( G @ X ) ) ) )
% 0.29/0.46 @ ( sigma_sets @ D3 @ M ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_equality_set
% 0.29/0.46 thf(fact_161_measurable__If__restrict__space__iff,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,M: sigma_measure @ A,P: A > $o,F: A > B,G: A > B,N2: sigma_measure @ B] :
% 0.29/0.46 ( ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( member @ ( A > B )
% 0.29/0.46 @ ^ [X: A] : ( if @ B @ ( P @ X ) @ ( F @ X ) @ ( G @ X ) )
% 0.29/0.46 @ ( sigma_measurable @ A @ B @ M @ N2 ) )
% 0.29/0.46 = ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ M @ ( collect @ A @ P ) ) @ N2 ) )
% 0.29/0.46 & ( member @ ( A > B ) @ G
% 0.29/0.46 @ ( sigma_measurable @ A @ B
% 0.29/0.46 @ ( sigma_restrict_space @ A @ M
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ~ ( P @ X ) ) )
% 0.29/0.46 @ N2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_If_restrict_space_iff
% 0.29/0.46 thf(fact_162_space__lebesgue__on,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( euclid925273238_space @ A )
% 0.29/0.46 => ! [S: set @ A] :
% 0.29/0.46 ( ( sigma_space @ A @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) )
% 0.29/0.46 = S ) ) ).
% 0.29/0.46
% 0.29/0.46 % space_lebesgue_on
% 0.29/0.46 thf(fact_163_sets__lebesgue__on__refl,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( euclid925273238_space @ A )
% 0.29/0.46 => ! [S: set @ A] : ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets_lebesgue_on_refl
% 0.29/0.46 thf(fact_164_space__lborel,axiom,
% 0.29/0.46 ! [B: $tType] :
% 0.29/0.46 ( ( euclid925273238_space @ B )
% 0.29/0.46 => ( ( sigma_space @ B @ ( lebesgue_lborel @ B ) )
% 0.29/0.46 = ( sigma_space @ B @ ( borel_1404511681_borel @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % space_lborel
% 0.29/0.46 thf(fact_165_measurable__lborel1,axiom,
% 0.29/0.46 ! [C3: $tType,D3: $tType] :
% 0.29/0.46 ( ( euclid925273238_space @ D3 )
% 0.29/0.46 => ! [M: sigma_measure @ C3] :
% 0.29/0.46 ( ( sigma_measurable @ C3 @ D3 @ M @ ( lebesgue_lborel @ D3 ) )
% 0.29/0.46 = ( sigma_measurable @ C3 @ D3 @ M @ ( borel_1404511681_borel @ D3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_lborel1
% 0.29/0.46 thf(fact_166_measurable__lborel2,axiom,
% 0.29/0.46 ! [E: $tType,C3: $tType] :
% 0.29/0.46 ( ( euclid925273238_space @ E )
% 0.29/0.46 => ! [M: sigma_measure @ C3] :
% 0.29/0.46 ( ( sigma_measurable @ E @ C3 @ ( lebesgue_lborel @ E ) @ M )
% 0.29/0.46 = ( sigma_measurable @ E @ C3 @ ( borel_1404511681_borel @ E ) @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_lborel2
% 0.29/0.46 thf(fact_167_sets_ODiff,axiom,
% 0.29/0.46 ! [A: $tType,A2: set @ A,M: sigma_measure @ A,B2: set @ A] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ A2 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( member @ ( set @ A ) @ B2 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( member @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( sigma_sets @ A @ M ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets.Diff
% 0.29/0.46 thf(fact_168_sets_Ocompl__sets,axiom,
% 0.29/0.46 ! [A: $tType,A2: set @ A,M: sigma_measure @ A] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ A2 @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( member @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ ( sigma_space @ A @ M ) @ A2 ) @ ( sigma_sets @ A @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets.compl_sets
% 0.29/0.46 thf(fact_169_sets__lborel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( euclid925273238_space @ A )
% 0.29/0.46 => ( ( sigma_sets @ A @ ( lebesgue_lborel @ A ) )
% 0.29/0.46 = ( sigma_sets @ A @ ( borel_1404511681_borel @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets_lborel
% 0.29/0.46 thf(fact_170_Int__Diff,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,B3: set @ A,C: set @ A] :
% 0.29/0.46 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) @ C )
% 0.29/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ B3 @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Int_Diff
% 0.29/0.46 thf(fact_171_Diff__Int2,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,C: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ C ) @ ( inf_inf @ ( set @ A ) @ B3 @ C ) )
% 0.29/0.46 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ C ) @ B3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Diff_Int2
% 0.29/0.46 thf(fact_172_Diff__Diff__Int,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( minus_minus @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 = ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Diff_Diff_Int
% 0.29/0.46 thf(fact_173_Diff__Int__distrib,axiom,
% 0.29/0.46 ! [A: $tType,C: set @ A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( inf_inf @ ( set @ A ) @ C @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ C @ A4 ) @ ( inf_inf @ ( set @ A ) @ C @ B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Diff_Int_distrib
% 0.29/0.46 thf(fact_174_Diff__Int__distrib2,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,B3: set @ A,C: set @ A] :
% 0.29/0.46 ( ( inf_inf @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) @ C )
% 0.29/0.46 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ C ) @ ( inf_inf @ ( set @ A ) @ B3 @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Diff_Int_distrib2
% 0.29/0.46 thf(fact_175_vimage__Diff,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,F: A > B,A4: set @ B,B3: set @ B] :
% 0.29/0.46 ( ( vimage @ A @ B @ F @ ( minus_minus @ ( set @ B ) @ A4 @ B3 ) )
% 0.29/0.46 = ( minus_minus @ ( set @ A ) @ ( vimage @ A @ B @ F @ A4 ) @ ( vimage @ A @ B @ F @ B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vimage_Diff
% 0.29/0.46 thf(fact_176_sets__restrict__space,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,Omega: set @ A] :
% 0.29/0.46 ( ( sigma_sets @ A @ ( sigma_restrict_space @ A @ M @ Omega ) )
% 0.29/0.46 = ( image @ ( set @ A ) @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ Omega ) @ ( sigma_sets @ A @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets_restrict_space
% 0.29/0.46 thf(fact_177_lborelD,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( euclid925273238_space @ A )
% 0.29/0.46 => ! [A4: set @ A] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ A4 @ ( sigma_sets @ A @ ( borel_1404511681_borel @ A ) ) )
% 0.29/0.46 => ( member @ ( set @ A ) @ A4 @ ( sigma_sets @ A @ ( lebesgue_lborel @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lborelD
% 0.29/0.46 thf(fact_178_measurable__lebesgue__cong,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( euclid925273238_space @ A )
% 0.29/0.46 => ! [S: set @ A,F: A > B,G: A > B,M: sigma_measure @ B] :
% 0.29/0.46 ( ! [X3: A] :
% 0.29/0.46 ( ( member @ A @ X3 @ S )
% 0.29/0.46 => ( ( F @ X3 )
% 0.29/0.46 = ( G @ X3 ) ) )
% 0.29/0.46 => ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ M ) )
% 0.29/0.46 = ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ M ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_lebesgue_cong
% 0.29/0.46 thf(fact_179_lborelD__Collect,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( euclid925273238_space @ A )
% 0.29/0.46 => ! [P: A > $o] :
% 0.29/0.46 ( ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ ( borel_1404511681_borel @ A ) ) )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ ( borel_1404511681_borel @ A ) ) )
% 0.29/0.46 => ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sigma_space @ A @ ( lebesgue_lborel @ A ) ) )
% 0.29/0.46 & ( P @ X ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ ( lebesgue_lborel @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lborelD_Collect
% 0.29/0.46 thf(fact_180_lebesgue__sets__translation,axiom,
% 0.29/0.46 ! [B: $tType] :
% 0.29/0.46 ( ( euclid925273238_space @ B )
% 0.29/0.46 => ! [S: set @ B,A2: B] :
% 0.29/0.46 ( ( member @ ( set @ B ) @ S @ ( sigma_sets @ B @ ( complete_completion @ B @ ( lebesgue_lborel @ B ) ) ) )
% 0.29/0.46 => ( member @ ( set @ B ) @ ( image @ B @ B @ ( plus_plus @ B @ A2 ) @ S ) @ ( sigma_sets @ B @ ( complete_completion @ B @ ( lebesgue_lborel @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lebesgue_sets_translation
% 0.29/0.46 thf(fact_181_lebesgue__measurable__vimage__borel,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( euclid925273238_space @ A )
% 0.29/0.46 & ( euclid925273238_space @ B ) )
% 0.29/0.46 => ! [F: A > B,T: set @ B] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( ( member @ ( set @ B ) @ T @ ( sigma_sets @ B @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] : ( member @ B @ ( F @ X ) @ T ) )
% 0.29/0.46 @ ( sigma_sets @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lebesgue_measurable_vimage_borel
% 0.29/0.46 thf(fact_182_borel__measurable__lebesgue__preimage__borel,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( ( euclid925273238_space @ B )
% 0.29/0.46 & ( euclid925273238_space @ A ) )
% 0.29/0.46 => ! [F: A > B] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 = ( ! [T2: set @ B] :
% 0.29/0.46 ( ( member @ ( set @ B ) @ T2 @ ( sigma_sets @ B @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] : ( member @ B @ ( F @ X ) @ T2 ) )
% 0.29/0.46 @ ( sigma_sets @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_lebesgue_preimage_borel
% 0.29/0.46 thf(fact_183_borel__measurable__vimage__borel,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( ( euclid925273238_space @ B )
% 0.29/0.46 & ( euclid925273238_space @ A ) )
% 0.29/0.46 => ! [F: A > B,S: set @ A] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 = ( ! [T2: set @ B] :
% 0.29/0.46 ( ( member @ ( set @ B ) @ T2 @ ( sigma_sets @ B @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( member @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ S )
% 0.29/0.46 & ( member @ B @ ( F @ X ) @ T2 ) ) )
% 0.29/0.46 @ ( sigma_sets @ A @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_vimage_borel
% 0.29/0.46 thf(fact_184_restrict__space__eq__vimage__algebra_H,axiom,
% 0.29/0.46 ! [A: $tType,M: sigma_measure @ A,Omega: set @ A] :
% 0.29/0.46 ( ( sigma_sets @ A @ ( sigma_restrict_space @ A @ M @ Omega ) )
% 0.29/0.46 = ( sigma_sets @ A
% 0.29/0.46 @ ( sigma_vimage_algebra @ A @ A @ ( inf_inf @ ( set @ A ) @ Omega @ ( sigma_space @ A @ M ) )
% 0.29/0.46 @ ^ [X: A] : X
% 0.29/0.46 @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % restrict_space_eq_vimage_algebra'
% 0.29/0.46 thf(fact_185_restrict__restrict__space,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,M: sigma_measure @ A,B3: set @ A] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ B3 @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) )
% 0.29/0.46 => ( ( sigma_restrict_space @ A @ ( sigma_restrict_space @ A @ M @ A4 ) @ B3 )
% 0.29/0.46 = ( sigma_restrict_space @ A @ M @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % restrict_restrict_space
% 0.29/0.46 thf(fact_186_is__borel__def,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( topolo503727757_space @ B )
% 0.29/0.46 => ( ( borel_is_borel @ A @ B )
% 0.29/0.46 = ( ^ [F2: A > B,M3: sigma_measure @ A] : ( member @ ( A > B ) @ F2 @ ( sigma_measurable @ A @ B @ M3 @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % is_borel_def
% 0.29/0.46 thf(fact_187_Diff__idemp,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) @ B3 )
% 0.29/0.46 = ( minus_minus @ ( set @ A ) @ A4 @ B3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Diff_idemp
% 0.29/0.46 thf(fact_188_Diff__iff,axiom,
% 0.29/0.46 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 = ( ( member @ A @ C2 @ A4 )
% 0.29/0.46 & ~ ( member @ A @ C2 @ B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Diff_iff
% 0.29/0.46 thf(fact_189_DiffI,axiom,
% 0.29/0.46 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( member @ A @ C2 @ A4 )
% 0.29/0.46 => ( ~ ( member @ A @ C2 @ B3 )
% 0.29/0.46 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % DiffI
% 0.29/0.46 thf(fact_190_set__diff__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( minus_minus @ ( set @ A ) )
% 0.29/0.46 = ( ^ [A6: set @ A,B4: set @ A] :
% 0.29/0.46 ( collect @ A
% 0.29/0.46 @ ^ [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ A6 )
% 0.29/0.46 & ~ ( member @ A @ X @ B4 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % set_diff_eq
% 0.29/0.46 thf(fact_191_minus__set__def,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( minus_minus @ ( set @ A ) )
% 0.29/0.46 = ( ^ [A6: set @ A,B4: set @ A] :
% 0.29/0.46 ( collect @ A
% 0.29/0.46 @ ( minus_minus @ ( A > $o )
% 0.29/0.46 @ ^ [X: A] : ( member @ A @ X @ A6 )
% 0.29/0.46 @ ^ [X: A] : ( member @ A @ X @ B4 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % minus_set_def
% 0.29/0.46 thf(fact_192_DiffD2,axiom,
% 0.29/0.46 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 => ~ ( member @ A @ C2 @ B3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % DiffD2
% 0.29/0.46 thf(fact_193_DiffD1,axiom,
% 0.29/0.46 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 => ( member @ A @ C2 @ A4 ) ) ).
% 0.29/0.46
% 0.29/0.46 % DiffD1
% 0.29/0.46 thf(fact_194_DiffE,axiom,
% 0.29/0.46 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 => ~ ( ( member @ A @ C2 @ A4 )
% 0.29/0.46 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % DiffE
% 0.29/0.46 thf(fact_195_sets__vimage__algebra__space,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,X4: set @ A,F: A > B,M: sigma_measure @ B] : ( member @ ( set @ A ) @ X4 @ ( sigma_sets @ A @ ( sigma_vimage_algebra @ A @ B @ X4 @ F @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sets_vimage_algebra_space
% 0.29/0.46 thf(fact_196_translation__subtract__diff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_group_add @ A )
% 0.29/0.46 => ! [A2: A,S2: set @ A,T3: set @ A] :
% 0.29/0.46 ( ( image @ A @ A
% 0.29/0.46 @ ^ [X: A] : ( minus_minus @ A @ X @ A2 )
% 0.29/0.46 @ ( minus_minus @ ( set @ A ) @ S2 @ T3 ) )
% 0.29/0.46 = ( minus_minus @ ( set @ A )
% 0.29/0.46 @ ( image @ A @ A
% 0.29/0.46 @ ^ [X: A] : ( minus_minus @ A @ X @ A2 )
% 0.29/0.46 @ S2 )
% 0.29/0.46 @ ( image @ A @ A
% 0.29/0.46 @ ^ [X: A] : ( minus_minus @ A @ X @ A2 )
% 0.29/0.46 @ T3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % translation_subtract_diff
% 0.29/0.46 thf(fact_197_translation__subtract__Int,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_group_add @ A )
% 0.29/0.46 => ! [A2: A,S2: set @ A,T3: set @ A] :
% 0.29/0.46 ( ( image @ A @ A
% 0.29/0.46 @ ^ [X: A] : ( minus_minus @ A @ X @ A2 )
% 0.29/0.46 @ ( inf_inf @ ( set @ A ) @ S2 @ T3 ) )
% 0.29/0.46 = ( inf_inf @ ( set @ A )
% 0.29/0.46 @ ( image @ A @ A
% 0.29/0.46 @ ^ [X: A] : ( minus_minus @ A @ X @ A2 )
% 0.29/0.46 @ S2 )
% 0.29/0.46 @ ( image @ A @ A
% 0.29/0.46 @ ^ [X: A] : ( minus_minus @ A @ X @ A2 )
% 0.29/0.46 @ T3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % translation_subtract_Int
% 0.29/0.46 thf(fact_198_translation__diff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_group_add @ A )
% 0.29/0.46 => ! [A2: A,S2: set @ A,T3: set @ A] :
% 0.29/0.46 ( ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ ( minus_minus @ ( set @ A ) @ S2 @ T3 ) )
% 0.29/0.46 = ( minus_minus @ ( set @ A ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ S2 ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ T3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % translation_diff
% 0.29/0.46 thf(fact_199_translation__Int,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_group_add @ A )
% 0.29/0.46 => ! [A2: A,S2: set @ A,T3: set @ A] :
% 0.29/0.46 ( ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ ( inf_inf @ ( set @ A ) @ S2 @ T3 ) )
% 0.29/0.46 = ( inf_inf @ ( set @ A ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ S2 ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ T3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % translation_Int
% 0.29/0.46 thf(fact_200_measurable__product__then__coordinatewise,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,C3: $tType] :
% 0.29/0.46 ( ( topolo503727757_space @ C3 )
% 0.29/0.46 => ! [F: A > B > C3,M: sigma_measure @ A,I: B] :
% 0.29/0.46 ( ( member @ ( A > B > C3 ) @ F @ ( sigma_measurable @ A @ ( B > C3 ) @ M @ ( borel_1404511681_borel @ ( B > C3 ) ) ) )
% 0.29/0.46 => ( member @ ( A > C3 )
% 0.29/0.46 @ ^ [X: A] : ( F @ X @ I )
% 0.29/0.46 @ ( sigma_measurable @ A @ C3 @ M @ ( borel_1404511681_borel @ C3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_product_then_coordinatewise
% 0.29/0.46 thf(fact_201_measurable__coordinatewise__then__product,axiom,
% 0.29/0.46 ! [A: $tType,C3: $tType,B: $tType] :
% 0.29/0.46 ( ( ( countable @ B )
% 0.29/0.46 & ( elemen1026692323pology @ C3 ) )
% 0.29/0.46 => ! [F: A > B > C3,M: sigma_measure @ A] :
% 0.29/0.46 ( ! [I2: B] :
% 0.29/0.46 ( member @ ( A > C3 )
% 0.29/0.46 @ ^ [X: A] : ( F @ X @ I2 )
% 0.29/0.46 @ ( sigma_measurable @ A @ C3 @ M @ ( borel_1404511681_borel @ C3 ) ) )
% 0.29/0.46 => ( member @ ( A > B > C3 ) @ F @ ( sigma_measurable @ A @ ( B > C3 ) @ M @ ( borel_1404511681_borel @ ( B > C3 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_coordinatewise_then_product
% 0.29/0.46 thf(fact_202_measurable__product__coordinates,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( topolo503727757_space @ B )
% 0.29/0.46 => ! [I: A] :
% 0.29/0.46 ( member @ ( ( A > B ) > B )
% 0.29/0.46 @ ^ [X: A > B] : ( X @ I )
% 0.29/0.46 @ ( sigma_measurable @ ( A > B ) @ B @ ( borel_1404511681_borel @ ( A > B ) ) @ ( borel_1404511681_borel @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measurable_product_coordinates
% 0.29/0.46 thf(fact_203_translation__invert,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_group_add @ A )
% 0.29/0.46 => ! [A2: A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ A4 )
% 0.29/0.46 = ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ B3 ) )
% 0.29/0.46 => ( A4 = B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % translation_invert
% 0.29/0.46 thf(fact_204_translation__assoc,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_group_add @ A )
% 0.29/0.46 => ! [B2: A,A2: A,S: set @ A] :
% 0.29/0.46 ( ( image @ A @ A @ ( plus_plus @ A @ B2 ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ S ) )
% 0.29/0.46 = ( image @ A @ A @ ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) ) @ S ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % translation_assoc
% 0.29/0.46 thf(fact_205_affine__parallel__expl__aux,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( real_V1076094709vector @ A )
% 0.29/0.46 => ! [S: set @ A,A2: A,T: set @ A] :
% 0.29/0.46 ( ! [X3: A] :
% 0.29/0.46 ( ( member @ A @ X3 @ S )
% 0.29/0.46 = ( member @ A @ ( plus_plus @ A @ A2 @ X3 ) @ T ) )
% 0.29/0.46 => ( T
% 0.29/0.46 = ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ S ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % affine_parallel_expl_aux
% 0.29/0.46 thf(fact_206_borel__measurable__if,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( ( euclid925273238_space @ B )
% 0.29/0.46 & ( euclid925273238_space @ A ) )
% 0.29/0.46 => ! [S: set @ A,F: A > B] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) ) )
% 0.29/0.46 => ( ( member @ ( A > B )
% 0.29/0.46 @ ^ [X: A] : ( if @ B @ ( member @ A @ X @ S ) @ ( F @ X ) @ ( zero_zero @ B ) )
% 0.29/0.46 @ ( sigma_measurable @ A @ B @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 = ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_if
% 0.29/0.46 thf(fact_207_add_Oleft__neutral,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( monoid_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.left_neutral
% 0.29/0.46 thf(fact_208_add_Oright__neutral,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( monoid_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.right_neutral
% 0.29/0.46 thf(fact_209_double__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord219039673up_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ A2 @ A2 )
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 = ( A2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % double_zero
% 0.29/0.46 thf(fact_210_double__zero__sym,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord219039673up_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ( zero_zero @ A )
% 0.29/0.46 = ( plus_plus @ A @ A2 @ A2 ) )
% 0.29/0.46 = ( A2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % double_zero_sym
% 0.29/0.46 thf(fact_211_add__cancel__left__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel1352612707id_add @ A )
% 0.29/0.46 => ! [B2: A,A2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.29/0.46 = A2 )
% 0.29/0.46 = ( B2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_cancel_left_left
% 0.29/0.46 thf(fact_212_add__cancel__left__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel1352612707id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.29/0.46 = A2 )
% 0.29/0.46 = ( B2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_cancel_left_right
% 0.29/0.46 thf(fact_213_add__cancel__right__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel1352612707id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( plus_plus @ A @ B2 @ A2 ) )
% 0.29/0.46 = ( B2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_cancel_right_left
% 0.29/0.46 thf(fact_214_add__cancel__right__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel1352612707id_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( plus_plus @ A @ A2 @ B2 ) )
% 0.29/0.46 = ( B2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_cancel_right_right
% 0.29/0.46 thf(fact_215_add__eq__0__iff__both__eq__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [X2: A,Y3: A] :
% 0.29/0.46 ( ( ( plus_plus @ A @ X2 @ Y3 )
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 = ( ( X2
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 & ( Y3
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_eq_0_iff_both_eq_0
% 0.29/0.46 thf(fact_216_zero__eq__add__iff__both__eq__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [X2: A,Y3: A] :
% 0.29/0.46 ( ( ( zero_zero @ A )
% 0.29/0.46 = ( plus_plus @ A @ X2 @ Y3 ) )
% 0.29/0.46 = ( ( X2
% 0.29/0.46 = ( zero_zero @ A ) )
% 0.29/0.46 & ( Y3
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_eq_add_iff_both_eq_0
% 0.29/0.46 thf(fact_217_diff__self,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ A2 @ A2 )
% 0.29/0.46 = ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_self
% 0.29/0.46 thf(fact_218_diff__0__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_0_right
% 0.29/0.46 thf(fact_219_zero__diff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( comm_monoid_diff @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 = ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_diff
% 0.29/0.46 thf(fact_220_diff__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel1352612707id_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_zero
% 0.29/0.46 thf(fact_221_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( cancel1352612707id_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ A2 @ A2 )
% 0.29/0.46 = ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.46 thf(fact_222_image__add__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( comm_monoid_add @ A )
% 0.29/0.46 => ! [S: set @ A] :
% 0.29/0.46 ( ( image @ A @ A @ ( plus_plus @ A @ ( zero_zero @ A ) ) @ S )
% 0.29/0.46 = S ) ) ).
% 0.29/0.46
% 0.29/0.46 % image_add_0
% 0.29/0.46 thf(fact_223_diff__add__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( comm_monoid_diff @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( minus_minus @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 0.29/0.46 = ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_add_zero
% 0.29/0.46 thf(fact_224_eq__add__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ab_group_add @ A )
% 0.29/0.46 => ! [X2: A,Y3: A] :
% 0.29/0.46 ( ( X2
% 0.29/0.46 = ( plus_plus @ A @ X2 @ Y3 ) )
% 0.29/0.46 = ( Y3
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % eq_add_iff
% 0.29/0.46 thf(fact_225_eq__iff__diff__eq__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.29/0.46 = ( ^ [A5: A,B5: A] :
% 0.29/0.46 ( ( minus_minus @ A @ A5 @ B5 )
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % eq_iff_diff_eq_0
% 0.29/0.46 thf(fact_226_comm__monoid__add__class_Oadd__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( comm_monoid_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % comm_monoid_add_class.add_0
% 0.29/0.46 thf(fact_227_add_Ocomm__neutral,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( comm_monoid_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.comm_neutral
% 0.29/0.46 thf(fact_228_add_Ogroup__left__neutral,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( group_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % add.group_left_neutral
% 0.29/0.46 thf(fact_229_zero__reorient,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( zero @ A )
% 0.29/0.46 => ! [X2: A] :
% 0.29/0.46 ( ( ( zero_zero @ A )
% 0.29/0.46 = X2 )
% 0.29/0.46 = ( X2
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_reorient
% 0.29/0.46 thf(fact_230_borel__measurable__if__D,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( ( euclid925273238_space @ B )
% 0.29/0.46 & ( euclid925273238_space @ A ) )
% 0.29/0.46 => ! [S: set @ A,F: A > B] :
% 0.29/0.46 ( ( member @ ( A > B )
% 0.29/0.46 @ ^ [X: A] : ( if @ B @ ( member @ A @ X @ S ) @ ( F @ X ) @ ( zero_zero @ B ) )
% 0.29/0.46 @ ( sigma_measurable @ A @ B @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ ( borel_1404511681_borel @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_if_D
% 0.29/0.46 thf(fact_231_borel__measurable__if__I,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( ( euclid925273238_space @ B )
% 0.29/0.46 & ( euclid925273238_space @ A ) )
% 0.29/0.46 => ! [F: A > B,S: set @ A] :
% 0.29/0.46 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 => ( ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) ) )
% 0.29/0.46 => ( member @ ( A > B )
% 0.29/0.46 @ ^ [X: A] : ( if @ B @ ( member @ A @ X @ S ) @ ( F @ X ) @ ( zero_zero @ B ) )
% 0.29/0.46 @ ( sigma_measurable @ A @ B @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_if_I
% 0.29/0.46 thf(fact_232_Least__eq__0,axiom,
% 0.29/0.46 ! [P: nat > $o] :
% 0.29/0.46 ( ( P @ ( zero_zero @ nat ) )
% 0.29/0.46 => ( ( ord_Least @ nat @ P )
% 0.29/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Least_eq_0
% 0.29/0.46 thf(fact_233_borel__measurable__if__lebesgue__on,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType] :
% 0.29/0.46 ( ( ( euclid925273238_space @ B )
% 0.29/0.46 & ( euclid925273238_space @ A ) )
% 0.29/0.46 => ! [S: set @ A,T: set @ A,F: A > B] :
% 0.29/0.46 ( ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) ) )
% 0.29/0.46 => ( ( member @ ( set @ A ) @ T @ ( sigma_sets @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) ) )
% 0.29/0.46 => ( ( ord_less_eq @ ( set @ A ) @ S @ T )
% 0.29/0.46 => ( ( member @ ( A > B )
% 0.29/0.46 @ ^ [X: A] : ( if @ B @ ( member @ A @ X @ S ) @ ( F @ X ) @ ( zero_zero @ B ) )
% 0.29/0.46 @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ T ) @ ( borel_1404511681_borel @ B ) ) )
% 0.29/0.46 = ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % borel_measurable_if_lebesgue_on
% 0.29/0.46 thf(fact_234_subsetI,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ! [X3: A] :
% 0.29/0.46 ( ( member @ A @ X3 @ A4 )
% 0.29/0.46 => ( member @ A @ X3 @ B3 ) )
% 0.29/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ B3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % subsetI
% 0.29/0.46 thf(fact_235_subset__antisym,axiom,
% 0.29/0.46 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 0.29/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A4 )
% 0.29/0.46 => ( A4 = B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % subset_antisym
% 0.29/0.46 thf(fact_236_diff__0__eq__0,axiom,
% 0.29/0.46 ! [N4: nat] :
% 0.29/0.46 ( ( minus_minus @ nat @ ( zero_zero @ nat ) @ N4 )
% 0.29/0.46 = ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_0_eq_0
% 0.29/0.46 thf(fact_237_diff__self__eq__0,axiom,
% 0.29/0.46 ! [M4: nat] :
% 0.29/0.46 ( ( minus_minus @ nat @ M4 @ M4 )
% 0.29/0.46 = ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_self_eq_0
% 0.29/0.46 thf(fact_238_le__zero__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( canoni770627133id_add @ A )
% 0.29/0.46 => ! [N4: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ N4 @ ( zero_zero @ A ) )
% 0.29/0.46 = ( N4
% 0.29/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_zero_eq
% 0.29/0.46 thf(fact_239_add__le__cancel__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere236663937imp_le @ A )
% 0.29/0.46 => ! [A2: A,C2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.29/0.46 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_cancel_right
% 0.29/0.46 thf(fact_240_add__le__cancel__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere236663937imp_le @ A )
% 0.29/0.46 => ! [C2: A,A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 0.29/0.46 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_cancel_left
% 0.29/0.46 thf(fact_241_le__inf__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [X2: A,Y3: A,Z: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ X2 @ ( inf_inf @ A @ Y3 @ Z ) )
% 0.29/0.46 = ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.29/0.46 & ( ord_less_eq @ A @ X2 @ Z ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_inf_iff
% 0.29/0.46 thf(fact_242_inf_Obounded__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A )
% 0.29/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) )
% 0.29/0.46 = ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.46 & ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf.bounded_iff
% 0.29/0.46 thf(fact_243_Int__subset__iff,axiom,
% 0.29/0.46 ! [A: $tType,C: set @ A,A4: set @ A,B3: set @ A] :
% 0.29/0.46 ( ( ord_less_eq @ ( set @ A ) @ C @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 0.29/0.46 = ( ( ord_less_eq @ ( set @ A ) @ C @ A4 )
% 0.29/0.46 & ( ord_less_eq @ ( set @ A ) @ C @ B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Int_subset_iff
% 0.29/0.46 thf(fact_244_set__plus__mono2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( plus @ A )
% 0.29/0.46 => ! [C: set @ A,D: set @ A,E2: set @ A,F3: set @ A] :
% 0.29/0.46 ( ( ord_less_eq @ ( set @ A ) @ C @ D )
% 0.29/0.46 => ( ( ord_less_eq @ ( set @ A ) @ E2 @ F3 )
% 0.29/0.46 => ( ord_less_eq @ ( set @ A ) @ ( plus_plus @ ( set @ A ) @ C @ E2 ) @ ( plus_plus @ ( set @ A ) @ D @ F3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % set_plus_mono2
% 0.29/0.46 thf(fact_245_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord219039673up_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.29/0.46 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_le_double_add_iff_zero_le_single_add
% 0.29/0.46 thf(fact_246_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord219039673up_add @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.29/0.46 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % double_add_le_zero_iff_single_add_le_zero
% 0.29/0.46 thf(fact_247_le__add__same__cancel2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere516151231imp_le @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 0.29/0.46 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_add_same_cancel2
% 0.29/0.46 thf(fact_248_le__add__same__cancel1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere516151231imp_le @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 0.29/0.46 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_add_same_cancel1
% 0.29/0.46 thf(fact_249_add__le__same__cancel2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere516151231imp_le @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.29/0.46 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_same_cancel2
% 0.29/0.46 thf(fact_250_add__le__same__cancel1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordere516151231imp_le @ A )
% 0.29/0.46 => ! [B2: A,A2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 0.29/0.46 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_same_cancel1
% 0.29/0.46 thf(fact_251_diff__ge__0__iff__ge,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ordered_ab_group_add @ A )
% 0.29/0.46 => ! [A2: A,B2: A] :
% 0.29/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A2 @ B2 ) )
% 0.29/0.46 = ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_ge_0_iff_ge
% 0.29/0.46 thf(fact_252_subset__translation__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( real_V1076094709vector @ A )
% 0.29/0.46 => ! [A2: A,S2: set @ A,T3: set @ A] :
% 0.29/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ S2 ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ T3 ) )
% 0.29/0.46 = ( ord_less_eq @ ( set @ A ) @ S2 @ T3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % subset_translation_eq
% 0.29/0.46 thf(fact_253_diffs0__imp__equal,axiom,
% 0.29/0.46 ! [M4: nat,N4: nat] :
% 0.29/0.46 ( ( ( minus_minus @ nat @ M4 @ N4 )
% 0.29/0.46 = ( zero_zero @ nat ) )
% 0.29/0.46 => ( ( ( minus_minus @ nat @ N4 @ M4 )
% 0.29/0.46 = ( zero_zero @ nat ) )
% 0.29/0.46 => ( M4 = N4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % diffs0_imp_equal
% 0.29/0.46 thf(fact_254_minus__nat_Odiff__0,axiom,
% 0.29/0.46 ! [M4: nat] :
% 0.29/0.46 ( ( minus_minus @ nat @ M4 @ ( zero_zero @ nat ) )
% 0.29/0.46 = M4 ) ).
% 0.29/0.46
% 0.29/0.46 % minus_nat.diff_0
% 0.29/0.46
% 0.29/0.46 % Subclasses (2)
% 0.29/0.46 thf(subcl_Finite__Set_Ofinite___HOL_Otype,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( finite_finite @ A )
% 0.29/0.46 => ( type @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Finite__Set_Ofinite___Countable_Ocountable,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( finite_finite @ A )
% 0.29/0.46 => ( countable @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % Type constructors (136)
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( ordere890947078_space @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( ordere890947078_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Ometric__space,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( real_V2090557954_space @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( real_V2090557954_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_1,axiom,
% 0.29/0.46 ordere890947078_space @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space_2,axiom,
% 0.29/0.46 real_V2090557954_space @ real ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Elementary__Topology_Osecond__countable__topology,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( countable @ A9 )
% 0.29/0.46 & ( elemen1026692323pology @ A10 ) )
% 0.29/0.46 => ( elemen1026692323pology @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Topological__Spaces_Otopological__space,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( topolo503727757_space @ A10 )
% 0.29/0.46 => ( topolo503727757_space @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( semilattice_inf @ A10 )
% 0.29/0.46 => ( semilattice_inf @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Countable_Ocountable,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( finite_finite @ A9 )
% 0.29/0.46 & ( countable @ A10 ) )
% 0.29/0.46 => ( countable @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( ( finite_finite @ A9 )
% 0.29/0.46 & ( finite_finite @ A10 ) )
% 0.29/0.46 => ( finite_finite @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( lattice @ A10 )
% 0.29/0.46 => ( lattice @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Groups_Ominus,axiom,
% 0.29/0.46 ! [A9: $tType,A10: $tType] :
% 0.29/0.46 ( ( minus @ A10 )
% 0.29/0.46 => ( minus @ ( A9 > A10 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 0.29/0.46 ordere516151231imp_le @ int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.29/0.46 ordere236663937imp_le @ int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Int_Oint___Topological__Spaces_Otopological__space_3,axiom,
% 0.29/0.46 topolo503727757_space @ int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Int_Oint___Topological__Spaces_Olinorder__topology,axiom,
% 0.29/0.46 topolo2117631714pology @ int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Int_Oint___Groups_Oordered__ab__semigroup__add,axiom,
% 0.29/0.46 ordere779506340up_add @ int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Int_Oint___Groups_Olinordered__ab__group__add,axiom,
% 0.29/0.46 linord219039673up_add @ int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.29/0.46 cancel146912293up_add @ int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Int_Oint___Limits_Otopological__monoid__add,axiom,
% 0.29/0.46 topolo1314133330id_add @ int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Int_Oint___Groups_Ocancel__comm__monoid__add,axiom,
% 0.29/0.46 cancel1352612707id_add @ int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Int_Oint___Topological__Spaces_Ot2__space,axiom,
% 0.29/0.46 topological_t2_space @ int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add,axiom,
% 0.29/0.46 ordered_ab_group_add @ int ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Int_Oint___Groups_Ocancel__semigroup__add,axiom,
% 0.29/0.47 cancel_semigroup_add @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Lattices_Osemilattice__inf_4,axiom,
% 0.29/0.47 semilattice_inf @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Oab__semigroup__add,axiom,
% 0.29/0.47 ab_semigroup_add @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Ocomm__monoid__add,axiom,
% 0.29/0.47 comm_monoid_add @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Osemigroup__add,axiom,
% 0.29/0.47 semigroup_add @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Oab__group__add,axiom,
% 0.29/0.47 ab_group_add @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Countable_Ocountable_5,axiom,
% 0.29/0.47 countable @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Omonoid__add,axiom,
% 0.29/0.47 monoid_add @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Lattices_Olattice_6,axiom,
% 0.29/0.47 lattice @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Ogroup__add,axiom,
% 0.29/0.47 group_add @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Nat_Oring__char__0,axiom,
% 0.29/0.47 ring_char_0 @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Ominus_7,axiom,
% 0.29/0.47 minus @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Ozero,axiom,
% 0.29/0.47 zero @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Oplus,axiom,
% 0.29/0.47 plus @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_8,axiom,
% 0.29/0.47 ordere516151231imp_le @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Elementary__Topology_Osecond__countable__topology_9,axiom,
% 0.29/0.47 elemen1026692323pology @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_10,axiom,
% 0.29/0.47 ordere236663937imp_le @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.29/0.47 canoni770627133id_add @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Topological__Spaces_Otopological__space_11,axiom,
% 0.29/0.47 topolo503727757_space @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Topological__Spaces_Olinorder__topology_12,axiom,
% 0.29/0.47 topolo2117631714pology @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_13,axiom,
% 0.29/0.47 ordere779506340up_add @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_14,axiom,
% 0.29/0.47 cancel146912293up_add @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Limits_Otopological__monoid__add_15,axiom,
% 0.29/0.47 topolo1314133330id_add @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_16,axiom,
% 0.29/0.47 cancel1352612707id_add @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Topological__Spaces_Ot2__space_17,axiom,
% 0.29/0.47 topological_t2_space @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add_18,axiom,
% 0.29/0.47 cancel_semigroup_add @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Lattices_Osemilattice__inf_19,axiom,
% 0.29/0.47 semilattice_inf @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 0.29/0.47 comm_monoid_diff @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add_20,axiom,
% 0.29/0.47 ab_semigroup_add @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add_21,axiom,
% 0.29/0.47 comm_monoid_add @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Osemigroup__add_22,axiom,
% 0.29/0.47 semigroup_add @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Countable_Ocountable_23,axiom,
% 0.29/0.47 countable @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Omonoid__add_24,axiom,
% 0.29/0.47 monoid_add @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Lattices_Olattice_25,axiom,
% 0.29/0.47 lattice @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Ominus_26,axiom,
% 0.29/0.47 minus @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Ozero_27,axiom,
% 0.29/0.47 zero @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Oplus_28,axiom,
% 0.29/0.47 plus @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_29,axiom,
% 0.29/0.47 ! [A9: $tType] : ( semilattice_inf @ ( set @ A9 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Groups_Oab__semigroup__add_30,axiom,
% 0.29/0.47 ! [A9: $tType] :
% 0.29/0.47 ( ( ab_semigroup_add @ A9 )
% 0.29/0.47 => ( ab_semigroup_add @ ( set @ A9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Groups_Ocomm__monoid__add_31,axiom,
% 0.29/0.47 ! [A9: $tType] :
% 0.29/0.47 ( ( comm_monoid_add @ A9 )
% 0.29/0.47 => ( comm_monoid_add @ ( set @ A9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Groups_Osemigroup__add_32,axiom,
% 0.29/0.47 ! [A9: $tType] :
% 0.29/0.47 ( ( semigroup_add @ A9 )
% 0.29/0.47 => ( semigroup_add @ ( set @ A9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Countable_Ocountable_33,axiom,
% 0.29/0.47 ! [A9: $tType] :
% 0.29/0.47 ( ( finite_finite @ A9 )
% 0.29/0.47 => ( countable @ ( set @ A9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Groups_Omonoid__add_34,axiom,
% 0.29/0.47 ! [A9: $tType] :
% 0.29/0.47 ( ( monoid_add @ A9 )
% 0.29/0.47 => ( monoid_add @ ( set @ A9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Finite__Set_Ofinite_35,axiom,
% 0.29/0.47 ! [A9: $tType] :
% 0.29/0.47 ( ( finite_finite @ A9 )
% 0.29/0.47 => ( finite_finite @ ( set @ A9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Lattices_Olattice_36,axiom,
% 0.29/0.47 ! [A9: $tType] : ( lattice @ ( set @ A9 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Groups_Ominus_37,axiom,
% 0.29/0.47 ! [A9: $tType] : ( minus @ ( set @ A9 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Groups_Ozero_38,axiom,
% 0.29/0.47 ! [A9: $tType] :
% 0.29/0.47 ( ( zero @ A9 )
% 0.29/0.47 => ( zero @ ( set @ A9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Groups_Oplus_39,axiom,
% 0.29/0.47 ! [A9: $tType] :
% 0.29/0.47 ( ( plus @ A9 )
% 0.29/0.47 => ( plus @ ( set @ A9 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_40,axiom,
% 0.29/0.47 topolo503727757_space @ $o ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_HOL_Obool___Topological__Spaces_Olinorder__topology_41,axiom,
% 0.29/0.47 topolo2117631714pology @ $o ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_HOL_Obool___Topological__Spaces_Ot2__space_42,axiom,
% 0.29/0.47 topological_t2_space @ $o ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_43,axiom,
% 0.29/0.47 semilattice_inf @ $o ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_HOL_Obool___Countable_Ocountable_44,axiom,
% 0.29/0.47 countable @ $o ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_HOL_Obool___Finite__Set_Ofinite_45,axiom,
% 0.29/0.47 finite_finite @ $o ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_HOL_Obool___Lattices_Olattice_46,axiom,
% 0.29/0.47 lattice @ $o ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_HOL_Obool___Groups_Ominus_47,axiom,
% 0.29/0.47 minus @ $o ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_48,axiom,
% 0.29/0.47 ordere516151231imp_le @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Elementary__Topology_Osecond__countable__topology_49,axiom,
% 0.29/0.47 elemen1026692323pology @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_50,axiom,
% 0.29/0.47 ordere236663937imp_le @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector,axiom,
% 0.29/0.47 real_V55928688vector @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Topological__Spaces_Otopological__space_51,axiom,
% 0.29/0.47 topolo503727757_space @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Topological__Spaces_Olinorder__topology_52,axiom,
% 0.29/0.47 topolo2117631714pology @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_53,axiom,
% 0.29/0.47 ordere779506340up_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Euclidean__Space_Oeuclidean__space,axiom,
% 0.29/0.47 euclid925273238_space @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector,axiom,
% 0.29/0.47 real_V1076094709vector @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add_54,axiom,
% 0.29/0.47 linord219039673up_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_55,axiom,
% 0.29/0.47 cancel146912293up_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Limits_Otopological__monoid__add_56,axiom,
% 0.29/0.47 topolo1314133330id_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_57,axiom,
% 0.29/0.47 cancel1352612707id_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Topological__Spaces_Ot2__space_58,axiom,
% 0.29/0.47 topological_t2_space @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add_59,axiom,
% 0.29/0.47 ordered_ab_group_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_60,axiom,
% 0.29/0.47 cancel_semigroup_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Lattices_Osemilattice__inf_61,axiom,
% 0.29/0.47 semilattice_inf @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_62,axiom,
% 0.29/0.47 ab_semigroup_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_63,axiom,
% 0.29/0.47 comm_monoid_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Osemigroup__add_64,axiom,
% 0.29/0.47 semigroup_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Oab__group__add_65,axiom,
% 0.29/0.47 ab_group_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Omonoid__add_66,axiom,
% 0.29/0.47 monoid_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Lattices_Olattice_67,axiom,
% 0.29/0.47 lattice @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Ogroup__add_68,axiom,
% 0.29/0.47 group_add @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Nat_Oring__char__0_69,axiom,
% 0.29/0.47 ring_char_0 @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Ominus_70,axiom,
% 0.29/0.47 minus @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Ozero_71,axiom,
% 0.29/0.47 zero @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Real_Oreal___Groups_Oplus_72,axiom,
% 0.29/0.47 plus @ real ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Sigma__Algebra_Omeasure___Lattices_Osemilattice__inf_73,axiom,
% 0.29/0.47 ! [A9: $tType] : ( semilattice_inf @ ( sigma_measure @ A9 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Sigma__Algebra_Omeasure___Lattices_Olattice_74,axiom,
% 0.29/0.47 ! [A9: $tType] : ( lattice @ ( sigma_measure @ A9 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__monoid__add__imp__le_75,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( ordere890947078_space @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( ordere516151231imp_le @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Elementary__Topology_Osecond__countable__topology_76,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( euclid925273238_space @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( elemen1026692323pology @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add__imp__le_77,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( ordere890947078_space @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( ordere236663937imp_le @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_78,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( real_V55928688vector @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( real_V55928688vector @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_79,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( topolo503727757_space @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( topolo503727757_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add_80,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( ordere890947078_space @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( ordere779506340up_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Euclidean__Space_Oeuclidean__space_81,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( euclid925273238_space @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( euclid925273238_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__vector_82,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( real_V1076094709vector @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( real_V1076094709vector @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__ab__semigroup__add_83,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( cancel146912293up_add @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( cancel146912293up_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Limits_Otopological__monoid__add_84,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( real_V55928688vector @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( topolo1314133330id_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__comm__monoid__add_85,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( cancel1352612707id_add @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( cancel1352612707id_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Ot2__space_86,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( real_V2090557954_space @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( topological_t2_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add_87,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( ordere890947078_space @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( ordered_ab_group_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__semigroup__add_88,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( cancel_semigroup_add @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( cancel_semigroup_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Osemilattice__inf_89,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( ordere890947078_space @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( semilattice_inf @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__semigroup__add_90,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( ab_semigroup_add @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( ab_semigroup_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocomm__monoid__add_91,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( comm_monoid_add @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( comm_monoid_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Osemigroup__add_92,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( semigroup_add @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( semigroup_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__group__add_93,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( ab_group_add @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( ab_group_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Countable_Ocountable_94,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( countable @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( countable @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Omonoid__add_95,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( monoid_add @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( monoid_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_96,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( finite_finite @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( finite_finite @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Olattice_97,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( ordere890947078_space @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( lattice @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ogroup__add_98,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( group_add @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( group_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Nat_Oring__char__0_99,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( ring_char_0 @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( ring_char_0 @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ominus_100,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( minus @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( minus @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ozero_101,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( zero @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( zero @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oplus_102,axiom,
% 0.29/0.47 ! [A9: $tType,A10: $tType] :
% 0.29/0.47 ( ( ( plus @ A9 )
% 0.29/0.47 & ( finite_finite @ A10 ) )
% 0.29/0.47 => ( plus @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Helper facts (3)
% 0.29/0.47 thf(help_If_3_1_T,axiom,
% 0.29/0.47 ! [P: $o] :
% 0.29/0.47 ( ( P = $true )
% 0.29/0.47 | ( P = $false ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_If_2_1_T,axiom,
% 0.29/0.47 ! [A: $tType,X2: A,Y3: A] :
% 0.29/0.47 ( ( if @ A @ $false @ X2 @ Y3 )
% 0.29/0.47 = Y3 ) ).
% 0.29/0.47
% 0.29/0.47 thf(help_If_1_1_T,axiom,
% 0.29/0.47 ! [A: $tType,X2: A,Y3: A] :
% 0.29/0.47 ( ( if @ A @ $true @ X2 @ Y3 )
% 0.29/0.47 = X2 ) ).
% 0.29/0.47
% 0.29/0.47 % Free types (1)
% 0.29/0.47 thf(tfree_0,hypothesis,
% 0.29/0.47 finite_finite @ n ).
% 0.29/0.47
% 0.29/0.47 % Conjectures (1)
% 0.29/0.47 thf(conj_0,conjecture,
% 0.29/0.47 ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
% 0.29/0.47 @ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
% 0.29/0.47 @ ^ [X: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ X @ ( minkow1937162798nt_vec @ n @ real @ a ) )
% 0.29/0.47 @ ( t2 @ a ) )
% 0.29/0.47 @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 2.99/1.50 ---- Embedded in THF ---
% 2.99/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.99/1.51 %%% Generated on Tue Feb 24 08:25:12 EST 2026
% 2.99/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 2.99/1.51 %%% Logic specification used:
% 2.99/1.51 %%% thf(spec, logic, $$dhol).
% 2.99/1.51
% 2.99/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3Wo9oJ6aQl/DTF2DTF12084.p
% 2.99/1.51 thf(ty_t_Finite__Cartesian__Product_Ovec, type, finite_Cartesian_vec: ($tType > ($tType > $tType))).
% 2.99/1.51 thf(ty_t_Sigma__Algebra_Omeasure, type, sigma_measure: ($tType > $tType)).
% 2.99/1.51 thf(ty_t_Real_Oreal, type, real: $tType).
% 2.99/1.51 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.99/1.51 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.99/1.51 thf(ty_t_Int_Oint, type, int: $tType).
% 2.99/1.51 thf(ty_tf_n, type, n: $tType).
% 2.99/1.51 thf(sy_cl_Real__Vector__Spaces_Ometric__space, type, real_V2090557954_space: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Ordered__Euclidean__Space_Oordered__euclidean__space, type, ordere890947078_space: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Oplus, type, plus: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Ominus, type, minus: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Nat_Oring__char__0, type, ring_char_0: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Omonoid__add, type, monoid_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Countable_Ocountable, type, countable: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Oab__group__add, type, ab_group_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Ocomm__monoid__diff, type, comm_monoid_diff: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Topological__Spaces_Ot2__space, type, topological_t2_space: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Limits_Otopological__monoid__add, type, topolo1314133330id_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Real__Vector__Spaces_Oreal__vector, type, real_V1076094709vector: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Euclidean__Space_Oeuclidean__space, type, euclid925273238_space: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Topological__Spaces_Olinorder__topology, type, topolo2117631714pology: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Topological__Spaces_Otopological__space, type, topolo503727757_space: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector, type, real_V55928688vector: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Elementary__Topology_Osecond__countable__topology, type, elemen1026692323pology: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le, type, ordere516151231imp_le: (!> [A:$tType]: ($o))).
% 2.99/1.51 thf(sy_c_Borel__Space_Ois__borel, type, borel_is_borel: (!> [A:$tType,B:$tType]: (((A > B) > ((sigma_measure @ A) > $o))))).
% 2.99/1.51 thf(sy_c_Borel__Space_Otopological__space__class_Oborel, type, borel_1404511681_borel: (!> [A:$tType]: ((sigma_measure @ A)))).
% 2.99/1.51 thf(sy_c_Complete__Measure_Ocompletion, type, complete_completion: (!> [A:$tType]: (((sigma_measure @ A) > (sigma_measure @ A))))).
% 2.99/1.51 thf(sy_c_Complete__Measure_Omain__part, type, complete_main_part: (!> [A:$tType]: (((sigma_measure @ A) > ((set @ A) > (set @ A)))))).
% 2.99/1.51 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.99/1.51 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.99/1.51 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.99/1.51 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.99/1.51 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 2.99/1.51 thf(sy_c_Lebesgue__Measure_Olborel, type, lebesgue_lborel: (!> [A:$tType]: ((sigma_measure @ A)))).
% 2.99/1.51 thf(sy_c_Minkowskis__Theorem__Mirabelle__jpyvdnlcjd_Oof__int__vec, type, minkow1937162798nt_vec: (!> [B:$tType,A:$tType]: ((((finite_Cartesian_vec @ int) @ B) > ((finite_Cartesian_vec @ A) @ B))))).
% 2.99/1.51 thf(sy_c_Orderings_Oord__class_OLeast, type, ord_Least: (!> [A:$tType]: (((A > $o) > A)))).
% 2.99/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.99/1.51 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.99/1.51 thf(sy_c_Set_Oimage, type, image: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > (set @ B)))))).
% 2.99/1.51 thf(sy_c_Set_Ovimage, type, vimage: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ B) > (set @ A)))))).
% 2.99/1.51 thf(sy_c_Sigma__Algebra_Omeasurable, type, sigma_measurable: (!> [A:$tType,B:$tType]: (((sigma_measure @ A) > ((sigma_measure @ B) > (set @ (A > B))))))).
% 2.99/1.51 thf(sy_c_Sigma__Algebra_Orestrict__space, type, sigma_restrict_space: (!> [A:$tType]: (((sigma_measure @ A) > ((set @ A) > (sigma_measure @ A)))))).
% 2.99/1.51 thf(sy_c_Sigma__Algebra_Osets, type, sigma_sets: (!> [A:$tType]: (((sigma_measure @ A) > (set @ (set @ A)))))).
% 2.99/1.51 thf(sy_c_Sigma__Algebra_Ospace, type, sigma_space: (!> [A:$tType]: (((sigma_measure @ A) > (set @ A))))).
% 2.99/1.51 thf(sy_c_Sigma__Algebra_Ovimage__algebra, type, sigma_vimage_algebra: (!> [A:$tType,B:$tType]: (((set @ A) > ((A > B) > ((sigma_measure @ B) > (sigma_measure @ A))))))).
% 2.99/1.51 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.99/1.51 thf(sy_v_R____, type, r: (((finite_Cartesian_vec @ int) @ n) > (set @ ((finite_Cartesian_vec @ real) @ n)))).
% 2.99/1.51 thf(sy_v_S, type, s: (set @ ((finite_Cartesian_vec @ real) @ n))).
% 2.99/1.51 thf(sy_v_T_H____, type, t: (((finite_Cartesian_vec @ int) @ n) > (set @ ((finite_Cartesian_vec @ real) @ n)))).
% 2.99/1.51 thf(sy_v_T____, type, t2: (((finite_Cartesian_vec @ int) @ n) > (set @ ((finite_Cartesian_vec @ real) @ n)))).
% 2.99/1.51 thf(sy_v_a____, type, a: ((finite_Cartesian_vec @ int) @ n)).
% 2.99/1.51 thf(fact_0_assms_I1_J, axiom, (((member @ (set @ ((finite_Cartesian_vec @ real) @ n))) @ s) @ ((sigma_sets @ ((finite_Cartesian_vec @ real) @ n)) @ ((complete_completion @ ((finite_Cartesian_vec @ real) @ n)) @ (lebesgue_lborel @ ((finite_Cartesian_vec @ real) @ n)))))).
% 2.99/1.51 thf(fact_1_of__int__vec__eq__iff, axiom, (! [A:$tType,N:$tType]: ((((finite_finite @ N) & (ring_char_0 @ A)) => (! [A2:((finite_Cartesian_vec @ int) @ N),B2:((finite_Cartesian_vec @ int) @ N)]: ((((((minkow1937162798nt_vec @ N) @ A) @ A2) = (((minkow1937162798nt_vec @ N) @ A) @ B2)) = (A2 = B2)))))))).
% 2.99/1.51 thf(fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062, axiom, (! [A3:((finite_Cartesian_vec @ int) @ n)]: (((((member @ (set @ ((finite_Cartesian_vec @ real) @ n))) @ (t2 @ A3)) @ ((sigma_sets @ ((finite_Cartesian_vec @ real) @ n)) @ ((complete_completion @ ((finite_Cartesian_vec @ real) @ n)) @ (lebesgue_lborel @ ((finite_Cartesian_vec @ real) @ n))))) => (((member @ (set @ ((finite_Cartesian_vec @ real) @ n))) @ (((inf_inf @ (set @ ((finite_Cartesian_vec @ real) @ n))) @ ((((vimage @ ((finite_Cartesian_vec @ real) @ n)) @ ((finite_Cartesian_vec @ real) @ n)) @ (^ [X:((finite_Cartesian_vec @ real) @ n)]: ((((plus_plus @ ((finite_Cartesian_vec @ real) @ n)) @ X) @ (((minkow1937162798nt_vec @ n) @ real) @ A3))))) @ (t2 @ A3))) @ ((sigma_space @ ((finite_Cartesian_vec @ real) @ n)) @ ((complete_completion @ ((finite_Cartesian_vec @ real) @ n)) @ (lebesgue_lborel @ ((finite_Cartesian_vec @ real) @ n)))))) @ ((sigma_sets @ ((finite_Cartesian_vec @ real) @ n)) @ ((complete_completion @ ((finite_Cartesian_vec @ real) @ n)) @ (lebesgue_lborel @ ((finite_Cartesian_vec @ real) @ n))))))))).
% 2.99/1.51 thf(fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, axiom, (! [A2:((finite_Cartesian_vec @ int) @ n)]: ((((member @ (set @ ((finite_Cartesian_vec @ real) @ n))) @ (t2 @ A2)) @ ((sigma_sets @ ((finite_Cartesian_vec @ real) @ n)) @ ((complete_completion @ ((finite_Cartesian_vec @ real) @ n)) @ (lebesgue_lborel @ ((finite_Cartesian_vec @ real) @ n)))))))).
% 2.99/1.51 thf(fact_4_T_H__altdef, axiom, (! [A2:((finite_Cartesian_vec @ int) @ n)]: (((t @ A2) = ((((vimage @ ((finite_Cartesian_vec @ real) @ n)) @ ((finite_Cartesian_vec @ real) @ n)) @ (^ [X:((finite_Cartesian_vec @ real) @ n)]: ((((plus_plus @ ((finite_Cartesian_vec @ real) @ n)) @ X) @ (((minkow1937162798nt_vec @ n) @ real) @ A2))))) @ (t2 @ A2)))))).
% 2.99/1.51 thf(fact_5__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, axiom, (! [A2:((finite_Cartesian_vec @ int) @ n)]: ((((member @ (set @ ((finite_Cartesian_vec @ real) @ n))) @ (r @ A2)) @ ((sigma_sets @ ((finite_Cartesian_vec @ real) @ n)) @ ((complete_completion @ ((finite_Cartesian_vec @ real) @ n)) @ (lebesgue_lborel @ ((finite_Cartesian_vec @ real) @ n)))))))).
% 2.99/1.51 thf(fact_6_sets__completionI__sets, axiom, (! [A:$tType,A4:(set @ A),M:(sigma_measure @ A)]: (((((member @ (set @ A)) @ A4) @ ((sigma_sets @ A) @ M)) => (((member @ (set @ A)) @ A4) @ ((sigma_sets @ A) @ ((complete_completion @ A) @ M))))))).
% 2.99/1.51 thf(fact_7__092_060open_062_092_060And_062a_O_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_092_060in_062_Alebesgue_A_092_060rightarrow_062_092_060_094sub_062M_Alebesgue_092_060close_062, axiom, (! [A2:((finite_Cartesian_vec @ int) @ n)]: ((((member @ (((finite_Cartesian_vec @ real) @ n) > ((finite_Cartesian_vec @ real) @ n))) @ (^ [X:((finite_Cartesian_vec @ real) @ n)]: ((((plus_plus @ ((finite_Cartesian_vec @ real) @ n)) @ X) @ (((minkow1937162798nt_vec @ n) @ real) @ A2))))) @ ((((sigma_measurable @ ((finite_Cartesian_vec @ real) @ n)) @ ((finite_Cartesian_vec @ real) @ n)) @ ((complete_completion @ ((finite_Cartesian_vec @ real) @ n)) @ (lebesgue_lborel @ ((finite_Cartesian_vec @ real) @ n)))) @ ((complete_completion @ ((finite_Cartesian_vec @ real) @ n)) @ (lebesgue_lborel @ ((finite_Cartesian_vec @ real) @ n)))))))).
% 2.99/1.51 thf(fact_8_vimage__ident, axiom, (! [A:$tType,Y:(set @ A)]: ((((((vimage @ A) @ A) @ (^ [X:A]: (X))) @ Y) = Y)))).
% 2.99/1.51 thf(fact_9_vimage__Collect__eq, axiom, (! [B:$tType,A:$tType,F:(A > B),P:(B > $o)]: ((((((vimage @ A) @ B) @ F) @ ((collect @ B) @ P)) = ((collect @ A) @ (^ [Y2:A]: ((P @ (F @ Y2))))))))).
% 2.99/1.51 thf(fact_10_vimageI, axiom, (! [B:$tType,A:$tType,F:(B > A),A2:B,B2:A,B3:(set @ A)]: ((((F @ A2) = B2) => ((((member @ A) @ B2) @ B3) => (((member @ B) @ A2) @ ((((vimage @ B) @ A) @ F) @ B3))))))).
% 2.99/1.51 thf(fact_11_vimage__eq, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),B3:(set @ B)]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ B3)) = (((member @ B) @ (F @ A2)) @ B3))))).
% 2.99/1.51 thf(fact_12_set__plus__intro, axiom, (! [A:$tType]: (((plus @ A) => (! [A2:A,C:(set @ A),B2:A,D:(set @ A)]: (((((member @ A) @ A2) @ C) => ((((member @ A) @ B2) @ D) => (((member @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ (((plus_plus @ (set @ A)) @ C) @ D)))))))))).
% 2.99/1.51 thf(fact_13_add__left__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C2)) = (B2 = C2)))))))).
% 2.99/1.51 thf(fact_14_add__right__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C2) @ A2)) = (B2 = C2)))))))).
% 2.99/1.51 thf(fact_15_vimage__def, axiom, (! [B:$tType,A:$tType]: ((((vimage @ A) @ B) = (^ [F2:(A > B),B4:(set @ B)]: (((collect @ A) @ (^ [X:A]: ((((member @ B) @ (F2 @ X)) @ B4)))))))))).
% 2.99/1.51 thf(fact_16_vimageD, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),A4:(set @ B)]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ A4)) => (((member @ B) @ (F @ A2)) @ A4))))).
% 2.99/1.51 thf(fact_17_vimageE, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),B3:(set @ B)]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ B3)) => (((member @ B) @ (F @ A2)) @ B3))))).
% 2.99/1.51 thf(fact_18_IntI, axiom, (! [A:$tType,C2:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ A4) => ((((member @ A) @ C2) @ B3) => (((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A4) @ B3))))))).
% 2.99/1.51 thf(fact_19_Int__iff, axiom, (! [A:$tType,C2:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) = ((((member @ A) @ C2) @ A4) & (((member @ A) @ C2) @ B3)))))).
% 2.99/1.51 thf(fact_20_space__completion, axiom, (! [A:$tType,M:(sigma_measure @ A)]: ((((sigma_space @ A) @ ((complete_completion @ A) @ M)) = ((sigma_space @ A) @ M))))).
% 2.99/1.51 thf(fact_21_vimage__Int, axiom, (! [A:$tType,B:$tType,F:(A > B),A4:(set @ B),B3:(set @ B)]: ((((((vimage @ A) @ B) @ F) @ (((inf_inf @ (set @ B)) @ A4) @ B3)) = (((inf_inf @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ A4)) @ ((((vimage @ A) @ B) @ F) @ B3)))))).
% 2.99/1.51 thf(fact_22_T__def, axiom, (t2 = (^ [A5:((finite_Cartesian_vec @ int) @ n)]: ((((inf_inf @ (set @ ((finite_Cartesian_vec @ real) @ n))) @ s) @ (r @ A5)))))).
% 2.99/1.51 thf(fact_23_IntE, axiom, (! [A:$tType,C2:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) => (~ (((((member @ A) @ C2) @ A4) => (~ ((((member @ A) @ C2) @ B3)))))))))).
% 2.99/1.51 thf(fact_24_IntD1, axiom, (! [A:$tType,C2:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) => (((member @ A) @ C2) @ A4))))).
% 2.99/1.51 thf(fact_25_IntD2, axiom, (! [A:$tType,C2:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) => (((member @ A) @ C2) @ B3))))).
% 2.99/1.51 thf(fact_26_Int__assoc, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A),C:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) @ C) = (((inf_inf @ (set @ A)) @ A4) @ (((inf_inf @ (set @ A)) @ B3) @ C)))))).
% 2.99/1.51 thf(fact_27_Int__absorb, axiom, (! [A:$tType,A4:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ A4) = A4)))).
% 2.99/1.51 thf(fact_28_Int__commute, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A6:(set @ A),B4:(set @ A)]: ((((inf_inf @ (set @ A)) @ B4) @ A6))))))).
% 2.99/1.51 thf(fact_29_Int__left__absorb, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) = (((inf_inf @ (set @ A)) @ A4) @ B3))))).
% 2.99/1.51 thf(fact_30_Int__left__commute, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A),C:(set @ A)]: (((((inf_inf @ (set @ A)) @ A4) @ (((inf_inf @ (set @ A)) @ B3) @ C)) = (((inf_inf @ (set @ A)) @ B3) @ (((inf_inf @ (set @ A)) @ A4) @ C)))))).
% 2.99/1.51 thf(fact_31_Collect__conj__eq, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: ((((collect @ A) @ (^ [X:A]: (((P @ X) & (Q @ X))))) = (((inf_inf @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.99/1.51 thf(fact_32_Int__Collect, axiom, (! [A:$tType,X2:A,A4:(set @ A),P:(A > $o)]: (((((member @ A) @ X2) @ (((inf_inf @ (set @ A)) @ A4) @ ((collect @ A) @ P))) = ((((member @ A) @ X2) @ A4) & (P @ X2)))))).
% 2.99/1.51 thf(fact_33_Int__def, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A6:(set @ A),B4:(set @ A)]: (((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ A6) & (((member @ A) @ X) @ B4))))))))))).
% 2.99/1.51 thf(fact_34_measurable__completion, axiom, (! [A:$tType,B:$tType,F:(A > B),M:(sigma_measure @ A),N2:(sigma_measure @ B)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ N2)) => (((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ ((complete_completion @ A) @ M)) @ N2)))))).
% 2.99/1.51 thf(fact_35_vimage__inter__cong, axiom, (! [B:$tType,A:$tType,S:(set @ A),F:(A > B),G:(A > B),Y3:(set @ B)]: (((! [W:A]: (((((member @ A) @ W) @ S) => ((F @ W) = (G @ W))))) => ((((inf_inf @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ Y3)) @ S) = (((inf_inf @ (set @ A)) @ ((((vimage @ A) @ B) @ G) @ Y3)) @ S)))))).
% 2.99/1.51 thf(fact_36_add__right__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C2) @ A2)) => (B2 = C2)))))))).
% 2.99/1.51 thf(fact_37_add__left__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C2)) => (B2 = C2)))))))).
% 2.99/1.51 thf(fact_38_add_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [B2:A,A2:A,C2:A]: (((((plus_plus @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C2)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.99/1.51 thf(fact_39_add_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => ((plus_plus @ A) = (^ [A5:A,B5:A]: ((((plus_plus @ A) @ B5) @ A5)))))))).
% 2.99/1.51 thf(fact_40_add_Oright__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [B2:A,A2:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C2) @ A2)) = (B2 = C2)))))))).
% 2.99/1.51 thf(fact_41_add_Oleft__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C2)) = (B2 = C2)))))))).
% 2.99/1.51 thf(fact_42_add_Oassoc, axiom, (! [A:$tType]: (((semigroup_add @ A) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.99/1.51 thf(fact_43_set__plus__elim, axiom, (! [A:$tType]: (((plus @ A) => (! [X2:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ X2) @ (((plus_plus @ (set @ A)) @ A4) @ B3)) => (~ ((! [A7:A,B6:A]: (((X2 = (((plus_plus @ A) @ A7) @ B6)) => ((((member @ A) @ A7) @ A4) => (~ ((((member @ A) @ B6) @ B3)))))))))))))))).
% 2.99/1.51 thf(fact_44_group__cancel_Oadd2, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [B3:A,K:A,B2:A,A2:A]: (((B3 = (((plus_plus @ A) @ K) @ B2)) => ((((plus_plus @ A) @ A2) @ B3) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.99/1.51 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.99/1.51 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A4)))) = A4)))).
% 2.99/1.51 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.99/1.51 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.99/1.51 thf(fact_49_group__cancel_Oadd1, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A4:A,K:A,A2:A,B2:A]: (((A4 = (((plus_plus @ A) @ K) @ A2)) => ((((plus_plus @ A) @ A4) @ B2) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.99/1.51 thf(fact_50_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (K = L)) => ((((plus_plus @ A) @ I) @ K) = (((plus_plus @ A) @ J) @ L))))))))).
% 2.99/1.51 thf(fact_51_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.99/1.51 thf(fact_52_vimage__Collect, axiom, (! [B:$tType,A:$tType,P:(B > $o),F:(A > B),Q:(A > $o)]: (((! [X3:A]: (((P @ (F @ X3)) = (Q @ X3)))) => (((((vimage @ A) @ B) @ F) @ ((collect @ B) @ P)) = ((collect @ A) @ Q)))))).
% 2.99/1.51 thf(fact_53_vimageI2, axiom, (! [B:$tType,A:$tType,F:(B > A),A2:B,A4:(set @ A)]: (((((member @ A) @ (F @ A2)) @ A4) => (((member @ B) @ A2) @ ((((vimage @ B) @ A) @ F) @ A4)))))).
% 2.99/1.51 thf(fact_54_sets_OInt__space__eq2, axiom, (! [A:$tType,X2:(set @ A),M:(sigma_measure @ A)]: (((((member @ (set @ A)) @ X2) @ ((sigma_sets @ A) @ M)) => ((((inf_inf @ (set @ A)) @ X2) @ ((sigma_space @ A) @ M)) = X2))))).
% 2.99/1.51 thf(fact_55_sets_OInt__space__eq1, axiom, (! [A:$tType,X2:(set @ A),M:(sigma_measure @ A)]: (((((member @ (set @ A)) @ X2) @ ((sigma_sets @ A) @ M)) => ((((inf_inf @ (set @ A)) @ ((sigma_space @ A) @ M)) @ X2) = X2))))).
% 2.99/1.51 thf(fact_56_measurable__sets, axiom, (! [B:$tType,A:$tType,F:(A > B),M:(sigma_measure @ A),A4:(sigma_measure @ B),S:(set @ B)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ A4)) => ((((member @ (set @ B)) @ S) @ ((sigma_sets @ B) @ A4)) => (((member @ (set @ A)) @ (((inf_inf @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ S)) @ ((sigma_space @ A) @ M))) @ ((sigma_sets @ A) @ M))))))).
% 2.99/1.51 thf(fact_57_measurableI, axiom, (! [A:$tType,B:$tType,M:(sigma_measure @ A),F:(A > B),N2:(sigma_measure @ B)]: (((! [X3:A]: (((((member @ A) @ X3) @ ((sigma_space @ A) @ M)) => (((member @ B) @ (F @ X3)) @ ((sigma_space @ B) @ N2))))) => ((! [A8:(set @ B)]: (((((member @ (set @ B)) @ A8) @ ((sigma_sets @ B) @ N2)) => (((member @ (set @ A)) @ (((inf_inf @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ A8)) @ ((sigma_space @ A) @ M))) @ ((sigma_sets @ A) @ M))))) => (((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ N2))))))).
% 2.99/1.51 thf(fact_58_sets_Otop, axiom, (! [A:$tType,M:(sigma_measure @ A)]: ((((member @ (set @ A)) @ ((sigma_space @ A) @ M)) @ ((sigma_sets @ A) @ M))))).
% 2.99/1.51 thf(fact_59_sets_OInt, axiom, (! [A:$tType,A2:(set @ A),M:(sigma_measure @ A),B2:(set @ A)]: (((((member @ (set @ A)) @ A2) @ ((sigma_sets @ A) @ M)) => ((((member @ (set @ A)) @ B2) @ ((sigma_sets @ A) @ M)) => (((member @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A2) @ B2)) @ ((sigma_sets @ A) @ M))))))).
% 2.99/1.51 thf(fact_60_measurable__If__set, axiom, (! [A:$tType,B:$tType,F:(A > B),M:(sigma_measure @ A),M2:(sigma_measure @ B),G:(A > B),A4:(set @ A)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ M2)) => ((((member @ (A > B)) @ G) @ ((((sigma_measurable @ A) @ B) @ M) @ M2)) => ((((member @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ ((sigma_space @ A) @ M))) @ ((sigma_sets @ A) @ M)) => (((member @ (A > B)) @ (^ [X:A]: (((((if @ B) @ (((member @ A) @ X) @ A4)) @ (F @ X)) @ (G @ X))))) @ ((((sigma_measurable @ A) @ B) @ M) @ M2)))))))).
% 2.99/1.51 thf(fact_61_measurable__sets__Collect, axiom, (! [B:$tType,A:$tType,F:(A > B),M:(sigma_measure @ A),N2:(sigma_measure @ B),P:(B > $o)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ N2)) => ((((member @ (set @ B)) @ ((collect @ B) @ (^ [X:B]: (((((member @ B) @ X) @ ((sigma_space @ B) @ N2)) & (P @ X)))))) @ ((sigma_sets @ B) @ N2)) => (((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & (P @ (F @ X))))))) @ ((sigma_sets @ A) @ M))))))).
% 2.99/1.51 thf(fact_62_measurable__If, axiom, (! [A:$tType,B:$tType,F:(A > B),M:(sigma_measure @ A),M2:(sigma_measure @ B),G:(A > B),P:(A > $o)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ M2)) => ((((member @ (A > B)) @ G) @ ((((sigma_measurable @ A) @ B) @ M) @ M2)) => ((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & (P @ X)))))) @ ((sigma_sets @ A) @ M)) => (((member @ (A > B)) @ (^ [X:A]: (((((if @ B) @ (P @ X)) @ (F @ X)) @ (G @ X))))) @ ((((sigma_measurable @ A) @ B) @ M) @ M2)))))))).
% 2.99/1.51 thf(fact_63_inf__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X:A]: ((((inf_inf @ B) @ (F2 @ X)) @ (G2 @ X))))))))).
% 2.99/1.51 thf(fact_64_inf__right__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X2:A,Y3:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X2) @ Y3)) @ Y3) = (((inf_inf @ A) @ X2) @ Y3)))))))).
% 2.99/1.51 thf(fact_65_inf_Oright__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ B2) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.99/1.51 thf(fact_66_inf__left__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X2:A,Y3:A]: (((((inf_inf @ A) @ X2) @ (((inf_inf @ A) @ X2) @ Y3)) = (((inf_inf @ A) @ X2) @ Y3)))))))).
% 2.99/1.51 thf(fact_67_inf_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ A2) @ B2)) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 2.99/1.51 thf(fact_68_inf__idem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X2:A]: (((((inf_inf @ A) @ X2) @ X2) = X2))))))).
% 2.99/1.51 thf(fact_69_inf_Oidem, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A]: (((((inf_inf @ A) @ A2) @ A2) = A2))))))).
% 2.99/1.51 thf(fact_70_inf__set__def, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A6:(set @ A),B4:(set @ A)]: (((collect @ A) @ (((inf_inf @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ A6)))) @ (^ [X:A]: ((((member @ A) @ X) @ B4))))))))))).
% 2.99/1.51 thf(fact_71_inf__left__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X2:A,Y3:A,Z:A]: (((((inf_inf @ A) @ X2) @ (((inf_inf @ A) @ Y3) @ Z)) = (((inf_inf @ A) @ Y3) @ (((inf_inf @ A) @ X2) @ Z))))))))).
% 2.99/1.51 thf(fact_72_inf_Oleft__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B2:A,A2:A,C2:A]: (((((inf_inf @ A) @ B2) @ (((inf_inf @ A) @ A2) @ C2)) = (((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2))))))))).
% 2.99/1.51 thf(fact_73_inf__commute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((inf_inf @ A) = (^ [X:A,Y2:A]: ((((inf_inf @ A) @ Y2) @ X)))))))).
% 2.99/1.51 thf(fact_74_inf_Ocommute, axiom, (! [A:$tType]: (((semilattice_inf @ A) => ((inf_inf @ A) = (^ [A5:A,B5:A]: ((((inf_inf @ A) @ B5) @ A5)))))))).
% 2.99/1.51 thf(fact_75_inf__assoc, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X2:A,Y3:A,Z:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X2) @ Y3)) @ Z) = (((inf_inf @ A) @ X2) @ (((inf_inf @ A) @ Y3) @ Z))))))))).
% 2.99/1.51 thf(fact_76_inf_Oassoc, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ C2) = (((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2))))))))).
% 2.99/1.51 thf(fact_77_boolean__algebra__cancel_Oinf2, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [B3:A,K:A,B2:A,A2:A]: (((B3 = (((inf_inf @ A) @ K) @ B2)) => ((((inf_inf @ A) @ A2) @ B3) = (((inf_inf @ A) @ K) @ (((inf_inf @ A) @ A2) @ B2)))))))))).
% 2.99/1.51 thf(fact_78_boolean__algebra__cancel_Oinf1, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A4:A,K:A,A2:A,B2:A]: (((A4 = (((inf_inf @ A) @ K) @ A2)) => ((((inf_inf @ A) @ A4) @ B2) = (((inf_inf @ A) @ K) @ (((inf_inf @ A) @ A2) @ B2)))))))))).
% 2.99/1.51 thf(fact_79_inf__fun__def, axiom, (! [B:$tType,A:$tType]: (((semilattice_inf @ B) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X:A]: ((((inf_inf @ B) @ (F2 @ X)) @ (G2 @ X))))))))).
% 2.99/1.51 thf(fact_80_inf__sup__aci_I1_J, axiom, (! [A:$tType]: (((lattice @ A) => ((inf_inf @ A) = (^ [X:A,Y2:A]: ((((inf_inf @ A) @ Y2) @ X)))))))).
% 2.99/1.51 thf(fact_81_inf__sup__aci_I2_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y3:A,Z:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X2) @ Y3)) @ Z) = (((inf_inf @ A) @ X2) @ (((inf_inf @ A) @ Y3) @ Z))))))))).
% 2.99/1.51 thf(fact_82_inf__sup__aci_I3_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y3:A,Z:A]: (((((inf_inf @ A) @ X2) @ (((inf_inf @ A) @ Y3) @ Z)) = (((inf_inf @ A) @ Y3) @ (((inf_inf @ A) @ X2) @ Z))))))))).
% 2.99/1.51 thf(fact_83_inf__sup__aci_I4_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y3:A]: (((((inf_inf @ A) @ X2) @ (((inf_inf @ A) @ X2) @ Y3)) = (((inf_inf @ A) @ X2) @ Y3)))))))).
% 2.99/1.51 thf(fact_84_measurable__compose__rev, axiom, (! [A:$tType,C3:$tType,B:$tType,F:(A > B),L2:(sigma_measure @ A),N2:(sigma_measure @ B),G:(C3 > A),M:(sigma_measure @ C3)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ L2) @ N2)) => ((((member @ (C3 > A)) @ G) @ ((((sigma_measurable @ C3) @ A) @ M) @ L2)) => (((member @ (C3 > B)) @ (^ [X:C3]: ((F @ (G @ X))))) @ ((((sigma_measurable @ C3) @ B) @ M) @ N2))))))).
% 2.99/1.51 thf(fact_85_measurable__compose, axiom, (! [B:$tType,A:$tType,C3:$tType,F:(A > B),M:(sigma_measure @ A),N2:(sigma_measure @ B),G:(B > C3),L2:(sigma_measure @ C3)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ N2)) => ((((member @ (B > C3)) @ G) @ ((((sigma_measurable @ B) @ C3) @ N2) @ L2)) => (((member @ (A > C3)) @ (^ [X:A]: ((G @ (F @ X))))) @ ((((sigma_measurable @ A) @ C3) @ M) @ L2))))))).
% 2.99/1.51 thf(fact_86_measurable__id, axiom, (! [A:$tType,M:(sigma_measure @ A)]: ((((member @ (A > A)) @ (^ [X:A]: (X))) @ ((((sigma_measurable @ A) @ A) @ M) @ M))))).
% 2.99/1.51 thf(fact_87_measurable__cong__sets, axiom, (! [A:$tType,B:$tType,M:(sigma_measure @ A),M2:(sigma_measure @ A),N2:(sigma_measure @ B),N3:(sigma_measure @ B)]: (((((sigma_sets @ A) @ M) = ((sigma_sets @ A) @ M2)) => ((((sigma_sets @ B) @ N2) = ((sigma_sets @ B) @ N3)) => (((((sigma_measurable @ A) @ B) @ M) @ N2) = ((((sigma_measurable @ A) @ B) @ M2) @ N3))))))).
% 2.99/1.51 thf(fact_88_sets__eq__imp__space__eq, axiom, (! [A:$tType,M:(sigma_measure @ A),M2:(sigma_measure @ A)]: (((((sigma_sets @ A) @ M) = ((sigma_sets @ A) @ M2)) => (((sigma_space @ A) @ M) = ((sigma_space @ A) @ M2)))))).
% 2.99/1.51 thf(fact_89_measurable__cong__simp, axiom, (! [A:$tType,B:$tType,M:(sigma_measure @ A),N2:(sigma_measure @ A),M2:(sigma_measure @ B),N3:(sigma_measure @ B),F:(A > B),G:(A > B)]: (((M = N2) => ((M2 = N3) => ((! [W:A]: (((((member @ A) @ W) @ ((sigma_space @ A) @ M)) => ((F @ W) = (G @ W))))) => ((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ M2)) = (((member @ (A > B)) @ G) @ ((((sigma_measurable @ A) @ B) @ N2) @ N3))))))))).
% 2.99/1.51 thf(fact_90_measurable__space, axiom, (! [A:$tType,B:$tType,F:(A > B),M:(sigma_measure @ A),A4:(sigma_measure @ B),X2:A]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ A4)) => ((((member @ A) @ X2) @ ((sigma_space @ A) @ M)) => (((member @ B) @ (F @ X2)) @ ((sigma_space @ B) @ A4))))))).
% 2.99/1.51 thf(fact_91_measurable__cong, axiom, (! [A:$tType,B:$tType,M:(sigma_measure @ A),F:(A > B),G:(A > B),M2:(sigma_measure @ B)]: (((! [W:A]: (((((member @ A) @ W) @ ((sigma_space @ A) @ M)) => ((F @ W) = (G @ W))))) => ((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ M2)) = (((member @ (A > B)) @ G) @ ((((sigma_measurable @ A) @ B) @ M) @ M2))))))).
% 2.99/1.51 thf(fact_92_measurable__ident__sets, axiom, (! [A:$tType,M:(sigma_measure @ A),M2:(sigma_measure @ A)]: (((((sigma_sets @ A) @ M) = ((sigma_sets @ A) @ M2)) => (((member @ (A > A)) @ (^ [X:A]: (X))) @ ((((sigma_measurable @ A) @ A) @ M) @ M2)))))).
% 2.99/1.51 thf(fact_93_sets_Osets__Collect_I5_J, axiom, (! [A:$tType,M:(sigma_measure @ A),Pb:$o]: ((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & Pb))))) @ ((sigma_sets @ A) @ M))))).
% 2.99/1.51 thf(fact_94_sets_Osets__Collect__imp, axiom, (! [A:$tType,M:(sigma_measure @ A),P:(A > $o),Q:(A > $o)]: (((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & (P @ X)))))) @ ((sigma_sets @ A) @ M)) => ((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & (Q @ X)))))) @ ((sigma_sets @ A) @ M)) => (((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & ((Q @ X) => (P @ X))))))) @ ((sigma_sets @ A) @ M))))))).
% 2.99/1.51 thf(fact_95_sets_Osets__Collect__neg, axiom, (! [A:$tType,M:(sigma_measure @ A),P:(A > $o)]: (((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & (P @ X)))))) @ ((sigma_sets @ A) @ M)) => (((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & (~ ((P @ X)))))))) @ ((sigma_sets @ A) @ M)))))).
% 2.99/1.51 thf(fact_96_sets_Osets__Collect__conj, axiom, (! [A:$tType,M:(sigma_measure @ A),P:(A > $o),Q:(A > $o)]: (((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & (P @ X)))))) @ ((sigma_sets @ A) @ M)) => ((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & (Q @ X)))))) @ ((sigma_sets @ A) @ M)) => (((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & ((Q @ X) & (P @ X))))))) @ ((sigma_sets @ A) @ M))))))).
% 2.99/1.51 thf(fact_97_sets_Osets__Collect__disj, axiom, (! [A:$tType,M:(sigma_measure @ A),P:(A > $o),Q:(A > $o)]: (((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & (P @ X)))))) @ ((sigma_sets @ A) @ M)) => ((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & (Q @ X)))))) @ ((sigma_sets @ A) @ M)) => (((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & ((Q @ X) | (P @ X))))))) @ ((sigma_sets @ A) @ M))))))).
% 2.99/1.51 thf(fact_98_sets_Osets__Collect__const, axiom, (! [A:$tType,M:(sigma_measure @ A),P:$o]: ((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & P))))) @ ((sigma_sets @ A) @ M))))).
% 2.99/1.51 thf(fact_99_measurable__const, axiom, (! [B:$tType,A:$tType,C2:A,M2:(sigma_measure @ A),M:(sigma_measure @ B)]: (((((member @ A) @ C2) @ ((sigma_space @ A) @ M2)) => (((member @ (B > A)) @ (^ [X:B]: (C2))) @ ((((sigma_measurable @ B) @ A) @ M) @ M2)))))).
% 2.99/1.51 thf(fact_100_T_H__def, axiom, (t = (^ [A5:((finite_Cartesian_vec @ int) @ n)]: (((((image @ ((finite_Cartesian_vec @ real) @ n)) @ ((finite_Cartesian_vec @ real) @ n)) @ (^ [X:((finite_Cartesian_vec @ real) @ n)]: ((((minus_minus @ ((finite_Cartesian_vec @ real) @ n)) @ X) @ (((minkow1937162798nt_vec @ n) @ real) @ A5))))) @ (t2 @ A5)))))).
% 2.99/1.51 thf(fact_101_inf__Int__eq, axiom, (! [A:$tType,R:(set @ A),S:(set @ A)]: (((((inf_inf @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ R)))) @ (^ [X:A]: ((((member @ A) @ X) @ S)))) = (^ [X:A]: ((((member @ A) @ X) @ (((inf_inf @ (set @ A)) @ R) @ S)))))))).
% 2.99/1.51 thf(fact_102_main__part__sets, axiom, (! [A:$tType,S:(set @ A),M:(sigma_measure @ A)]: (((((member @ (set @ A)) @ S) @ ((sigma_sets @ A) @ ((complete_completion @ A) @ M))) => (((member @ (set @ A)) @ (((complete_main_part @ A) @ M) @ S)) @ ((sigma_sets @ A) @ M)))))).
% 2.99/1.51 thf(fact_103_measurable__restrict__space__iff, axiom, (! [A:$tType,B:$tType,Omega:(set @ A),M:(sigma_measure @ A),C2:B,N2:(sigma_measure @ B),F:(A > B)]: (((((member @ (set @ A)) @ (((inf_inf @ (set @ A)) @ Omega) @ ((sigma_space @ A) @ M))) @ ((sigma_sets @ A) @ M)) => ((((member @ B) @ C2) @ ((sigma_space @ B) @ N2)) => ((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ (((sigma_restrict_space @ A) @ M) @ Omega)) @ N2)) = (((member @ (A > B)) @ (^ [X:A]: (((((if @ B) @ (((member @ A) @ X) @ Omega)) @ (F @ X)) @ C2)))) @ ((((sigma_measurable @ A) @ B) @ M) @ N2)))))))).
% 2.99/1.51 thf(fact_104_sets__Least, axiom, (! [A:$tType,M:(sigma_measure @ A),P:(nat > (A > $o)),A4:(set @ nat)]: (((! [I2:nat]: ((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & ((P @ I2) @ X)))))) @ ((sigma_sets @ A) @ M)))) => (((member @ (set @ A)) @ (((inf_inf @ (set @ A)) @ ((((vimage @ A) @ nat) @ (^ [X:A]: (((ord_Least @ nat) @ (^ [J2:nat]: (((P @ J2) @ X))))))) @ A4)) @ ((sigma_space @ A) @ M))) @ ((sigma_sets @ A) @ M)))))).
% 2.99/1.51 thf(fact_105_in__vimage__algebra, axiom, (! [B:$tType,A:$tType,A4:(set @ A),M:(sigma_measure @ A),F:(B > A),X4:(set @ B)]: (((((member @ (set @ A)) @ A4) @ ((sigma_sets @ A) @ M)) => (((member @ (set @ B)) @ (((inf_inf @ (set @ B)) @ ((((vimage @ B) @ A) @ F) @ A4)) @ X4)) @ ((sigma_sets @ B) @ (((((sigma_vimage_algebra @ B) @ A) @ X4) @ F) @ M))))))).
% 2.99/1.51 thf(fact_106_in__borel__measurable__borel, axiom, (! [A:$tType,B:$tType]: (((topolo503727757_space @ B) => (! [F:(A > B),M:(sigma_measure @ A)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))) = (! [X:(set @ B)]: (((((member @ (set @ B)) @ X) @ ((sigma_sets @ B) @ (borel_1404511681_borel @ B))) => (((member @ (set @ A)) @ (((inf_inf @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ X)) @ ((sigma_space @ A) @ M))) @ ((sigma_sets @ A) @ M)))))))))))).
% 2.99/1.51 thf(fact_107_image__eqI, axiom, (! [A:$tType,B:$tType,B2:A,F:(B > A),X2:B,A4:(set @ B)]: (((B2 = (F @ X2)) => ((((member @ B) @ X2) @ A4) => (((member @ A) @ B2) @ ((((image @ B) @ A) @ F) @ A4))))))).
% 2.99/1.51 thf(fact_108_minus__apply, axiom, (! [B:$tType,A:$tType]: (((minus @ B) => ((minus_minus @ (A > B)) = (^ [A6:(A > B),B4:(A > B),X:A]: ((((minus_minus @ B) @ (A6 @ X)) @ (B4 @ X))))))))).
% 2.99/1.51 thf(fact_109_inf1I, axiom, (! [A:$tType,A4:(A > $o),X2:A,B3:(A > $o)]: (((A4 @ X2) => ((B3 @ X2) => ((((inf_inf @ (A > $o)) @ A4) @ B3) @ X2)))))).
% 2.99/1.51 thf(fact_110_image__ident, axiom, (! [A:$tType,Y:(set @ A)]: ((((((image @ A) @ A) @ (^ [X:A]: (X))) @ Y) = Y)))).
% 2.99/1.51 thf(fact_111_add__diff__cancel__right_H, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A2:A,B2:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ B2) = A2))))))).
% 2.99/1.51 thf(fact_112_add__diff__cancel__right, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A2:A,C2:A,B2:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ C2)) = (((minus_minus @ A) @ A2) @ B2)))))))).
% 2.99/1.51 thf(fact_113_add__diff__cancel__left_H, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A2:A,B2:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ A2) = B2))))))).
% 2.99/1.51 thf(fact_114_add__diff__cancel__left, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [C2:A,A2:A,B2:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B2)) = (((minus_minus @ A) @ A2) @ B2)))))))).
% 2.99/1.51 thf(fact_115_diff__add__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A]: (((((plus_plus @ A) @ (((minus_minus @ A) @ A2) @ B2)) @ B2) = A2))))))).
% 2.99/1.51 thf(fact_116_add__diff__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ B2) = A2))))))).
% 2.99/1.51 thf(fact_117_space__vimage__algebra, axiom, (! [B:$tType,A:$tType,X4:(set @ A),F:(A > B),M:(sigma_measure @ B)]: ((((sigma_space @ A) @ (((((sigma_vimage_algebra @ A) @ B) @ X4) @ F) @ M)) = X4)))).
% 2.99/1.51 thf(fact_118_main__part, axiom, (! [A:$tType,S:(set @ A),M:(sigma_measure @ A)]: (((((member @ (set @ A)) @ S) @ ((sigma_sets @ A) @ M)) => ((((complete_main_part @ A) @ M) @ S) = S))))).
% 2.99/1.51 thf(fact_119_space__restrict__space2, axiom, (! [A:$tType,Omega:(set @ A),M:(sigma_measure @ A)]: (((((member @ (set @ A)) @ Omega) @ ((sigma_sets @ A) @ M)) => (((sigma_space @ A) @ (((sigma_restrict_space @ A) @ M) @ Omega)) = Omega))))).
% 2.99/1.51 thf(fact_120_inf1E, axiom, (! [A:$tType,A4:(A > $o),B3:(A > $o),X2:A]: ((((((inf_inf @ (A > $o)) @ A4) @ B3) @ X2) => (~ (((A4 @ X2) => (~ ((B3 @ X2)))))))))).
% 2.99/1.51 thf(fact_121_inf1D1, axiom, (! [A:$tType,A4:(A > $o),B3:(A > $o),X2:A]: ((((((inf_inf @ (A > $o)) @ A4) @ B3) @ X2) => (A4 @ X2))))).
% 2.99/1.51 thf(fact_122_inf1D2, axiom, (! [A:$tType,A4:(A > $o),B3:(A > $o),X2:A]: ((((((inf_inf @ (A > $o)) @ A4) @ B3) @ X2) => (B3 @ X2))))).
% 2.99/1.51 thf(fact_123_borel__measurable__diff, axiom, (! [A:$tType,B:$tType]: ((((elemen1026692323pology @ B) & (real_V55928688vector @ B)) => (! [F:(A > B),M:(sigma_measure @ A),G:(A > B)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))) => ((((member @ (A > B)) @ G) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))) => (((member @ (A > B)) @ (^ [X:A]: ((((minus_minus @ B) @ (F @ X)) @ (G @ X))))) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))))))))))).
% 2.99/1.51 thf(fact_124_fun__diff__def, axiom, (! [B:$tType,A:$tType]: (((minus @ B) => ((minus_minus @ (A > B)) = (^ [A6:(A > B),B4:(A > B),X:A]: ((((minus_minus @ B) @ (A6 @ X)) @ (B4 @ X))))))))).
% 2.99/1.51 thf(fact_125_Compr__image__eq, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(set @ B),P:(A > $o)]: ((((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((((image @ B) @ A) @ F) @ A4)) & (P @ X))))) = ((((image @ B) @ A) @ F) @ ((collect @ B) @ (^ [X:B]: (((((member @ B) @ X) @ A4) & (P @ (F @ X))))))))))).
% 2.99/1.51 thf(fact_126_image__image, axiom, (! [A:$tType,B:$tType,C3:$tType,F:(B > A),G:(C3 > B),A4:(set @ C3)]: ((((((image @ B) @ A) @ F) @ ((((image @ C3) @ B) @ G) @ A4)) = ((((image @ C3) @ A) @ (^ [X:C3]: ((F @ (G @ X))))) @ A4))))).
% 2.99/1.51 thf(fact_127_imageE, axiom, (! [A:$tType,B:$tType,B2:A,F:(B > A),A4:(set @ B)]: (((((member @ A) @ B2) @ ((((image @ B) @ A) @ F) @ A4)) => (~ ((! [X3:B]: (((B2 = (F @ X3)) => (~ ((((member @ B) @ X3) @ A4)))))))))))).
% 2.99/1.51 thf(fact_128_diff__right__commute, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A2:A,C2:A,B2:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ C2)) @ B2) = (((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ B2)) @ C2)))))))).
% 2.99/1.51 thf(fact_129_diff__eq__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A,C2:A,D2:A]: ((((((minus_minus @ A) @ A2) @ B2) = (((minus_minus @ A) @ C2) @ D2)) => ((A2 = B2) = (C2 = D2))))))))).
% 2.99/1.51 thf(fact_130_rev__image__eqI, axiom, (! [B:$tType,A:$tType,X2:A,A4:(set @ A),B2:B,F:(A > B)]: (((((member @ A) @ X2) @ A4) => ((B2 = (F @ X2)) => (((member @ B) @ B2) @ ((((image @ A) @ B) @ F) @ A4))))))).
% 2.99/1.51 thf(fact_131_ball__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(set @ B),P:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ ((((image @ B) @ A) @ F) @ A4)) => (P @ X3)))) => (! [X5:B]: (((((member @ B) @ X5) @ A4) => (P @ (F @ X5))))))))).
% 2.99/1.51 thf(fact_132_image__cong, axiom, (! [B:$tType,A:$tType,M:(set @ A),N2:(set @ A),F:(A > B),G:(A > B)]: (((M = N2) => ((! [X3:A]: (((((member @ A) @ X3) @ N2) => ((F @ X3) = (G @ X3))))) => (((((image @ A) @ B) @ F) @ M) = ((((image @ A) @ B) @ G) @ N2))))))).
% 2.99/1.51 thf(fact_133_bex__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(set @ B),P:(A > $o)]: (((? [X5:A]: (((((member @ A) @ X5) @ ((((image @ B) @ A) @ F) @ A4)) & (P @ X5)))) => (? [X3:B]: (((((member @ B) @ X3) @ A4) & (P @ (F @ X3))))))))).
% 2.99/1.51 thf(fact_134_image__iff, axiom, (! [A:$tType,B:$tType,Z:A,F:(B > A),A4:(set @ B)]: (((((member @ A) @ Z) @ ((((image @ B) @ A) @ F) @ A4)) = (? [X:B]: (((((member @ B) @ X) @ A4) & (Z = (F @ X))))))))).
% 2.99/1.51 thf(fact_135_imageI, axiom, (! [B:$tType,A:$tType,X2:A,A4:(set @ A),F:(A > B)]: (((((member @ A) @ X2) @ A4) => (((member @ B) @ (F @ X2)) @ ((((image @ A) @ B) @ F) @ A4)))))).
% 2.99/1.51 thf(fact_136_borel__measurable__const, axiom, (! [A:$tType,B:$tType]: (((topolo503727757_space @ B) => (! [C2:B,M:(sigma_measure @ A)]: ((((member @ (A > B)) @ (^ [X:A]: (C2))) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))))))))).
% 2.99/1.51 thf(fact_137_sets__restrict__space__cong, axiom, (! [A:$tType,M:(sigma_measure @ A),N2:(sigma_measure @ A),Omega:(set @ A)]: (((((sigma_sets @ A) @ M) = ((sigma_sets @ A) @ N2)) => (((sigma_sets @ A) @ (((sigma_restrict_space @ A) @ M) @ Omega)) = ((sigma_sets @ A) @ (((sigma_restrict_space @ A) @ N2) @ Omega))))))).
% 2.99/1.51 thf(fact_138_restrict__space__sets__cong, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A),M:(sigma_measure @ A),N2:(sigma_measure @ A)]: (((A4 = B3) => ((((sigma_sets @ A) @ M) = ((sigma_sets @ A) @ N2)) => (((sigma_sets @ A) @ (((sigma_restrict_space @ A) @ M) @ A4)) = ((sigma_sets @ A) @ (((sigma_restrict_space @ A) @ N2) @ B3)))))))).
% 2.99/1.51 thf(fact_139_measurable__restrict__space1, axiom, (! [A:$tType,B:$tType,F:(A > B),M:(sigma_measure @ A),N2:(sigma_measure @ B),Omega:(set @ A)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ N2)) => (((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ (((sigma_restrict_space @ A) @ M) @ Omega)) @ N2)))))).
% 2.99/1.51 thf(fact_140_add__implies__diff, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [C2:A,B2:A,A2:A]: ((((((plus_plus @ A) @ C2) @ B2) = A2) => (C2 = (((minus_minus @ A) @ A2) @ B2))))))))).
% 2.99/1.51 thf(fact_141_diff__diff__add, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A2:A,B2:A,C2:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ B2)) @ C2) = (((minus_minus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.99/1.51 thf(fact_142_diff__add__eq__diff__diff__swap, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A,C2:A]: (((((minus_minus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2)) = (((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ C2)) @ B2)))))))).
% 2.99/1.51 thf(fact_143_diff__add__eq, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((minus_minus @ A) @ A2) @ B2)) @ C2) = (((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ B2)))))))).
% 2.99/1.51 thf(fact_144_diff__diff__eq2, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A,C2:A]: (((((minus_minus @ A) @ A2) @ (((minus_minus @ A) @ B2) @ C2)) = (((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ B2)))))))).
% 2.99/1.51 thf(fact_145_add__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ A2) @ (((minus_minus @ A) @ B2) @ C2)) = (((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2)))))))).
% 2.99/1.51 thf(fact_146_eq__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,C2:A,B2:A]: (((A2 = (((minus_minus @ A) @ C2) @ B2)) = ((((plus_plus @ A) @ A2) @ B2) = C2)))))))).
% 2.99/1.51 thf(fact_147_diff__eq__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A,C2:A]: ((((((minus_minus @ A) @ A2) @ B2) = C2) = (A2 = (((plus_plus @ A) @ C2) @ B2))))))))).
% 2.99/1.51 thf(fact_148_group__cancel_Osub1, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [A4:A,K:A,A2:A,B2:A]: (((A4 = (((plus_plus @ A) @ K) @ A2)) => ((((minus_minus @ A) @ A4) @ B2) = (((plus_plus @ A) @ K) @ (((minus_minus @ A) @ A2) @ B2)))))))))).
% 2.99/1.51 thf(fact_149_sets__vimage__algebra__cong, axiom, (! [B:$tType,A:$tType,M:(sigma_measure @ A),N2:(sigma_measure @ A),X4:(set @ B),F:(B > A)]: (((((sigma_sets @ A) @ M) = ((sigma_sets @ A) @ N2)) => (((sigma_sets @ B) @ (((((sigma_vimage_algebra @ B) @ A) @ X4) @ F) @ M)) = ((sigma_sets @ B) @ (((((sigma_vimage_algebra @ B) @ A) @ X4) @ F) @ N2))))))).
% 2.99/1.51 thf(fact_150_vimage__algebra__cong, axiom, (! [A:$tType,B:$tType,X4:(set @ A),Y:(set @ A),F:(A > B),G:(A > B),M:(sigma_measure @ B),N2:(sigma_measure @ B)]: (((X4 = Y) => ((! [X3:A]: (((((member @ A) @ X3) @ Y) => ((F @ X3) = (G @ X3))))) => ((((sigma_sets @ B) @ M) = ((sigma_sets @ B) @ N2)) => ((((((sigma_vimage_algebra @ A) @ B) @ X4) @ F) @ M) = (((((sigma_vimage_algebra @ A) @ B) @ Y) @ G) @ N2)))))))).
% 2.99/1.51 thf(fact_151_borel__measurable__const__add, axiom, (! [B:$tType,A:$tType]: (((real_V55928688vector @ A) => (! [F:(B > A),M:(sigma_measure @ B),A2:A]: (((((member @ (B > A)) @ F) @ ((((sigma_measurable @ B) @ A) @ M) @ (borel_1404511681_borel @ A))) => (((member @ (B > A)) @ (^ [X:B]: ((((plus_plus @ A) @ A2) @ (F @ X))))) @ ((((sigma_measurable @ B) @ A) @ M) @ (borel_1404511681_borel @ A)))))))))).
% 2.99/1.51 thf(fact_152_borel__measurable__add, axiom, (! [A:$tType,B:$tType]: ((((elemen1026692323pology @ B) & (topolo1314133330id_add @ B)) => (! [F:(A > B),M:(sigma_measure @ A),G:(A > B)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))) => ((((member @ (A > B)) @ G) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))) => (((member @ (A > B)) @ (^ [X:A]: ((((plus_plus @ B) @ (F @ X)) @ (G @ X))))) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))))))))))).
% 2.99/1.51 thf(fact_153_borel__measurable__inf, axiom, (! [A:$tType,B:$tType]: ((((elemen1026692323pology @ B) & ((lattice @ B) & (topolo2117631714pology @ B))) => (! [F:(A > B),M:(sigma_measure @ A),G:(A > B)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))) => ((((member @ (A > B)) @ G) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))) => (((member @ (A > B)) @ (^ [X:A]: ((((inf_inf @ B) @ (G @ X)) @ (F @ X))))) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))))))))))).
% 2.99/1.51 thf(fact_154_sets__restrict__restrict__space, axiom, (! [A:$tType,M:(sigma_measure @ A),A4:(set @ A),B3:(set @ A)]: ((((sigma_sets @ A) @ (((sigma_restrict_space @ A) @ (((sigma_restrict_space @ A) @ M) @ A4)) @ B3)) = ((sigma_sets @ A) @ (((sigma_restrict_space @ A) @ M) @ (((inf_inf @ (set @ A)) @ A4) @ B3))))))).
% 2.99/1.51 thf(fact_155_space__restrict__space, axiom, (! [A:$tType,M:(sigma_measure @ A),Omega:(set @ A)]: ((((sigma_space @ A) @ (((sigma_restrict_space @ A) @ M) @ Omega)) = (((inf_inf @ (set @ A)) @ Omega) @ ((sigma_space @ A) @ M)))))).
% 2.99/1.51 thf(fact_156_measurable__sets__borel, axiom, (! [B:$tType,A:$tType]: (((topolo503727757_space @ A) => (! [F:(A > B),M:(sigma_measure @ B),A4:(set @ B)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ (borel_1404511681_borel @ A)) @ M)) => ((((member @ (set @ B)) @ A4) @ ((sigma_sets @ B) @ M)) => (((member @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ A4)) @ ((sigma_sets @ A) @ (borel_1404511681_borel @ A))))))))))).
% 2.99/1.51 thf(fact_157_sets__Collect__restrict__space__iff, axiom, (! [A:$tType,S:(set @ A),M:(sigma_measure @ A),P:(A > $o)]: (((((member @ (set @ A)) @ S) @ ((sigma_sets @ A) @ M)) => ((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ (((sigma_restrict_space @ A) @ M) @ S))) & (P @ X)))))) @ ((sigma_sets @ A) @ (((sigma_restrict_space @ A) @ M) @ S))) = (((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & ((((member @ A) @ X) @ S) & (P @ X))))))) @ ((sigma_sets @ A) @ M))))))).
% 2.99/1.51 thf(fact_158_borel__measurable__eq, axiom, (! [B:$tType,A:$tType]: ((((elemen1026692323pology @ B) & (topolo2117631714pology @ B)) => (! [F:(A > B),M:(sigma_measure @ A),G:(A > B)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))) => ((((member @ (A > B)) @ G) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))) => (((member @ (set @ A)) @ ((collect @ A) @ (^ [W2:A]: (((((member @ A) @ W2) @ ((sigma_space @ A) @ M)) & ((F @ W2) = (G @ W2))))))) @ ((sigma_sets @ A) @ M)))))))))).
% 2.99/1.51 thf(fact_159_borel__measurable__neq, axiom, (! [B:$tType,A:$tType]: ((((elemen1026692323pology @ B) & (topolo2117631714pology @ B)) => (! [F:(A > B),M:(sigma_measure @ A),G:(A > B)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))) => ((((member @ (A > B)) @ G) @ ((((sigma_measurable @ A) @ B) @ M) @ (borel_1404511681_borel @ B))) => (((member @ (set @ A)) @ ((collect @ A) @ (^ [W2:A]: (((((member @ A) @ W2) @ ((sigma_space @ A) @ M)) & ((F @ W2) != (G @ W2))))))) @ ((sigma_sets @ A) @ M)))))))))).
% 2.99/1.51 thf(fact_160_measurable__equality__set, axiom, (! [A:$tType,D3:$tType]: ((((elemen1026692323pology @ A) & (topological_t2_space @ A)) => (! [F:(D3 > A),M:(sigma_measure @ D3),G:(D3 > A)]: (((((member @ (D3 > A)) @ F) @ ((((sigma_measurable @ D3) @ A) @ M) @ (borel_1404511681_borel @ A))) => ((((member @ (D3 > A)) @ G) @ ((((sigma_measurable @ D3) @ A) @ M) @ (borel_1404511681_borel @ A))) => (((member @ (set @ D3)) @ ((collect @ D3) @ (^ [X:D3]: (((((member @ D3) @ X) @ ((sigma_space @ D3) @ M)) & ((F @ X) = (G @ X))))))) @ ((sigma_sets @ D3) @ M)))))))))).
% 2.99/1.51 thf(fact_161_measurable__If__restrict__space__iff, axiom, (! [A:$tType,B:$tType,M:(sigma_measure @ A),P:(A > $o),F:(A > B),G:(A > B),N2:(sigma_measure @ B)]: (((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ M)) & (P @ X)))))) @ ((sigma_sets @ A) @ M)) => ((((member @ (A > B)) @ (^ [X:A]: (((((if @ B) @ (P @ X)) @ (F @ X)) @ (G @ X))))) @ ((((sigma_measurable @ A) @ B) @ M) @ N2)) = ((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ (((sigma_restrict_space @ A) @ M) @ ((collect @ A) @ P))) @ N2)) & (((member @ (A > B)) @ G) @ ((((sigma_measurable @ A) @ B) @ (((sigma_restrict_space @ A) @ M) @ ((collect @ A) @ (^ [X:A]: ((~ ((P @ X)))))))) @ N2)))))))).
% 2.99/1.51 thf(fact_162_space__lebesgue__on, axiom, (! [A:$tType]: (((euclid925273238_space @ A) => (! [S:(set @ A)]: ((((sigma_space @ A) @ (((sigma_restrict_space @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ S)) = S))))))).
% 2.99/1.51 thf(fact_163_sets__lebesgue__on__refl, axiom, (! [A:$tType]: (((euclid925273238_space @ A) => (! [S:(set @ A)]: ((((member @ (set @ A)) @ S) @ ((sigma_sets @ A) @ (((sigma_restrict_space @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ S))))))))).
% 2.99/1.51 thf(fact_164_space__lborel, axiom, (! [B:$tType]: (((euclid925273238_space @ B) => (((sigma_space @ B) @ (lebesgue_lborel @ B)) = ((sigma_space @ B) @ (borel_1404511681_borel @ B))))))).
% 2.99/1.51 thf(fact_165_measurable__lborel1, axiom, (! [C3:$tType,D3:$tType]: (((euclid925273238_space @ D3) => (! [M:(sigma_measure @ C3)]: ((((((sigma_measurable @ C3) @ D3) @ M) @ (lebesgue_lborel @ D3)) = ((((sigma_measurable @ C3) @ D3) @ M) @ (borel_1404511681_borel @ D3))))))))).
% 2.99/1.51 thf(fact_166_measurable__lborel2, axiom, (! [E:$tType,C3:$tType]: (((euclid925273238_space @ E) => (! [M:(sigma_measure @ C3)]: ((((((sigma_measurable @ E) @ C3) @ (lebesgue_lborel @ E)) @ M) = ((((sigma_measurable @ E) @ C3) @ (borel_1404511681_borel @ E)) @ M)))))))).
% 2.99/1.51 thf(fact_167_sets_ODiff, axiom, (! [A:$tType,A2:(set @ A),M:(sigma_measure @ A),B2:(set @ A)]: (((((member @ (set @ A)) @ A2) @ ((sigma_sets @ A) @ M)) => ((((member @ (set @ A)) @ B2) @ ((sigma_sets @ A) @ M)) => (((member @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ ((sigma_sets @ A) @ M))))))).
% 2.99/1.51 thf(fact_168_sets_Ocompl__sets, axiom, (! [A:$tType,A2:(set @ A),M:(sigma_measure @ A)]: (((((member @ (set @ A)) @ A2) @ ((sigma_sets @ A) @ M)) => (((member @ (set @ A)) @ (((minus_minus @ (set @ A)) @ ((sigma_space @ A) @ M)) @ A2)) @ ((sigma_sets @ A) @ M)))))).
% 2.99/1.51 thf(fact_169_sets__lborel, axiom, (! [A:$tType]: (((euclid925273238_space @ A) => (((sigma_sets @ A) @ (lebesgue_lborel @ A)) = ((sigma_sets @ A) @ (borel_1404511681_borel @ A))))))).
% 2.99/1.51 thf(fact_170_Int__Diff, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A),C:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) @ C) = (((inf_inf @ (set @ A)) @ A4) @ (((minus_minus @ (set @ A)) @ B3) @ C)))))).
% 2.99/1.51 thf(fact_171_Diff__Int2, axiom, (! [A:$tType,A4:(set @ A),C:(set @ A),B3:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ C)) @ (((inf_inf @ (set @ A)) @ B3) @ C)) = (((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ C)) @ B3))))).
% 2.99/1.51 thf(fact_172_Diff__Diff__Int, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ (((minus_minus @ (set @ A)) @ A4) @ B3)) = (((inf_inf @ (set @ A)) @ A4) @ B3))))).
% 2.99/1.51 thf(fact_173_Diff__Int__distrib, axiom, (! [A:$tType,C:(set @ A),A4:(set @ A),B3:(set @ A)]: (((((inf_inf @ (set @ A)) @ C) @ (((minus_minus @ (set @ A)) @ A4) @ B3)) = (((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ C) @ A4)) @ (((inf_inf @ (set @ A)) @ C) @ B3)))))).
% 2.99/1.51 thf(fact_174_Diff__Int__distrib2, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A),C:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ B3)) @ C) = (((minus_minus @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ C)) @ (((inf_inf @ (set @ A)) @ B3) @ C)))))).
% 2.99/1.51 thf(fact_175_vimage__Diff, axiom, (! [A:$tType,B:$tType,F:(A > B),A4:(set @ B),B3:(set @ B)]: ((((((vimage @ A) @ B) @ F) @ (((minus_minus @ (set @ B)) @ A4) @ B3)) = (((minus_minus @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ A4)) @ ((((vimage @ A) @ B) @ F) @ B3)))))).
% 2.99/1.51 thf(fact_176_sets__restrict__space, axiom, (! [A:$tType,M:(sigma_measure @ A),Omega:(set @ A)]: ((((sigma_sets @ A) @ (((sigma_restrict_space @ A) @ M) @ Omega)) = ((((image @ (set @ A)) @ (set @ A)) @ ((inf_inf @ (set @ A)) @ Omega)) @ ((sigma_sets @ A) @ M)))))).
% 2.99/1.51 thf(fact_177_lborelD, axiom, (! [A:$tType]: (((euclid925273238_space @ A) => (! [A4:(set @ A)]: (((((member @ (set @ A)) @ A4) @ ((sigma_sets @ A) @ (borel_1404511681_borel @ A))) => (((member @ (set @ A)) @ A4) @ ((sigma_sets @ A) @ (lebesgue_lborel @ A)))))))))).
% 2.99/1.51 thf(fact_178_measurable__lebesgue__cong, axiom, (! [A:$tType,B:$tType]: (((euclid925273238_space @ A) => (! [S:(set @ A),F:(A > B),G:(A > B),M:(sigma_measure @ B)]: (((! [X3:A]: (((((member @ A) @ X3) @ S) => ((F @ X3) = (G @ X3))))) => ((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ (((sigma_restrict_space @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ S)) @ M)) = (((member @ (A > B)) @ G) @ ((((sigma_measurable @ A) @ B) @ (((sigma_restrict_space @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ S)) @ M)))))))))).
% 2.99/1.51 thf(fact_179_lborelD__Collect, axiom, (! [A:$tType]: (((euclid925273238_space @ A) => (! [P:(A > $o)]: (((((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ (borel_1404511681_borel @ A))) & (P @ X)))))) @ ((sigma_sets @ A) @ (borel_1404511681_borel @ A))) => (((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ ((sigma_space @ A) @ (lebesgue_lborel @ A))) & (P @ X)))))) @ ((sigma_sets @ A) @ (lebesgue_lborel @ A)))))))))).
% 2.99/1.51 thf(fact_180_lebesgue__sets__translation, axiom, (! [B:$tType]: (((euclid925273238_space @ B) => (! [S:(set @ B),A2:B]: (((((member @ (set @ B)) @ S) @ ((sigma_sets @ B) @ ((complete_completion @ B) @ (lebesgue_lborel @ B)))) => (((member @ (set @ B)) @ ((((image @ B) @ B) @ ((plus_plus @ B) @ A2)) @ S)) @ ((sigma_sets @ B) @ ((complete_completion @ B) @ (lebesgue_lborel @ B))))))))))).
% 2.99/1.51 thf(fact_181_lebesgue__measurable__vimage__borel, axiom, (! [B:$tType,A:$tType]: ((((euclid925273238_space @ A) & (euclid925273238_space @ B)) => (! [F:(A > B),T:(set @ B)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ (borel_1404511681_borel @ B))) => ((((member @ (set @ B)) @ T) @ ((sigma_sets @ B) @ (borel_1404511681_borel @ B))) => (((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: ((((member @ B) @ (F @ X)) @ T))))) @ ((sigma_sets @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A)))))))))))).
% 2.99/1.51 thf(fact_182_borel__measurable__lebesgue__preimage__borel, axiom, (! [A:$tType,B:$tType]: ((((euclid925273238_space @ B) & (euclid925273238_space @ A)) => (! [F:(A > B)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ (borel_1404511681_borel @ B))) = (! [T2:(set @ B)]: (((((member @ (set @ B)) @ T2) @ ((sigma_sets @ B) @ (borel_1404511681_borel @ B))) => (((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: ((((member @ B) @ (F @ X)) @ T2))))) @ ((sigma_sets @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A)))))))))))))).
% 2.99/1.51 thf(fact_183_borel__measurable__vimage__borel, axiom, (! [A:$tType,B:$tType]: ((((euclid925273238_space @ B) & (euclid925273238_space @ A)) => (! [F:(A > B),S:(set @ A)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ (((sigma_restrict_space @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ S)) @ (borel_1404511681_borel @ B))) = (! [T2:(set @ B)]: (((((member @ (set @ B)) @ T2) @ ((sigma_sets @ B) @ (borel_1404511681_borel @ B))) => (((member @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ S) & (((member @ B) @ (F @ X)) @ T2)))))) @ ((sigma_sets @ A) @ (((sigma_restrict_space @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ S))))))))))))).
% 2.99/1.51 thf(fact_184_restrict__space__eq__vimage__algebra_H, axiom, (! [A:$tType,M:(sigma_measure @ A),Omega:(set @ A)]: ((((sigma_sets @ A) @ (((sigma_restrict_space @ A) @ M) @ Omega)) = ((sigma_sets @ A) @ (((((sigma_vimage_algebra @ A) @ A) @ (((inf_inf @ (set @ A)) @ Omega) @ ((sigma_space @ A) @ M))) @ (^ [X:A]: (X))) @ M)))))).
% 2.99/1.51 thf(fact_185_restrict__restrict__space, axiom, (! [A:$tType,A4:(set @ A),M:(sigma_measure @ A),B3:(set @ A)]: (((((member @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A4) @ ((sigma_space @ A) @ M))) @ ((sigma_sets @ A) @ M)) => ((((member @ (set @ A)) @ (((inf_inf @ (set @ A)) @ B3) @ ((sigma_space @ A) @ M))) @ ((sigma_sets @ A) @ M)) => ((((sigma_restrict_space @ A) @ (((sigma_restrict_space @ A) @ M) @ A4)) @ B3) = (((sigma_restrict_space @ A) @ M) @ (((inf_inf @ (set @ A)) @ A4) @ B3)))))))).
% 2.99/1.51 thf(fact_186_is__borel__def, axiom, (! [B:$tType,A:$tType]: (((topolo503727757_space @ B) => (((borel_is_borel @ A) @ B) = (^ [F2:(A > B),M3:(sigma_measure @ A)]: ((((member @ (A > B)) @ F2) @ ((((sigma_measurable @ A) @ B) @ M3) @ (borel_1404511681_borel @ B)))))))))).
% 2.99/1.51 thf(fact_187_Diff__idemp, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ B3)) @ B3) = (((minus_minus @ (set @ A)) @ A4) @ B3))))).
% 2.99/1.51 thf(fact_188_Diff__iff, axiom, (! [A:$tType,C2:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B3)) = ((((member @ A) @ C2) @ A4) & (~ ((((member @ A) @ C2) @ B3)))))))).
% 2.99/1.51 thf(fact_189_DiffI, axiom, (! [A:$tType,C2:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ A4) => ((~ ((((member @ A) @ C2) @ B3))) => (((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B3))))))).
% 2.99/1.51 thf(fact_190_set__diff__eq, axiom, (! [A:$tType]: (((minus_minus @ (set @ A)) = (^ [A6:(set @ A),B4:(set @ A)]: (((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ A6) & (~ ((((member @ A) @ X) @ B4))))))))))))).
% 2.99/1.51 thf(fact_191_minus__set__def, axiom, (! [A:$tType]: (((minus_minus @ (set @ A)) = (^ [A6:(set @ A),B4:(set @ A)]: (((collect @ A) @ (((minus_minus @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ A6)))) @ (^ [X:A]: ((((member @ A) @ X) @ B4))))))))))).
% 2.99/1.51 thf(fact_192_DiffD2, axiom, (! [A:$tType,C2:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B3)) => (~ ((((member @ A) @ C2) @ B3))))))).
% 2.99/1.51 thf(fact_193_DiffD1, axiom, (! [A:$tType,C2:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B3)) => (((member @ A) @ C2) @ A4))))).
% 2.99/1.51 thf(fact_194_DiffE, axiom, (! [A:$tType,C2:A,A4:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B3)) => (~ (((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ B3)))))))).
% 2.99/1.51 thf(fact_195_sets__vimage__algebra__space, axiom, (! [A:$tType,B:$tType,X4:(set @ A),F:(A > B),M:(sigma_measure @ B)]: ((((member @ (set @ A)) @ X4) @ ((sigma_sets @ A) @ (((((sigma_vimage_algebra @ A) @ B) @ X4) @ F) @ M)))))).
% 2.99/1.51 thf(fact_196_translation__subtract__diff, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [A2:A,S2:(set @ A),T3:(set @ A)]: ((((((image @ A) @ A) @ (^ [X:A]: ((((minus_minus @ A) @ X) @ A2)))) @ (((minus_minus @ (set @ A)) @ S2) @ T3)) = (((minus_minus @ (set @ A)) @ ((((image @ A) @ A) @ (^ [X:A]: ((((minus_minus @ A) @ X) @ A2)))) @ S2)) @ ((((image @ A) @ A) @ (^ [X:A]: ((((minus_minus @ A) @ X) @ A2)))) @ T3))))))))).
% 2.99/1.51 thf(fact_197_translation__subtract__Int, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [A2:A,S2:(set @ A),T3:(set @ A)]: ((((((image @ A) @ A) @ (^ [X:A]: ((((minus_minus @ A) @ X) @ A2)))) @ (((inf_inf @ (set @ A)) @ S2) @ T3)) = (((inf_inf @ (set @ A)) @ ((((image @ A) @ A) @ (^ [X:A]: ((((minus_minus @ A) @ X) @ A2)))) @ S2)) @ ((((image @ A) @ A) @ (^ [X:A]: ((((minus_minus @ A) @ X) @ A2)))) @ T3))))))))).
% 2.99/1.51 thf(fact_198_translation__diff, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [A2:A,S2:(set @ A),T3:(set @ A)]: ((((((image @ A) @ A) @ ((plus_plus @ A) @ A2)) @ (((minus_minus @ (set @ A)) @ S2) @ T3)) = (((minus_minus @ (set @ A)) @ ((((image @ A) @ A) @ ((plus_plus @ A) @ A2)) @ S2)) @ ((((image @ A) @ A) @ ((plus_plus @ A) @ A2)) @ T3))))))))).
% 2.99/1.51 thf(fact_199_translation__Int, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [A2:A,S2:(set @ A),T3:(set @ A)]: ((((((image @ A) @ A) @ ((plus_plus @ A) @ A2)) @ (((inf_inf @ (set @ A)) @ S2) @ T3)) = (((inf_inf @ (set @ A)) @ ((((image @ A) @ A) @ ((plus_plus @ A) @ A2)) @ S2)) @ ((((image @ A) @ A) @ ((plus_plus @ A) @ A2)) @ T3))))))))).
% 2.99/1.51 thf(fact_200_measurable__product__then__coordinatewise, axiom, (! [B:$tType,A:$tType,C3:$tType]: (((topolo503727757_space @ C3) => (! [F:(A > (B > C3)),M:(sigma_measure @ A),I:B]: (((((member @ (A > (B > C3))) @ F) @ ((((sigma_measurable @ A) @ (B > C3)) @ M) @ (borel_1404511681_borel @ (B > C3)))) => (((member @ (A > C3)) @ (^ [X:A]: (((F @ X) @ I)))) @ ((((sigma_measurable @ A) @ C3) @ M) @ (borel_1404511681_borel @ C3)))))))))).
% 2.99/1.51 thf(fact_201_measurable__coordinatewise__then__product, axiom, (! [A:$tType,C3:$tType,B:$tType]: ((((countable @ B) & (elemen1026692323pology @ C3)) => (! [F:(A > (B > C3)),M:(sigma_measure @ A)]: (((! [I2:B]: ((((member @ (A > C3)) @ (^ [X:A]: (((F @ X) @ I2)))) @ ((((sigma_measurable @ A) @ C3) @ M) @ (borel_1404511681_borel @ C3))))) => (((member @ (A > (B > C3))) @ F) @ ((((sigma_measurable @ A) @ (B > C3)) @ M) @ (borel_1404511681_borel @ (B > C3))))))))))).
% 2.99/1.51 thf(fact_202_measurable__product__coordinates, axiom, (! [A:$tType,B:$tType]: (((topolo503727757_space @ B) => (! [I:A]: ((((member @ ((A > B) > B)) @ (^ [X:(A > B)]: ((X @ I)))) @ ((((sigma_measurable @ (A > B)) @ B) @ (borel_1404511681_borel @ (A > B))) @ (borel_1404511681_borel @ B))))))))).
% 2.99/1.51 thf(fact_203_translation__invert, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [A2:A,A4:(set @ A),B3:(set @ A)]: (((((((image @ A) @ A) @ ((plus_plus @ A) @ A2)) @ A4) = ((((image @ A) @ A) @ ((plus_plus @ A) @ A2)) @ B3)) => (A4 = B3)))))))).
% 2.99/1.51 thf(fact_204_translation__assoc, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [B2:A,A2:A,S:(set @ A)]: ((((((image @ A) @ A) @ ((plus_plus @ A) @ B2)) @ ((((image @ A) @ A) @ ((plus_plus @ A) @ A2)) @ S)) = ((((image @ A) @ A) @ ((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2))) @ S)))))))).
% 2.99/1.51 thf(fact_205_affine__parallel__expl__aux, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [S:(set @ A),A2:A,T:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ S) = (((member @ A) @ (((plus_plus @ A) @ A2) @ X3)) @ T)))) => (T = ((((image @ A) @ A) @ ((plus_plus @ A) @ A2)) @ S))))))))).
% 2.99/1.51 thf(fact_206_borel__measurable__if, axiom, (! [A:$tType,B:$tType]: ((((euclid925273238_space @ B) & (euclid925273238_space @ A)) => (! [S:(set @ A),F:(A > B)]: (((((member @ (set @ A)) @ S) @ ((sigma_sets @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A)))) => ((((member @ (A > B)) @ (^ [X:A]: (((((if @ B) @ (((member @ A) @ X) @ S)) @ (F @ X)) @ (zero_zero @ B))))) @ ((((sigma_measurable @ A) @ B) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ (borel_1404511681_borel @ B))) = (((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ (((sigma_restrict_space @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ S)) @ (borel_1404511681_borel @ B))))))))))).
% 2.99/1.51 thf(fact_207_add_Oleft__neutral, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.99/1.51 thf(fact_208_add_Oright__neutral, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.99/1.51 thf(fact_209_double__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: ((((((plus_plus @ A) @ A2) @ A2) = (zero_zero @ A)) = (A2 = (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_210_double__zero__sym, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ A2) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_211_add__cancel__left__left, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [B2:A,A2:A]: ((((((plus_plus @ A) @ B2) @ A2) = A2) = (B2 = (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_212_add__cancel__left__right, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: ((((((plus_plus @ A) @ A2) @ B2) = A2) = (B2 = (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_213_add__cancel__right__left, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ B2) @ A2)) = (B2 = (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_214_add__cancel__right__right, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ A2) @ B2)) = (B2 = (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_215_add__eq__0__iff__both__eq__0, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X2:A,Y3:A]: ((((((plus_plus @ A) @ X2) @ Y3) = (zero_zero @ A)) = ((X2 = (zero_zero @ A)) & (Y3 = (zero_zero @ A)))))))))).
% 2.99/1.51 thf(fact_216_zero__eq__add__iff__both__eq__0, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X2:A,Y3:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ X2) @ Y3)) = ((X2 = (zero_zero @ A)) & (Y3 = (zero_zero @ A)))))))))).
% 2.99/1.51 thf(fact_217_diff__self, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: (((((minus_minus @ A) @ A2) @ A2) = (zero_zero @ A)))))))).
% 2.99/1.51 thf(fact_218_diff__0__right, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: (((((minus_minus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.99/1.51 thf(fact_219_zero__diff, axiom, (! [A:$tType]: (((comm_monoid_diff @ A) => (! [A2:A]: (((((minus_minus @ A) @ (zero_zero @ A)) @ A2) = (zero_zero @ A)))))))).
% 2.99/1.51 thf(fact_220_diff__zero, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A]: (((((minus_minus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.99/1.51 thf(fact_221_cancel__comm__monoid__add__class_Odiff__cancel, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A]: (((((minus_minus @ A) @ A2) @ A2) = (zero_zero @ A)))))))).
% 2.99/1.51 thf(fact_222_image__add__0, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [S:(set @ A)]: ((((((image @ A) @ A) @ ((plus_plus @ A) @ (zero_zero @ A))) @ S) = S))))))).
% 2.99/1.51 thf(fact_223_diff__add__zero, axiom, (! [A:$tType]: (((comm_monoid_diff @ A) => (! [A2:A,B2:A]: (((((minus_minus @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B2)) = (zero_zero @ A)))))))).
% 2.99/1.51 thf(fact_224_eq__add__iff, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [X2:A,Y3:A]: (((X2 = (((plus_plus @ A) @ X2) @ Y3)) = (Y3 = (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_225_eq__iff__diff__eq__0, axiom, (! [A:$tType]: (((group_add @ A) => ((^ [Y4:A,Z2:A]: ((Y4 = Z2))) = (^ [A5:A,B5:A]: (((((minus_minus @ A) @ A5) @ B5) = (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_226_comm__monoid__add__class_Oadd__0, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.99/1.51 thf(fact_227_add_Ocomm__neutral, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.99/1.51 thf(fact_228_add_Ogroup__left__neutral, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.99/1.51 thf(fact_229_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X2:A]: ((((zero_zero @ A) = X2) = (X2 = (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_230_borel__measurable__if__D, axiom, (! [A:$tType,B:$tType]: ((((euclid925273238_space @ B) & (euclid925273238_space @ A)) => (! [S:(set @ A),F:(A > B)]: (((((member @ (A > B)) @ (^ [X:A]: (((((if @ B) @ (((member @ A) @ X) @ S)) @ (F @ X)) @ (zero_zero @ B))))) @ ((((sigma_measurable @ A) @ B) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ (borel_1404511681_borel @ B))) => (((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ (((sigma_restrict_space @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ S)) @ (borel_1404511681_borel @ B)))))))))).
% 2.99/1.51 thf(fact_231_borel__measurable__if__I, axiom, (! [A:$tType,B:$tType]: ((((euclid925273238_space @ B) & (euclid925273238_space @ A)) => (! [F:(A > B),S:(set @ A)]: (((((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ (((sigma_restrict_space @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ S)) @ (borel_1404511681_borel @ B))) => ((((member @ (set @ A)) @ S) @ ((sigma_sets @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A)))) => (((member @ (A > B)) @ (^ [X:A]: (((((if @ B) @ (((member @ A) @ X) @ S)) @ (F @ X)) @ (zero_zero @ B))))) @ ((((sigma_measurable @ A) @ B) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ (borel_1404511681_borel @ B))))))))))).
% 2.99/1.51 thf(fact_232_Least__eq__0, axiom, (! [P:(nat > $o)]: (((P @ (zero_zero @ nat)) => (((ord_Least @ nat) @ P) = (zero_zero @ nat)))))).
% 2.99/1.51 thf(fact_233_borel__measurable__if__lebesgue__on, axiom, (! [A:$tType,B:$tType]: ((((euclid925273238_space @ B) & (euclid925273238_space @ A)) => (! [S:(set @ A),T:(set @ A),F:(A > B)]: (((((member @ (set @ A)) @ S) @ ((sigma_sets @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A)))) => ((((member @ (set @ A)) @ T) @ ((sigma_sets @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A)))) => ((((ord_less_eq @ (set @ A)) @ S) @ T) => ((((member @ (A > B)) @ (^ [X:A]: (((((if @ B) @ (((member @ A) @ X) @ S)) @ (F @ X)) @ (zero_zero @ B))))) @ ((((sigma_measurable @ A) @ B) @ (((sigma_restrict_space @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ T)) @ (borel_1404511681_borel @ B))) = (((member @ (A > B)) @ F) @ ((((sigma_measurable @ A) @ B) @ (((sigma_restrict_space @ A) @ ((complete_completion @ A) @ (lebesgue_lborel @ A))) @ S)) @ (borel_1404511681_borel @ B))))))))))))).
% 2.99/1.51 thf(fact_234_subsetI, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A4) => (((member @ A) @ X3) @ B3)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B3))))).
% 2.99/1.51 thf(fact_235_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ A4) => (A4 = B3)))))).
% 2.99/1.51 thf(fact_236_diff__0__eq__0, axiom, (! [N4:nat]: (((((minus_minus @ nat) @ (zero_zero @ nat)) @ N4) = (zero_zero @ nat))))).
% 2.99/1.51 thf(fact_237_diff__self__eq__0, axiom, (! [M4:nat]: (((((minus_minus @ nat) @ M4) @ M4) = (zero_zero @ nat))))).
% 2.99/1.51 thf(fact_238_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N4:A]: (((((ord_less_eq @ A) @ N4) @ (zero_zero @ A)) = (N4 = (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_239_add__le__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B2) @ C2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.99/1.51 thf(fact_240_add__le__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C2:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.99/1.51 thf(fact_241_le__inf__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [X2:A,Y3:A,Z:A]: (((((ord_less_eq @ A) @ X2) @ (((inf_inf @ A) @ Y3) @ Z)) = ((((ord_less_eq @ A) @ X2) @ Y3) & (((ord_less_eq @ A) @ X2) @ Z))))))))).
% 2.99/1.51 thf(fact_242_inf_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_inf @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C2)) = ((((ord_less_eq @ A) @ A2) @ B2) & (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.99/1.51 thf(fact_243_Int__subset__iff, axiom, (! [A:$tType,C:(set @ A),A4:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C) @ (((inf_inf @ (set @ A)) @ A4) @ B3)) = ((((ord_less_eq @ (set @ A)) @ C) @ A4) & (((ord_less_eq @ (set @ A)) @ C) @ B3)))))).
% 2.99/1.51 thf(fact_244_set__plus__mono2, axiom, (! [A:$tType]: (((plus @ A) => (! [C:(set @ A),D:(set @ A),E2:(set @ A),F3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C) @ D) => ((((ord_less_eq @ (set @ A)) @ E2) @ F3) => (((ord_less_eq @ (set @ A)) @ (((plus_plus @ (set @ A)) @ C) @ E2)) @ (((plus_plus @ (set @ A)) @ D) @ F3)))))))))).
% 2.99/1.51 thf(fact_245_zero__le__double__add__iff__zero__le__single__add, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ A2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ A2)))))))).
% 2.99/1.51 thf(fact_246_double__add__le__zero__iff__single__add__le__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ A2)) @ (zero_zero @ A)) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_247_le__add__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ B2) @ A2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))).
% 2.99/1.51 thf(fact_248_le__add__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))).
% 2.99/1.51 thf(fact_249_add__le__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ B2) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_250_add__le__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ B2) @ A2)) @ B2) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.99/1.51 thf(fact_251_diff__ge__0__iff__ge, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((minus_minus @ A) @ A2) @ B2)) = (((ord_less_eq @ A) @ B2) @ A2)))))))).
% 2.99/1.51 thf(fact_252_subset__translation__eq, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [A2:A,S2:(set @ A),T3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((((image @ A) @ A) @ ((plus_plus @ A) @ A2)) @ S2)) @ ((((image @ A) @ A) @ ((plus_plus @ A) @ A2)) @ T3)) = (((ord_less_eq @ (set @ A)) @ S2) @ T3)))))))).
% 2.99/1.51 thf(fact_253_diffs0__imp__equal, axiom, (! [M4:nat,N4:nat]: ((((((minus_minus @ nat) @ M4) @ N4) = (zero_zero @ nat)) => (((((minus_minus @ nat) @ N4) @ M4) = (zero_zero @ nat)) => (M4 = N4)))))).
% 2.99/1.51 thf(fact_254_minus__nat_Odiff__0, axiom, (! [M4:nat]: (((((minus_minus @ nat) @ M4) @ (zero_zero @ nat)) = M4)))).
% 2.99/1.51 thf(subcl_Finite__Set_Ofinite___HOL_Otype, axiom, (! [A:$tType]: (((finite_finite @ A) => (type @ A))))).
% 2.99/1.51 thf(subcl_Finite__Set_Ofinite___Countable_Ocountable, axiom, (! [A:$tType]: (((finite_finite @ A) => (countable @ A))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space, axiom, (! [A9:$tType,A10:$tType]: ((((ordere890947078_space @ A9) & (finite_finite @ A10)) => (ordere890947078_space @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Ometric__space, axiom, (! [A9:$tType,A10:$tType]: ((((real_V2090557954_space @ A9) & (finite_finite @ A10)) => (real_V2090557954_space @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_1, axiom, (ordere890947078_space @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space_2, axiom, (real_V2090557954_space @ real)).
% 2.99/1.51 thf(tcon_fun___Elementary__Topology_Osecond__countable__topology, axiom, (! [A9:$tType,A10:$tType]: ((((countable @ A9) & (elemen1026692323pology @ A10)) => (elemen1026692323pology @ (A9 > A10)))))).
% 2.99/1.51 thf(tcon_fun___Topological__Spaces_Otopological__space, axiom, (! [A9:$tType,A10:$tType]: (((topolo503727757_space @ A10) => (topolo503727757_space @ (A9 > A10)))))).
% 2.99/1.51 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A9:$tType,A10:$tType]: (((semilattice_inf @ A10) => (semilattice_inf @ (A9 > A10)))))).
% 2.99/1.51 thf(tcon_fun___Countable_Ocountable, axiom, (! [A9:$tType,A10:$tType]: ((((finite_finite @ A9) & (countable @ A10)) => (countable @ (A9 > A10)))))).
% 2.99/1.51 thf(tcon_fun___Finite__Set_Ofinite, axiom, (! [A9:$tType,A10:$tType]: ((((finite_finite @ A9) & (finite_finite @ A10)) => (finite_finite @ (A9 > A10)))))).
% 2.99/1.51 thf(tcon_fun___Lattices_Olattice, axiom, (! [A9:$tType,A10:$tType]: (((lattice @ A10) => (lattice @ (A9 > A10)))))).
% 2.99/1.51 thf(tcon_fun___Groups_Ominus, axiom, (! [A9:$tType,A10:$tType]: (((minus @ A10) => (minus @ (A9 > A10)))))).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le, axiom, (ordere516151231imp_le @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, axiom, (ordere236663937imp_le @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Topological__Spaces_Otopological__space_3, axiom, (topolo503727757_space @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Topological__Spaces_Olinorder__topology, axiom, (topolo2117631714pology @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Oordered__ab__semigroup__add, axiom, (ordere779506340up_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Olinordered__ab__group__add, axiom, (linord219039673up_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add, axiom, (cancel146912293up_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Limits_Otopological__monoid__add, axiom, (topolo1314133330id_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Ocancel__comm__monoid__add, axiom, (cancel1352612707id_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Topological__Spaces_Ot2__space, axiom, (topological_t2_space @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add, axiom, (ordered_ab_group_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Ocancel__semigroup__add, axiom, (cancel_semigroup_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Lattices_Osemilattice__inf_4, axiom, (semilattice_inf @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Oab__semigroup__add, axiom, (ab_semigroup_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Ocomm__monoid__add, axiom, (comm_monoid_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Osemigroup__add, axiom, (semigroup_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Oab__group__add, axiom, (ab_group_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Countable_Ocountable_5, axiom, (countable @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Omonoid__add, axiom, (monoid_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Lattices_Olattice_6, axiom, (lattice @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Ogroup__add, axiom, (group_add @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Nat_Oring__char__0, axiom, (ring_char_0 @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Ominus_7, axiom, (minus @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Ozero, axiom, (zero @ int)).
% 2.99/1.51 thf(tcon_Int_Oint___Groups_Oplus, axiom, (plus @ int)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_8, axiom, (ordere516151231imp_le @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Elementary__Topology_Osecond__countable__topology_9, axiom, (elemen1026692323pology @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_10, axiom, (ordere236663937imp_le @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Topological__Spaces_Otopological__space_11, axiom, (topolo503727757_space @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Topological__Spaces_Olinorder__topology_12, axiom, (topolo2117631714pology @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_13, axiom, (ordere779506340up_add @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_14, axiom, (cancel146912293up_add @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Limits_Otopological__monoid__add_15, axiom, (topolo1314133330id_add @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_16, axiom, (cancel1352612707id_add @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Topological__Spaces_Ot2__space_17, axiom, (topological_t2_space @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add_18, axiom, (cancel_semigroup_add @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Lattices_Osemilattice__inf_19, axiom, (semilattice_inf @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff, axiom, (comm_monoid_diff @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add_20, axiom, (ab_semigroup_add @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add_21, axiom, (comm_monoid_add @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Osemigroup__add_22, axiom, (semigroup_add @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Countable_Ocountable_23, axiom, (countable @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Omonoid__add_24, axiom, (monoid_add @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Lattices_Olattice_25, axiom, (lattice @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Ominus_26, axiom, (minus @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Ozero_27, axiom, (zero @ nat)).
% 2.99/1.51 thf(tcon_Nat_Onat___Groups_Oplus_28, axiom, (plus @ nat)).
% 2.99/1.51 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_29, axiom, (! [A9:$tType]: ((semilattice_inf @ (set @ A9))))).
% 2.99/1.51 thf(tcon_Set_Oset___Groups_Oab__semigroup__add_30, axiom, (! [A9:$tType]: (((ab_semigroup_add @ A9) => (ab_semigroup_add @ (set @ A9)))))).
% 2.99/1.51 thf(tcon_Set_Oset___Groups_Ocomm__monoid__add_31, axiom, (! [A9:$tType]: (((comm_monoid_add @ A9) => (comm_monoid_add @ (set @ A9)))))).
% 2.99/1.51 thf(tcon_Set_Oset___Groups_Osemigroup__add_32, axiom, (! [A9:$tType]: (((semigroup_add @ A9) => (semigroup_add @ (set @ A9)))))).
% 2.99/1.51 thf(tcon_Set_Oset___Countable_Ocountable_33, axiom, (! [A9:$tType]: (((finite_finite @ A9) => (countable @ (set @ A9)))))).
% 2.99/1.51 thf(tcon_Set_Oset___Groups_Omonoid__add_34, axiom, (! [A9:$tType]: (((monoid_add @ A9) => (monoid_add @ (set @ A9)))))).
% 2.99/1.51 thf(tcon_Set_Oset___Finite__Set_Ofinite_35, axiom, (! [A9:$tType]: (((finite_finite @ A9) => (finite_finite @ (set @ A9)))))).
% 2.99/1.51 thf(tcon_Set_Oset___Lattices_Olattice_36, axiom, (! [A9:$tType]: ((lattice @ (set @ A9))))).
% 2.99/1.51 thf(tcon_Set_Oset___Groups_Ominus_37, axiom, (! [A9:$tType]: ((minus @ (set @ A9))))).
% 2.99/1.51 thf(tcon_Set_Oset___Groups_Ozero_38, axiom, (! [A9:$tType]: (((zero @ A9) => (zero @ (set @ A9)))))).
% 2.99/1.51 thf(tcon_Set_Oset___Groups_Oplus_39, axiom, (! [A9:$tType]: (((plus @ A9) => (plus @ (set @ A9)))))).
% 2.99/1.51 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_40, axiom, (topolo503727757_space @ $o)).
% 2.99/1.51 thf(tcon_HOL_Obool___Topological__Spaces_Olinorder__topology_41, axiom, (topolo2117631714pology @ $o)).
% 2.99/1.51 thf(tcon_HOL_Obool___Topological__Spaces_Ot2__space_42, axiom, (topological_t2_space @ $o)).
% 2.99/1.51 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_43, axiom, (semilattice_inf @ $o)).
% 2.99/1.51 thf(tcon_HOL_Obool___Countable_Ocountable_44, axiom, (countable @ $o)).
% 2.99/1.51 thf(tcon_HOL_Obool___Finite__Set_Ofinite_45, axiom, (finite_finite @ $o)).
% 2.99/1.51 thf(tcon_HOL_Obool___Lattices_Olattice_46, axiom, (lattice @ $o)).
% 2.99/1.51 thf(tcon_HOL_Obool___Groups_Ominus_47, axiom, (minus @ $o)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_48, axiom, (ordere516151231imp_le @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Elementary__Topology_Osecond__countable__topology_49, axiom, (elemen1026692323pology @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_50, axiom, (ordere236663937imp_le @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector, axiom, (real_V55928688vector @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Topological__Spaces_Otopological__space_51, axiom, (topolo503727757_space @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Topological__Spaces_Olinorder__topology_52, axiom, (topolo2117631714pology @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_53, axiom, (ordere779506340up_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Euclidean__Space_Oeuclidean__space, axiom, (euclid925273238_space @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector, axiom, (real_V1076094709vector @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add_54, axiom, (linord219039673up_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_55, axiom, (cancel146912293up_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Limits_Otopological__monoid__add_56, axiom, (topolo1314133330id_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_57, axiom, (cancel1352612707id_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Topological__Spaces_Ot2__space_58, axiom, (topological_t2_space @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add_59, axiom, (ordered_ab_group_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_60, axiom, (cancel_semigroup_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Lattices_Osemilattice__inf_61, axiom, (semilattice_inf @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_62, axiom, (ab_semigroup_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_63, axiom, (comm_monoid_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Osemigroup__add_64, axiom, (semigroup_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Oab__group__add_65, axiom, (ab_group_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Omonoid__add_66, axiom, (monoid_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Lattices_Olattice_67, axiom, (lattice @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Ogroup__add_68, axiom, (group_add @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Nat_Oring__char__0_69, axiom, (ring_char_0 @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Ominus_70, axiom, (minus @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Ozero_71, axiom, (zero @ real)).
% 2.99/1.51 thf(tcon_Real_Oreal___Groups_Oplus_72, axiom, (plus @ real)).
% 2.99/1.51 thf(tcon_Sigma__Algebra_Omeasure___Lattices_Osemilattice__inf_73, axiom, (! [A9:$tType]: ((semilattice_inf @ (sigma_measure @ A9))))).
% 2.99/1.51 thf(tcon_Sigma__Algebra_Omeasure___Lattices_Olattice_74, axiom, (! [A9:$tType]: ((lattice @ (sigma_measure @ A9))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__monoid__add__imp__le_75, axiom, (! [A9:$tType,A10:$tType]: ((((ordere890947078_space @ A9) & (finite_finite @ A10)) => (ordere516151231imp_le @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Elementary__Topology_Osecond__countable__topology_76, axiom, (! [A9:$tType,A10:$tType]: ((((euclid925273238_space @ A9) & (finite_finite @ A10)) => (elemen1026692323pology @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add__imp__le_77, axiom, (! [A9:$tType,A10:$tType]: ((((ordere890947078_space @ A9) & (finite_finite @ A10)) => (ordere236663937imp_le @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_78, axiom, (! [A9:$tType,A10:$tType]: ((((real_V55928688vector @ A9) & (finite_finite @ A10)) => (real_V55928688vector @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_79, axiom, (! [A9:$tType,A10:$tType]: ((((topolo503727757_space @ A9) & (finite_finite @ A10)) => (topolo503727757_space @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add_80, axiom, (! [A9:$tType,A10:$tType]: ((((ordere890947078_space @ A9) & (finite_finite @ A10)) => (ordere779506340up_add @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Euclidean__Space_Oeuclidean__space_81, axiom, (! [A9:$tType,A10:$tType]: ((((euclid925273238_space @ A9) & (finite_finite @ A10)) => (euclid925273238_space @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__vector_82, axiom, (! [A9:$tType,A10:$tType]: ((((real_V1076094709vector @ A9) & (finite_finite @ A10)) => (real_V1076094709vector @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__ab__semigroup__add_83, axiom, (! [A9:$tType,A10:$tType]: ((((cancel146912293up_add @ A9) & (finite_finite @ A10)) => (cancel146912293up_add @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Limits_Otopological__monoid__add_84, axiom, (! [A9:$tType,A10:$tType]: ((((real_V55928688vector @ A9) & (finite_finite @ A10)) => (topolo1314133330id_add @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__comm__monoid__add_85, axiom, (! [A9:$tType,A10:$tType]: ((((cancel1352612707id_add @ A9) & (finite_finite @ A10)) => (cancel1352612707id_add @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Ot2__space_86, axiom, (! [A9:$tType,A10:$tType]: ((((real_V2090557954_space @ A9) & (finite_finite @ A10)) => (topological_t2_space @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add_87, axiom, (! [A9:$tType,A10:$tType]: ((((ordere890947078_space @ A9) & (finite_finite @ A10)) => (ordered_ab_group_add @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__semigroup__add_88, axiom, (! [A9:$tType,A10:$tType]: ((((cancel_semigroup_add @ A9) & (finite_finite @ A10)) => (cancel_semigroup_add @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Osemilattice__inf_89, axiom, (! [A9:$tType,A10:$tType]: ((((ordere890947078_space @ A9) & (finite_finite @ A10)) => (semilattice_inf @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__semigroup__add_90, axiom, (! [A9:$tType,A10:$tType]: ((((ab_semigroup_add @ A9) & (finite_finite @ A10)) => (ab_semigroup_add @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocomm__monoid__add_91, axiom, (! [A9:$tType,A10:$tType]: ((((comm_monoid_add @ A9) & (finite_finite @ A10)) => (comm_monoid_add @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Osemigroup__add_92, axiom, (! [A9:$tType,A10:$tType]: ((((semigroup_add @ A9) & (finite_finite @ A10)) => (semigroup_add @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__group__add_93, axiom, (! [A9:$tType,A10:$tType]: ((((ab_group_add @ A9) & (finite_finite @ A10)) => (ab_group_add @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Countable_Ocountable_94, axiom, (! [A9:$tType,A10:$tType]: ((((countable @ A9) & (finite_finite @ A10)) => (countable @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Omonoid__add_95, axiom, (! [A9:$tType,A10:$tType]: ((((monoid_add @ A9) & (finite_finite @ A10)) => (monoid_add @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_96, axiom, (! [A9:$tType,A10:$tType]: ((((finite_finite @ A9) & (finite_finite @ A10)) => (finite_finite @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Olattice_97, axiom, (! [A9:$tType,A10:$tType]: ((((ordere890947078_space @ A9) & (finite_finite @ A10)) => (lattice @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ogroup__add_98, axiom, (! [A9:$tType,A10:$tType]: ((((group_add @ A9) & (finite_finite @ A10)) => (group_add @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Nat_Oring__char__0_99, axiom, (! [A9:$tType,A10:$tType]: ((((ring_char_0 @ A9) & (finite_finite @ A10)) => (ring_char_0 @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ominus_100, axiom, (! [A9:$tType,A10:$tType]: ((((minus @ A9) & (finite_finite @ A10)) => (minus @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ozero_101, axiom, (! [A9:$tType,A10:$tType]: ((((zero @ A9) & (finite_finite @ A10)) => (zero @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oplus_102, axiom, (! [A9:$tType,A10:$tType]: ((((plus @ A9) & (finite_finite @ A10)) => (plus @ ((finite_Cartesian_vec @ A9) @ A10)))))).
% 2.99/1.51 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.99/1.51 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y3:A]: ((((((if @ A) @ $false) @ X2) @ Y3) = Y3)))).
% 2.99/1.51 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y3:A]: ((((((if @ A) @ $true) @ X2) @ Y3) = X2)))).
% 2.99/1.51 thf(tfree_0, hypothesis, (finite_finite @ n)).
% 2.99/1.51 thf(conj_0, conjecture, (((member @ (set @ ((finite_Cartesian_vec @ real) @ n))) @ ((((vimage @ ((finite_Cartesian_vec @ real) @ n)) @ ((finite_Cartesian_vec @ real) @ n)) @ (^ [X:((finite_Cartesian_vec @ real) @ n)]: ((((plus_plus @ ((finite_Cartesian_vec @ real) @ n)) @ X) @ (((minkow1937162798nt_vec @ n) @ real) @ a))))) @ (t2 @ a))) @ ((sigma_sets @ ((finite_Cartesian_vec @ real) @ n)) @ ((complete_completion @ ((finite_Cartesian_vec @ real) @ n)) @ (lebesgue_lborel @ ((finite_Cartesian_vec @ real) @ n)))))).
% 2.99/1.51 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.3Wo9oJ6aQl/DTF2DTF12084.p
% 2.99/1.51 ------------------------
% 2.99/1.54 ---- Cleaned THF ---
% 2.99/1.54 thf(ty_t_Finite__Cartesian__Product_Ovec,type,
% 2.99/1.54 finite_Cartesian_vec: $tType > $tType > $tType ).
% 2.99/1.54
% 2.99/1.54 thf(ty_t_Sigma__Algebra_Omeasure,type,
% 2.99/1.54 sigma_measure: $tType > $tType ).
% 2.99/1.54
% 2.99/1.54 thf(ty_t_Real_Oreal,type,
% 2.99/1.54 real: $tType ).
% 2.99/1.54
% 2.99/1.54 thf(ty_t_Set_Oset,type,
% 2.99/1.54 set: $tType > $tType ).
% 2.99/1.54
% 2.99/1.54 thf(ty_t_Nat_Onat,type,
% 2.99/1.54 nat: $tType ).
% 2.99/1.54
% 2.99/1.54 thf(ty_t_Int_Oint,type,
% 2.99/1.54 int: $tType ).
% 2.99/1.54
% 2.99/1.54 thf(ty_tf_n,type,
% 2.99/1.54 n: $tType ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Real__Vector__Spaces_Ometric__space,type,
% 2.99/1.54 real_V2090557954_space:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Ordered__Euclidean__Space_Oordered__euclidean__space,type,
% 2.99/1.54 ordere890947078_space:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_HOL_Otype,type,
% 2.99/1.54 type:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Oplus,type,
% 2.99/1.54 plus:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Ozero,type,
% 2.99/1.54 zero:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Ominus,type,
% 2.99/1.54 minus:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Nat_Oring__char__0,type,
% 2.99/1.54 ring_char_0:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Ogroup__add,type,
% 2.99/1.54 group_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Lattices_Olattice,type,
% 2.99/1.54 lattice:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Finite__Set_Ofinite,type,
% 2.99/1.54 finite_finite:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Omonoid__add,type,
% 2.99/1.54 monoid_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Countable_Ocountable,type,
% 2.99/1.54 countable:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Oab__group__add,type,
% 2.99/1.54 ab_group_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Osemigroup__add,type,
% 2.99/1.54 semigroup_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 2.99/1.54 comm_monoid_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 2.99/1.54 ab_semigroup_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 2.99/1.54 comm_monoid_diff:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 2.99/1.54 semilattice_inf:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.99/1.54 cancel_semigroup_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.99/1.54 ordered_ab_group_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Topological__Spaces_Ot2__space,type,
% 2.99/1.54 topological_t2_space:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 2.99/1.54 cancel1352612707id_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Limits_Otopological__monoid__add,type,
% 2.99/1.54 topolo1314133330id_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 2.99/1.54 cancel146912293up_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 2.99/1.54 linord219039673up_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Real__Vector__Spaces_Oreal__vector,type,
% 2.99/1.54 real_V1076094709vector:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Euclidean__Space_Oeuclidean__space,type,
% 2.99/1.54 euclid925273238_space:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.99/1.54 ordere779506340up_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Topological__Spaces_Olinorder__topology,type,
% 2.99/1.54 topolo2117631714pology:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Topological__Spaces_Otopological__space,type,
% 2.99/1.54 topolo503727757_space:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.99/1.54 canoni770627133id_add:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector,type,
% 2.99/1.54 real_V55928688vector:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.99/1.54 ordere236663937imp_le:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Elementary__Topology_Osecond__countable__topology,type,
% 2.99/1.54 elemen1026692323pology:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 2.99/1.54 ordere516151231imp_le:
% 2.99/1.54 !>[A: $tType] : $o ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Borel__Space_Ois__borel,type,
% 2.99/1.54 borel_is_borel:
% 2.99/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > ( sigma_measure @ A ) > $o ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Borel__Space_Otopological__space__class_Oborel,type,
% 2.99/1.54 borel_1404511681_borel:
% 2.99/1.54 !>[A: $tType] : ( sigma_measure @ A ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Complete__Measure_Ocompletion,type,
% 2.99/1.54 complete_completion:
% 2.99/1.54 !>[A: $tType] : ( ( sigma_measure @ A ) > ( sigma_measure @ A ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Complete__Measure_Omain__part,type,
% 2.99/1.54 complete_main_part:
% 2.99/1.54 !>[A: $tType] : ( ( sigma_measure @ A ) > ( set @ A ) > ( set @ A ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.99/1.54 minus_minus:
% 2.99/1.54 !>[A: $tType] : ( A > A > A ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.99/1.54 plus_plus:
% 2.99/1.54 !>[A: $tType] : ( A > A > A ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.99/1.54 zero_zero:
% 2.99/1.54 !>[A: $tType] : A ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_If,type,
% 2.99/1.54 if:
% 2.99/1.54 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 2.99/1.54 inf_inf:
% 2.99/1.54 !>[A: $tType] : ( A > A > A ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Lebesgue__Measure_Olborel,type,
% 2.99/1.54 lebesgue_lborel:
% 2.99/1.54 !>[A: $tType] : ( sigma_measure @ A ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Minkowskis__Theorem__Mirabelle__jpyvdnlcjd_Oof__int__vec,type,
% 2.99/1.54 minkow1937162798nt_vec:
% 2.99/1.54 !>[B: $tType,A: $tType] : ( ( finite_Cartesian_vec @ int @ B ) > ( finite_Cartesian_vec @ A @ B ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Orderings_Oord__class_OLeast,type,
% 2.99/1.54 ord_Least:
% 2.99/1.54 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.99/1.54 ord_less_eq:
% 2.99/1.54 !>[A: $tType] : ( A > A > $o ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Set_OCollect,type,
% 2.99/1.54 collect:
% 2.99/1.54 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Set_Oimage,type,
% 2.99/1.54 image:
% 2.99/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Set_Ovimage,type,
% 2.99/1.54 vimage:
% 2.99/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Sigma__Algebra_Omeasurable,type,
% 2.99/1.54 sigma_measurable:
% 2.99/1.54 !>[A: $tType,B: $tType] : ( ( sigma_measure @ A ) > ( sigma_measure @ B ) > ( set @ ( A > B ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Sigma__Algebra_Orestrict__space,type,
% 2.99/1.54 sigma_restrict_space:
% 2.99/1.54 !>[A: $tType] : ( ( sigma_measure @ A ) > ( set @ A ) > ( sigma_measure @ A ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Sigma__Algebra_Osets,type,
% 2.99/1.54 sigma_sets:
% 2.99/1.54 !>[A: $tType] : ( ( sigma_measure @ A ) > ( set @ ( set @ A ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Sigma__Algebra_Ospace,type,
% 2.99/1.54 sigma_space:
% 2.99/1.54 !>[A: $tType] : ( ( sigma_measure @ A ) > ( set @ A ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_Sigma__Algebra_Ovimage__algebra,type,
% 2.99/1.54 sigma_vimage_algebra:
% 2.99/1.54 !>[A: $tType,B: $tType] : ( ( set @ A ) > ( A > B ) > ( sigma_measure @ B ) > ( sigma_measure @ A ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_c_member,type,
% 2.99/1.54 member:
% 2.99/1.54 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_v_R____,type,
% 2.99/1.54 r: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_v_S,type,
% 2.99/1.54 s: set @ ( finite_Cartesian_vec @ real @ n ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_v_T_H____,type,
% 2.99/1.54 t: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_v_T____,type,
% 2.99/1.54 t2: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(sy_v_a____,type,
% 2.99/1.54 a: finite_Cartesian_vec @ int @ n ).
% 2.99/1.54
% 2.99/1.54 thf(fact_0_assms_I1_J,axiom,
% 2.99/1.54 member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_1_of__int__vec__eq__iff,axiom,
% 2.99/1.54 ! [A: $tType,N: $tType] :
% 2.99/1.54 ( ( ( finite_finite @ N )
% 2.99/1.54 & ( ring_char_0 @ A ) )
% 2.99/1.54 => ! [A2: finite_Cartesian_vec @ int @ N,B2: finite_Cartesian_vec @ int @ N] :
% 2.99/1.54 ( ( ( minkow1937162798nt_vec @ N @ A @ A2 )
% 2.99/1.54 = ( minkow1937162798nt_vec @ N @ A @ B2 ) )
% 2.99/1.54 = ( A2 = B2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
% 2.99/1.54 ! [A3: finite_Cartesian_vec @ int @ n] :
% 2.99/1.54 ( ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A3 ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
% 2.99/1.54 => ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
% 2.99/1.54 @ ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
% 2.99/1.54 @ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
% 2.99/1.54 @ ^ [X: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ X @ ( minkow1937162798nt_vec @ n @ real @ A3 ) )
% 2.99/1.54 @ ( t2 @ A3 ) )
% 2.99/1.54 @ ( sigma_space @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
% 2.99/1.54 @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
% 2.99/1.54 ! [A2: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A2 ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_4_T_H__altdef,axiom,
% 2.99/1.54 ! [A2: finite_Cartesian_vec @ int @ n] :
% 2.99/1.54 ( ( t @ A2 )
% 2.99/1.54 = ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
% 2.99/1.54 @ ^ [X: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ X @ ( minkow1937162798nt_vec @ n @ real @ A2 ) )
% 2.99/1.54 @ ( t2 @ A2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_5__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
% 2.99/1.54 ! [A2: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( r @ A2 ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_6_sets__completionI__sets,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,M: sigma_measure @ A] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ A4 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( member @ ( set @ A ) @ A4 @ ( sigma_sets @ A @ ( complete_completion @ A @ M ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_7__092_060open_062_092_060And_062a_O_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_092_060in_062_Alebesgue_A_092_060rightarrow_062_092_060_094sub_062M_Alebesgue_092_060close_062,axiom,
% 2.99/1.54 ! [A2: finite_Cartesian_vec @ int @ n] :
% 2.99/1.54 ( member @ ( ( finite_Cartesian_vec @ real @ n ) > ( finite_Cartesian_vec @ real @ n ) )
% 2.99/1.54 @ ^ [X: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ X @ ( minkow1937162798nt_vec @ n @ real @ A2 ) )
% 2.99/1.54 @ ( sigma_measurable @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_8_vimage__ident,axiom,
% 2.99/1.54 ! [A: $tType,Y: set @ A] :
% 2.99/1.54 ( ( vimage @ A @ A
% 2.99/1.54 @ ^ [X: A] : X
% 2.99/1.54 @ Y )
% 2.99/1.54 = Y ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_9_vimage__Collect__eq,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,F: A > B,P: B > $o] :
% 2.99/1.54 ( ( vimage @ A @ B @ F @ ( collect @ B @ P ) )
% 2.99/1.54 = ( collect @ A
% 2.99/1.54 @ ^ [Y2: A] : ( P @ ( F @ Y2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_10_vimageI,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,F: B > A,A2: B,B2: A,B3: set @ A] :
% 2.99/1.54 ( ( ( F @ A2 )
% 2.99/1.54 = B2 )
% 2.99/1.54 => ( ( member @ A @ B2 @ B3 )
% 2.99/1.54 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ B3 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_11_vimage__eq,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 2.99/1.54 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 2.99/1.54 = ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_12_set__plus__intro,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( plus @ A )
% 2.99/1.54 => ! [A2: A,C: set @ A,B2: A,D: set @ A] :
% 2.99/1.54 ( ( member @ A @ A2 @ C )
% 2.99/1.54 => ( ( member @ A @ B2 @ D )
% 2.99/1.54 => ( member @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( plus_plus @ ( set @ A ) @ C @ D ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_13_add__left__cancel,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel_semigroup_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.99/1.54 = ( plus_plus @ A @ A2 @ C2 ) )
% 2.99/1.54 = ( B2 = C2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_14_add__right__cancel,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel_semigroup_add @ A )
% 2.99/1.54 => ! [B2: A,A2: A,C2: A] :
% 2.99/1.54 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.99/1.54 = ( plus_plus @ A @ C2 @ A2 ) )
% 2.99/1.54 = ( B2 = C2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_15_vimage__def,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType] :
% 2.99/1.54 ( ( vimage @ A @ B )
% 2.99/1.54 = ( ^ [F2: A > B,B4: set @ B] :
% 2.99/1.54 ( collect @ A
% 2.99/1.54 @ ^ [X: A] : ( member @ B @ ( F2 @ X ) @ B4 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_16_vimageD,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,A2: A,F: A > B,A4: set @ B] :
% 2.99/1.54 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ A4 ) )
% 2.99/1.54 => ( member @ B @ ( F @ A2 ) @ A4 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_17_vimageE,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 2.99/1.54 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 2.99/1.54 => ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_18_IntI,axiom,
% 2.99/1.54 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( member @ A @ C2 @ A4 )
% 2.99/1.54 => ( ( member @ A @ C2 @ B3 )
% 2.99/1.54 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_19_Int__iff,axiom,
% 2.99/1.54 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 = ( ( member @ A @ C2 @ A4 )
% 2.99/1.54 & ( member @ A @ C2 @ B3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_20_space__completion,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A] :
% 2.99/1.54 ( ( sigma_space @ A @ ( complete_completion @ A @ M ) )
% 2.99/1.54 = ( sigma_space @ A @ M ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_21_vimage__Int,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,F: A > B,A4: set @ B,B3: set @ B] :
% 2.99/1.54 ( ( vimage @ A @ B @ F @ ( inf_inf @ ( set @ B ) @ A4 @ B3 ) )
% 2.99/1.54 = ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ A4 ) @ ( vimage @ A @ B @ F @ B3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_22_T__def,axiom,
% 2.99/1.54 ( t2
% 2.99/1.54 = ( ^ [A5: finite_Cartesian_vec @ int @ n] : ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( r @ A5 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_23_IntE,axiom,
% 2.99/1.54 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 => ~ ( ( member @ A @ C2 @ A4 )
% 2.99/1.54 => ~ ( member @ A @ C2 @ B3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_24_IntD1,axiom,
% 2.99/1.54 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 => ( member @ A @ C2 @ A4 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_25_IntD2,axiom,
% 2.99/1.54 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 => ( member @ A @ C2 @ B3 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_26_Int__assoc,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,B3: set @ A,C: set @ A] :
% 2.99/1.54 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) @ C )
% 2.99/1.54 = ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ B3 @ C ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_27_Int__absorb,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A] :
% 2.99/1.54 ( ( inf_inf @ ( set @ A ) @ A4 @ A4 )
% 2.99/1.54 = A4 ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_28_Int__commute,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( inf_inf @ ( set @ A ) )
% 2.99/1.54 = ( ^ [A6: set @ A,B4: set @ A] : ( inf_inf @ ( set @ A ) @ B4 @ A6 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_29_Int__left__absorb,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 = ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_30_Int__left__commute,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,B3: set @ A,C: set @ A] :
% 2.99/1.54 ( ( inf_inf @ ( set @ A ) @ A4 @ ( inf_inf @ ( set @ A ) @ B3 @ C ) )
% 2.99/1.54 = ( inf_inf @ ( set @ A ) @ B3 @ ( inf_inf @ ( set @ A ) @ A4 @ C ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_31_Collect__conj__eq,axiom,
% 2.99/1.54 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.99/1.54 ( ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( P @ X )
% 2.99/1.54 & ( Q @ X ) ) )
% 2.99/1.54 = ( inf_inf @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_32_Int__Collect,axiom,
% 2.99/1.54 ! [A: $tType,X2: A,A4: set @ A,P: A > $o] :
% 2.99/1.54 ( ( member @ A @ X2 @ ( inf_inf @ ( set @ A ) @ A4 @ ( collect @ A @ P ) ) )
% 2.99/1.54 = ( ( member @ A @ X2 @ A4 )
% 2.99/1.54 & ( P @ X2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_33_Int__def,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( inf_inf @ ( set @ A ) )
% 2.99/1.54 = ( ^ [A6: set @ A,B4: set @ A] :
% 2.99/1.54 ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ A6 )
% 2.99/1.54 & ( member @ A @ X @ B4 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_34_measurable__completion,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,F: A > B,M: sigma_measure @ A,N2: sigma_measure @ B] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ N2 ) )
% 2.99/1.54 => ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( complete_completion @ A @ M ) @ N2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_35_vimage__inter__cong,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,S: set @ A,F: A > B,G: A > B,Y3: set @ B] :
% 2.99/1.54 ( ! [W: A] :
% 2.99/1.54 ( ( member @ A @ W @ S )
% 2.99/1.54 => ( ( F @ W )
% 2.99/1.54 = ( G @ W ) ) )
% 2.99/1.54 => ( ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ Y3 ) @ S )
% 2.99/1.54 = ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ G @ Y3 ) @ S ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_36_add__right__imp__eq,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel_semigroup_add @ A )
% 2.99/1.54 => ! [B2: A,A2: A,C2: A] :
% 2.99/1.54 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.99/1.54 = ( plus_plus @ A @ C2 @ A2 ) )
% 2.99/1.54 => ( B2 = C2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_37_add__left__imp__eq,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel_semigroup_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.99/1.54 = ( plus_plus @ A @ A2 @ C2 ) )
% 2.99/1.54 => ( B2 = C2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_38_add_Oleft__commute,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ab_semigroup_add @ A )
% 2.99/1.54 => ! [B2: A,A2: A,C2: A] :
% 2.99/1.54 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
% 2.99/1.54 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_39_add_Ocommute,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ab_semigroup_add @ A )
% 2.99/1.54 => ( ( plus_plus @ A )
% 2.99/1.54 = ( ^ [A5: A,B5: A] : ( plus_plus @ A @ B5 @ A5 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_40_add_Oright__cancel,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [B2: A,A2: A,C2: A] :
% 2.99/1.54 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.99/1.54 = ( plus_plus @ A @ C2 @ A2 ) )
% 2.99/1.54 = ( B2 = C2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_41_add_Oleft__cancel,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.99/1.54 = ( plus_plus @ A @ A2 @ C2 ) )
% 2.99/1.54 = ( B2 = C2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_42_add_Oassoc,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semigroup_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 2.99/1.54 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_43_set__plus__elim,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( plus @ A )
% 2.99/1.54 => ! [X2: A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( member @ A @ X2 @ ( plus_plus @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 => ~ ! [A7: A,B6: A] :
% 2.99/1.54 ( ( X2
% 2.99/1.54 = ( plus_plus @ A @ A7 @ B6 ) )
% 2.99/1.54 => ( ( member @ A @ A7 @ A4 )
% 2.99/1.54 => ~ ( member @ A @ B6 @ B3 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_44_group__cancel_Oadd2,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( comm_monoid_add @ A )
% 2.99/1.54 => ! [B3: A,K: A,B2: A,A2: A] :
% 2.99/1.54 ( ( B3
% 2.99/1.54 = ( plus_plus @ A @ K @ B2 ) )
% 2.99/1.54 => ( ( plus_plus @ A @ A2 @ B3 )
% 2.99/1.54 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_45_mem__Collect__eq,axiom,
% 2.99/1.54 ! [A: $tType,A2: A,P: A > $o] :
% 2.99/1.54 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.99/1.54 = ( P @ A2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_46_Collect__mem__eq,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A] :
% 2.99/1.54 ( ( collect @ A
% 2.99/1.54 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 2.99/1.54 = A4 ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_47_Collect__cong,axiom,
% 2.99/1.54 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.99/1.54 ( ! [X3: A] :
% 2.99/1.54 ( ( P @ X3 )
% 2.99/1.54 = ( Q @ X3 ) )
% 2.99/1.54 => ( ( collect @ A @ P )
% 2.99/1.54 = ( collect @ A @ Q ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_48_ext,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.99/1.54 ( ! [X3: A] :
% 2.99/1.54 ( ( F @ X3 )
% 2.99/1.54 = ( G @ X3 ) )
% 2.99/1.54 => ( F = G ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_49_group__cancel_Oadd1,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( comm_monoid_add @ A )
% 2.99/1.54 => ! [A4: A,K: A,A2: A,B2: A] :
% 2.99/1.54 ( ( A4
% 2.99/1.54 = ( plus_plus @ A @ K @ A2 ) )
% 2.99/1.54 => ( ( plus_plus @ A @ A4 @ B2 )
% 2.99/1.54 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_50_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ordere779506340up_add @ A )
% 2.99/1.54 => ! [I: A,J: A,K: A,L: A] :
% 2.99/1.54 ( ( ( I = J )
% 2.99/1.54 & ( K = L ) )
% 2.99/1.54 => ( ( plus_plus @ A @ I @ K )
% 2.99/1.54 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_51_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ab_semigroup_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 2.99/1.54 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_52_vimage__Collect,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,P: B > $o,F: A > B,Q: A > $o] :
% 2.99/1.54 ( ! [X3: A] :
% 2.99/1.54 ( ( P @ ( F @ X3 ) )
% 2.99/1.54 = ( Q @ X3 ) )
% 2.99/1.54 => ( ( vimage @ A @ B @ F @ ( collect @ B @ P ) )
% 2.99/1.54 = ( collect @ A @ Q ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_53_vimageI2,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,F: B > A,A2: B,A4: set @ A] :
% 2.99/1.54 ( ( member @ A @ ( F @ A2 ) @ A4 )
% 2.99/1.54 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ A4 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_54_sets_OInt__space__eq2,axiom,
% 2.99/1.54 ! [A: $tType,X2: set @ A,M: sigma_measure @ A] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ X2 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( inf_inf @ ( set @ A ) @ X2 @ ( sigma_space @ A @ M ) )
% 2.99/1.54 = X2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_55_sets_OInt__space__eq1,axiom,
% 2.99/1.54 ! [A: $tType,X2: set @ A,M: sigma_measure @ A] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ X2 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( inf_inf @ ( set @ A ) @ ( sigma_space @ A @ M ) @ X2 )
% 2.99/1.54 = X2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_56_measurable__sets,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,F: A > B,M: sigma_measure @ A,A4: sigma_measure @ B,S: set @ B] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ A4 ) )
% 2.99/1.54 => ( ( member @ ( set @ B ) @ S @ ( sigma_sets @ B @ A4 ) )
% 2.99/1.54 => ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ S ) @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_57_measurableI,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,M: sigma_measure @ A,F: A > B,N2: sigma_measure @ B] :
% 2.99/1.54 ( ! [X3: A] :
% 2.99/1.54 ( ( member @ A @ X3 @ ( sigma_space @ A @ M ) )
% 2.99/1.54 => ( member @ B @ ( F @ X3 ) @ ( sigma_space @ B @ N2 ) ) )
% 2.99/1.54 => ( ! [A8: set @ B] :
% 2.99/1.54 ( ( member @ ( set @ B ) @ A8 @ ( sigma_sets @ B @ N2 ) )
% 2.99/1.54 => ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ A8 ) @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) ) )
% 2.99/1.54 => ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ N2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_58_sets_Otop,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A] : ( member @ ( set @ A ) @ ( sigma_space @ A @ M ) @ ( sigma_sets @ A @ M ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_59_sets_OInt,axiom,
% 2.99/1.54 ! [A: $tType,A2: set @ A,M: sigma_measure @ A,B2: set @ A] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ A2 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( member @ ( set @ A ) @ B2 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A2 @ B2 ) @ ( sigma_sets @ A @ M ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_60_measurable__If__set,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,F: A > B,M: sigma_measure @ A,M2: sigma_measure @ B,G: A > B,A4: set @ A] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ M2 ) )
% 2.99/1.54 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ M2 ) )
% 2.99/1.54 => ( ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( member @ ( A > B )
% 2.99/1.54 @ ^ [X: A] : ( if @ B @ ( member @ A @ X @ A4 ) @ ( F @ X ) @ ( G @ X ) )
% 2.99/1.54 @ ( sigma_measurable @ A @ B @ M @ M2 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_61_measurable__sets__Collect,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,F: A > B,M: sigma_measure @ A,N2: sigma_measure @ B,P: B > $o] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ N2 ) )
% 2.99/1.54 => ( ( member @ ( set @ B )
% 2.99/1.54 @ ( collect @ B
% 2.99/1.54 @ ^ [X: B] :
% 2.99/1.54 ( ( member @ B @ X @ ( sigma_space @ B @ N2 ) )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ B @ N2 ) )
% 2.99/1.54 => ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( P @ ( F @ X ) ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_62_measurable__If,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,F: A > B,M: sigma_measure @ A,M2: sigma_measure @ B,G: A > B,P: A > $o] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ M2 ) )
% 2.99/1.54 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ M2 ) )
% 2.99/1.54 => ( ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( member @ ( A > B )
% 2.99/1.54 @ ^ [X: A] : ( if @ B @ ( P @ X ) @ ( F @ X ) @ ( G @ X ) )
% 2.99/1.54 @ ( sigma_measurable @ A @ B @ M @ M2 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_63_inf__apply,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ B )
% 2.99/1.54 => ( ( inf_inf @ ( A > B ) )
% 2.99/1.54 = ( ^ [F2: A > B,G2: A > B,X: A] : ( inf_inf @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_64_inf__right__idem,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [X2: A,Y3: A] :
% 2.99/1.54 ( ( inf_inf @ A @ ( inf_inf @ A @ X2 @ Y3 ) @ Y3 )
% 2.99/1.54 = ( inf_inf @ A @ X2 @ Y3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_65_inf_Oright__idem,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 2.99/1.54 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_66_inf__left__idem,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [X2: A,Y3: A] :
% 2.99/1.54 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ X2 @ Y3 ) )
% 2.99/1.54 = ( inf_inf @ A @ X2 @ Y3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_67_inf_Oleft__idem,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 2.99/1.54 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_68_inf__idem,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [X2: A] :
% 2.99/1.54 ( ( inf_inf @ A @ X2 @ X2 )
% 2.99/1.54 = X2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_69_inf_Oidem,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( inf_inf @ A @ A2 @ A2 )
% 2.99/1.54 = A2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_70_inf__set__def,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( inf_inf @ ( set @ A ) )
% 2.99/1.54 = ( ^ [A6: set @ A,B4: set @ A] :
% 2.99/1.54 ( collect @ A
% 2.99/1.54 @ ( inf_inf @ ( A > $o )
% 2.99/1.54 @ ^ [X: A] : ( member @ A @ X @ A6 )
% 2.99/1.54 @ ^ [X: A] : ( member @ A @ X @ B4 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_71_inf__left__commute,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [X2: A,Y3: A,Z: A] :
% 2.99/1.54 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y3 @ Z ) )
% 2.99/1.54 = ( inf_inf @ A @ Y3 @ ( inf_inf @ A @ X2 @ Z ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_72_inf_Oleft__commute,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [B2: A,A2: A,C2: A] :
% 2.99/1.54 ( ( inf_inf @ A @ B2 @ ( inf_inf @ A @ A2 @ C2 ) )
% 2.99/1.54 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_73_inf__commute,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ( ( inf_inf @ A )
% 2.99/1.54 = ( ^ [X: A,Y2: A] : ( inf_inf @ A @ Y2 @ X ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_74_inf_Ocommute,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ( ( inf_inf @ A )
% 2.99/1.54 = ( ^ [A5: A,B5: A] : ( inf_inf @ A @ B5 @ A5 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_75_inf__assoc,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [X2: A,Y3: A,Z: A] :
% 2.99/1.54 ( ( inf_inf @ A @ ( inf_inf @ A @ X2 @ Y3 ) @ Z )
% 2.99/1.54 = ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y3 @ Z ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_76_inf_Oassoc,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C2 )
% 2.99/1.54 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_77_boolean__algebra__cancel_Oinf2,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [B3: A,K: A,B2: A,A2: A] :
% 2.99/1.54 ( ( B3
% 2.99/1.54 = ( inf_inf @ A @ K @ B2 ) )
% 2.99/1.54 => ( ( inf_inf @ A @ A2 @ B3 )
% 2.99/1.54 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_78_boolean__algebra__cancel_Oinf1,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [A4: A,K: A,A2: A,B2: A] :
% 2.99/1.54 ( ( A4
% 2.99/1.54 = ( inf_inf @ A @ K @ A2 ) )
% 2.99/1.54 => ( ( inf_inf @ A @ A4 @ B2 )
% 2.99/1.54 = ( inf_inf @ A @ K @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_79_inf__fun__def,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ B )
% 2.99/1.54 => ( ( inf_inf @ ( A > B ) )
% 2.99/1.54 = ( ^ [F2: A > B,G2: A > B,X: A] : ( inf_inf @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_80_inf__sup__aci_I1_J,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( lattice @ A )
% 2.99/1.54 => ( ( inf_inf @ A )
% 2.99/1.54 = ( ^ [X: A,Y2: A] : ( inf_inf @ A @ Y2 @ X ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_81_inf__sup__aci_I2_J,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( lattice @ A )
% 2.99/1.54 => ! [X2: A,Y3: A,Z: A] :
% 2.99/1.54 ( ( inf_inf @ A @ ( inf_inf @ A @ X2 @ Y3 ) @ Z )
% 2.99/1.54 = ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y3 @ Z ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_82_inf__sup__aci_I3_J,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( lattice @ A )
% 2.99/1.54 => ! [X2: A,Y3: A,Z: A] :
% 2.99/1.54 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ Y3 @ Z ) )
% 2.99/1.54 = ( inf_inf @ A @ Y3 @ ( inf_inf @ A @ X2 @ Z ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_83_inf__sup__aci_I4_J,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( lattice @ A )
% 2.99/1.54 => ! [X2: A,Y3: A] :
% 2.99/1.54 ( ( inf_inf @ A @ X2 @ ( inf_inf @ A @ X2 @ Y3 ) )
% 2.99/1.54 = ( inf_inf @ A @ X2 @ Y3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_84_measurable__compose__rev,axiom,
% 2.99/1.54 ! [A: $tType,C3: $tType,B: $tType,F: A > B,L2: sigma_measure @ A,N2: sigma_measure @ B,G: C3 > A,M: sigma_measure @ C3] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ L2 @ N2 ) )
% 2.99/1.54 => ( ( member @ ( C3 > A ) @ G @ ( sigma_measurable @ C3 @ A @ M @ L2 ) )
% 2.99/1.54 => ( member @ ( C3 > B )
% 2.99/1.54 @ ^ [X: C3] : ( F @ ( G @ X ) )
% 2.99/1.54 @ ( sigma_measurable @ C3 @ B @ M @ N2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_85_measurable__compose,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,C3: $tType,F: A > B,M: sigma_measure @ A,N2: sigma_measure @ B,G: B > C3,L2: sigma_measure @ C3] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ N2 ) )
% 2.99/1.54 => ( ( member @ ( B > C3 ) @ G @ ( sigma_measurable @ B @ C3 @ N2 @ L2 ) )
% 2.99/1.54 => ( member @ ( A > C3 )
% 2.99/1.54 @ ^ [X: A] : ( G @ ( F @ X ) )
% 2.99/1.54 @ ( sigma_measurable @ A @ C3 @ M @ L2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_86_measurable__id,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A] :
% 2.99/1.54 ( member @ ( A > A )
% 2.99/1.54 @ ^ [X: A] : X
% 2.99/1.54 @ ( sigma_measurable @ A @ A @ M @ M ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_87_measurable__cong__sets,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,M: sigma_measure @ A,M2: sigma_measure @ A,N2: sigma_measure @ B,N3: sigma_measure @ B] :
% 2.99/1.54 ( ( ( sigma_sets @ A @ M )
% 2.99/1.54 = ( sigma_sets @ A @ M2 ) )
% 2.99/1.54 => ( ( ( sigma_sets @ B @ N2 )
% 2.99/1.54 = ( sigma_sets @ B @ N3 ) )
% 2.99/1.54 => ( ( sigma_measurable @ A @ B @ M @ N2 )
% 2.99/1.54 = ( sigma_measurable @ A @ B @ M2 @ N3 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_88_sets__eq__imp__space__eq,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,M2: sigma_measure @ A] :
% 2.99/1.54 ( ( ( sigma_sets @ A @ M )
% 2.99/1.54 = ( sigma_sets @ A @ M2 ) )
% 2.99/1.54 => ( ( sigma_space @ A @ M )
% 2.99/1.54 = ( sigma_space @ A @ M2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_89_measurable__cong__simp,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,M: sigma_measure @ A,N2: sigma_measure @ A,M2: sigma_measure @ B,N3: sigma_measure @ B,F: A > B,G: A > B] :
% 2.99/1.54 ( ( M = N2 )
% 2.99/1.54 => ( ( M2 = N3 )
% 2.99/1.54 => ( ! [W: A] :
% 2.99/1.54 ( ( member @ A @ W @ ( sigma_space @ A @ M ) )
% 2.99/1.54 => ( ( F @ W )
% 2.99/1.54 = ( G @ W ) ) )
% 2.99/1.54 => ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ M2 ) )
% 2.99/1.54 = ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ N2 @ N3 ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_90_measurable__space,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,F: A > B,M: sigma_measure @ A,A4: sigma_measure @ B,X2: A] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ A4 ) )
% 2.99/1.54 => ( ( member @ A @ X2 @ ( sigma_space @ A @ M ) )
% 2.99/1.54 => ( member @ B @ ( F @ X2 ) @ ( sigma_space @ B @ A4 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_91_measurable__cong,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,M: sigma_measure @ A,F: A > B,G: A > B,M2: sigma_measure @ B] :
% 2.99/1.54 ( ! [W: A] :
% 2.99/1.54 ( ( member @ A @ W @ ( sigma_space @ A @ M ) )
% 2.99/1.54 => ( ( F @ W )
% 2.99/1.54 = ( G @ W ) ) )
% 2.99/1.54 => ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ M2 ) )
% 2.99/1.54 = ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ M2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_92_measurable__ident__sets,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,M2: sigma_measure @ A] :
% 2.99/1.54 ( ( ( sigma_sets @ A @ M )
% 2.99/1.54 = ( sigma_sets @ A @ M2 ) )
% 2.99/1.54 => ( member @ ( A > A )
% 2.99/1.54 @ ^ [X: A] : X
% 2.99/1.54 @ ( sigma_measurable @ A @ A @ M @ M2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_93_sets_Osets__Collect_I5_J,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,Pb: $o] :
% 2.99/1.54 ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & Pb ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_94_sets_Osets__Collect__imp,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,P: A > $o,Q: A > $o] :
% 2.99/1.54 ( ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( Q @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( ( Q @ X )
% 2.99/1.54 => ( P @ X ) ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_95_sets_Osets__Collect__neg,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,P: A > $o] :
% 2.99/1.54 ( ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ~ ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_96_sets_Osets__Collect__conj,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,P: A > $o,Q: A > $o] :
% 2.99/1.54 ( ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( Q @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( Q @ X )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_97_sets_Osets__Collect__disj,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,P: A > $o,Q: A > $o] :
% 2.99/1.54 ( ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( Q @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( ( Q @ X )
% 2.99/1.54 | ( P @ X ) ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_98_sets_Osets__Collect__const,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,P: $o] :
% 2.99/1.54 ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & P ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_99_measurable__const,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,C2: A,M2: sigma_measure @ A,M: sigma_measure @ B] :
% 2.99/1.54 ( ( member @ A @ C2 @ ( sigma_space @ A @ M2 ) )
% 2.99/1.54 => ( member @ ( B > A )
% 2.99/1.54 @ ^ [X: B] : C2
% 2.99/1.54 @ ( sigma_measurable @ B @ A @ M @ M2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_100_T_H__def,axiom,
% 2.99/1.54 ( t
% 2.99/1.54 = ( ^ [A5: finite_Cartesian_vec @ int @ n] :
% 2.99/1.54 ( image @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
% 2.99/1.54 @ ^ [X: finite_Cartesian_vec @ real @ n] : ( minus_minus @ ( finite_Cartesian_vec @ real @ n ) @ X @ ( minkow1937162798nt_vec @ n @ real @ A5 ) )
% 2.99/1.54 @ ( t2 @ A5 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_101_inf__Int__eq,axiom,
% 2.99/1.54 ! [A: $tType,R: set @ A,S: set @ A] :
% 2.99/1.54 ( ( inf_inf @ ( A > $o )
% 2.99/1.54 @ ^ [X: A] : ( member @ A @ X @ R )
% 2.99/1.54 @ ^ [X: A] : ( member @ A @ X @ S ) )
% 2.99/1.54 = ( ^ [X: A] : ( member @ A @ X @ ( inf_inf @ ( set @ A ) @ R @ S ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_102_main__part__sets,axiom,
% 2.99/1.54 ! [A: $tType,S: set @ A,M: sigma_measure @ A] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ ( complete_completion @ A @ M ) ) )
% 2.99/1.54 => ( member @ ( set @ A ) @ ( complete_main_part @ A @ M @ S ) @ ( sigma_sets @ A @ M ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_103_measurable__restrict__space__iff,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,Omega: set @ A,M: sigma_measure @ A,C2: B,N2: sigma_measure @ B,F: A > B] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ Omega @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( member @ B @ C2 @ ( sigma_space @ B @ N2 ) )
% 2.99/1.54 => ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ M @ Omega ) @ N2 ) )
% 2.99/1.54 = ( member @ ( A > B )
% 2.99/1.54 @ ^ [X: A] : ( if @ B @ ( member @ A @ X @ Omega ) @ ( F @ X ) @ C2 )
% 2.99/1.54 @ ( sigma_measurable @ A @ B @ M @ N2 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_104_sets__Least,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,P: nat > A > $o,A4: set @ nat] :
% 2.99/1.54 ( ! [I2: nat] :
% 2.99/1.54 ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( P @ I2 @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( member @ ( set @ A )
% 2.99/1.54 @ ( inf_inf @ ( set @ A )
% 2.99/1.54 @ ( vimage @ A @ nat
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ord_Least @ nat
% 2.99/1.54 @ ^ [J2: nat] : ( P @ J2 @ X ) )
% 2.99/1.54 @ A4 )
% 2.99/1.54 @ ( sigma_space @ A @ M ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_105_in__vimage__algebra,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,A4: set @ A,M: sigma_measure @ A,F: B > A,X4: set @ B] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ A4 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( member @ ( set @ B ) @ ( inf_inf @ ( set @ B ) @ ( vimage @ B @ A @ F @ A4 ) @ X4 ) @ ( sigma_sets @ B @ ( sigma_vimage_algebra @ B @ A @ X4 @ F @ M ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_106_in__borel__measurable__borel,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( topolo503727757_space @ B )
% 2.99/1.54 => ! [F: A > B,M: sigma_measure @ A] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 = ( ! [X: set @ B] :
% 2.99/1.54 ( ( member @ ( set @ B ) @ X @ ( sigma_sets @ B @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ X ) @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_107_image__eqI,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,B2: A,F: B > A,X2: B,A4: set @ B] :
% 2.99/1.54 ( ( B2
% 2.99/1.54 = ( F @ X2 ) )
% 2.99/1.54 => ( ( member @ B @ X2 @ A4 )
% 2.99/1.54 => ( member @ A @ B2 @ ( image @ B @ A @ F @ A4 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_108_minus__apply,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType] :
% 2.99/1.54 ( ( minus @ B )
% 2.99/1.54 => ( ( minus_minus @ ( A > B ) )
% 2.99/1.54 = ( ^ [A6: A > B,B4: A > B,X: A] : ( minus_minus @ B @ ( A6 @ X ) @ ( B4 @ X ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_109_inf1I,axiom,
% 2.99/1.54 ! [A: $tType,A4: A > $o,X2: A,B3: A > $o] :
% 2.99/1.54 ( ( A4 @ X2 )
% 2.99/1.54 => ( ( B3 @ X2 )
% 2.99/1.54 => ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_110_image__ident,axiom,
% 2.99/1.54 ! [A: $tType,Y: set @ A] :
% 2.99/1.54 ( ( image @ A @ A
% 2.99/1.54 @ ^ [X: A] : X
% 2.99/1.54 @ Y )
% 2.99/1.54 = Y ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_111_add__diff__cancel__right_H,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel146912293up_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 2.99/1.54 = A2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_112_add__diff__cancel__right,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel146912293up_add @ A )
% 2.99/1.54 => ! [A2: A,C2: A,B2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.99/1.54 = ( minus_minus @ A @ A2 @ B2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_113_add__diff__cancel__left_H,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel146912293up_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ A2 )
% 2.99/1.54 = B2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_114_add__diff__cancel__left,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel146912293up_add @ A )
% 2.99/1.54 => ! [C2: A,A2: A,B2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 2.99/1.54 = ( minus_minus @ A @ A2 @ B2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_115_diff__add__cancel,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B2 ) @ B2 )
% 2.99/1.54 = A2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_116_add__diff__cancel,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 2.99/1.54 = A2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_117_space__vimage__algebra,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,X4: set @ A,F: A > B,M: sigma_measure @ B] :
% 2.99/1.54 ( ( sigma_space @ A @ ( sigma_vimage_algebra @ A @ B @ X4 @ F @ M ) )
% 2.99/1.54 = X4 ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_118_main__part,axiom,
% 2.99/1.54 ! [A: $tType,S: set @ A,M: sigma_measure @ A] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( complete_main_part @ A @ M @ S )
% 2.99/1.54 = S ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_119_space__restrict__space2,axiom,
% 2.99/1.54 ! [A: $tType,Omega: set @ A,M: sigma_measure @ A] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ Omega @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( sigma_space @ A @ ( sigma_restrict_space @ A @ M @ Omega ) )
% 2.99/1.54 = Omega ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_120_inf1E,axiom,
% 2.99/1.54 ! [A: $tType,A4: A > $o,B3: A > $o,X2: A] :
% 2.99/1.54 ( ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X2 )
% 2.99/1.54 => ~ ( ( A4 @ X2 )
% 2.99/1.54 => ~ ( B3 @ X2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_121_inf1D1,axiom,
% 2.99/1.54 ! [A: $tType,A4: A > $o,B3: A > $o,X2: A] :
% 2.99/1.54 ( ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X2 )
% 2.99/1.54 => ( A4 @ X2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_122_inf1D2,axiom,
% 2.99/1.54 ! [A: $tType,A4: A > $o,B3: A > $o,X2: A] :
% 2.99/1.54 ( ( inf_inf @ ( A > $o ) @ A4 @ B3 @ X2 )
% 2.99/1.54 => ( B3 @ X2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_123_borel__measurable__diff,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( ( elemen1026692323pology @ B )
% 2.99/1.54 & ( real_V55928688vector @ B ) )
% 2.99/1.54 => ! [F: A > B,M: sigma_measure @ A,G: A > B] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( member @ ( A > B )
% 2.99/1.54 @ ^ [X: A] : ( minus_minus @ B @ ( F @ X ) @ ( G @ X ) )
% 2.99/1.54 @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_124_fun__diff__def,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType] :
% 2.99/1.54 ( ( minus @ B )
% 2.99/1.54 => ( ( minus_minus @ ( A > B ) )
% 2.99/1.54 = ( ^ [A6: A > B,B4: A > B,X: A] : ( minus_minus @ B @ ( A6 @ X ) @ ( B4 @ X ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_125_Compr__image__eq,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 2.99/1.54 ( ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( image @ B @ A @ F @ A4 ) )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 = ( image @ B @ A @ F
% 2.99/1.54 @ ( collect @ B
% 2.99/1.54 @ ^ [X: B] :
% 2.99/1.54 ( ( member @ B @ X @ A4 )
% 2.99/1.54 & ( P @ ( F @ X ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_126_image__image,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,C3: $tType,F: B > A,G: C3 > B,A4: set @ C3] :
% 2.99/1.54 ( ( image @ B @ A @ F @ ( image @ C3 @ B @ G @ A4 ) )
% 2.99/1.54 = ( image @ C3 @ A
% 2.99/1.54 @ ^ [X: C3] : ( F @ ( G @ X ) )
% 2.99/1.54 @ A4 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_127_imageE,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,B2: A,F: B > A,A4: set @ B] :
% 2.99/1.54 ( ( member @ A @ B2 @ ( image @ B @ A @ F @ A4 ) )
% 2.99/1.54 => ~ ! [X3: B] :
% 2.99/1.54 ( ( B2
% 2.99/1.54 = ( F @ X3 ) )
% 2.99/1.54 => ~ ( member @ B @ X3 @ A4 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_128_diff__right__commute,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel146912293up_add @ A )
% 2.99/1.54 => ! [A2: A,C2: A,B2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C2 ) @ B2 )
% 2.99/1.54 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B2 ) @ C2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_129_diff__eq__diff__eq,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A,D2: A] :
% 2.99/1.54 ( ( ( minus_minus @ A @ A2 @ B2 )
% 2.99/1.54 = ( minus_minus @ A @ C2 @ D2 ) )
% 2.99/1.54 => ( ( A2 = B2 )
% 2.99/1.54 = ( C2 = D2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_130_rev__image__eqI,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,X2: A,A4: set @ A,B2: B,F: A > B] :
% 2.99/1.54 ( ( member @ A @ X2 @ A4 )
% 2.99/1.54 => ( ( B2
% 2.99/1.54 = ( F @ X2 ) )
% 2.99/1.54 => ( member @ B @ B2 @ ( image @ A @ B @ F @ A4 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_131_ball__imageD,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 2.99/1.54 ( ! [X3: A] :
% 2.99/1.54 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A4 ) )
% 2.99/1.54 => ( P @ X3 ) )
% 2.99/1.54 => ! [X5: B] :
% 2.99/1.54 ( ( member @ B @ X5 @ A4 )
% 2.99/1.54 => ( P @ ( F @ X5 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_132_image__cong,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,M: set @ A,N2: set @ A,F: A > B,G: A > B] :
% 2.99/1.54 ( ( M = N2 )
% 2.99/1.54 => ( ! [X3: A] :
% 2.99/1.54 ( ( member @ A @ X3 @ N2 )
% 2.99/1.54 => ( ( F @ X3 )
% 2.99/1.54 = ( G @ X3 ) ) )
% 2.99/1.54 => ( ( image @ A @ B @ F @ M )
% 2.99/1.54 = ( image @ A @ B @ G @ N2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_133_bex__imageD,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 2.99/1.54 ( ? [X5: A] :
% 2.99/1.54 ( ( member @ A @ X5 @ ( image @ B @ A @ F @ A4 ) )
% 2.99/1.54 & ( P @ X5 ) )
% 2.99/1.54 => ? [X3: B] :
% 2.99/1.54 ( ( member @ B @ X3 @ A4 )
% 2.99/1.54 & ( P @ ( F @ X3 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_134_image__iff,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,Z: A,F: B > A,A4: set @ B] :
% 2.99/1.54 ( ( member @ A @ Z @ ( image @ B @ A @ F @ A4 ) )
% 2.99/1.54 = ( ? [X: B] :
% 2.99/1.54 ( ( member @ B @ X @ A4 )
% 2.99/1.54 & ( Z
% 2.99/1.54 = ( F @ X ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_135_imageI,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,X2: A,A4: set @ A,F: A > B] :
% 2.99/1.54 ( ( member @ A @ X2 @ A4 )
% 2.99/1.54 => ( member @ B @ ( F @ X2 ) @ ( image @ A @ B @ F @ A4 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_136_borel__measurable__const,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( topolo503727757_space @ B )
% 2.99/1.54 => ! [C2: B,M: sigma_measure @ A] :
% 2.99/1.54 ( member @ ( A > B )
% 2.99/1.54 @ ^ [X: A] : C2
% 2.99/1.54 @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_137_sets__restrict__space__cong,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,N2: sigma_measure @ A,Omega: set @ A] :
% 2.99/1.54 ( ( ( sigma_sets @ A @ M )
% 2.99/1.54 = ( sigma_sets @ A @ N2 ) )
% 2.99/1.54 => ( ( sigma_sets @ A @ ( sigma_restrict_space @ A @ M @ Omega ) )
% 2.99/1.54 = ( sigma_sets @ A @ ( sigma_restrict_space @ A @ N2 @ Omega ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_138_restrict__space__sets__cong,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,B3: set @ A,M: sigma_measure @ A,N2: sigma_measure @ A] :
% 2.99/1.54 ( ( A4 = B3 )
% 2.99/1.54 => ( ( ( sigma_sets @ A @ M )
% 2.99/1.54 = ( sigma_sets @ A @ N2 ) )
% 2.99/1.54 => ( ( sigma_sets @ A @ ( sigma_restrict_space @ A @ M @ A4 ) )
% 2.99/1.54 = ( sigma_sets @ A @ ( sigma_restrict_space @ A @ N2 @ B3 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_139_measurable__restrict__space1,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,F: A > B,M: sigma_measure @ A,N2: sigma_measure @ B,Omega: set @ A] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ N2 ) )
% 2.99/1.54 => ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ M @ Omega ) @ N2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_140_add__implies__diff,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel1352612707id_add @ A )
% 2.99/1.54 => ! [C2: A,B2: A,A2: A] :
% 2.99/1.54 ( ( ( plus_plus @ A @ C2 @ B2 )
% 2.99/1.54 = A2 )
% 2.99/1.54 => ( C2
% 2.99/1.54 = ( minus_minus @ A @ A2 @ B2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_141_diff__diff__add,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel146912293up_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B2 ) @ C2 )
% 2.99/1.54 = ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_142_diff__add__eq__diff__diff__swap,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.99/1.54 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C2 ) @ B2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_143_diff__add__eq,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ab_group_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B2 ) @ C2 )
% 2.99/1.54 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_144_diff__diff__eq2,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ A2 @ ( minus_minus @ A @ B2 @ C2 ) )
% 2.99/1.54 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C2 ) @ B2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_145_add__diff__eq,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B2 @ C2 ) )
% 2.99/1.54 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_146_eq__diff__eq,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [A2: A,C2: A,B2: A] :
% 2.99/1.54 ( ( A2
% 2.99/1.54 = ( minus_minus @ A @ C2 @ B2 ) )
% 2.99/1.54 = ( ( plus_plus @ A @ A2 @ B2 )
% 2.99/1.54 = C2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_147_diff__eq__eq,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( ( minus_minus @ A @ A2 @ B2 )
% 2.99/1.54 = C2 )
% 2.99/1.54 = ( A2
% 2.99/1.54 = ( plus_plus @ A @ C2 @ B2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_148_group__cancel_Osub1,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ab_group_add @ A )
% 2.99/1.54 => ! [A4: A,K: A,A2: A,B2: A] :
% 2.99/1.54 ( ( A4
% 2.99/1.54 = ( plus_plus @ A @ K @ A2 ) )
% 2.99/1.54 => ( ( minus_minus @ A @ A4 @ B2 )
% 2.99/1.54 = ( plus_plus @ A @ K @ ( minus_minus @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_149_sets__vimage__algebra__cong,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,M: sigma_measure @ A,N2: sigma_measure @ A,X4: set @ B,F: B > A] :
% 2.99/1.54 ( ( ( sigma_sets @ A @ M )
% 2.99/1.54 = ( sigma_sets @ A @ N2 ) )
% 2.99/1.54 => ( ( sigma_sets @ B @ ( sigma_vimage_algebra @ B @ A @ X4 @ F @ M ) )
% 2.99/1.54 = ( sigma_sets @ B @ ( sigma_vimage_algebra @ B @ A @ X4 @ F @ N2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_150_vimage__algebra__cong,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,X4: set @ A,Y: set @ A,F: A > B,G: A > B,M: sigma_measure @ B,N2: sigma_measure @ B] :
% 2.99/1.54 ( ( X4 = Y )
% 2.99/1.54 => ( ! [X3: A] :
% 2.99/1.54 ( ( member @ A @ X3 @ Y )
% 2.99/1.54 => ( ( F @ X3 )
% 2.99/1.54 = ( G @ X3 ) ) )
% 2.99/1.54 => ( ( ( sigma_sets @ B @ M )
% 2.99/1.54 = ( sigma_sets @ B @ N2 ) )
% 2.99/1.54 => ( ( sigma_vimage_algebra @ A @ B @ X4 @ F @ M )
% 2.99/1.54 = ( sigma_vimage_algebra @ A @ B @ Y @ G @ N2 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_151_borel__measurable__const__add,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType] :
% 2.99/1.54 ( ( real_V55928688vector @ A )
% 2.99/1.54 => ! [F: B > A,M: sigma_measure @ B,A2: A] :
% 2.99/1.54 ( ( member @ ( B > A ) @ F @ ( sigma_measurable @ B @ A @ M @ ( borel_1404511681_borel @ A ) ) )
% 2.99/1.54 => ( member @ ( B > A )
% 2.99/1.54 @ ^ [X: B] : ( plus_plus @ A @ A2 @ ( F @ X ) )
% 2.99/1.54 @ ( sigma_measurable @ B @ A @ M @ ( borel_1404511681_borel @ A ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_152_borel__measurable__add,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( ( elemen1026692323pology @ B )
% 2.99/1.54 & ( topolo1314133330id_add @ B ) )
% 2.99/1.54 => ! [F: A > B,M: sigma_measure @ A,G: A > B] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( member @ ( A > B )
% 2.99/1.54 @ ^ [X: A] : ( plus_plus @ B @ ( F @ X ) @ ( G @ X ) )
% 2.99/1.54 @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_153_borel__measurable__inf,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( ( elemen1026692323pology @ B )
% 2.99/1.54 & ( lattice @ B )
% 2.99/1.54 & ( topolo2117631714pology @ B ) )
% 2.99/1.54 => ! [F: A > B,M: sigma_measure @ A,G: A > B] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( member @ ( A > B )
% 2.99/1.54 @ ^ [X: A] : ( inf_inf @ B @ ( G @ X ) @ ( F @ X ) )
% 2.99/1.54 @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_154_sets__restrict__restrict__space,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( sigma_sets @ A @ ( sigma_restrict_space @ A @ ( sigma_restrict_space @ A @ M @ A4 ) @ B3 ) )
% 2.99/1.54 = ( sigma_sets @ A @ ( sigma_restrict_space @ A @ M @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_155_space__restrict__space,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,Omega: set @ A] :
% 2.99/1.54 ( ( sigma_space @ A @ ( sigma_restrict_space @ A @ M @ Omega ) )
% 2.99/1.54 = ( inf_inf @ ( set @ A ) @ Omega @ ( sigma_space @ A @ M ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_156_measurable__sets__borel,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType] :
% 2.99/1.54 ( ( topolo503727757_space @ A )
% 2.99/1.54 => ! [F: A > B,M: sigma_measure @ B,A4: set @ B] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( borel_1404511681_borel @ A ) @ M ) )
% 2.99/1.54 => ( ( member @ ( set @ B ) @ A4 @ ( sigma_sets @ B @ M ) )
% 2.99/1.54 => ( member @ ( set @ A ) @ ( vimage @ A @ B @ F @ A4 ) @ ( sigma_sets @ A @ ( borel_1404511681_borel @ A ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_157_sets__Collect__restrict__space__iff,axiom,
% 2.99/1.54 ! [A: $tType,S: set @ A,M: sigma_measure @ A,P: A > $o] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ ( sigma_restrict_space @ A @ M @ S ) ) )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ ( sigma_restrict_space @ A @ M @ S ) ) )
% 2.99/1.54 = ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( member @ A @ X @ S )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_158_borel__measurable__eq,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType] :
% 2.99/1.54 ( ( ( elemen1026692323pology @ B )
% 2.99/1.54 & ( topolo2117631714pology @ B ) )
% 2.99/1.54 => ! [F: A > B,M: sigma_measure @ A,G: A > B] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [W2: A] :
% 2.99/1.54 ( ( member @ A @ W2 @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( ( F @ W2 )
% 2.99/1.54 = ( G @ W2 ) ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_159_borel__measurable__neq,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType] :
% 2.99/1.54 ( ( ( elemen1026692323pology @ B )
% 2.99/1.54 & ( topolo2117631714pology @ B ) )
% 2.99/1.54 => ! [F: A > B,M: sigma_measure @ A,G: A > B] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ M @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [W2: A] :
% 2.99/1.54 ( ( member @ A @ W2 @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( ( F @ W2 )
% 2.99/1.54 != ( G @ W2 ) ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_160_measurable__equality__set,axiom,
% 2.99/1.54 ! [A: $tType,D3: $tType] :
% 2.99/1.54 ( ( ( elemen1026692323pology @ A )
% 2.99/1.54 & ( topological_t2_space @ A ) )
% 2.99/1.54 => ! [F: D3 > A,M: sigma_measure @ D3,G: D3 > A] :
% 2.99/1.54 ( ( member @ ( D3 > A ) @ F @ ( sigma_measurable @ D3 @ A @ M @ ( borel_1404511681_borel @ A ) ) )
% 2.99/1.54 => ( ( member @ ( D3 > A ) @ G @ ( sigma_measurable @ D3 @ A @ M @ ( borel_1404511681_borel @ A ) ) )
% 2.99/1.54 => ( member @ ( set @ D3 )
% 2.99/1.54 @ ( collect @ D3
% 2.99/1.54 @ ^ [X: D3] :
% 2.99/1.54 ( ( member @ D3 @ X @ ( sigma_space @ D3 @ M ) )
% 2.99/1.54 & ( ( F @ X )
% 2.99/1.54 = ( G @ X ) ) ) )
% 2.99/1.54 @ ( sigma_sets @ D3 @ M ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_161_measurable__If__restrict__space__iff,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,M: sigma_measure @ A,P: A > $o,F: A > B,G: A > B,N2: sigma_measure @ B] :
% 2.99/1.54 ( ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ M ) )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( member @ ( A > B )
% 2.99/1.54 @ ^ [X: A] : ( if @ B @ ( P @ X ) @ ( F @ X ) @ ( G @ X ) )
% 2.99/1.54 @ ( sigma_measurable @ A @ B @ M @ N2 ) )
% 2.99/1.54 = ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ M @ ( collect @ A @ P ) ) @ N2 ) )
% 2.99/1.54 & ( member @ ( A > B ) @ G
% 2.99/1.54 @ ( sigma_measurable @ A @ B
% 2.99/1.54 @ ( sigma_restrict_space @ A @ M
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ~ ( P @ X ) ) )
% 2.99/1.54 @ N2 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_162_space__lebesgue__on,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( euclid925273238_space @ A )
% 2.99/1.54 => ! [S: set @ A] :
% 2.99/1.54 ( ( sigma_space @ A @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) )
% 2.99/1.54 = S ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_163_sets__lebesgue__on__refl,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( euclid925273238_space @ A )
% 2.99/1.54 => ! [S: set @ A] : ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_164_space__lborel,axiom,
% 2.99/1.54 ! [B: $tType] :
% 2.99/1.54 ( ( euclid925273238_space @ B )
% 2.99/1.54 => ( ( sigma_space @ B @ ( lebesgue_lborel @ B ) )
% 2.99/1.54 = ( sigma_space @ B @ ( borel_1404511681_borel @ B ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_165_measurable__lborel1,axiom,
% 2.99/1.54 ! [C3: $tType,D3: $tType] :
% 2.99/1.54 ( ( euclid925273238_space @ D3 )
% 2.99/1.54 => ! [M: sigma_measure @ C3] :
% 2.99/1.54 ( ( sigma_measurable @ C3 @ D3 @ M @ ( lebesgue_lborel @ D3 ) )
% 2.99/1.54 = ( sigma_measurable @ C3 @ D3 @ M @ ( borel_1404511681_borel @ D3 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_166_measurable__lborel2,axiom,
% 2.99/1.54 ! [E: $tType,C3: $tType] :
% 2.99/1.54 ( ( euclid925273238_space @ E )
% 2.99/1.54 => ! [M: sigma_measure @ C3] :
% 2.99/1.54 ( ( sigma_measurable @ E @ C3 @ ( lebesgue_lborel @ E ) @ M )
% 2.99/1.54 = ( sigma_measurable @ E @ C3 @ ( borel_1404511681_borel @ E ) @ M ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_167_sets_ODiff,axiom,
% 2.99/1.54 ! [A: $tType,A2: set @ A,M: sigma_measure @ A,B2: set @ A] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ A2 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( member @ ( set @ A ) @ B2 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( member @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ ( sigma_sets @ A @ M ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_168_sets_Ocompl__sets,axiom,
% 2.99/1.54 ! [A: $tType,A2: set @ A,M: sigma_measure @ A] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ A2 @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( member @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ ( sigma_space @ A @ M ) @ A2 ) @ ( sigma_sets @ A @ M ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_169_sets__lborel,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( euclid925273238_space @ A )
% 2.99/1.54 => ( ( sigma_sets @ A @ ( lebesgue_lborel @ A ) )
% 2.99/1.54 = ( sigma_sets @ A @ ( borel_1404511681_borel @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_170_Int__Diff,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,B3: set @ A,C: set @ A] :
% 2.99/1.54 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) @ C )
% 2.99/1.54 = ( inf_inf @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ B3 @ C ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_171_Diff__Int2,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,C: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ C ) @ ( inf_inf @ ( set @ A ) @ B3 @ C ) )
% 2.99/1.54 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ C ) @ B3 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_172_Diff__Diff__Int,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( minus_minus @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 = ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_173_Diff__Int__distrib,axiom,
% 2.99/1.54 ! [A: $tType,C: set @ A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( inf_inf @ ( set @ A ) @ C @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ C @ A4 ) @ ( inf_inf @ ( set @ A ) @ C @ B3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_174_Diff__Int__distrib2,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,B3: set @ A,C: set @ A] :
% 2.99/1.54 ( ( inf_inf @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) @ C )
% 2.99/1.54 = ( minus_minus @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ C ) @ ( inf_inf @ ( set @ A ) @ B3 @ C ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_175_vimage__Diff,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,F: A > B,A4: set @ B,B3: set @ B] :
% 2.99/1.54 ( ( vimage @ A @ B @ F @ ( minus_minus @ ( set @ B ) @ A4 @ B3 ) )
% 2.99/1.54 = ( minus_minus @ ( set @ A ) @ ( vimage @ A @ B @ F @ A4 ) @ ( vimage @ A @ B @ F @ B3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_176_sets__restrict__space,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,Omega: set @ A] :
% 2.99/1.54 ( ( sigma_sets @ A @ ( sigma_restrict_space @ A @ M @ Omega ) )
% 2.99/1.54 = ( image @ ( set @ A ) @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ Omega ) @ ( sigma_sets @ A @ M ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_177_lborelD,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( euclid925273238_space @ A )
% 2.99/1.54 => ! [A4: set @ A] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ A4 @ ( sigma_sets @ A @ ( borel_1404511681_borel @ A ) ) )
% 2.99/1.54 => ( member @ ( set @ A ) @ A4 @ ( sigma_sets @ A @ ( lebesgue_lborel @ A ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_178_measurable__lebesgue__cong,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( euclid925273238_space @ A )
% 2.99/1.54 => ! [S: set @ A,F: A > B,G: A > B,M: sigma_measure @ B] :
% 2.99/1.54 ( ! [X3: A] :
% 2.99/1.54 ( ( member @ A @ X3 @ S )
% 2.99/1.54 => ( ( F @ X3 )
% 2.99/1.54 = ( G @ X3 ) ) )
% 2.99/1.54 => ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ M ) )
% 2.99/1.54 = ( member @ ( A > B ) @ G @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ M ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_179_lborelD__Collect,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( euclid925273238_space @ A )
% 2.99/1.54 => ! [P: A > $o] :
% 2.99/1.54 ( ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ ( borel_1404511681_borel @ A ) ) )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ ( borel_1404511681_borel @ A ) ) )
% 2.99/1.54 => ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ ( sigma_space @ A @ ( lebesgue_lborel @ A ) ) )
% 2.99/1.54 & ( P @ X ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ ( lebesgue_lborel @ A ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_180_lebesgue__sets__translation,axiom,
% 2.99/1.54 ! [B: $tType] :
% 2.99/1.54 ( ( euclid925273238_space @ B )
% 2.99/1.54 => ! [S: set @ B,A2: B] :
% 2.99/1.54 ( ( member @ ( set @ B ) @ S @ ( sigma_sets @ B @ ( complete_completion @ B @ ( lebesgue_lborel @ B ) ) ) )
% 2.99/1.54 => ( member @ ( set @ B ) @ ( image @ B @ B @ ( plus_plus @ B @ A2 ) @ S ) @ ( sigma_sets @ B @ ( complete_completion @ B @ ( lebesgue_lborel @ B ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_181_lebesgue__measurable__vimage__borel,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType] :
% 2.99/1.54 ( ( ( euclid925273238_space @ A )
% 2.99/1.54 & ( euclid925273238_space @ B ) )
% 2.99/1.54 => ! [F: A > B,T: set @ B] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( ( member @ ( set @ B ) @ T @ ( sigma_sets @ B @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] : ( member @ B @ ( F @ X ) @ T ) )
% 2.99/1.54 @ ( sigma_sets @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_182_borel__measurable__lebesgue__preimage__borel,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( ( euclid925273238_space @ B )
% 2.99/1.54 & ( euclid925273238_space @ A ) )
% 2.99/1.54 => ! [F: A > B] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 = ( ! [T2: set @ B] :
% 2.99/1.54 ( ( member @ ( set @ B ) @ T2 @ ( sigma_sets @ B @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] : ( member @ B @ ( F @ X ) @ T2 ) )
% 2.99/1.54 @ ( sigma_sets @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_183_borel__measurable__vimage__borel,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( ( euclid925273238_space @ B )
% 2.99/1.54 & ( euclid925273238_space @ A ) )
% 2.99/1.54 => ! [F: A > B,S: set @ A] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 = ( ! [T2: set @ B] :
% 2.99/1.54 ( ( member @ ( set @ B ) @ T2 @ ( sigma_sets @ B @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( member @ ( set @ A )
% 2.99/1.54 @ ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ S )
% 2.99/1.54 & ( member @ B @ ( F @ X ) @ T2 ) ) )
% 2.99/1.54 @ ( sigma_sets @ A @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_184_restrict__space__eq__vimage__algebra_H,axiom,
% 2.99/1.54 ! [A: $tType,M: sigma_measure @ A,Omega: set @ A] :
% 2.99/1.54 ( ( sigma_sets @ A @ ( sigma_restrict_space @ A @ M @ Omega ) )
% 2.99/1.54 = ( sigma_sets @ A
% 2.99/1.54 @ ( sigma_vimage_algebra @ A @ A @ ( inf_inf @ ( set @ A ) @ Omega @ ( sigma_space @ A @ M ) )
% 2.99/1.54 @ ^ [X: A] : X
% 2.99/1.54 @ M ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_185_restrict__restrict__space,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,M: sigma_measure @ A,B3: set @ A] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A4 @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( member @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ B3 @ ( sigma_space @ A @ M ) ) @ ( sigma_sets @ A @ M ) )
% 2.99/1.54 => ( ( sigma_restrict_space @ A @ ( sigma_restrict_space @ A @ M @ A4 ) @ B3 )
% 2.99/1.54 = ( sigma_restrict_space @ A @ M @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_186_is__borel__def,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType] :
% 2.99/1.54 ( ( topolo503727757_space @ B )
% 2.99/1.54 => ( ( borel_is_borel @ A @ B )
% 2.99/1.54 = ( ^ [F2: A > B,M3: sigma_measure @ A] : ( member @ ( A > B ) @ F2 @ ( sigma_measurable @ A @ B @ M3 @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_187_Diff__idemp,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) @ B3 )
% 2.99/1.54 = ( minus_minus @ ( set @ A ) @ A4 @ B3 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_188_Diff__iff,axiom,
% 2.99/1.54 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 = ( ( member @ A @ C2 @ A4 )
% 2.99/1.54 & ~ ( member @ A @ C2 @ B3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_189_DiffI,axiom,
% 2.99/1.54 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( member @ A @ C2 @ A4 )
% 2.99/1.54 => ( ~ ( member @ A @ C2 @ B3 )
% 2.99/1.54 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_190_set__diff__eq,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( minus_minus @ ( set @ A ) )
% 2.99/1.54 = ( ^ [A6: set @ A,B4: set @ A] :
% 2.99/1.54 ( collect @ A
% 2.99/1.54 @ ^ [X: A] :
% 2.99/1.54 ( ( member @ A @ X @ A6 )
% 2.99/1.54 & ~ ( member @ A @ X @ B4 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_191_minus__set__def,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( minus_minus @ ( set @ A ) )
% 2.99/1.54 = ( ^ [A6: set @ A,B4: set @ A] :
% 2.99/1.54 ( collect @ A
% 2.99/1.54 @ ( minus_minus @ ( A > $o )
% 2.99/1.54 @ ^ [X: A] : ( member @ A @ X @ A6 )
% 2.99/1.54 @ ^ [X: A] : ( member @ A @ X @ B4 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_192_DiffD2,axiom,
% 2.99/1.54 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 => ~ ( member @ A @ C2 @ B3 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_193_DiffD1,axiom,
% 2.99/1.54 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 => ( member @ A @ C2 @ A4 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_194_DiffE,axiom,
% 2.99/1.54 ! [A: $tType,C2: A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 => ~ ( ( member @ A @ C2 @ A4 )
% 2.99/1.54 => ( member @ A @ C2 @ B3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_195_sets__vimage__algebra__space,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType,X4: set @ A,F: A > B,M: sigma_measure @ B] : ( member @ ( set @ A ) @ X4 @ ( sigma_sets @ A @ ( sigma_vimage_algebra @ A @ B @ X4 @ F @ M ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_196_translation__subtract__diff,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ab_group_add @ A )
% 2.99/1.54 => ! [A2: A,S2: set @ A,T3: set @ A] :
% 2.99/1.54 ( ( image @ A @ A
% 2.99/1.54 @ ^ [X: A] : ( minus_minus @ A @ X @ A2 )
% 2.99/1.54 @ ( minus_minus @ ( set @ A ) @ S2 @ T3 ) )
% 2.99/1.54 = ( minus_minus @ ( set @ A )
% 2.99/1.54 @ ( image @ A @ A
% 2.99/1.54 @ ^ [X: A] : ( minus_minus @ A @ X @ A2 )
% 2.99/1.54 @ S2 )
% 2.99/1.54 @ ( image @ A @ A
% 2.99/1.54 @ ^ [X: A] : ( minus_minus @ A @ X @ A2 )
% 2.99/1.54 @ T3 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_197_translation__subtract__Int,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ab_group_add @ A )
% 2.99/1.54 => ! [A2: A,S2: set @ A,T3: set @ A] :
% 2.99/1.54 ( ( image @ A @ A
% 2.99/1.54 @ ^ [X: A] : ( minus_minus @ A @ X @ A2 )
% 2.99/1.54 @ ( inf_inf @ ( set @ A ) @ S2 @ T3 ) )
% 2.99/1.54 = ( inf_inf @ ( set @ A )
% 2.99/1.54 @ ( image @ A @ A
% 2.99/1.54 @ ^ [X: A] : ( minus_minus @ A @ X @ A2 )
% 2.99/1.54 @ S2 )
% 2.99/1.54 @ ( image @ A @ A
% 2.99/1.54 @ ^ [X: A] : ( minus_minus @ A @ X @ A2 )
% 2.99/1.54 @ T3 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_198_translation__diff,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ab_group_add @ A )
% 2.99/1.54 => ! [A2: A,S2: set @ A,T3: set @ A] :
% 2.99/1.54 ( ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ ( minus_minus @ ( set @ A ) @ S2 @ T3 ) )
% 2.99/1.54 = ( minus_minus @ ( set @ A ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ S2 ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ T3 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_199_translation__Int,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ab_group_add @ A )
% 2.99/1.54 => ! [A2: A,S2: set @ A,T3: set @ A] :
% 2.99/1.54 ( ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ ( inf_inf @ ( set @ A ) @ S2 @ T3 ) )
% 2.99/1.54 = ( inf_inf @ ( set @ A ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ S2 ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ T3 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_200_measurable__product__then__coordinatewise,axiom,
% 2.99/1.54 ! [B: $tType,A: $tType,C3: $tType] :
% 2.99/1.54 ( ( topolo503727757_space @ C3 )
% 2.99/1.54 => ! [F: A > B > C3,M: sigma_measure @ A,I: B] :
% 2.99/1.54 ( ( member @ ( A > B > C3 ) @ F @ ( sigma_measurable @ A @ ( B > C3 ) @ M @ ( borel_1404511681_borel @ ( B > C3 ) ) ) )
% 2.99/1.54 => ( member @ ( A > C3 )
% 2.99/1.54 @ ^ [X: A] : ( F @ X @ I )
% 2.99/1.54 @ ( sigma_measurable @ A @ C3 @ M @ ( borel_1404511681_borel @ C3 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_201_measurable__coordinatewise__then__product,axiom,
% 2.99/1.54 ! [A: $tType,C3: $tType,B: $tType] :
% 2.99/1.54 ( ( ( countable @ B )
% 2.99/1.54 & ( elemen1026692323pology @ C3 ) )
% 2.99/1.54 => ! [F: A > B > C3,M: sigma_measure @ A] :
% 2.99/1.54 ( ! [I2: B] :
% 2.99/1.54 ( member @ ( A > C3 )
% 2.99/1.54 @ ^ [X: A] : ( F @ X @ I2 )
% 2.99/1.54 @ ( sigma_measurable @ A @ C3 @ M @ ( borel_1404511681_borel @ C3 ) ) )
% 2.99/1.54 => ( member @ ( A > B > C3 ) @ F @ ( sigma_measurable @ A @ ( B > C3 ) @ M @ ( borel_1404511681_borel @ ( B > C3 ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_202_measurable__product__coordinates,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( topolo503727757_space @ B )
% 2.99/1.54 => ! [I: A] :
% 2.99/1.54 ( member @ ( ( A > B ) > B )
% 2.99/1.54 @ ^ [X: A > B] : ( X @ I )
% 2.99/1.54 @ ( sigma_measurable @ ( A > B ) @ B @ ( borel_1404511681_borel @ ( A > B ) ) @ ( borel_1404511681_borel @ B ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_203_translation__invert,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ab_group_add @ A )
% 2.99/1.54 => ! [A2: A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ A4 )
% 2.99/1.54 = ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ B3 ) )
% 2.99/1.54 => ( A4 = B3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_204_translation__assoc,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ab_group_add @ A )
% 2.99/1.54 => ! [B2: A,A2: A,S: set @ A] :
% 2.99/1.54 ( ( image @ A @ A @ ( plus_plus @ A @ B2 ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ S ) )
% 2.99/1.54 = ( image @ A @ A @ ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) ) @ S ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_205_affine__parallel__expl__aux,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( real_V1076094709vector @ A )
% 2.99/1.54 => ! [S: set @ A,A2: A,T: set @ A] :
% 2.99/1.54 ( ! [X3: A] :
% 2.99/1.54 ( ( member @ A @ X3 @ S )
% 2.99/1.54 = ( member @ A @ ( plus_plus @ A @ A2 @ X3 ) @ T ) )
% 2.99/1.54 => ( T
% 2.99/1.54 = ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ S ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_206_borel__measurable__if,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( ( euclid925273238_space @ B )
% 2.99/1.54 & ( euclid925273238_space @ A ) )
% 2.99/1.54 => ! [S: set @ A,F: A > B] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) ) )
% 2.99/1.54 => ( ( member @ ( A > B )
% 2.99/1.54 @ ^ [X: A] : ( if @ B @ ( member @ A @ X @ S ) @ ( F @ X ) @ ( zero_zero @ B ) )
% 2.99/1.54 @ ( sigma_measurable @ A @ B @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 = ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_207_add_Oleft__neutral,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( monoid_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.99/1.54 = A2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_208_add_Oright__neutral,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( monoid_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.99/1.54 = A2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_209_double__zero,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( linord219039673up_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( ( plus_plus @ A @ A2 @ A2 )
% 2.99/1.54 = ( zero_zero @ A ) )
% 2.99/1.54 = ( A2
% 2.99/1.54 = ( zero_zero @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_210_double__zero__sym,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( linord219039673up_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( ( zero_zero @ A )
% 2.99/1.54 = ( plus_plus @ A @ A2 @ A2 ) )
% 2.99/1.54 = ( A2
% 2.99/1.54 = ( zero_zero @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_211_add__cancel__left__left,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel1352612707id_add @ A )
% 2.99/1.54 => ! [B2: A,A2: A] :
% 2.99/1.54 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.99/1.54 = A2 )
% 2.99/1.54 = ( B2
% 2.99/1.54 = ( zero_zero @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_212_add__cancel__left__right,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel1352612707id_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.99/1.54 = A2 )
% 2.99/1.54 = ( B2
% 2.99/1.54 = ( zero_zero @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_213_add__cancel__right__left,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel1352612707id_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( A2
% 2.99/1.54 = ( plus_plus @ A @ B2 @ A2 ) )
% 2.99/1.54 = ( B2
% 2.99/1.54 = ( zero_zero @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_214_add__cancel__right__right,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel1352612707id_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( A2
% 2.99/1.54 = ( plus_plus @ A @ A2 @ B2 ) )
% 2.99/1.54 = ( B2
% 2.99/1.54 = ( zero_zero @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_215_add__eq__0__iff__both__eq__0,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( canoni770627133id_add @ A )
% 2.99/1.54 => ! [X2: A,Y3: A] :
% 2.99/1.54 ( ( ( plus_plus @ A @ X2 @ Y3 )
% 2.99/1.54 = ( zero_zero @ A ) )
% 2.99/1.54 = ( ( X2
% 2.99/1.54 = ( zero_zero @ A ) )
% 2.99/1.54 & ( Y3
% 2.99/1.54 = ( zero_zero @ A ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_216_zero__eq__add__iff__both__eq__0,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( canoni770627133id_add @ A )
% 2.99/1.54 => ! [X2: A,Y3: A] :
% 2.99/1.54 ( ( ( zero_zero @ A )
% 2.99/1.54 = ( plus_plus @ A @ X2 @ Y3 ) )
% 2.99/1.54 = ( ( X2
% 2.99/1.54 = ( zero_zero @ A ) )
% 2.99/1.54 & ( Y3
% 2.99/1.54 = ( zero_zero @ A ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_217_diff__self,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ A2 @ A2 )
% 2.99/1.54 = ( zero_zero @ A ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_218_diff__0__right,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 2.99/1.54 = A2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_219_zero__diff,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( comm_monoid_diff @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A2 )
% 2.99/1.54 = ( zero_zero @ A ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_220_diff__zero,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel1352612707id_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 2.99/1.54 = A2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_221_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( cancel1352612707id_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ A2 @ A2 )
% 2.99/1.54 = ( zero_zero @ A ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_222_image__add__0,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( comm_monoid_add @ A )
% 2.99/1.54 => ! [S: set @ A] :
% 2.99/1.54 ( ( image @ A @ A @ ( plus_plus @ A @ ( zero_zero @ A ) ) @ S )
% 2.99/1.54 = S ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_223_diff__add__zero,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( comm_monoid_diff @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( minus_minus @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 2.99/1.54 = ( zero_zero @ A ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_224_eq__add__iff,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ab_group_add @ A )
% 2.99/1.54 => ! [X2: A,Y3: A] :
% 2.99/1.54 ( ( X2
% 2.99/1.54 = ( plus_plus @ A @ X2 @ Y3 ) )
% 2.99/1.54 = ( Y3
% 2.99/1.54 = ( zero_zero @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_225_eq__iff__diff__eq__0,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 2.99/1.54 = ( ^ [A5: A,B5: A] :
% 2.99/1.54 ( ( minus_minus @ A @ A5 @ B5 )
% 2.99/1.54 = ( zero_zero @ A ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_226_comm__monoid__add__class_Oadd__0,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( comm_monoid_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.99/1.54 = A2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_227_add_Ocomm__neutral,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( comm_monoid_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.99/1.54 = A2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_228_add_Ogroup__left__neutral,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( group_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.99/1.54 = A2 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_229_zero__reorient,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( zero @ A )
% 2.99/1.54 => ! [X2: A] :
% 2.99/1.54 ( ( ( zero_zero @ A )
% 2.99/1.54 = X2 )
% 2.99/1.54 = ( X2
% 2.99/1.54 = ( zero_zero @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_230_borel__measurable__if__D,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( ( euclid925273238_space @ B )
% 2.99/1.54 & ( euclid925273238_space @ A ) )
% 2.99/1.54 => ! [S: set @ A,F: A > B] :
% 2.99/1.54 ( ( member @ ( A > B )
% 2.99/1.54 @ ^ [X: A] : ( if @ B @ ( member @ A @ X @ S ) @ ( F @ X ) @ ( zero_zero @ B ) )
% 2.99/1.54 @ ( sigma_measurable @ A @ B @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ ( borel_1404511681_borel @ B ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_231_borel__measurable__if__I,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( ( euclid925273238_space @ B )
% 2.99/1.54 & ( euclid925273238_space @ A ) )
% 2.99/1.54 => ! [F: A > B,S: set @ A] :
% 2.99/1.54 ( ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 => ( ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) ) )
% 2.99/1.54 => ( member @ ( A > B )
% 2.99/1.54 @ ^ [X: A] : ( if @ B @ ( member @ A @ X @ S ) @ ( F @ X ) @ ( zero_zero @ B ) )
% 2.99/1.54 @ ( sigma_measurable @ A @ B @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_232_Least__eq__0,axiom,
% 2.99/1.54 ! [P: nat > $o] :
% 2.99/1.54 ( ( P @ ( zero_zero @ nat ) )
% 2.99/1.54 => ( ( ord_Least @ nat @ P )
% 2.99/1.54 = ( zero_zero @ nat ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_233_borel__measurable__if__lebesgue__on,axiom,
% 2.99/1.54 ! [A: $tType,B: $tType] :
% 2.99/1.54 ( ( ( euclid925273238_space @ B )
% 2.99/1.54 & ( euclid925273238_space @ A ) )
% 2.99/1.54 => ! [S: set @ A,T: set @ A,F: A > B] :
% 2.99/1.54 ( ( member @ ( set @ A ) @ S @ ( sigma_sets @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) ) )
% 2.99/1.54 => ( ( member @ ( set @ A ) @ T @ ( sigma_sets @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) ) )
% 2.99/1.54 => ( ( ord_less_eq @ ( set @ A ) @ S @ T )
% 2.99/1.54 => ( ( member @ ( A > B )
% 2.99/1.54 @ ^ [X: A] : ( if @ B @ ( member @ A @ X @ S ) @ ( F @ X ) @ ( zero_zero @ B ) )
% 2.99/1.54 @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ T ) @ ( borel_1404511681_borel @ B ) ) )
% 2.99/1.54 = ( member @ ( A > B ) @ F @ ( sigma_measurable @ A @ B @ ( sigma_restrict_space @ A @ ( complete_completion @ A @ ( lebesgue_lborel @ A ) ) @ S ) @ ( borel_1404511681_borel @ B ) ) ) ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_234_subsetI,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ! [X3: A] :
% 2.99/1.54 ( ( member @ A @ X3 @ A4 )
% 2.99/1.54 => ( member @ A @ X3 @ B3 ) )
% 2.99/1.54 => ( ord_less_eq @ ( set @ A ) @ A4 @ B3 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_235_subset__antisym,axiom,
% 2.99/1.54 ! [A: $tType,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B3 )
% 2.99/1.54 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A4 )
% 2.99/1.54 => ( A4 = B3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_236_diff__0__eq__0,axiom,
% 2.99/1.54 ! [N4: nat] :
% 2.99/1.54 ( ( minus_minus @ nat @ ( zero_zero @ nat ) @ N4 )
% 2.99/1.54 = ( zero_zero @ nat ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_237_diff__self__eq__0,axiom,
% 2.99/1.54 ! [M4: nat] :
% 2.99/1.54 ( ( minus_minus @ nat @ M4 @ M4 )
% 2.99/1.54 = ( zero_zero @ nat ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_238_le__zero__eq,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( canoni770627133id_add @ A )
% 2.99/1.54 => ! [N4: A] :
% 2.99/1.54 ( ( ord_less_eq @ A @ N4 @ ( zero_zero @ A ) )
% 2.99/1.54 = ( N4
% 2.99/1.54 = ( zero_zero @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_239_add__le__cancel__right,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ordere236663937imp_le @ A )
% 2.99/1.54 => ! [A2: A,C2: A,B2: A] :
% 2.99/1.54 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.99/1.54 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_240_add__le__cancel__left,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ordere236663937imp_le @ A )
% 2.99/1.54 => ! [C2: A,A2: A,B2: A] :
% 2.99/1.54 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B2 ) )
% 2.99/1.54 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_241_le__inf__iff,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [X2: A,Y3: A,Z: A] :
% 2.99/1.54 ( ( ord_less_eq @ A @ X2 @ ( inf_inf @ A @ Y3 @ Z ) )
% 2.99/1.54 = ( ( ord_less_eq @ A @ X2 @ Y3 )
% 2.99/1.54 & ( ord_less_eq @ A @ X2 @ Z ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_242_inf_Obounded__iff,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A )
% 2.99/1.54 => ! [A2: A,B2: A,C2: A] :
% 2.99/1.54 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C2 ) )
% 2.99/1.54 = ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.99/1.54 & ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_243_Int__subset__iff,axiom,
% 2.99/1.54 ! [A: $tType,C: set @ A,A4: set @ A,B3: set @ A] :
% 2.99/1.54 ( ( ord_less_eq @ ( set @ A ) @ C @ ( inf_inf @ ( set @ A ) @ A4 @ B3 ) )
% 2.99/1.54 = ( ( ord_less_eq @ ( set @ A ) @ C @ A4 )
% 2.99/1.54 & ( ord_less_eq @ ( set @ A ) @ C @ B3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_244_set__plus__mono2,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( plus @ A )
% 2.99/1.54 => ! [C: set @ A,D: set @ A,E2: set @ A,F3: set @ A] :
% 2.99/1.54 ( ( ord_less_eq @ ( set @ A ) @ C @ D )
% 2.99/1.54 => ( ( ord_less_eq @ ( set @ A ) @ E2 @ F3 )
% 2.99/1.54 => ( ord_less_eq @ ( set @ A ) @ ( plus_plus @ ( set @ A ) @ C @ E2 ) @ ( plus_plus @ ( set @ A ) @ D @ F3 ) ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_245_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( linord219039673up_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 2.99/1.54 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_246_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( linord219039673up_add @ A )
% 2.99/1.54 => ! [A2: A] :
% 2.99/1.54 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 2.99/1.54 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_247_le__add__same__cancel2,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ordere516151231imp_le @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 2.99/1.54 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_248_le__add__same__cancel1,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ordere516151231imp_le @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 2.99/1.54 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_249_add__le__same__cancel2,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ordere516151231imp_le @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 2.99/1.54 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_250_add__le__same__cancel1,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ordere516151231imp_le @ A )
% 2.99/1.54 => ! [B2: A,A2: A] :
% 2.99/1.54 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 2.99/1.54 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_251_diff__ge__0__iff__ge,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( ordered_ab_group_add @ A )
% 2.99/1.54 => ! [A2: A,B2: A] :
% 2.99/1.54 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A2 @ B2 ) )
% 2.99/1.54 = ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_252_subset__translation__eq,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( real_V1076094709vector @ A )
% 2.99/1.54 => ! [A2: A,S2: set @ A,T3: set @ A] :
% 2.99/1.54 ( ( ord_less_eq @ ( set @ A ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ S2 ) @ ( image @ A @ A @ ( plus_plus @ A @ A2 ) @ T3 ) )
% 2.99/1.54 = ( ord_less_eq @ ( set @ A ) @ S2 @ T3 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_253_diffs0__imp__equal,axiom,
% 2.99/1.54 ! [M4: nat,N4: nat] :
% 2.99/1.54 ( ( ( minus_minus @ nat @ M4 @ N4 )
% 2.99/1.54 = ( zero_zero @ nat ) )
% 2.99/1.54 => ( ( ( minus_minus @ nat @ N4 @ M4 )
% 2.99/1.54 = ( zero_zero @ nat ) )
% 2.99/1.54 => ( M4 = N4 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(fact_254_minus__nat_Odiff__0,axiom,
% 2.99/1.54 ! [M4: nat] :
% 2.99/1.54 ( ( minus_minus @ nat @ M4 @ ( zero_zero @ nat ) )
% 2.99/1.54 = M4 ) ).
% 2.99/1.54
% 2.99/1.54 thf(subcl_Finite__Set_Ofinite___HOL_Otype,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( finite_finite @ A )
% 2.99/1.54 => ( type @ A ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(subcl_Finite__Set_Ofinite___Countable_Ocountable,axiom,
% 2.99/1.54 ! [A: $tType] :
% 2.99/1.54 ( ( finite_finite @ A )
% 2.99/1.54 => ( countable @ A ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( ordere890947078_space @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( ordere890947078_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Ometric__space,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( real_V2090557954_space @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( real_V2090557954_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_1,axiom,
% 2.99/1.54 ordere890947078_space @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space_2,axiom,
% 2.99/1.54 real_V2090557954_space @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_fun___Elementary__Topology_Osecond__countable__topology,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( countable @ A9 )
% 2.99/1.54 & ( elemen1026692323pology @ A10 ) )
% 2.99/1.54 => ( elemen1026692323pology @ ( A9 > A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_fun___Topological__Spaces_Otopological__space,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( topolo503727757_space @ A10 )
% 2.99/1.54 => ( topolo503727757_space @ ( A9 > A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( semilattice_inf @ A10 )
% 2.99/1.54 => ( semilattice_inf @ ( A9 > A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_fun___Countable_Ocountable,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( finite_finite @ A9 )
% 2.99/1.54 & ( countable @ A10 ) )
% 2.99/1.54 => ( countable @ ( A9 > A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( finite_finite @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( finite_finite @ ( A9 > A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( lattice @ A10 )
% 2.99/1.54 => ( lattice @ ( A9 > A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_fun___Groups_Ominus,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( minus @ A10 )
% 2.99/1.54 => ( minus @ ( A9 > A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 2.99/1.54 ordere516151231imp_le @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.99/1.54 ordere236663937imp_le @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Topological__Spaces_Otopological__space_3,axiom,
% 2.99/1.54 topolo503727757_space @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Topological__Spaces_Olinorder__topology,axiom,
% 2.99/1.54 topolo2117631714pology @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Oordered__ab__semigroup__add,axiom,
% 2.99/1.54 ordere779506340up_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Olinordered__ab__group__add,axiom,
% 2.99/1.54 linord219039673up_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add,axiom,
% 2.99/1.54 cancel146912293up_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Limits_Otopological__monoid__add,axiom,
% 2.99/1.54 topolo1314133330id_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Ocancel__comm__monoid__add,axiom,
% 2.99/1.54 cancel1352612707id_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Topological__Spaces_Ot2__space,axiom,
% 2.99/1.54 topological_t2_space @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add,axiom,
% 2.99/1.54 ordered_ab_group_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Ocancel__semigroup__add,axiom,
% 2.99/1.54 cancel_semigroup_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Lattices_Osemilattice__inf_4,axiom,
% 2.99/1.54 semilattice_inf @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Oab__semigroup__add,axiom,
% 2.99/1.54 ab_semigroup_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Ocomm__monoid__add,axiom,
% 2.99/1.54 comm_monoid_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Osemigroup__add,axiom,
% 2.99/1.54 semigroup_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Oab__group__add,axiom,
% 2.99/1.54 ab_group_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Countable_Ocountable_5,axiom,
% 2.99/1.54 countable @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Omonoid__add,axiom,
% 2.99/1.54 monoid_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Lattices_Olattice_6,axiom,
% 2.99/1.54 lattice @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Ogroup__add,axiom,
% 2.99/1.54 group_add @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Nat_Oring__char__0,axiom,
% 2.99/1.54 ring_char_0 @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Ominus_7,axiom,
% 2.99/1.54 minus @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Ozero,axiom,
% 2.99/1.54 zero @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Int_Oint___Groups_Oplus,axiom,
% 2.99/1.54 plus @ int ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_8,axiom,
% 2.99/1.54 ordere516151231imp_le @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Elementary__Topology_Osecond__countable__topology_9,axiom,
% 2.99/1.54 elemen1026692323pology @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_10,axiom,
% 2.99/1.54 ordere236663937imp_le @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.99/1.54 canoni770627133id_add @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Topological__Spaces_Otopological__space_11,axiom,
% 2.99/1.54 topolo503727757_space @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Topological__Spaces_Olinorder__topology_12,axiom,
% 2.99/1.54 topolo2117631714pology @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_13,axiom,
% 2.99/1.54 ordere779506340up_add @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_14,axiom,
% 2.99/1.54 cancel146912293up_add @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Limits_Otopological__monoid__add_15,axiom,
% 2.99/1.54 topolo1314133330id_add @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_16,axiom,
% 2.99/1.54 cancel1352612707id_add @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Topological__Spaces_Ot2__space_17,axiom,
% 2.99/1.54 topological_t2_space @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add_18,axiom,
% 2.99/1.54 cancel_semigroup_add @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Lattices_Osemilattice__inf_19,axiom,
% 2.99/1.54 semilattice_inf @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 2.99/1.54 comm_monoid_diff @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add_20,axiom,
% 2.99/1.54 ab_semigroup_add @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add_21,axiom,
% 2.99/1.54 comm_monoid_add @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Osemigroup__add_22,axiom,
% 2.99/1.54 semigroup_add @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Countable_Ocountable_23,axiom,
% 2.99/1.54 countable @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Omonoid__add_24,axiom,
% 2.99/1.54 monoid_add @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Lattices_Olattice_25,axiom,
% 2.99/1.54 lattice @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Ominus_26,axiom,
% 2.99/1.54 minus @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Ozero_27,axiom,
% 2.99/1.54 zero @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Nat_Onat___Groups_Oplus_28,axiom,
% 2.99/1.54 plus @ nat ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_29,axiom,
% 2.99/1.54 ! [A9: $tType] : ( semilattice_inf @ ( set @ A9 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Set_Oset___Groups_Oab__semigroup__add_30,axiom,
% 2.99/1.54 ! [A9: $tType] :
% 2.99/1.54 ( ( ab_semigroup_add @ A9 )
% 2.99/1.54 => ( ab_semigroup_add @ ( set @ A9 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Set_Oset___Groups_Ocomm__monoid__add_31,axiom,
% 2.99/1.54 ! [A9: $tType] :
% 2.99/1.54 ( ( comm_monoid_add @ A9 )
% 2.99/1.54 => ( comm_monoid_add @ ( set @ A9 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Set_Oset___Groups_Osemigroup__add_32,axiom,
% 2.99/1.54 ! [A9: $tType] :
% 2.99/1.54 ( ( semigroup_add @ A9 )
% 2.99/1.54 => ( semigroup_add @ ( set @ A9 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Set_Oset___Countable_Ocountable_33,axiom,
% 2.99/1.54 ! [A9: $tType] :
% 2.99/1.54 ( ( finite_finite @ A9 )
% 2.99/1.54 => ( countable @ ( set @ A9 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Set_Oset___Groups_Omonoid__add_34,axiom,
% 2.99/1.54 ! [A9: $tType] :
% 2.99/1.54 ( ( monoid_add @ A9 )
% 2.99/1.54 => ( monoid_add @ ( set @ A9 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Set_Oset___Finite__Set_Ofinite_35,axiom,
% 2.99/1.54 ! [A9: $tType] :
% 2.99/1.54 ( ( finite_finite @ A9 )
% 2.99/1.54 => ( finite_finite @ ( set @ A9 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Set_Oset___Lattices_Olattice_36,axiom,
% 2.99/1.54 ! [A9: $tType] : ( lattice @ ( set @ A9 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Set_Oset___Groups_Ominus_37,axiom,
% 2.99/1.54 ! [A9: $tType] : ( minus @ ( set @ A9 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Set_Oset___Groups_Ozero_38,axiom,
% 2.99/1.54 ! [A9: $tType] :
% 2.99/1.54 ( ( zero @ A9 )
% 2.99/1.54 => ( zero @ ( set @ A9 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Set_Oset___Groups_Oplus_39,axiom,
% 2.99/1.54 ! [A9: $tType] :
% 2.99/1.54 ( ( plus @ A9 )
% 2.99/1.54 => ( plus @ ( set @ A9 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_HOL_Obool___Topological__Spaces_Otopological__space_40,axiom,
% 2.99/1.54 topolo503727757_space @ $o ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_HOL_Obool___Topological__Spaces_Olinorder__topology_41,axiom,
% 2.99/1.54 topolo2117631714pology @ $o ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_HOL_Obool___Topological__Spaces_Ot2__space_42,axiom,
% 2.99/1.54 topological_t2_space @ $o ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_43,axiom,
% 2.99/1.54 semilattice_inf @ $o ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_HOL_Obool___Countable_Ocountable_44,axiom,
% 2.99/1.54 countable @ $o ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_HOL_Obool___Finite__Set_Ofinite_45,axiom,
% 2.99/1.54 finite_finite @ $o ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_HOL_Obool___Lattices_Olattice_46,axiom,
% 2.99/1.54 lattice @ $o ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_HOL_Obool___Groups_Ominus_47,axiom,
% 2.99/1.54 minus @ $o ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_48,axiom,
% 2.99/1.54 ordere516151231imp_le @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Elementary__Topology_Osecond__countable__topology_49,axiom,
% 2.99/1.54 elemen1026692323pology @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_50,axiom,
% 2.99/1.54 ordere236663937imp_le @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector,axiom,
% 2.99/1.54 real_V55928688vector @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Topological__Spaces_Otopological__space_51,axiom,
% 2.99/1.54 topolo503727757_space @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Topological__Spaces_Olinorder__topology_52,axiom,
% 2.99/1.54 topolo2117631714pology @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_53,axiom,
% 2.99/1.54 ordere779506340up_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Euclidean__Space_Oeuclidean__space,axiom,
% 2.99/1.54 euclid925273238_space @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector,axiom,
% 2.99/1.54 real_V1076094709vector @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add_54,axiom,
% 2.99/1.54 linord219039673up_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_55,axiom,
% 2.99/1.54 cancel146912293up_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Limits_Otopological__monoid__add_56,axiom,
% 2.99/1.54 topolo1314133330id_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_57,axiom,
% 2.99/1.54 cancel1352612707id_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Topological__Spaces_Ot2__space_58,axiom,
% 2.99/1.54 topological_t2_space @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add_59,axiom,
% 2.99/1.54 ordered_ab_group_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_60,axiom,
% 2.99/1.54 cancel_semigroup_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Lattices_Osemilattice__inf_61,axiom,
% 2.99/1.54 semilattice_inf @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_62,axiom,
% 2.99/1.54 ab_semigroup_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_63,axiom,
% 2.99/1.54 comm_monoid_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Osemigroup__add_64,axiom,
% 2.99/1.54 semigroup_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Oab__group__add_65,axiom,
% 2.99/1.54 ab_group_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Omonoid__add_66,axiom,
% 2.99/1.54 monoid_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Lattices_Olattice_67,axiom,
% 2.99/1.54 lattice @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Ogroup__add_68,axiom,
% 2.99/1.54 group_add @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Nat_Oring__char__0_69,axiom,
% 2.99/1.54 ring_char_0 @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Ominus_70,axiom,
% 2.99/1.54 minus @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Ozero_71,axiom,
% 2.99/1.54 zero @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Real_Oreal___Groups_Oplus_72,axiom,
% 2.99/1.54 plus @ real ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Sigma__Algebra_Omeasure___Lattices_Osemilattice__inf_73,axiom,
% 2.99/1.54 ! [A9: $tType] : ( semilattice_inf @ ( sigma_measure @ A9 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Sigma__Algebra_Omeasure___Lattices_Olattice_74,axiom,
% 2.99/1.54 ! [A9: $tType] : ( lattice @ ( sigma_measure @ A9 ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__monoid__add__imp__le_75,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( ordere890947078_space @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( ordere516151231imp_le @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Elementary__Topology_Osecond__countable__topology_76,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( euclid925273238_space @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( elemen1026692323pology @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add__imp__le_77,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( ordere890947078_space @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( ordere236663937imp_le @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_78,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( real_V55928688vector @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( real_V55928688vector @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_79,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( topolo503727757_space @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( topolo503727757_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add_80,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( ordere890947078_space @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( ordere779506340up_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Euclidean__Space_Oeuclidean__space_81,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( euclid925273238_space @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( euclid925273238_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__vector_82,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( real_V1076094709vector @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( real_V1076094709vector @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__ab__semigroup__add_83,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( cancel146912293up_add @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( cancel146912293up_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Limits_Otopological__monoid__add_84,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( real_V55928688vector @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( topolo1314133330id_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__comm__monoid__add_85,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( cancel1352612707id_add @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( cancel1352612707id_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Ot2__space_86,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( real_V2090557954_space @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( topological_t2_space @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add_87,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( ordere890947078_space @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( ordered_ab_group_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__semigroup__add_88,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( cancel_semigroup_add @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( cancel_semigroup_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Osemilattice__inf_89,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( ordere890947078_space @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( semilattice_inf @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__semigroup__add_90,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( ab_semigroup_add @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( ab_semigroup_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ocomm__monoid__add_91,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( comm_monoid_add @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( comm_monoid_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Osemigroup__add_92,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( semigroup_add @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( semigroup_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__group__add_93,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( ab_group_add @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( ab_group_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Countable_Ocountable_94,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( countable @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( countable @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Omonoid__add_95,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( monoid_add @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( monoid_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_96,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( finite_finite @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( finite_finite @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Lattices_Olattice_97,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( ordere890947078_space @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( lattice @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ogroup__add_98,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( group_add @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( group_add @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Nat_Oring__char__0_99,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( ring_char_0 @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( ring_char_0 @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ominus_100,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( minus @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( minus @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Ozero_101,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( zero @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( zero @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(tcon_Finite__Cartesian__Product_Ovec___Groups_Oplus_102,axiom,
% 2.99/1.54 ! [A9: $tType,A10: $tType] :
% 2.99/1.54 ( ( ( plus @ A9 )
% 2.99/1.54 & ( finite_finite @ A10 ) )
% 2.99/1.54 => ( plus @ ( finite_Cartesian_vec @ A9 @ A10 ) ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(help_If_3_1_T,axiom,
% 2.99/1.54 ! [P: $o] :
% 2.99/1.54 ( ( P = $true )
% 2.99/1.54 | ( P = $false ) ) ).
% 2.99/1.54
% 2.99/1.54 thf(help_If_2_1_T,axiom,
% 2.99/1.54 ! [A: $tType,X2: A,Y3: A] :
% 2.99/1.54 ( ( if @ A @ $false @ X2 @ Y3 )
% 2.99/1.54 = Y3 ) ).
% 2.99/1.54
% 2.99/1.54 thf(help_If_1_1_T,axiom,
% 2.99/1.54 ! [A: $tType,X2: A,Y3: A] :
% 2.99/1.54 ( ( if @ A @ $true @ X2 @ Y3 )
% 2.99/1.54 = X2 ) ).
% 2.99/1.54
% 2.99/1.54 thf(tfree_0,hypothesis,
% 2.99/1.54 finite_finite @ n ).
% 2.99/1.54
% 2.99/1.54 thf(conj_0,conjecture,
% 2.99/1.54 ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
% 2.99/1.54 @ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
% 2.99/1.54 @ ^ [X: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ X @ ( minkow1937162798nt_vec @ n @ real @ a ) )
% 2.99/1.54 @ ( t2 @ a ) )
% 2.99/1.54 @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ).
% 2.99/1.54 ------------------------
% 2.99/1.56 % (12289)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_12084 for (2999ds/275Mi)
% 2.99/1.56 % (12285)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_12084 for (2999ds/4Mi)
% 2.99/1.56 % (12287)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/2Mi)
% 2.99/1.56 % (12286)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_12084 for (2999ds/27Mi)
% 2.99/1.57 % (12287)Instruction limit reached!
% 2.99/1.57 % (12287)------------------------------
% 2.99/1.57 % (12287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.57 % (12287)Termination reason: Unknown
% 2.99/1.57 % (12287)Termination phase: shuffling
% 2.99/1.57
% 2.99/1.57 % (12287)Memory used [KB]: 1407
% 2.99/1.57 % (12287)Time elapsed: 0.002 s
% 2.99/1.57 % (12287)Instructions burned: 2 (million)
% 2.99/1.57 % (12287)------------------------------
% 2.99/1.57 % (12287)------------------------------
% 2.99/1.57 % (12288)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_12084 for (2999ds/2Mi)
% 2.99/1.57 % (12285)Instruction limit reached!
% 2.99/1.57 % (12285)------------------------------
% 2.99/1.57 % (12285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.57 % (12285)Termination reason: Unknown
% 2.99/1.57 % (12285)Termination phase: shuffling
% 2.99/1.57
% 2.99/1.57 % (12285)Memory used [KB]: 1407
% 2.99/1.57 % (12285)Time elapsed: 0.003 s
% 2.99/1.57 % (12285)Instructions burned: 4 (million)
% 2.99/1.57 % (12285)------------------------------
% 2.99/1.57 % (12285)------------------------------
% 2.99/1.57 % (12288)Instruction limit reached!
% 2.99/1.57 % (12288)------------------------------
% 2.99/1.57 % (12288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.57 % (12288)Termination reason: Unknown
% 2.99/1.57 % (12288)Termination phase: shuffling
% 2.99/1.57
% 2.99/1.57 % (12288)Memory used [KB]: 1407
% 2.99/1.57 % (12288)Time elapsed: 0.003 s
% 2.99/1.57 % (12288)Instructions burned: 3 (million)
% 2.99/1.57 % (12288)------------------------------
% 2.99/1.57 % (12288)------------------------------
% 2.99/1.57 % (12284)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/183Mi)
% 2.99/1.58 % (12290)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/18Mi)
% 2.99/1.58 % (12286)Instruction limit reached!
% 2.99/1.58 % (12286)------------------------------
% 2.99/1.58 % (12286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.58 % (12286)Termination reason: Unknown
% 2.99/1.58 % (12286)Termination phase: shuffling
% 2.99/1.58
% 2.99/1.58 % (12286)Memory used [KB]: 2046
% 2.99/1.58 % (12286)Time elapsed: 0.018 s
% 2.99/1.58 % (12286)Instructions burned: 27 (million)
% 2.99/1.58 % (12286)------------------------------
% 2.99/1.58 % (12286)------------------------------
% 2.99/1.58 % (12298)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/3Mi)
% 2.99/1.58 % (12299)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_12084 for (2999ds/37Mi)
% 2.99/1.58 % (12298)Instruction limit reached!
% 2.99/1.58 % (12298)------------------------------
% 2.99/1.58 % (12298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.58 % (12298)Termination reason: Unknown
% 2.99/1.58 % (12298)Termination phase: shuffling
% 2.99/1.58
% 2.99/1.58 % (12298)Memory used [KB]: 1535
% 2.99/1.58 % (12298)Time elapsed: 0.003 s
% 2.99/1.58 % (12298)Instructions burned: 3 (million)
% 2.99/1.58 % (12298)------------------------------
% 2.99/1.58 % (12298)------------------------------
% 2.99/1.58 % (12290)Instruction limit reached!
% 2.99/1.58 % (12290)------------------------------
% 2.99/1.58 % (12290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.58 % (12290)Termination reason: Unknown
% 2.99/1.58 % (12290)Termination phase: shuffling
% 2.99/1.58
% 2.99/1.58 % (12290)Memory used [KB]: 1791
% 2.99/1.58 % (12290)Time elapsed: 0.009 s
% 2.99/1.58 % (12290)Instructions burned: 19 (million)
% 2.99/1.58 % (12290)------------------------------
% 2.99/1.58 % (12290)------------------------------
% 2.99/1.59 % (12300)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_12084 for (2999ds/15Mi)
% 2.99/1.60 % (12300)Instruction limit reached!
% 2.99/1.60 % (12300)------------------------------
% 2.99/1.60 % (12300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.60 % (12300)Termination reason: Unknown
% 2.99/1.60 % (12300)Termination phase: shuffling
% 2.99/1.60
% 2.99/1.60 % (12300)Memory used [KB]: 1791
% 2.99/1.60 % (12300)Time elapsed: 0.007 s
% 2.99/1.60 % (12300)Instructions burned: 17 (million)
% 2.99/1.60 % (12300)------------------------------
% 2.99/1.60 % (12300)------------------------------
% 3.05/1.60 % (12299)Instruction limit reached!
% 3.05/1.60 % (12299)------------------------------
% 3.05/1.60 % (12299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.60 % (12299)Termination reason: Unknown
% 3.05/1.60 % (12299)Termination phase: shuffling
% 3.05/1.60
% 3.05/1.60 % (12299)Memory used [KB]: 2174
% 3.05/1.60 % (12299)Time elapsed: 0.018 s
% 3.05/1.60 % (12299)Instructions burned: 37 (million)
% 3.05/1.60 % (12299)------------------------------
% 3.05/1.60 % (12299)------------------------------
% 3.05/1.60 % (12305)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_12084 for (2999ds/1041Mi)
% 3.05/1.60 % (12306)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/7Mi)
% 3.05/1.60 % (12304)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_12084 for (2999ds/3Mi)
% 3.05/1.60 % (12304)Instruction limit reached!
% 3.05/1.60 % (12304)------------------------------
% 3.05/1.60 % (12304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.60 % (12304)Termination reason: Unknown
% 3.05/1.60 % (12304)Termination phase: shuffling
% 3.05/1.60
% 3.05/1.60 % (12304)Memory used [KB]: 1407
% 3.05/1.60 % (12304)Time elapsed: 0.003 s
% 3.05/1.60 % (12304)Instructions burned: 3 (million)
% 3.05/1.60 % (12304)------------------------------
% 3.05/1.60 % (12304)------------------------------
% 3.05/1.60 % (12306)Instruction limit reached!
% 3.05/1.60 % (12306)------------------------------
% 3.05/1.60 % (12306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.60 % (12306)Termination reason: Unknown
% 3.05/1.60 % (12306)Termination phase: shuffling
% 3.05/1.60
% 3.05/1.60 % (12306)Memory used [KB]: 1535
% 3.05/1.60 % (12306)Time elapsed: 0.005 s
% 3.05/1.60 % (12306)Instructions burned: 7 (million)
% 3.05/1.60 % (12306)------------------------------
% 3.05/1.60 % (12306)------------------------------
% 3.05/1.60 % (12289)Refutation not found, incomplete strategy
% 3.05/1.60 % (12289)------------------------------
% 3.05/1.60 % (12289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.60 % (12289)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.60
% 3.05/1.60
% 3.05/1.60 % (12289)Memory used [KB]: 6908
% 3.05/1.60 % (12289)Time elapsed: 0.042 s
% 3.05/1.60 % (12289)Instructions burned: 76 (million)
% 3.05/1.60 % (12289)------------------------------
% 3.05/1.60 % (12289)------------------------------
% 3.05/1.60 % (12309)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/16Mi)
% 3.05/1.61 % (12309)Instruction limit reached!
% 3.05/1.61 % (12309)------------------------------
% 3.05/1.61 % (12309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.61 % (12309)Termination reason: Unknown
% 3.05/1.61 % (12309)Termination phase: shuffling
% 3.05/1.61
% 3.05/1.61 % (12309)Memory used [KB]: 1791
% 3.05/1.61 % (12309)Time elapsed: 0.007 s
% 3.05/1.61 % (12309)Instructions burned: 16 (million)
% 3.05/1.61 % (12309)------------------------------
% 3.05/1.61 % (12309)------------------------------
% 3.05/1.62 % (12311)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_12084 for (2999ds/3Mi)
% 3.05/1.62 % (12312)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_12084 for (2999ds/3Mi)
% 3.05/1.62 % (12311)Instruction limit reached!
% 3.05/1.62 % (12311)------------------------------
% 3.05/1.62 % (12311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.62 % (12311)Termination reason: Unknown
% 3.05/1.62 % (12311)Termination phase: shuffling
% 3.05/1.62
% 3.05/1.62 % (12311)Memory used [KB]: 1535
% 3.05/1.62 % (12311)Time elapsed: 0.004 s
% 3.05/1.62 % (12311)Instructions burned: 4 (million)
% 3.05/1.62 % (12311)------------------------------
% 3.05/1.62 % (12311)------------------------------
% 3.05/1.62 % (12312)Instruction limit reached!
% 3.05/1.62 % (12312)------------------------------
% 3.05/1.62 % (12312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.62 % (12312)Termination reason: Unknown
% 3.05/1.62 % (12312)Termination phase: shuffling
% 3.05/1.62
% 3.05/1.62 % (12312)Memory used [KB]: 1535
% 3.05/1.62 % (12312)Time elapsed: 0.003 s
% 3.05/1.62 % (12312)Instructions burned: 5 (million)
% 3.05/1.62 % (12312)------------------------------
% 3.05/1.62 % (12312)------------------------------
% 3.05/1.62 % (12314)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/7Mi)
% 3.05/1.62 % (12314)Instruction limit reached!
% 3.05/1.62 % (12314)------------------------------
% 3.05/1.62 % (12314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.62 % (12314)Termination reason: Unknown
% 3.05/1.62 % (12314)Termination phase: shuffling
% 3.05/1.62
% 3.05/1.62 % (12314)Memory used [KB]: 1535
% 3.05/1.62 % (12314)Time elapsed: 0.005 s
% 3.05/1.62 % (12314)Instructions burned: 7 (million)
% 3.05/1.62 % (12314)------------------------------
% 3.05/1.62 % (12314)------------------------------
% 3.05/1.63 % (12315)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/3Mi)
% 3.05/1.63 % (12315)Instruction limit reached!
% 3.05/1.63 % (12315)------------------------------
% 3.05/1.63 % (12315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.63 % (12315)Termination reason: Unknown
% 3.05/1.63 % (12315)Termination phase: shuffling
% 3.05/1.63
% 3.05/1.63 % (12315)Memory used [KB]: 1407
% 3.05/1.63 % (12315)Time elapsed: 0.004 s
% 3.05/1.63 % (12315)Instructions burned: 4 (million)
% 3.05/1.63 % (12315)------------------------------
% 3.05/1.63 % (12315)------------------------------
% 3.05/1.63 % (12317)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/4Mi)
% 3.05/1.63 % (12321)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/710Mi)
% 3.05/1.63 % (12320)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/18Mi)
% 3.05/1.63 % (12317)Instruction limit reached!
% 3.05/1.63 % (12317)------------------------------
% 3.05/1.63 % (12317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.63 % (12317)Termination reason: Unknown
% 3.05/1.63 % (12317)Termination phase: shuffling
% 3.05/1.63
% 3.05/1.63 % (12317)Memory used [KB]: 1535
% 3.05/1.63 % (12317)Time elapsed: 0.003 s
% 3.05/1.63 % (12317)Instructions burned: 4 (million)
% 3.05/1.63 % (12317)------------------------------
% 3.05/1.63 % (12317)------------------------------
% 3.05/1.64 % (12323)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/6Mi)
% 3.05/1.64 % (12323)Instruction limit reached!
% 3.05/1.64 % (12323)------------------------------
% 3.05/1.64 % (12323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.64 % (12323)Termination reason: Unknown
% 3.05/1.64 % (12323)Termination phase: shuffling
% 3.05/1.64
% 3.05/1.64 % (12323)Memory used [KB]: 1535
% 3.05/1.64 % (12323)Time elapsed: 0.003 s
% 3.05/1.64 % (12323)Instructions burned: 6 (million)
% 3.05/1.64 % (12323)------------------------------
% 3.05/1.64 % (12323)------------------------------
% 3.05/1.64 % (12320)Instruction limit reached!
% 3.05/1.64 % (12320)------------------------------
% 3.05/1.64 % (12320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.64 % (12320)Termination reason: Unknown
% 3.05/1.64 % (12320)Termination phase: shuffling
% 3.05/1.64
% 3.05/1.64 % (12320)Memory used [KB]: 1791
% 3.05/1.64 % (12320)Time elapsed: 0.011 s
% 3.05/1.64 % (12320)Instructions burned: 19 (million)
% 3.05/1.64 % (12320)------------------------------
% 3.05/1.64 % (12320)------------------------------
% 3.05/1.64 % (12325)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_12084 for (2999ds/902Mi)
% 3.05/1.64 % (12327)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_12084 for (2999ds/21Mi)
% 3.05/1.65 % (12284)Instruction limit reached!
% 3.05/1.65 % (12284)------------------------------
% 3.05/1.65 % (12284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (12284)Termination reason: Unknown
% 3.05/1.65 % (12284)Termination phase: Saturation
% 3.05/1.65
% 3.05/1.65 % (12284)Memory used [KB]: 7291
% 3.05/1.65 % (12284)Time elapsed: 0.076 s
% 3.05/1.65 % (12284)Instructions burned: 185 (million)
% 3.05/1.65 % (12284)------------------------------
% 3.05/1.65 % (12284)------------------------------
% 3.05/1.65 % (12330)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_12084 for (2999ds/6Mi)
% 3.05/1.65 % (12329)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/5Mi)
% 3.05/1.65 % (12327)Instruction limit reached!
% 3.05/1.65 % (12327)------------------------------
% 3.05/1.65 % (12327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (12327)Termination reason: Unknown
% 3.05/1.65 % (12327)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (12327)Memory used [KB]: 1918
% 3.05/1.65 % (12327)Time elapsed: 0.009 s
% 3.05/1.65 % (12327)Instructions burned: 22 (million)
% 3.05/1.65 % (12327)------------------------------
% 3.05/1.65 % (12327)------------------------------
% 3.05/1.65 % (12329)Instruction limit reached!
% 3.05/1.65 % (12329)------------------------------
% 3.05/1.65 % (12329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (12329)Termination reason: Unknown
% 3.05/1.65 % (12329)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (12329)Memory used [KB]: 1535
% 3.05/1.65 % (12329)Time elapsed: 0.003 s
% 3.05/1.65 % (12329)Instructions burned: 6 (million)
% 3.05/1.65 % (12329)------------------------------
% 3.05/1.65 % (12329)------------------------------
% 3.05/1.65 % (12330)Instruction limit reached!
% 3.05/1.65 % (12330)------------------------------
% 3.05/1.65 % (12330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (12330)Termination reason: Unknown
% 3.05/1.65 % (12330)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (12330)Memory used [KB]: 1535
% 3.05/1.65 % (12330)Time elapsed: 0.004 s
% 3.05/1.65 % (12330)Instructions burned: 7 (million)
% 3.05/1.65 % (12330)------------------------------
% 3.05/1.65 % (12330)------------------------------
% 3.05/1.66 % (12332)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/377Mi)
% 3.05/1.66 % (12334)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_12084 for (2999ds/19Mi)
% 3.05/1.66 % (12335)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_12084 for (2999ds/879Mi)
% 3.05/1.66 % (12333)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_12084 for (2999ds/779Mi)
% 3.05/1.67 % (12334)Instruction limit reached!
% 3.05/1.67 % (12334)------------------------------
% 3.05/1.67 % (12334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.67 % (12334)Termination reason: Unknown
% 3.05/1.67 % (12334)Termination phase: shuffling
% 3.05/1.67
% 3.05/1.67 % (12334)Memory used [KB]: 1791
% 3.05/1.67 % (12334)Time elapsed: 0.009 s
% 3.05/1.67 % (12334)Instructions burned: 19 (million)
% 3.05/1.67 % (12334)------------------------------
% 3.05/1.67 % (12334)------------------------------
% 3.05/1.68 % (12336)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_12084 for (2998ds/17Mi)
% 3.05/1.69 % (12336)Instruction limit reached!
% 3.05/1.69 % (12336)------------------------------
% 3.05/1.69 % (12336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (12336)Termination reason: Unknown
% 3.05/1.69 % (12336)Termination phase: shuffling
% 3.05/1.69
% 3.05/1.69 % (12336)Memory used [KB]: 1791
% 3.05/1.69 % (12336)Time elapsed: 0.007 s
% 3.05/1.69 % (12336)Instructions burned: 18 (million)
% 3.05/1.69 % (12336)------------------------------
% 3.05/1.69 % (12336)------------------------------
% 3.05/1.69 % (12325)Refutation not found, incomplete strategy
% 3.05/1.69 % (12325)------------------------------
% 3.05/1.69 % (12325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (12325)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.69
% 3.05/1.69
% 3.05/1.69 % (12325)Memory used [KB]: 7419
% 3.05/1.69 % (12325)Time elapsed: 0.048 s
% 3.05/1.69 % (12325)Instructions burned: 151 (million)
% 3.05/1.69 % (12325)------------------------------
% 3.05/1.69 % (12325)------------------------------
% 3.05/1.69 % (12337)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_12084 for (2998ds/3Mi)
% 3.05/1.70 % (12337)Instruction limit reached!
% 3.05/1.70 % (12337)------------------------------
% 3.05/1.70 % (12337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.70 % (12337)Termination reason: Unknown
% 3.05/1.70 % (12337)Termination phase: shuffling
% 3.05/1.70
% 3.05/1.70 % (12337)Memory used [KB]: 1535
% 3.05/1.70 % (12337)Time elapsed: 0.003 s
% 3.05/1.70 % (12337)Instructions burned: 5 (million)
% 3.05/1.70 % (12337)------------------------------
% 3.05/1.70 % (12337)------------------------------
% 3.05/1.70 % (12338)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_12084 for (2998ds/30Mi)
% 3.05/1.71 % (12339)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_12084 for (2998ds/127Mi)
% 3.05/1.71 % (12338)Instruction limit reached!
% 3.05/1.71 % (12338)------------------------------
% 3.05/1.71 % (12338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.71 % (12338)Termination reason: Unknown
% 3.05/1.71 % (12338)Termination phase: shuffling
% 3.05/1.71
% 3.05/1.71 % (12338)Memory used [KB]: 2046
% 3.05/1.71 % (12338)Time elapsed: 0.011 s
% 3.05/1.71 % (12338)Instructions burned: 31 (million)
% 3.05/1.71 % (12338)------------------------------
% 3.05/1.71 % (12338)------------------------------
% 3.05/1.72 % (12341)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_12084 for (2998ds/100Mi)
% 3.05/1.74 % (12339)Instruction limit reached!
% 3.05/1.74 % (12339)------------------------------
% 3.05/1.74 % (12339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.74 % (12339)Termination reason: Unknown
% 3.05/1.74 % (12339)Termination phase: Saturation
% 3.05/1.74
% 3.05/1.74 % (12339)Memory used [KB]: 6908
% 3.05/1.74 % (12339)Time elapsed: 0.040 s
% 3.05/1.74 % (12339)Instructions burned: 127 (million)
% 3.05/1.74 % (12339)------------------------------
% 3.05/1.74 % (12339)------------------------------
% 3.05/1.75 % (12341)Instruction limit reached!
% 3.05/1.75 % (12341)------------------------------
% 3.05/1.75 % (12341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.75 % (12341)Termination reason: Unknown
% 3.05/1.75 % (12341)Termination phase: Property scanning
% 3.05/1.75
% 3.05/1.75 % (12341)Memory used [KB]: 2814
% 3.05/1.75 % (12341)Time elapsed: 0.031 s
% 3.05/1.75 % (12341)Instructions burned: 102 (million)
% 3.05/1.75 % (12341)------------------------------
% 3.05/1.75 % (12341)------------------------------
% 3.05/1.75 % (12355)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_12084 for (2997ds/3Mi)
% 3.05/1.76 % (12355)Instruction limit reached!
% 3.05/1.76 % (12355)------------------------------
% 3.05/1.76 % (12355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.76 % (12355)Termination reason: Unknown
% 3.05/1.76 % (12355)Termination phase: shuffling
% 3.05/1.76
% 3.05/1.76 % (12355)Memory used [KB]: 1407
% 3.05/1.76 % (12355)Time elapsed: 0.002 s
% 3.05/1.76 % (12355)Instructions burned: 3 (million)
% 3.05/1.76 % (12355)------------------------------
% 3.05/1.76 % (12355)------------------------------
% 3.05/1.76 % (12359)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_12084 for (2997ds/20Mi)
% 3.05/1.76 % (12361)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_12084 for (2997ds/86Mi)
% 3.05/1.77 % (12359)Instruction limit reached!
% 3.05/1.77 % (12359)------------------------------
% 3.05/1.77 % (12359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.77 % (12359)Termination reason: Unknown
% 3.05/1.77 % (12359)Termination phase: shuffling
% 3.05/1.77
% 3.05/1.77 % (12359)Memory used [KB]: 1918
% 3.05/1.77 % (12359)Time elapsed: 0.008 s
% 3.05/1.77 % (12359)Instructions burned: 21 (million)
% 3.05/1.77 % (12359)------------------------------
% 3.05/1.77 % (12359)------------------------------
% 3.05/1.78 % (12332)Instruction limit reached!
% 3.05/1.78 % (12332)------------------------------
% 3.05/1.78 % (12332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.78 % (12332)Termination reason: Unknown
% 3.05/1.78 % (12332)Termination phase: Saturation
% 3.05/1.78
% 3.05/1.78 % (12332)Memory used [KB]: 7931
% 3.05/1.78 % (12332)Time elapsed: 0.142 s
% 3.05/1.78 % (12332)Instructions burned: 379 (million)
% 3.05/1.78 % (12332)------------------------------
% 3.05/1.78 % (12332)------------------------------
% 3.05/1.78 % (12367)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_12084 for (2997ds/107Mi)
% 3.05/1.79 % (12371)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_12084 for (2997ds/39Mi)
% 3.05/1.79 % (12361)Instruction limit reached!
% 3.05/1.79 % (12361)------------------------------
% 3.05/1.79 % (12361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.79 % (12361)Termination reason: Unknown
% 3.05/1.79 % (12361)Termination phase: Property scanning
% 3.05/1.79
% 3.05/1.79 % (12361)Memory used [KB]: 2430
% 3.05/1.79 % (12361)Time elapsed: 0.027 s
% 3.05/1.79 % (12361)Instructions burned: 87 (million)
% 3.05/1.79 % (12361)------------------------------
% 3.05/1.79 % (12361)------------------------------
% 3.05/1.80 % (12371)Instruction limit reached!
% 3.05/1.80 % (12371)------------------------------
% 3.05/1.80 % (12371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.80 % (12371)Termination reason: Unknown
% 3.05/1.80 % (12371)Termination phase: shuffling
% 3.05/1.80
% 3.05/1.80 % (12371)Memory used [KB]: 2174
% 3.05/1.80 % (12371)Time elapsed: 0.012 s
% 3.05/1.80 % (12371)Instructions burned: 39 (million)
% 3.05/1.80 % (12371)------------------------------
% 3.05/1.80 % (12371)------------------------------
% 3.05/1.80 % (12380)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_12084 for (2997ds/448Mi)
% 3.05/1.81 % (12384)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_12084 for (2997ds/46Mi)
% 3.05/1.81 % (12367)Instruction limit reached!
% 3.05/1.81 % (12367)------------------------------
% 3.05/1.81 % (12367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.81 % (12367)Termination reason: Unknown
% 3.05/1.81 % (12367)Termination phase: Saturation
% 3.05/1.81
% 3.05/1.81 % (12367)Memory used [KB]: 6908
% 3.05/1.81 % (12367)Time elapsed: 0.034 s
% 3.05/1.81 % (12367)Instructions burned: 109 (million)
% 3.05/1.81 % (12367)------------------------------
% 3.05/1.81 % (12367)------------------------------
% 3.05/1.82 % (12388)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_12084 for (2997ds/98Mi)
% 3.05/1.82 % (12384)Instruction limit reached!
% 3.05/1.82 % (12384)------------------------------
% 3.05/1.82 % (12384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.82 % (12384)Termination reason: Unknown
% 3.05/1.82 % (12384)Termination phase: SInE selection
% 3.05/1.82
% 3.05/1.82 % (12384)Memory used [KB]: 2046
% 3.05/1.82 % (12384)Time elapsed: 0.016 s
% 3.05/1.82 % (12384)Instructions burned: 47 (million)
% 3.05/1.82 % (12384)------------------------------
% 3.05/1.82 % (12384)------------------------------
% 3.05/1.83 % (12393)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_12084 for (2997ds/507Mi)
% 3.05/1.85 % (12388)Instruction limit reached!
% 3.05/1.85 % (12388)------------------------------
% 3.05/1.85 % (12388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.85 % (12388)Termination reason: Unknown
% 3.05/1.85 % (12388)Termination phase: Property scanning
% 3.05/1.85
% 3.05/1.85 % (12388)Memory used [KB]: 2814
% 3.05/1.85 % (12388)Time elapsed: 0.029 s
% 3.05/1.85 % (12388)Instructions burned: 101 (million)
% 3.05/1.85 % (12388)------------------------------
% 3.05/1.85 % (12388)------------------------------
% 3.05/1.85 % (12321)Instruction limit reached!
% 3.05/1.85 % (12321)------------------------------
% 3.05/1.85 % (12321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.85 % (12321)Termination reason: Unknown
% 3.05/1.85 % (12321)Termination phase: Saturation
% 3.05/1.85
% 3.05/1.85 % (12321)Memory used [KB]: 8955
% 3.05/1.85 % (12321)Time elapsed: 0.225 s
% 3.05/1.85 % (12321)Instructions burned: 711 (million)
% 3.05/1.85 % (12321)------------------------------
% 3.05/1.85 % (12321)------------------------------
% 3.05/1.86 % (12405)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_12084 for (2996ds/149Mi)
% 3.05/1.86 % (12408)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_12084 for (2996ds/39Mi)
% 3.05/1.88 % (12408)Instruction limit reached!
% 3.05/1.88 % (12408)------------------------------
% 3.05/1.88 % (12408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.88 % (12408)Termination reason: Unknown
% 3.05/1.88 % (12408)Termination phase: Property scanning
% 3.05/1.88
% 3.05/1.88 % (12408)Memory used [KB]: 2046
% 3.05/1.88 % (12408)Time elapsed: 0.014 s
% 3.05/1.88 % (12408)Instructions burned: 42 (million)
% 3.05/1.88 % (12408)------------------------------
% 3.05/1.88 % (12408)------------------------------
% 3.05/1.89 % (12418)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_12084 for (2996ds/6Mi)
% 3.05/1.89 % (12418)Instruction limit reached!
% 3.05/1.89 % (12418)------------------------------
% 3.05/1.89 % (12418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.89 % (12418)Termination reason: Unknown
% 3.05/1.89 % (12418)Termination phase: shuffling
% 3.05/1.89
% 3.05/1.89 % (12418)Memory used [KB]: 1535
% 3.05/1.89 % (12418)Time elapsed: 0.003 s
% 3.05/1.89 % (12418)Instructions burned: 6 (million)
% 3.05/1.89 % (12418)------------------------------
% 3.05/1.89 % (12418)------------------------------
% 3.05/1.90 % (12419)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_12084 for (2996ds/1087Mi)
% 3.05/1.90 % (12405)Instruction limit reached!
% 3.05/1.90 % (12405)------------------------------
% 3.05/1.90 % (12405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.90 % (12405)Termination reason: Unknown
% 3.05/1.90 % (12405)Termination phase: Saturation
% 3.05/1.90
% 3.05/1.90 % (12405)Memory used [KB]: 7164
% 3.05/1.90 % (12405)Time elapsed: 0.047 s
% 3.05/1.90 % (12405)Instructions burned: 149 (million)
% 3.05/1.90 % (12405)------------------------------
% 3.05/1.90 % (12405)------------------------------
% 3.05/1.91 % (12333)Instruction limit reached!
% 3.05/1.91 % (12333)------------------------------
% 3.05/1.91 % (12333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.91 % (12333)Termination reason: Unknown
% 3.05/1.91 % (12333)Termination phase: Saturation
% 3.05/1.91
% 3.05/1.91 % (12333)Memory used [KB]: 9083
% 3.05/1.91 % (12333)Time elapsed: 0.265 s
% 3.05/1.91 % (12333)Instructions burned: 780 (million)
% 3.05/1.91 % (12333)------------------------------
% 3.05/1.91 % (12333)------------------------------
% 3.05/1.91 % (12430)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_12084 for (2996ds/47Mi)
% 3.05/1.92 % (12432)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_12084 for (2996ds/44Mi)
% 3.05/1.93 % (12430)Instruction limit reached!
% 3.05/1.93 % (12430)------------------------------
% 3.05/1.93 % (12430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.93 % (12430)Termination reason: Unknown
% 3.05/1.93 % (12430)Termination phase: Preprocessing 1
% 3.05/1.93
% 3.05/1.93 % (12430)Memory used [KB]: 2046
% 3.05/1.93 % (12430)Time elapsed: 0.017 s
% 3.05/1.93 % (12430)Instructions burned: 49 (million)
% 3.05/1.93 % (12430)------------------------------
% 3.05/1.93 % (12430)------------------------------
% 3.05/1.93 % (12432)Instruction limit reached!
% 3.05/1.93 % (12432)------------------------------
% 3.05/1.93 % (12432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.93 % (12432)Termination reason: Unknown
% 3.05/1.93 % (12432)Termination phase: Property scanning
% 3.05/1.93
% 3.05/1.93 % (12432)Memory used [KB]: 2302
% 3.05/1.93 % (12432)Time elapsed: 0.015 s
% 3.05/1.93 % (12432)Instructions burned: 47 (million)
% 3.05/1.93 % (12432)------------------------------
% 3.05/1.93 % (12432)------------------------------
% 3.05/1.93 % (12335)Instruction limit reached!
% 3.05/1.93 % (12335)------------------------------
% 3.05/1.93 % (12335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.93 % (12335)Termination reason: Unknown
% 3.05/1.93 % (12335)Termination phase: Saturation
% 3.05/1.93
% 3.05/1.93 % (12335)Memory used [KB]: 8571
% 3.05/1.93 % (12335)Time elapsed: 0.292 s
% 3.05/1.93 % (12335)Instructions burned: 879 (million)
% 3.05/1.93 % (12335)------------------------------
% 3.05/1.93 % (12335)------------------------------
% 3.05/1.93 % (12305)Instruction limit reached!
% 3.05/1.93 % (12305)------------------------------
% 3.05/1.93 % (12305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.93 % (12305)Termination reason: Unknown
% 3.05/1.93 % (12305)Termination phase: Saturation
% 3.05/1.93
% 3.05/1.93 % (12305)Memory used [KB]: 9978
% 3.05/1.93 % (12305)Time elapsed: 0.335 s
% 3.05/1.93 % (12305)Instructions burned: 1042 (million)
% 3.05/1.93 % (12305)------------------------------
% 3.05/1.93 % (12305)------------------------------
% 3.05/1.94 % (12380)Instruction limit reached!
% 3.05/1.94 % (12380)------------------------------
% 3.05/1.94 % (12380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.94 % (12380)Termination reason: Unknown
% 3.05/1.94 % (12380)Termination phase: Saturation
% 3.05/1.94
% 3.05/1.94 % (12380)Memory used [KB]: 8827
% 3.05/1.94 % (12380)Time elapsed: 0.137 s
% 3.05/1.94 % (12380)Instructions burned: 450 (million)
% 3.05/1.94 % (12380)------------------------------
% 3.05/1.94 % (12380)------------------------------
% 3.05/1.94 % (12442)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_12084 for (2996ds/432Mi)
% 3.05/1.94 % (12443)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_12084 for (2996ds/62Mi)
% 3.05/1.94 % (12444)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_12084 for (2996ds/31Mi)
% 3.05/1.94 % (12445)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_12084 for (2996ds/96Mi)
% 3.05/1.95 % (12446)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_12084 for (2996ds/453Mi)
% 3.05/1.95 % (12444)Instruction limit reached!
% 3.05/1.95 % (12444)------------------------------
% 3.05/1.95 % (12444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.95 % (12444)Termination reason: Unknown
% 3.05/1.95 % (12444)Termination phase: Property scanning
% 3.05/1.95
% 3.05/1.95 % (12444)Memory used [KB]: 2046
% 3.05/1.95 % (12444)Time elapsed: 0.012 s
% 3.05/1.95 % (12444)Instructions burned: 33 (million)
% 3.05/1.95 % (12444)------------------------------
% 3.05/1.95 % (12444)------------------------------
% 3.05/1.96 % (12443)Instruction limit reached!
% 3.05/1.96 % (12443)------------------------------
% 3.05/1.96 % (12443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.96 % (12443)Termination reason: Unknown
% 3.05/1.96 % (12443)Termination phase: Property scanning
% 3.05/1.96
% 3.05/1.96 % (12443)Memory used [KB]: 2302
% 3.05/1.96 % (12443)Time elapsed: 0.018 s
% 3.05/1.96 % (12443)Instructions burned: 62 (million)
% 3.05/1.96 % (12443)------------------------------
% 3.05/1.96 % (12443)------------------------------
% 3.05/1.96 % (12460)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_12084 for (2995ds/71Mi)
% 3.05/1.97 % (12463)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_12084 for (2995ds/83Mi)
% 3.05/1.97 % (12445)Instruction limit reached!
% 3.05/1.97 % (12445)------------------------------
% 3.05/1.97 % (12445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.97 % (12445)Termination reason: Unknown
% 3.05/1.97 % (12445)Termination phase: Saturation
% 3.05/1.97
% 3.05/1.97 % (12445)Memory used [KB]: 6908
% 3.05/1.97 % (12445)Time elapsed: 0.030 s
% 3.05/1.97 % (12445)Instructions burned: 98 (million)
% 3.05/1.97 % (12445)------------------------------
% 3.05/1.97 % (12445)------------------------------
% 3.05/1.98 % (12473)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_12084 for (2995ds/11Mi)
% 3.05/1.98 % (12393)Instruction limit reached!
% 3.05/1.98 % (12393)------------------------------
% 3.05/1.98 % (12393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.98 % (12393)Termination reason: Unknown
% 3.05/1.98 % (12393)Termination phase: Saturation
% 3.05/1.98
% 3.05/1.98 % (12393)Memory used [KB]: 8315
% 3.05/1.98 % (12393)Time elapsed: 0.154 s
% 3.05/1.98 % (12393)Instructions burned: 509 (million)
% 3.05/1.98 % (12393)------------------------------
% 3.05/1.98 % (12393)------------------------------
% 3.05/1.98 % (12460)Instruction limit reached!
% 3.05/1.98 % (12460)------------------------------
% 3.05/1.98 % (12460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.98 % (12460)Termination reason: Unknown
% 3.05/1.98 % (12460)Termination phase: Property scanning
% 3.05/1.98
% 3.05/1.98 % (12460)Memory used [KB]: 2302
% 3.05/1.98 % (12460)Time elapsed: 0.023 s
% 3.05/1.98 % (12460)Instructions burned: 72 (million)
% 3.05/1.98 % (12460)------------------------------
% 3.05/1.98 % (12460)------------------------------
% 3.05/1.99 % (12473)Instruction limit reached!
% 3.05/1.99 % (12473)------------------------------
% 3.05/1.99 % (12473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.99 % (12473)Termination reason: Unknown
% 3.05/1.99 % (12473)Termination phase: shuffling
% 3.05/1.99
% 3.05/1.99 % (12473)Memory used [KB]: 1663
% 3.05/1.99 % (12473)Time elapsed: 0.005 s
% 3.05/1.99 % (12473)Instructions burned: 14 (million)
% 3.05/1.99 % (12473)------------------------------
% 3.05/1.99 % (12473)------------------------------
% 3.05/1.99 % (12463)Instruction limit reached!
% 3.05/1.99 % (12463)------------------------------
% 3.05/1.99 % (12463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.99 % (12463)Termination reason: Unknown
% 3.05/1.99 % (12463)Termination phase: Saturation
% 3.05/1.99
% 3.05/1.99 % (12463)Memory used [KB]: 6780
% 3.05/1.99 % (12463)Time elapsed: 0.028 s
% 3.05/1.99 % (12463)Instructions burned: 85 (million)
% 3.05/1.99 % (12463)------------------------------
% 3.05/1.99 % (12463)------------------------------
% 3.05/1.99 % (12474)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_12084 for (2995ds/41Mi)
% 3.05/1.99 % (12475)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12084 for (2995ds/6Mi)
% 3.05/1.99 % (12476)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_12084 for (2995ds/150Mi)
% 3.05/2.00 % (12475)Instruction limit reached!
% 3.05/2.00 % (12475)------------------------------
% 3.05/2.00 % (12475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/2.00 % (12475)Termination reason: Unknown
% 3.05/2.00 % (12475)Termination phase: shuffling
% 3.05/2.00
% 3.05/2.00 % (12475)Memory used [KB]: 1535
% 3.05/2.00 % (12475)Time elapsed: 0.004 s
% 3.05/2.00 % (12475)Instructions burned: 8 (million)
% 3.05/2.00 % (12475)------------------------------
% 3.05/2.00 % (12475)------------------------------
% 3.05/2.00 % (12482)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_12084 for (2995ds/343Mi)
% 3.05/2.00 % (12474)Instruction limit reached!
% 3.05/2.00 % (12474)------------------------------
% 3.05/2.00 % (12474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/2.00 % (12474)Termination reason: Unknown
% 3.05/2.00 % (12474)Termination phase: shuffling
% 3.05/2.00
% 3.05/2.00 % (12474)Memory used [KB]: 2302
% 3.05/2.00 % (12474)Time elapsed: 0.013 s
% 3.05/2.00 % (12474)Instructions burned: 42 (million)
% 3.05/2.00 % (12474)------------------------------
% 3.05/2.00 % (12474)------------------------------
% 3.05/2.01 % (12488)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_12084 for (2995ds/109Mi)
% 3.05/2.01 % (12494)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_12084 for (2995ds/253Mi)
% 6.20/2.04 % (12488)Instruction limit reached!
% 6.20/2.04 % (12488)------------------------------
% 6.20/2.04 % (12488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.04 % (12488)Termination reason: Unknown
% 6.20/2.04 % (12488)Termination phase: Saturation
% 6.20/2.04
% 6.20/2.04 % (12488)Memory used [KB]: 6908
% 6.20/2.04 % (12488)Time elapsed: 0.033 s
% 6.20/2.04 % (12488)Instructions burned: 109 (million)
% 6.20/2.04 % (12488)------------------------------
% 6.20/2.04 % (12488)------------------------------
% 6.20/2.04 % (12476)Instruction limit reached!
% 6.20/2.04 % (12476)------------------------------
% 6.20/2.04 % (12476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.04 % (12476)Termination reason: Unknown
% 6.20/2.04 % (12476)Termination phase: Saturation
% 6.20/2.04
% 6.20/2.04 % (12476)Memory used [KB]: 7164
% 6.20/2.04 % (12476)Time elapsed: 0.047 s
% 6.20/2.04 % (12476)Instructions burned: 150 (million)
% 6.20/2.04 % (12476)------------------------------
% 6.20/2.04 % (12476)------------------------------
% 6.20/2.05 % (12508)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_12084 for (2995ds/140Mi)
% 6.20/2.05 % (12510)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_12084 for (2995ds/614Mi)
% 6.20/2.07 % (12442)Instruction limit reached!
% 6.20/2.07 % (12442)------------------------------
% 6.20/2.07 % (12442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.07 % (12442)Termination reason: Unknown
% 6.20/2.07 % (12442)Termination phase: Saturation
% 6.20/2.07
% 6.20/2.07 % (12442)Memory used [KB]: 4733
% 6.20/2.07 % (12442)Time elapsed: 0.133 s
% 6.20/2.07 % (12442)Instructions burned: 435 (million)
% 6.20/2.07 % (12442)------------------------------
% 6.20/2.07 % (12442)------------------------------
% 6.20/2.07 % (12446)Instruction limit reached!
% 6.20/2.07 % (12446)------------------------------
% 6.20/2.07 % (12446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.07 % (12446)Termination reason: Unknown
% 6.20/2.07 % (12446)Termination phase: Saturation
% 6.20/2.07
% 6.20/2.07 % (12446)Memory used [KB]: 7931
% 6.20/2.07 % (12446)Time elapsed: 0.129 s
% 6.20/2.07 % (12446)Instructions burned: 454 (million)
% 6.20/2.07 % (12446)------------------------------
% 6.20/2.07 % (12446)------------------------------
% 6.20/2.08 % (12520)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_12084 for (2994ds/202Mi)
% 6.20/2.08 % (12521)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_12084 for (2994ds/339Mi)
% 6.20/2.09 % (12494)Instruction limit reached!
% 6.20/2.09 % (12494)------------------------------
% 6.20/2.09 % (12494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.09 % (12494)Termination reason: Unknown
% 6.20/2.09 % (12494)Termination phase: Saturation
% 6.20/2.09
% 6.20/2.09 % (12494)Memory used [KB]: 7419
% 6.20/2.09 % (12494)Time elapsed: 0.079 s
% 6.20/2.09 % (12494)Instructions burned: 254 (million)
% 6.20/2.09 % (12494)------------------------------
% 6.20/2.09 % (12494)------------------------------
% 6.20/2.09 % (12508)Instruction limit reached!
% 6.20/2.09 % (12508)------------------------------
% 6.20/2.09 % (12508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.09 % (12508)Termination reason: Unknown
% 6.20/2.09 % (12508)Termination phase: Saturation
% 6.20/2.09
% 6.20/2.09 % (12508)Memory used [KB]: 7291
% 6.20/2.09 % (12508)Time elapsed: 0.047 s
% 6.20/2.09 % (12508)Instructions burned: 141 (million)
% 6.20/2.09 % (12508)------------------------------
% 6.20/2.09 % (12508)------------------------------
% 6.20/2.10 % (12528)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_12084 for (2994ds/283Mi)
% 6.20/2.10 % (12529)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_12084 for (2994ds/134Mi)
% 6.20/2.11 % (12520)Refutation not found, incomplete strategy
% 6.20/2.11 % (12520)------------------------------
% 6.20/2.11 % (12520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.11 % (12520)Termination reason: Refutation not found, incomplete strategy
% 6.20/2.11
% 6.20/2.11
% 6.20/2.11 % (12520)Memory used [KB]: 7036
% 6.20/2.11 % (12520)Time elapsed: 0.031 s
% 6.20/2.11 % (12520)Instructions burned: 94 (million)
% 6.20/2.11 % (12520)------------------------------
% 6.20/2.11 % (12520)------------------------------
% 6.20/2.11 % (12482)Instruction limit reached!
% 6.20/2.11 % (12482)------------------------------
% 6.20/2.11 % (12482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.11 % (12482)Termination reason: Unknown
% 6.20/2.11 % (12482)Termination phase: Saturation
% 6.20/2.11
% 6.20/2.11 % (12482)Memory used [KB]: 7675
% 6.20/2.11 % (12482)Time elapsed: 0.109 s
% 6.20/2.11 % (12482)Instructions burned: 344 (million)
% 6.20/2.11 % (12482)------------------------------
% 6.20/2.11 % (12482)------------------------------
% 6.20/2.12 % (12536)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_12084 for (2994ds/298Mi)
% 6.20/2.12 % (12537)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_12084 for (2994ds/192Mi)
% 6.76/2.14 % (12529)Instruction limit reached!
% 6.76/2.14 % (12529)------------------------------
% 6.76/2.14 % (12529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.14 % (12529)Termination reason: Unknown
% 6.76/2.14 % (12529)Termination phase: Saturation
% 6.76/2.14
% 6.76/2.14 % (12529)Memory used [KB]: 7036
% 6.76/2.14 % (12529)Time elapsed: 0.043 s
% 6.76/2.14 % (12529)Instructions burned: 136 (million)
% 6.76/2.14 % (12529)------------------------------
% 6.76/2.14 % (12529)------------------------------
% 6.76/2.15 % (12549)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_12084 for (2994ds/258Mi)
% 6.76/2.18 % (12537)Instruction limit reached!
% 6.76/2.18 % (12537)------------------------------
% 6.76/2.18 % (12537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.18 % (12537)Termination reason: Unknown
% 6.76/2.18 % (12537)Termination phase: Saturation
% 6.76/2.18
% 6.76/2.18 % (12537)Memory used [KB]: 7931
% 6.76/2.18 % (12537)Time elapsed: 0.061 s
% 6.76/2.18 % (12537)Instructions burned: 192 (million)
% 6.76/2.18 % (12537)------------------------------
% 6.76/2.18 % (12537)------------------------------
% 6.76/2.19 % (12528)Instruction limit reached!
% 6.76/2.19 % (12528)------------------------------
% 6.76/2.19 % (12528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.19 % (12528)Termination reason: Unknown
% 6.76/2.19 % (12528)Termination phase: Saturation
% 6.76/2.19
% 6.76/2.19 % (12528)Memory used [KB]: 7803
% 6.76/2.19 % (12528)Time elapsed: 0.086 s
% 6.76/2.19 % (12528)Instructions burned: 285 (million)
% 6.76/2.19 % (12528)------------------------------
% 6.76/2.19 % (12528)------------------------------
% 6.76/2.19 % (12561)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_12084 for (2993ds/90Mi)
% 6.76/2.19 % (12521)Instruction limit reached!
% 6.76/2.19 % (12521)------------------------------
% 6.76/2.19 % (12521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.19 % (12521)Termination reason: Unknown
% 6.76/2.19 % (12521)Termination phase: Saturation
% 6.76/2.19
% 6.76/2.19 % (12521)Memory used [KB]: 7803
% 6.76/2.19 % (12521)Time elapsed: 0.109 s
% 6.76/2.19 % (12521)Instructions burned: 341 (million)
% 6.76/2.19 % (12521)------------------------------
% 6.76/2.19 % (12521)------------------------------
% 6.76/2.20 % (12562)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_12084 for (2993ds/231Mi)
% 7.17/2.20 % (12566)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_12084 for (2993ds/458Mi)
% 7.17/2.20 % (12536)Instruction limit reached!
% 7.17/2.20 % (12536)------------------------------
% 7.17/2.20 % (12536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.20 % (12536)Termination reason: Unknown
% 7.17/2.20 % (12536)Termination phase: Saturation
% 7.17/2.20
% 7.17/2.20 % (12536)Memory used [KB]: 7931
% 7.17/2.20 % (12536)Time elapsed: 0.086 s
% 7.17/2.20 % (12536)Instructions burned: 298 (million)
% 7.17/2.20 % (12536)------------------------------
% 7.17/2.20 % (12536)------------------------------
% 7.17/2.21 % (12570)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_12084 for (2993ds/31Mi)
% 7.17/2.22 % (12561)Instruction limit reached!
% 7.17/2.22 % (12561)------------------------------
% 7.17/2.22 % (12561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.22 % (12561)Termination reason: Unknown
% 7.17/2.22 % (12561)Termination phase: Property scanning
% 7.17/2.22
% 7.17/2.22 % (12561)Memory used [KB]: 2430
% 7.17/2.22 % (12561)Time elapsed: 0.028 s
% 7.17/2.22 % (12561)Instructions burned: 91 (million)
% 7.17/2.22 % (12561)------------------------------
% 7.17/2.22 % (12561)------------------------------
% 7.17/2.22 % (12570)Instruction limit reached!
% 7.17/2.22 % (12570)------------------------------
% 7.17/2.22 % (12570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.22 % (12570)Termination reason: Unknown
% 7.17/2.22 % (12570)Termination phase: Property scanning
% 7.17/2.22
% 7.17/2.22 % (12570)Memory used [KB]: 2046
% 7.17/2.22 % (12570)Time elapsed: 0.012 s
% 7.17/2.22 % (12570)Instructions burned: 33 (million)
% 7.17/2.22 % (12570)------------------------------
% 7.17/2.22 % (12570)------------------------------
% 7.17/2.23 % (12574)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_12084 for (2993ds/297Mi)
% 7.17/2.23 % (12419)Instruction limit reached!
% 7.17/2.23 % (12419)------------------------------
% 7.17/2.23 % (12419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.23 % (12419)Termination reason: Unknown
% 7.17/2.23 % (12419)Termination phase: Saturation
% 7.17/2.23
% 7.17/2.23 % (12419)Memory used [KB]: 7931
% 7.17/2.23 % (12419)Time elapsed: 0.330 s
% 7.17/2.23 % (12419)Instructions burned: 1089 (million)
% 7.17/2.23 % (12419)------------------------------
% 7.17/2.23 % (12419)------------------------------
% 7.17/2.23 % (12576)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_12084 for (2993ds/987Mi)
% 7.17/2.24 % (12549)Instruction limit reached!
% 7.17/2.24 % (12549)------------------------------
% 7.17/2.24 % (12549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.24 % (12549)Termination reason: Unknown
% 7.17/2.24 % (12549)Termination phase: Saturation
% 7.17/2.24
% 7.17/2.24 % (12549)Memory used [KB]: 7803
% 7.17/2.24 % (12549)Time elapsed: 0.082 s
% 7.17/2.24 % (12549)Instructions burned: 260 (million)
% 7.17/2.24 % (12549)------------------------------
% 7.17/2.24 % (12549)------------------------------
% 7.17/2.24 % (12578)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_12084 for (2993ds/182Mi)
% 7.17/2.25 % (12583)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_12084 for (2993ds/182Mi)
% 7.17/2.25 % (12510)Instruction limit reached!
% 7.17/2.25 % (12510)------------------------------
% 7.17/2.25 % (12510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.25 % (12510)Termination reason: Unknown
% 7.17/2.25 % (12510)Termination phase: Saturation
% 7.17/2.25
% 7.17/2.25 % (12510)Memory used [KB]: 8699
% 7.17/2.25 % (12510)Time elapsed: 0.197 s
% 7.17/2.25 % (12510)Instructions burned: 616 (million)
% 7.17/2.25 % (12510)------------------------------
% 7.17/2.25 % (12510)------------------------------
% 7.17/2.26 % (12591)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_12084 for (2992ds/154Mi)
% 7.17/2.26 % (12562)Instruction limit reached!
% 7.17/2.26 % (12562)------------------------------
% 7.17/2.26 % (12562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.26 % (12562)Termination reason: Unknown
% 7.17/2.26 % (12562)Termination phase: Saturation
% 7.17/2.26
% 7.17/2.26 % (12562)Memory used [KB]: 7419
% 7.17/2.26 % (12562)Time elapsed: 0.064 s
% 7.17/2.26 % (12562)Instructions burned: 232 (million)
% 7.17/2.26 % (12562)------------------------------
% 7.17/2.26 % (12562)------------------------------
% 7.17/2.27 % (12599)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_12084 for (2992ds/79Mi)
% 7.17/2.29 % (12578)Instruction limit reached!
% 7.17/2.29 % (12578)------------------------------
% 7.17/2.29 % (12578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.29 % (12578)Termination reason: Unknown
% 7.17/2.29 % (12578)Termination phase: Saturation
% 7.17/2.29
% 7.17/2.29 % (12578)Memory used [KB]: 7291
% 7.17/2.29 % (12578)Time elapsed: 0.057 s
% 7.17/2.29 % (12578)Instructions burned: 182 (million)
% 7.17/2.29 % (12578)------------------------------
% 7.17/2.29 % (12578)------------------------------
% 7.17/2.29 % (12599)Instruction limit reached!
% 7.17/2.29 % (12599)------------------------------
% 7.17/2.29 % (12599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.17/2.29 % (12599)Termination reason: Unknown
% 7.17/2.29 % (12599)Termination phase: Function definition elimination
% 7.17/2.29
% 7.17/2.29 % (12599)Memory used [KB]: 2302
% 7.17/2.29 % (12599)Time elapsed: 0.025 s
% 7.17/2.29 % (12599)Instructions burned: 79 (million)
% 7.17/2.29 % (12599)------------------------------
% 7.17/2.29 % (12599)------------------------------
% 7.84/2.30 % (12591)Instruction limit reached!
% 7.84/2.30 % (12591)------------------------------
% 7.84/2.30 % (12591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.30 % (12591)Termination reason: Unknown
% 7.84/2.30 % (12591)Termination phase: Property scanning
% 7.84/2.30
% 7.84/2.30 % (12591)Memory used [KB]: 2814
% 7.84/2.30 % (12591)Time elapsed: 0.043 s
% 7.84/2.30 % (12591)Instructions burned: 155 (million)
% 7.84/2.30 % (12591)------------------------------
% 7.84/2.30 % (12591)------------------------------
% 7.84/2.30 % (12583)Instruction limit reached!
% 7.84/2.30 % (12583)------------------------------
% 7.84/2.30 % (12583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.30 % (12583)Termination reason: Unknown
% 7.84/2.30 % (12583)Termination phase: Saturation
% 7.84/2.30
% 7.84/2.30 % (12583)Memory used [KB]: 7419
% 7.84/2.30 % (12583)Time elapsed: 0.057 s
% 7.84/2.30 % (12583)Instructions burned: 182 (million)
% 7.84/2.30 % (12583)------------------------------
% 7.84/2.30 % (12583)------------------------------
% 7.84/2.30 % (12615)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_12084 for (2992ds/216Mi)
% 7.84/2.30 % (12616)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_12084 for (2992ds/114Mi)
% 7.84/2.31 % (12617)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_12084 for (2992ds/922Mi)
% 7.84/2.31 % (12619)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_12084 for (2992ds/182Mi)
% 7.84/2.32 % (12574)Instruction limit reached!
% 7.84/2.32 % (12574)------------------------------
% 7.84/2.32 % (12574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.32 % (12574)Termination reason: Unknown
% 7.84/2.32 % (12574)Termination phase: Saturation
% 7.84/2.32
% 7.84/2.32 % (12574)Memory used [KB]: 7931
% 7.84/2.32 % (12574)Time elapsed: 0.092 s
% 7.84/2.32 % (12574)Instructions burned: 297 (million)
% 7.84/2.32 % (12574)------------------------------
% 7.84/2.32 % (12574)------------------------------
% 7.84/2.33 % (12624)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_12084 for (2992ds/164Mi)
% 7.84/2.34 % (12616)Instruction limit reached!
% 7.84/2.34 % (12616)------------------------------
% 7.84/2.34 % (12616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.34 % (12616)Termination reason: Unknown
% 7.84/2.34 % (12616)Termination phase: Saturation
% 7.84/2.34
% 7.84/2.34 % (12616)Memory used [KB]: 6908
% 7.84/2.34 % (12616)Time elapsed: 0.035 s
% 7.84/2.34 % (12616)Instructions burned: 114 (million)
% 7.84/2.34 % (12616)------------------------------
% 7.84/2.34 % (12616)------------------------------
% 7.84/2.35 % (12625)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_12084 for (2992ds/50Mi)
% 7.84/2.35 % (12566)Instruction limit reached!
% 7.84/2.35 % (12566)------------------------------
% 7.84/2.35 % (12566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.35 % (12566)Termination reason: Unknown
% 7.84/2.35 % (12566)Termination phase: Saturation
% 7.84/2.35
% 7.84/2.35 % (12566)Memory used [KB]: 7931
% 7.84/2.35 % (12566)Time elapsed: 0.147 s
% 7.84/2.35 % (12566)Instructions burned: 460 (million)
% 7.84/2.35 % (12566)------------------------------
% 7.84/2.35 % (12566)------------------------------
% 7.84/2.36 % (12626)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_12084 for (2991ds/368Mi)
% 7.84/2.36 % (12625)Instruction limit reached!
% 7.84/2.36 % (12625)------------------------------
% 7.84/2.36 % (12625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.36 % (12625)Termination reason: Unknown
% 7.84/2.36 % (12625)Termination phase: Property scanning
% 7.84/2.36
% 7.84/2.36 % (12625)Memory used [KB]: 2302
% 7.84/2.36 % (12625)Time elapsed: 0.016 s
% 7.84/2.36 % (12625)Instructions burned: 53 (million)
% 7.84/2.36 % (12625)------------------------------
% 7.84/2.36 % (12625)------------------------------
% 7.84/2.36 % (12619)Instruction limit reached!
% 7.84/2.36 % (12619)------------------------------
% 7.84/2.36 % (12619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.36 % (12619)Termination reason: Unknown
% 7.84/2.36 % (12619)Termination phase: Saturation
% 7.84/2.36
% 7.84/2.36 % (12619)Memory used [KB]: 7291
% 7.84/2.36 % (12619)Time elapsed: 0.052 s
% 7.84/2.36 % (12619)Instructions burned: 185 (million)
% 7.84/2.36 % (12619)------------------------------
% 7.84/2.36 % (12619)------------------------------
% 7.84/2.36 % (12615)Instruction limit reached!
% 7.84/2.36 % (12615)------------------------------
% 7.84/2.36 % (12615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.36 % (12615)Termination reason: Unknown
% 7.84/2.36 % (12615)Termination phase: Saturation
% 7.84/2.36
% 7.84/2.36 % (12615)Memory used [KB]: 7547
% 7.84/2.36 % (12615)Time elapsed: 0.063 s
% 7.84/2.36 % (12615)Instructions burned: 217 (million)
% 7.84/2.36 % (12615)------------------------------
% 7.84/2.36 % (12615)------------------------------
% 7.84/2.37 % (12627)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_12084 for (2991ds/1021Mi)
% 7.84/2.37 % (12628)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_12084 for (2991ds/267Mi)
% 7.84/2.37 % (12629)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_12084 for (2991ds/204Mi)
% 7.84/2.37 % (12624)Instruction limit reached!
% 7.84/2.37 % (12624)------------------------------
% 7.84/2.37 % (12624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.37 % (12624)Termination reason: Unknown
% 7.84/2.37 % (12624)Termination phase: Saturation
% 7.84/2.37
% 7.84/2.37 % (12624)Memory used [KB]: 2814
% 7.84/2.37 % (12624)Time elapsed: 0.049 s
% 7.84/2.37 % (12624)Instructions burned: 166 (million)
% 7.84/2.37 % (12624)------------------------------
% 7.84/2.37 % (12624)------------------------------
% 7.84/2.38 % (12630)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_12084 for (2991ds/26Mi)
% 7.84/2.39 % (12630)Instruction limit reached!
% 7.84/2.39 % (12630)------------------------------
% 7.84/2.39 % (12630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.39 % (12630)Termination reason: Unknown
% 7.84/2.39 % (12630)Termination phase: shuffling
% 7.84/2.39
% 7.84/2.39 % (12630)Memory used [KB]: 2046
% 7.84/2.39 % (12630)Time elapsed: 0.009 s
% 7.84/2.39 % (12630)Instructions burned: 28 (million)
% 7.84/2.39 % (12630)------------------------------
% 7.84/2.39 % (12630)------------------------------
% 8.49/2.40 % (12631)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_12084 for (2991ds/53Mi)
% 8.49/2.42 % (12631)Instruction limit reached!
% 8.49/2.42 % (12631)------------------------------
% 8.49/2.42 % (12631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.49/2.42 % (12631)Termination reason: Unknown
% 8.49/2.42 % (12631)Termination phase: Property scanning
% 8.49/2.42
% 8.49/2.42 % (12631)Memory used [KB]: 2302
% 8.49/2.42 % (12631)Time elapsed: 0.016 s
% 8.49/2.42 % (12631)Instructions burned: 55 (million)
% 8.49/2.42 % (12631)------------------------------
% 8.49/2.42 % (12631)------------------------------
% 8.49/2.43 % (12632)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_12084 for (2991ds/4436Mi)
% 8.49/2.44 % (12629)Instruction limit reached!
% 8.49/2.44 % (12629)------------------------------
% 8.49/2.44 % (12629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.49/2.44 % (12629)Termination reason: Unknown
% 8.49/2.44 % (12629)Termination phase: Saturation
% 8.49/2.44
% 8.49/2.44 % (12629)Memory used [KB]: 7291
% 8.49/2.44 % (12629)Time elapsed: 0.064 s
% 8.49/2.44 % (12629)Instructions burned: 204 (million)
% 8.49/2.44 % (12629)------------------------------
% 8.49/2.44 % (12629)------------------------------
% 8.49/2.45 % (12633)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_12084 for (2991ds/1539Mi)
% 8.49/2.45 % (12628)Instruction limit reached!
% 8.49/2.45 % (12628)------------------------------
% 8.49/2.45 % (12628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.49/2.45 % (12628)Termination reason: Unknown
% 8.49/2.45 % (12628)Termination phase: Saturation
% 8.49/2.45
% 8.49/2.45 % (12628)Memory used [KB]: 7803
% 8.49/2.45 % (12628)Time elapsed: 0.080 s
% 8.49/2.45 % (12628)Instructions burned: 268 (million)
% 8.49/2.45 % (12628)------------------------------
% 8.49/2.45 % (12628)------------------------------
% 8.49/2.46 % (12634)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_12084 for (2990ds/408Mi)
% 8.49/2.48 % (12626)Instruction limit reached!
% 8.49/2.48 % (12626)------------------------------
% 8.49/2.48 % (12626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.49/2.48 % (12626)Termination reason: Unknown
% 8.49/2.48 % (12626)Termination phase: Saturation
% 8.49/2.48
% 8.49/2.48 % (12626)Memory used [KB]: 9210
% 8.49/2.48 % (12626)Time elapsed: 0.120 s
% 8.49/2.48 % (12626)Instructions burned: 368 (million)
% 8.49/2.48 % (12626)------------------------------
% 8.49/2.48 % (12626)------------------------------
% 8.49/2.49 % (12635)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_12084 for (2990ds/5205Mi)
% 8.80/2.54 % (12576)Instruction limit reached!
% 8.80/2.54 % (12576)------------------------------
% 8.80/2.54 % (12576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.54 % (12576)Termination reason: Unknown
% 8.80/2.54 % (12576)Termination phase: Saturation
% 8.80/2.54
% 8.80/2.54 % (12576)Memory used [KB]: 9722
% 8.80/2.54 % (12576)Time elapsed: 0.307 s
% 8.80/2.54 % (12576)Instructions burned: 989 (million)
% 8.80/2.54 % (12576)------------------------------
% 8.80/2.54 % (12576)------------------------------
% 8.80/2.55 % (12636)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_12084 for (2990ds/1913Mi)
% 8.80/2.59 % (12634)Instruction limit reached!
% 8.80/2.59 % (12634)------------------------------
% 8.80/2.59 % (12634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.59 % (12634)Termination reason: Unknown
% 8.80/2.59 % (12634)Termination phase: Saturation
% 8.80/2.59
% 8.80/2.59 % (12634)Memory used [KB]: 8443
% 8.80/2.59 % (12634)Time elapsed: 0.128 s
% 8.80/2.59 % (12634)Instructions burned: 410 (million)
% 8.80/2.59 % (12634)------------------------------
% 8.80/2.59 % (12634)------------------------------
% 8.80/2.59 % (12617)Instruction limit reached!
% 8.80/2.59 % (12617)------------------------------
% 8.80/2.59 % (12617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.59 % (12617)Termination reason: Unknown
% 8.80/2.59 % (12617)Termination phase: Saturation
% 8.80/2.59
% 8.80/2.59 % (12617)Memory used [KB]: 7803
% 8.80/2.59 % (12617)Time elapsed: 0.286 s
% 8.80/2.59 % (12617)Instructions burned: 924 (million)
% 8.80/2.59 % (12617)------------------------------
% 8.80/2.59 % (12617)------------------------------
% 8.80/2.60 % (12637)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_12084 for (2989ds/4350Mi)
% 9.54/2.60 % (12638)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_12084 for (2989ds/68Mi)
% 9.54/2.62 % (12638)Instruction limit reached!
% 9.54/2.62 % (12638)------------------------------
% 9.54/2.62 % (12638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.54/2.62 % (12638)Termination reason: Unknown
% 9.54/2.62 % (12638)Termination phase: Preprocessing 3
% 9.54/2.62
% 9.54/2.62 % (12638)Memory used [KB]: 2302
% 9.54/2.62 % (12638)Time elapsed: 0.022 s
% 9.54/2.62 % (12638)Instructions burned: 68 (million)
% 9.54/2.62 % (12638)------------------------------
% 9.54/2.62 % (12638)------------------------------
% 9.54/2.63 % (12639)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_12084 for (2989ds/358Mi)
% 9.54/2.68 % (12627)Instruction limit reached!
% 9.54/2.68 % (12627)------------------------------
% 9.54/2.68 % (12627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.54/2.68 % (12627)Termination reason: Unknown
% 9.54/2.68 % (12627)Termination phase: Saturation
% 9.54/2.68
% 9.54/2.68 % (12627)Memory used [KB]: 8699
% 9.54/2.68 % (12627)Time elapsed: 0.312 s
% 9.54/2.68 % (12627)Instructions burned: 1021 (million)
% 9.54/2.68 % (12627)------------------------------
% 9.54/2.68 % (12627)------------------------------
% 9.54/2.69 % (12640)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_12084 for (2988ds/31Mi)
% 9.90/2.70 % (12640)Instruction limit reached!
% 9.90/2.70 % (12640)------------------------------
% 9.90/2.70 % (12640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.90/2.70 % (12640)Termination reason: Unknown
% 9.90/2.70 % (12640)Termination phase: Property scanning
% 9.90/2.70
% 9.90/2.70 % (12640)Memory used [KB]: 2046
% 9.90/2.70 % (12640)Time elapsed: 0.012 s
% 9.90/2.70 % (12640)Instructions burned: 32 (million)
% 9.90/2.70 % (12640)------------------------------
% 9.90/2.70 % (12640)------------------------------
% 9.90/2.71 % (12641)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_12084 for (2988ds/279Mi)
% 9.90/2.74 % (12639)Instruction limit reached!
% 9.90/2.74 % (12639)------------------------------
% 9.90/2.74 % (12639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.90/2.74 % (12639)Termination reason: Unknown
% 9.90/2.74 % (12639)Termination phase: Saturation
% 9.90/2.74
% 9.90/2.74 % (12639)Memory used [KB]: 7547
% 9.90/2.74 % (12639)Time elapsed: 0.111 s
% 9.90/2.74 % (12639)Instructions burned: 358 (million)
% 9.90/2.74 % (12639)------------------------------
% 9.90/2.74 % (12639)------------------------------
% 9.90/2.75 % (12642)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_12084 for (2988ds/258Mi)
% 9.90/2.80 % (12641)Instruction limit reached!
% 9.90/2.80 % (12641)------------------------------
% 9.90/2.80 % (12641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.90/2.80 % (12641)Termination reason: Unknown
% 9.90/2.80 % (12641)Termination phase: Saturation
% 9.90/2.80
% 9.90/2.80 % (12641)Memory used [KB]: 8059
% 9.90/2.80 % (12641)Time elapsed: 0.085 s
% 9.90/2.80 % (12641)Instructions burned: 282 (million)
% 9.90/2.80 % (12641)------------------------------
% 9.90/2.80 % (12641)------------------------------
% 10.14/2.80 % (12643)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_12084 for (2987ds/26Mi)
% 10.14/2.81 % (12643)Instruction limit reached!
% 10.14/2.81 % (12643)------------------------------
% 10.14/2.81 % (12643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.14/2.81 % (12643)Termination reason: Unknown
% 10.14/2.81 % (12643)Termination phase: shuffling
% 10.14/2.81
% 10.14/2.81 % (12643)Memory used [KB]: 2046
% 10.14/2.81 % (12643)Time elapsed: 0.009 s
% 10.14/2.81 % (12643)Instructions burned: 27 (million)
% 10.14/2.81 % (12643)------------------------------
% 10.14/2.81 % (12643)------------------------------
% 10.14/2.82 % (12644)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_12084 for (2987ds/995Mi)
% 10.14/2.83 % (12642)Instruction limit reached!
% 10.14/2.83 % (12642)------------------------------
% 10.14/2.83 % (12642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.14/2.83 % (12642)Termination reason: Unknown
% 10.14/2.83 % (12642)Termination phase: Saturation
% 10.14/2.83
% 10.14/2.83 % (12642)Memory used [KB]: 7547
% 10.14/2.83 % (12642)Time elapsed: 0.081 s
% 10.14/2.83 % (12642)Instructions burned: 260 (million)
% 10.14/2.83 % (12642)------------------------------
% 10.14/2.83 % (12642)------------------------------
% 10.14/2.84 % (12645)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_12084 for (2987ds/373Mi)
% 10.24/2.92 % (12633)Instruction limit reached!
% 10.24/2.92 % (12633)------------------------------
% 10.24/2.92 % (12633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.24/2.92 % (12633)Termination reason: Unknown
% 10.24/2.92 % (12633)Termination phase: Saturation
% 10.24/2.92
% 10.24/2.92 % (12633)Memory used [KB]: 10490
% 10.24/2.92 % (12633)Time elapsed: 0.476 s
% 10.24/2.92 % (12633)Instructions burned: 1540 (million)
% 10.24/2.92 % (12633)------------------------------
% 10.24/2.92 % (12633)------------------------------
% 10.24/2.93 % (12646)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_12084 for (2986ds/253Mi)
% 10.24/2.96 % (12645)Instruction limit reached!
% 10.24/2.96 % (12645)------------------------------
% 10.24/2.96 % (12645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.24/2.96 % (12645)Termination reason: Unknown
% 10.24/2.96 % (12645)Termination phase: Saturation
% 10.24/2.96
% 10.24/2.96 % (12645)Memory used [KB]: 8315
% 10.24/2.96 % (12645)Time elapsed: 0.120 s
% 10.24/2.96 % (12645)Instructions burned: 373 (million)
% 10.24/2.96 % (12645)------------------------------
% 10.24/2.96 % (12645)------------------------------
% 10.24/2.97 % (12647)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_12084 for (2985ds/832Mi)
% 10.24/3.00 % (12646)Instruction limit reached!
% 10.24/3.00 % (12646)------------------------------
% 10.24/3.00 % (12646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.24/3.00 % (12646)Termination reason: Unknown
% 10.24/3.00 % (12646)Termination phase: Saturation
% 10.24/3.00
% 10.24/3.00 % (12646)Memory used [KB]: 7675
% 10.24/3.00 % (12646)Time elapsed: 0.071 s
% 10.24/3.00 % (12646)Instructions burned: 253 (million)
% 10.24/3.00 % (12646)------------------------------
% 10.24/3.00 % (12646)------------------------------
% 10.24/3.01 % (12648)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_12084 for (2985ds/668Mi)
% 10.24/3.02 % (12647)Refutation not found, incomplete strategy
% 10.24/3.02 % (12647)------------------------------
% 10.24/3.02 % (12647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.24/3.02 % (12647)Termination reason: Refutation not found, incomplete strategy
% 10.24/3.02
% 10.24/3.02
% 10.24/3.02 % (12647)Memory used [KB]: 7675
% 10.24/3.02 % (12647)Time elapsed: 0.051 s
% 10.24/3.02 % (12647)Instructions burned: 164 (million)
% 10.24/3.02 % (12647)------------------------------
% 10.24/3.02 % (12647)------------------------------
% 13.21/3.03 % (12649)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_12084 for (2985ds/40Mi)
% 13.21/3.04 % (12649)Instruction limit reached!
% 13.21/3.04 % (12649)------------------------------
% 13.21/3.04 % (12649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.21/3.04 % (12649)Termination reason: Unknown
% 13.21/3.04 % (12649)Termination phase: shuffling
% 13.21/3.04
% 13.21/3.04 % (12649)Memory used [KB]: 2174
% 13.21/3.04 % (12649)Time elapsed: 0.013 s
% 13.21/3.04 % (12649)Instructions burned: 41 (million)
% 13.21/3.04 % (12649)------------------------------
% 13.21/3.04 % (12649)------------------------------
% 13.21/3.05 % (12650)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_12084 for (2985ds/294Mi)
% 13.21/3.12 % (12644)Instruction limit reached!
% 13.21/3.12 % (12644)------------------------------
% 13.21/3.12 % (12644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.21/3.12 % (12644)Termination reason: Unknown
% 13.21/3.12 % (12644)Termination phase: Saturation
% 13.21/3.12
% 13.21/3.12 % (12644)Memory used [KB]: 9850
% 13.21/3.12 % (12644)Time elapsed: 0.298 s
% 13.21/3.12 % (12644)Instructions burned: 995 (million)
% 13.21/3.12 % (12644)------------------------------
% 13.21/3.12 % (12644)------------------------------
% 13.76/3.13 % (12651)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_12084 for (2984ds/187Mi)
% 13.76/3.14 % (12650)Instruction limit reached!
% 13.76/3.14 % (12650)------------------------------
% 13.76/3.14 % (12650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/3.14 % (12650)Termination reason: Unknown
% 13.76/3.14 % (12650)Termination phase: Saturation
% 13.76/3.14
% 13.76/3.14 % (12650)Memory used [KB]: 8059
% 13.76/3.14 % (12650)Time elapsed: 0.110 s
% 13.76/3.14 % (12650)Instructions burned: 294 (million)
% 13.76/3.14 % (12650)------------------------------
% 13.76/3.14 % (12650)------------------------------
% 13.76/3.15 % (12652)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_12084 for (2984ds/371Mi)
% 13.76/3.15 % (12636)Instruction limit reached!
% 13.76/3.15 % (12636)------------------------------
% 13.76/3.15 % (12636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/3.15 % (12636)Termination reason: Unknown
% 13.76/3.15 % (12636)Termination phase: Saturation
% 13.76/3.15
% 13.76/3.15 % (12636)Memory used [KB]: 7164
% 13.76/3.15 % (12636)Time elapsed: 0.603 s
% 13.76/3.15 % (12636)Instructions burned: 1915 (million)
% 13.76/3.15 % (12636)------------------------------
% 13.76/3.15 % (12636)------------------------------
% 13.76/3.16 % (12653)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_12084 for (2983ds/1827Mi)
% 13.76/3.19 % (12651)Instruction limit reached!
% 13.76/3.19 % (12651)------------------------------
% 13.76/3.19 % (12651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.76/3.19 % (12651)Termination reason: Unknown
% 13.76/3.19 % (12651)Termination phase: Saturation
% 13.76/3.19
% 13.76/3.19 % (12651)Memory used [KB]: 7419
% 13.76/3.19 % (12651)Time elapsed: 0.086 s
% 13.76/3.19 % (12651)Instructions burned: 189 (million)
% 13.76/3.19 % (12651)------------------------------
% 13.76/3.19 % (12651)------------------------------
% 14.19/3.20 % (12654)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_12084 for (2983ds/70Mi)
% 14.19/3.21 % (12648)Instruction limit reached!
% 14.19/3.21 % (12648)------------------------------
% 14.19/3.21 % (12648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.19/3.21 % (12648)Termination reason: Unknown
% 14.19/3.21 % (12648)Termination phase: Saturation
% 14.19/3.21
% 14.19/3.21 % (12648)Memory used [KB]: 14200
% 14.19/3.21 % (12648)Time elapsed: 0.200 s
% 14.19/3.21 % (12648)Instructions burned: 668 (million)
% 14.19/3.21 % (12648)------------------------------
% 14.19/3.21 % (12648)------------------------------
% 14.19/3.22 % (12654)Instruction limit reached!
% 14.19/3.22 % (12654)------------------------------
% 14.19/3.22 % (12654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.19/3.22 % (12654)Termination reason: Unknown
% 14.19/3.22 % (12654)Termination phase: Property scanning
% 14.19/3.22
% 14.19/3.22 % (12654)Memory used [KB]: 2302
% 14.19/3.22 % (12654)Time elapsed: 0.021 s
% 14.19/3.22 % (12654)Instructions burned: 71 (million)
% 14.19/3.22 % (12654)------------------------------
% 14.19/3.22 % (12654)------------------------------
% 14.19/3.22 % (12655)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_12084 for (2983ds/316Mi)
% 14.19/3.23 % (12656)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_12084 for (2983ds/932Mi)
% 14.19/3.25 % (12652)Refutation not found, non-redundant clauses discarded% (12652)------------------------------
% 14.19/3.25 % (12652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.19/3.25 % (12652)Termination reason: Refutation not found, non-redundant clauses discarded
% 14.19/3.25
% 14.19/3.25 % (12652)Memory used [KB]: 7931
% 14.19/3.25 % (12652)Time elapsed: 0.107 s
% 14.19/3.25 % (12652)Instructions burned: 334 (million)
% 14.19/3.25 % (12652)------------------------------
% 14.19/3.25 % (12652)------------------------------
% 14.19/3.27 % (12657)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_12084 for (2982ds/4714Mi)
% 14.83/3.31 % (12655)Instruction limit reached!
% 14.83/3.31 % (12655)------------------------------
% 14.83/3.31 % (12655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.83/3.31 % (12655)Termination reason: Unknown
% 14.83/3.31 % (12655)Termination phase: Saturation
% 14.83/3.31
% 14.83/3.31 % (12655)Memory used [KB]: 8187
% 14.83/3.31 % (12655)Time elapsed: 0.090 s
% 14.83/3.31 % (12655)Instructions burned: 318 (million)
% 14.83/3.31 % (12655)------------------------------
% 14.83/3.31 % (12655)------------------------------
% 14.83/3.32 % (12658)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_12084 for (2982ds/8250Mi)
% 15.54/3.50 % (12656)Instruction limit reached!
% 15.54/3.50 % (12656)------------------------------
% 15.54/3.50 % (12656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/3.50 % (12656)Termination reason: Unknown
% 15.54/3.50 % (12656)Termination phase: Saturation
% 15.54/3.50
% 15.54/3.50 % (12656)Memory used [KB]: 10362
% 15.54/3.50 % (12656)Time elapsed: 0.273 s
% 15.54/3.50 % (12656)Instructions burned: 933 (million)
% 15.54/3.50 % (12656)------------------------------
% 15.54/3.50 % (12656)------------------------------
% 15.54/3.51 % (12659)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_12084 for (2980ds/770Mi)
% 15.54/3.53 % (12659)Refutation not found, incomplete strategy
% 15.54/3.53 % (12659)------------------------------
% 15.54/3.53 % (12659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/3.53 % (12659)Termination reason: Refutation not found, incomplete strategy
% 15.54/3.53
% 15.54/3.53
% 15.54/3.53 % (12659)Memory used [KB]: 6780
% 15.54/3.53 % (12659)Time elapsed: 0.023 s
% 15.54/3.53 % (12659)Instructions burned: 69 (million)
% 15.54/3.53 % (12659)------------------------------
% 15.54/3.53 % (12659)------------------------------
% 15.54/3.54 % (12660)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_12084 for (2980ds/794Mi)
% 16.48/3.73 % (12653)Instruction limit reached!
% 16.48/3.73 % (12653)------------------------------
% 16.48/3.73 % (12653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.48/3.73 % (12653)Termination reason: Unknown
% 16.48/3.73 % (12653)Termination phase: Saturation
% 16.48/3.73
% 16.48/3.73 % (12653)Memory used [KB]: 10746
% 16.48/3.73 % (12653)Time elapsed: 0.570 s
% 16.48/3.73 % (12653)Instructions burned: 1828 (million)
% 16.48/3.73 % (12653)------------------------------
% 16.48/3.73 % (12653)------------------------------
% 16.48/3.74 % (12661)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_12084 for (2978ds/464Mi)
% 16.48/3.77 % (12632)Instruction limit reached!
% 16.48/3.77 % (12632)------------------------------
% 16.48/3.77 % (12632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.48/3.77 % (12632)Termination reason: Unknown
% 16.48/3.77 % (12632)Termination phase: Saturation
% 16.48/3.77
% 16.48/3.77 % (12632)Memory used [KB]: 10490
% 16.48/3.77 % (12632)Time elapsed: 1.347 s
% 16.48/3.77 % (12632)Instructions burned: 4436 (million)
% 16.48/3.77 % (12632)------------------------------
% 16.48/3.77 % (12632)------------------------------
% 16.48/3.78 % (12662)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_12084 for (2977ds/1376Mi)
% 17.34/3.80 % (12660)Instruction limit reached!
% 17.34/3.80 % (12660)------------------------------
% 17.34/3.80 % (12660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.34/3.80 % (12660)Termination reason: Unknown
% 17.34/3.80 % (12660)Termination phase: Saturation
% 17.34/3.80
% 17.34/3.80 % (12660)Memory used [KB]: 5373
% 17.34/3.80 % (12660)Time elapsed: 0.256 s
% 17.34/3.80 % (12660)Instructions burned: 794 (million)
% 17.34/3.80 % (12660)------------------------------
% 17.34/3.80 % (12660)------------------------------
% 17.34/3.81 % (12663)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_12084 for (2977ds/906Mi)
% 17.34/3.89 % (12661)Instruction limit reached!
% 17.34/3.89 % (12661)------------------------------
% 17.34/3.89 % (12661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.34/3.89 % (12661)Termination reason: Unknown
% 17.34/3.89 % (12661)Termination phase: Saturation
% 17.34/3.89
% 17.34/3.89 % (12661)Memory used [KB]: 8059
% 17.34/3.89 % (12661)Time elapsed: 0.147 s
% 17.34/3.89 % (12661)Instructions burned: 466 (million)
% 17.34/3.89 % (12661)------------------------------
% 17.34/3.89 % (12661)------------------------------
% 17.97/3.90 % (12664)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_12084 for (2976ds/434Mi)
% 17.97/3.92 % (12664)Refutation not found, incomplete strategy
% 17.97/3.92 % (12664)------------------------------
% 17.97/3.92 % (12664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.97/3.92 % (12664)Termination reason: Refutation not found, incomplete strategy
% 17.97/3.92
% 17.97/3.92
% 17.97/3.92 % (12664)Memory used [KB]: 6908
% 17.97/3.92 % (12664)Time elapsed: 0.026 s
% 17.97/3.92 % (12664)Instructions burned: 80 (million)
% 17.97/3.92 % (12664)------------------------------
% 17.97/3.92 % (12664)------------------------------
% 17.97/3.93 % (12665)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_12084 for (2976ds/865Mi)
% 17.97/3.96 % (12637)Instruction limit reached!
% 17.97/3.96 % (12637)------------------------------
% 17.97/3.96 % (12637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.97/3.96 % (12637)Termination reason: Unknown
% 17.97/3.96 % (12637)Termination phase: Saturation
% 17.97/3.96
% 17.97/3.96 % (12637)Memory used [KB]: 13688
% 17.97/3.96 % (12637)Time elapsed: 1.366 s
% 17.97/3.96 % (12637)Instructions burned: 4351 (million)
% 17.97/3.96 % (12637)------------------------------
% 17.97/3.96 % (12637)------------------------------
% 17.97/3.97 % (12666)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_12084 for (2975ds/593Mi)
% 17.97/4.01 % (12635)Instruction limit reached!
% 17.97/4.01 % (12635)------------------------------
% 17.97/4.01 % (12635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.97/4.01 % (12635)Termination reason: Unknown
% 17.97/4.01 % (12635)Termination phase: Saturation
% 17.97/4.01
% 17.97/4.01 % (12635)Memory used [KB]: 16502
% 17.97/4.01 % (12635)Time elapsed: 1.525 s
% 17.97/4.01 % (12635)Instructions burned: 5206 (million)
% 17.97/4.01 % (12635)------------------------------
% 17.97/4.01 % (12635)------------------------------
% 17.97/4.02 % (12667)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_12084 for (2975ds/443Mi)
% 20.24/4.12 % (12663)Instruction limit reached!
% 20.24/4.12 % (12663)------------------------------
% 20.24/4.12 % (12663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.24/4.12 % (12663)Termination reason: Unknown
% 20.24/4.12 % (12663)Termination phase: Saturation
% 20.24/4.12
% 20.24/4.12 % (12663)Memory used [KB]: 10490
% 20.24/4.12 % (12663)Time elapsed: 0.314 s
% 20.24/4.12 % (12663)Instructions burned: 906 (million)
% 20.24/4.12 % (12663)------------------------------
% 20.24/4.12 % (12663)------------------------------
% 20.85/4.13 % (12668)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_12084 for (2974ds/594Mi)
% 20.85/4.15 % (12666)Instruction limit reached!
% 20.85/4.15 % (12666)------------------------------
% 20.85/4.15 % (12666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.85/4.15 % (12666)Termination reason: Unknown
% 20.85/4.15 % (12666)Termination phase: Saturation
% 20.85/4.15
% 20.85/4.15 % (12666)Memory used [KB]: 9338
% 20.85/4.15 % (12666)Time elapsed: 0.177 s
% 20.85/4.15 % (12666)Instructions burned: 594 (million)
% 20.85/4.15 % (12666)------------------------------
% 20.85/4.15 % (12666)------------------------------
% 20.85/4.16 % (12669)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_12084 for (2973ds/327Mi)
% 20.85/4.17 % (12667)Instruction limit reached!
% 20.85/4.17 % (12667)------------------------------
% 20.85/4.17 % (12667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.85/4.17 % (12667)Termination reason: Unknown
% 20.85/4.17 % (12667)Termination phase: Saturation
% 20.85/4.17
% 20.85/4.17 % (12667)Memory used [KB]: 8187
% 20.85/4.17 % (12667)Time elapsed: 0.165 s
% 20.85/4.17 % (12667)Instructions burned: 444 (million)
% 20.85/4.17 % (12667)------------------------------
% 20.85/4.17 % (12667)------------------------------
% 20.85/4.17 % (12670)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_12084 for (2973ds/5411Mi)
% 20.85/4.18 % (12665)Instruction limit reached!
% 20.85/4.18 % (12665)------------------------------
% 20.85/4.18 % (12665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.85/4.18 % (12665)Termination reason: Unknown
% 20.85/4.18 % (12665)Termination phase: Saturation
% 20.85/4.18
% 20.85/4.18 % (12665)Memory used [KB]: 9338
% 20.85/4.18 % (12665)Time elapsed: 0.246 s
% 20.85/4.18 % (12665)Instructions burned: 866 (million)
% 20.85/4.18 % (12665)------------------------------
% 20.85/4.18 % (12665)------------------------------
% 20.85/4.19 % (12671)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_12084 for (2973ds/1762Mi)
% 21.34/4.20 % (12670)Refutation not found, incomplete strategy
% 21.34/4.20 % (12670)------------------------------
% 21.34/4.20 % (12670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.34/4.20 % (12670)Termination reason: Refutation not found, incomplete strategy
% 21.34/4.20
% 21.34/4.20
% 21.34/4.20 % (12670)Memory used [KB]: 6908
% 21.34/4.20 % (12670)Time elapsed: 0.025 s
% 21.34/4.20 % (12670)Instructions burned: 78 (million)
% 21.34/4.20 % (12670)------------------------------
% 21.34/4.20 % (12670)------------------------------
% 21.34/4.20 % (12662)Instruction limit reached!
% 21.34/4.20 % (12662)------------------------------
% 21.34/4.20 % (12662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.34/4.20 % (12662)Termination reason: Unknown
% 21.34/4.20 % (12662)Termination phase: Saturation
% 21.34/4.20
% 21.34/4.20 % (12662)Memory used [KB]: 14456
% 21.34/4.20 % (12662)Time elapsed: 0.420 s
% 21.34/4.20 % (12662)Instructions burned: 1378 (million)
% 21.34/4.20 % (12662)------------------------------
% 21.34/4.20 % (12662)------------------------------
% 21.34/4.21 % (12672)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_12084 for (2973ds/96Mi)
% 21.34/4.21 % (12673)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_12084 for (2973ds/503Mi)
% 21.34/4.24 % (12672)Instruction limit reached!
% 21.34/4.24 % (12672)------------------------------
% 21.34/4.24 % (12672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.34/4.24 % (12672)Termination reason: Unknown
% 21.34/4.24 % (12672)Termination phase: Preprocessing 3
% 21.34/4.24
% 21.34/4.24 % (12672)Memory used [KB]: 2814
% 21.34/4.24 % (12672)Time elapsed: 0.029 s
% 21.34/4.24 % (12672)Instructions burned: 96 (million)
% 21.34/4.24 % (12672)------------------------------
% 21.34/4.24 % (12672)------------------------------
% 21.34/4.25 % (12674)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_12084 for (2973ds/90Mi)
% 21.34/4.26 % (12669)Instruction limit reached!
% 21.34/4.26 % (12669)------------------------------
% 21.34/4.26 % (12669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.34/4.26 % (12669)Termination reason: Unknown
% 21.34/4.26 % (12669)Termination phase: Saturation
% 21.34/4.26
% 21.34/4.26 % (12669)Memory used [KB]: 7931
% 21.34/4.26 % (12669)Time elapsed: 0.107 s
% 21.34/4.26 % (12669)Instructions burned: 327 (million)
% 21.34/4.26 % (12669)------------------------------
% 21.34/4.26 % (12669)------------------------------
% 21.34/4.27 % (12675)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_12084 for (2972ds/593Mi)
% 21.34/4.27 % (12674)Instruction limit reached!
% 21.34/4.27 % (12674)------------------------------
% 21.34/4.27 % (12674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.34/4.27 % (12674)Termination reason: Unknown
% 21.34/4.27 % (12674)Termination phase: Property scanning
% 21.34/4.27
% 21.34/4.27 % (12674)Memory used [KB]: 2430
% 21.34/4.27 % (12674)Time elapsed: 0.029 s
% 21.34/4.27 % (12674)Instructions burned: 92 (million)
% 21.34/4.27 % (12674)------------------------------
% 21.34/4.27 % (12674)------------------------------
% 21.34/4.28 % (12676)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_12084 for (2972ds/1512Mi)
% 21.80/4.32 % (12668)Instruction limit reached!
% 21.80/4.32 % (12668)------------------------------
% 21.80/4.32 % (12668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.80/4.32 % (12668)Termination reason: Unknown
% 21.80/4.32 % (12668)Termination phase: Saturation
% 21.80/4.32
% 21.80/4.32 % (12668)Memory used [KB]: 8699
% 21.80/4.32 % (12668)Time elapsed: 0.192 s
% 21.80/4.32 % (12668)Instructions burned: 594 (million)
% 21.80/4.32 % (12668)------------------------------
% 21.80/4.32 % (12668)------------------------------
% 21.80/4.33 % (12677)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_12084 for (2972ds/569Mi)
% 21.80/4.34 % (12676)Refutation not found, incomplete strategy
% 21.80/4.34 % (12676)------------------------------
% 21.80/4.34 % (12676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.80/4.34 % (12676)Termination reason: Refutation not found, incomplete strategy
% 21.80/4.34
% 21.80/4.34
% 21.80/4.34 % (12676)Memory used [KB]: 7803
% 21.80/4.34 % (12676)Time elapsed: 0.055 s
% 21.80/4.34 % (12676)Instructions burned: 177 (million)
% 21.80/4.34 % (12676)------------------------------
% 21.80/4.34 % (12676)------------------------------
% 21.80/4.35 % (12678)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_12084 for (2972ds/501Mi)
% 21.80/4.37 % (12673)Instruction limit reached!
% 21.80/4.37 % (12673)------------------------------
% 21.80/4.37 % (12673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.80/4.37 % (12673)Termination reason: Unknown
% 21.80/4.37 % (12673)Termination phase: Saturation
% 21.80/4.37
% 21.80/4.37 % (12673)Memory used [KB]: 7931
% 21.80/4.37 % (12673)Time elapsed: 0.164 s
% 21.80/4.37 % (12673)Instructions burned: 504 (million)
% 21.80/4.37 % (12673)------------------------------
% 21.80/4.37 % (12673)------------------------------
% 21.80/4.38 % (12679)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_12084 for (2971ds/562Mi)
% 22.43/4.46 % (12675)Instruction limit reached!
% 22.43/4.46 % (12675)------------------------------
% 22.43/4.46 % (12675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.43/4.46 % (12675)Termination reason: Unknown
% 22.43/4.46 % (12675)Termination phase: Saturation
% 22.43/4.46
% 22.43/4.46 % (12675)Memory used [KB]: 8699
% 22.43/4.46 % (12675)Time elapsed: 0.193 s
% 22.43/4.46 % (12675)Instructions burned: 595 (million)
% 22.43/4.46 % (12675)------------------------------
% 22.43/4.46 % (12675)------------------------------
% 22.43/4.48 % (12680)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_12084 for (2970ds/406Mi)
% 22.82/4.50 % (12677)Instruction limit reached!
% 22.82/4.50 % (12677)------------------------------
% 22.82/4.50 % (12677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.82/4.50 % (12677)Termination reason: Unknown
% 22.82/4.50 % (12677)Termination phase: Saturation
% 22.82/4.50
% 22.82/4.50 % (12677)Memory used [KB]: 8827
% 22.82/4.50 % (12677)Time elapsed: 0.169 s
% 22.82/4.50 % (12677)Instructions burned: 569 (million)
% 22.82/4.50 % (12677)------------------------------
% 22.82/4.50 % (12677)------------------------------
% 22.82/4.51 % (12678)Instruction limit reached!
% 22.82/4.51 % (12678)------------------------------
% 22.82/4.51 % (12678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.82/4.51 % (12678)Termination reason: Unknown
% 22.82/4.51 % (12678)Termination phase: Saturation
% 22.82/4.51
% 22.82/4.51 % (12678)Memory used [KB]: 8827
% 22.82/4.51 % (12678)Time elapsed: 0.158 s
% 22.82/4.51 % (12678)Instructions burned: 502 (million)
% 22.82/4.51 % (12678)------------------------------
% 22.82/4.51 % (12678)------------------------------
% 22.82/4.51 % (12681)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_12084 for (2970ds/582Mi)
% 22.82/4.52 % (12682)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_12084 for (2970ds/456Mi)
% 22.82/4.56 % (12679)Instruction limit reached!
% 22.82/4.56 % (12679)------------------------------
% 22.82/4.56 % (12679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.82/4.56 % (12679)Termination reason: Unknown
% 22.82/4.56 % (12679)Termination phase: Saturation
% 22.82/4.56
% 22.82/4.56 % (12679)Memory used [KB]: 8059
% 22.82/4.56 % (12679)Time elapsed: 0.174 s
% 22.82/4.56 % (12679)Instructions burned: 564 (million)
% 22.82/4.56 % (12679)------------------------------
% 22.82/4.56 % (12679)------------------------------
% 22.82/4.57 % (12683)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_12084 for (2969ds/393Mi)
% 23.56/4.60 % (12680)Instruction limit reached!
% 23.56/4.60 % (12680)------------------------------
% 23.56/4.60 % (12680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.60 % (12680)Termination reason: Unknown
% 23.56/4.60 % (12680)Termination phase: Saturation
% 23.56/4.60
% 23.56/4.60 % (12680)Memory used [KB]: 7931
% 23.56/4.60 % (12680)Time elapsed: 0.131 s
% 23.56/4.60 % (12680)Instructions burned: 408 (million)
% 23.56/4.60 % (12680)------------------------------
% 23.56/4.60 % (12680)------------------------------
% 23.56/4.61 % (12684)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_12084 for (2969ds/1335Mi)
% 23.56/4.66 % (12682)Instruction limit reached!
% 23.56/4.66 % (12682)------------------------------
% 23.56/4.66 % (12682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.66 % (12682)Termination reason: Unknown
% 23.56/4.66 % (12682)Termination phase: Saturation
% 23.56/4.66
% 23.56/4.66 % (12682)Memory used [KB]: 8571
% 23.56/4.66 % (12682)Time elapsed: 0.142 s
% 23.56/4.66 % (12682)Instructions burned: 457 (million)
% 23.56/4.66 % (12682)------------------------------
% 23.56/4.66 % (12682)------------------------------
% 23.56/4.66 % (12657)Instruction limit reached!
% 23.56/4.66 % (12657)------------------------------
% 23.56/4.66 % (12657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.66 % (12657)Termination reason: Unknown
% 23.56/4.66 % (12657)Termination phase: Saturation
% 23.56/4.66
% 23.56/4.66 % (12657)Memory used [KB]: 20468
% 23.56/4.66 % (12657)Time elapsed: 1.399 s
% 23.56/4.66 % (12657)Instructions burned: 4715 (million)
% 23.56/4.66 % (12657)------------------------------
% 23.56/4.66 % (12657)------------------------------
% 23.56/4.67 % (12685)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_12084 for (2968ds/3373Mi)
% 23.56/4.67 % (12686)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_12084 for (2968ds/474Mi)
% 23.56/4.68 % (12683)Instruction limit reached!
% 23.56/4.68 % (12683)------------------------------
% 23.56/4.68 % (12683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.68 % (12683)Termination reason: Unknown
% 23.56/4.68 % (12683)Termination phase: Saturation
% 23.56/4.68
% 23.56/4.68 % (12683)Memory used [KB]: 7803
% 23.56/4.68 % (12683)Time elapsed: 0.112 s
% 23.56/4.68 % (12683)Instructions burned: 393 (million)
% 23.56/4.68 % (12683)------------------------------
% 23.56/4.68 % (12683)------------------------------
% 23.56/4.69 % (12687)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_12084 for (2968ds/157Mi)
% 23.56/4.70 % (12681)Instruction limit reached!
% 23.56/4.70 % (12681)------------------------------
% 23.56/4.70 % (12681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.70 % (12681)Termination reason: Unknown
% 23.56/4.70 % (12681)Termination phase: Saturation
% 23.56/4.70
% 23.56/4.70 % (12681)Memory used [KB]: 9466
% 23.56/4.70 % (12681)Time elapsed: 0.188 s
% 23.56/4.70 % (12681)Instructions burned: 582 (million)
% 23.56/4.70 % (12681)------------------------------
% 23.56/4.70 % (12681)------------------------------
% 24.33/4.71 % (12688)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_12084 for (2968ds/590Mi)
% 24.33/4.73 % (12687)Instruction limit reached!
% 24.33/4.73 % (12687)------------------------------
% 24.33/4.73 % (12687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.33/4.73 % (12687)Termination reason: Unknown
% 24.33/4.73 % (12687)Termination phase: Property scanning
% 24.33/4.73
% 24.33/4.73 % (12687)Memory used [KB]: 2814
% 24.33/4.73 % (12687)Time elapsed: 0.044 s
% 24.33/4.73 % (12687)Instructions burned: 159 (million)
% 24.33/4.73 % (12687)------------------------------
% 24.33/4.73 % (12687)------------------------------
% 24.33/4.74 % (12671)Instruction limit reached!
% 24.33/4.74 % (12671)------------------------------
% 24.33/4.74 % (12671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.33/4.74 % (12671)Termination reason: Unknown
% 24.33/4.74 % (12671)Termination phase: Saturation
% 24.33/4.74
% 24.33/4.74 % (12671)Memory used [KB]: 14072
% 24.33/4.74 % (12671)Time elapsed: 0.553 s
% 24.33/4.74 % (12671)Instructions burned: 1765 (million)
% 24.33/4.74 % (12671)------------------------------
% 24.33/4.74 % (12671)------------------------------
% 24.33/4.74 % (12689)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_12084 for (2968ds/104Mi)
% 24.33/4.75 % (12690)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_12084 for (2968ds/414Mi)
% 24.33/4.77 % (12689)Instruction limit reached!
% 24.33/4.77 % (12689)------------------------------
% 24.33/4.77 % (12689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.33/4.77 % (12689)Termination reason: Unknown
% 24.33/4.77 % (12689)Termination phase: Saturation
% 24.33/4.77
% 24.33/4.77 % (12689)Memory used [KB]: 2558
% 24.33/4.77 % (12689)Time elapsed: 0.032 s
% 24.33/4.77 % (12689)Instructions burned: 106 (million)
% 24.33/4.77 % (12689)------------------------------
% 24.33/4.77 % (12689)------------------------------
% 24.33/4.78 % (12691)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_12084 for (2967ds/715Mi)
% 25.09/4.82 % (12686)Instruction limit reached!
% 25.09/4.82 % (12686)------------------------------
% 25.09/4.82 % (12686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.09/4.82 % (12686)Termination reason: Unknown
% 25.09/4.82 % (12686)Termination phase: Saturation
% 25.09/4.82
% 25.09/4.82 % (12686)Memory used [KB]: 8571
% 25.09/4.82 % (12686)Time elapsed: 0.146 s
% 25.09/4.82 % (12686)Instructions burned: 476 (million)
% 25.09/4.82 % (12686)------------------------------
% 25.09/4.82 % (12686)------------------------------
% 25.09/4.83 % (12692)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_12084 for (2967ds/961Mi)
% 25.09/4.87 % (12690)Instruction limit reached!
% 25.09/4.87 % (12690)------------------------------
% 25.09/4.87 % (12690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.09/4.87 % (12690)Termination reason: Unknown
% 25.09/4.87 % (12690)Termination phase: Saturation
% 25.09/4.87
% 25.09/4.87 % (12690)Memory used [KB]: 7931
% 25.09/4.87 % (12690)Time elapsed: 0.120 s
% 25.09/4.87 % (12690)Instructions burned: 414 (million)
% 25.09/4.87 % (12690)------------------------------
% 25.09/4.87 % (12690)------------------------------
% 25.09/4.88 % (12693)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_12084 for (2966ds/1213Mi)
% 25.09/4.89 % (12688)Instruction limit reached!
% 25.09/4.89 % (12688)------------------------------
% 25.09/4.89 % (12688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.09/4.89 % (12688)Termination reason: Unknown
% 25.09/4.89 % (12688)Termination phase: Saturation
% 25.09/4.89
% 25.09/4.89 % (12688)Memory used [KB]: 8187
% 25.09/4.89 % (12688)Time elapsed: 0.183 s
% 25.09/4.89 % (12688)Instructions burned: 590 (million)
% 25.09/4.89 % (12688)------------------------------
% 25.09/4.89 % (12688)------------------------------
% 25.66/4.90 % (12694)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_12084 for (2966ds/1979Mi)
% 25.66/4.97 % (12684)Refutation not found, non-redundant clauses discarded% (12684)------------------------------
% 25.66/4.97 % (12684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.66/4.97 % (12684)Termination reason: Refutation not found, non-redundant clauses discarded
% 25.66/4.97
% 25.66/4.97 % (12684)Memory used [KB]: 9338
% 25.66/4.97 % (12684)Time elapsed: 0.361 s
% 25.66/4.97 % (12684)Instructions burned: 1178 (million)
% 25.66/4.97 % (12684)------------------------------
% 25.66/4.97 % (12684)------------------------------
% 25.66/4.99 % (12695)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_12084 for (2965ds/481Mi)
% 25.66/5.01 % (12691)Instruction limit reached!
% 25.66/5.01 % (12691)------------------------------
% 25.66/5.01 % (12691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.66/5.01 % (12691)Termination reason: Unknown
% 25.66/5.01 % (12691)Termination phase: Saturation
% 25.66/5.01
% 25.66/5.01 % (12691)Memory used [KB]: 4605
% 25.66/5.01 % (12691)Time elapsed: 0.255 s
% 25.66/5.01 % (12691)Instructions burned: 716 (million)
% 25.66/5.01 % (12691)------------------------------
% 25.66/5.01 % (12691)------------------------------
% 25.66/5.02 % (12696)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_12084 for (2965ds/783Mi)
% 27.89/5.13 % (12692)Instruction limit reached!
% 27.89/5.13 % (12692)------------------------------
% 27.89/5.13 % (12692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.89/5.13 % (12692)Termination reason: Unknown
% 27.89/5.13 % (12692)Termination phase: Saturation
% 27.89/5.13
% 27.89/5.13 % (12692)Memory used [KB]: 8443
% 27.89/5.13 % (12692)Time elapsed: 0.322 s
% 27.89/5.13 % (12692)Instructions burned: 963 (million)
% 27.89/5.13 % (12692)------------------------------
% 27.89/5.13 % (12692)------------------------------
% 27.89/5.13 % (12695)Instruction limit reached!
% 27.89/5.13 % (12695)------------------------------
% 27.89/5.13 % (12695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.89/5.13 % (12695)Termination reason: Unknown
% 27.89/5.13 % (12695)Termination phase: Saturation
% 27.89/5.13
% 27.89/5.13 % (12695)Memory used [KB]: 8571
% 27.89/5.13 % (12695)Time elapsed: 0.167 s
% 27.89/5.13 % (12695)Instructions burned: 482 (million)
% 27.89/5.13 % (12695)------------------------------
% 27.89/5.13 % (12695)------------------------------
% 27.89/5.14 % (12697)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_12084 for (2964ds/432Mi)
% 27.89/5.14 % (12698)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_12084 for (2964ds/1670Mi)
% 28.20/5.26 % (12693)Instruction limit reached!
% 28.20/5.26 % (12693)------------------------------
% 28.20/5.26 % (12693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.20/5.26 % (12693)Termination reason: Unknown
% 28.20/5.26 % (12693)Termination phase: Saturation
% 28.20/5.26
% 28.20/5.26 % (12693)Memory used [KB]: 8955
% 28.20/5.26 % (12693)Time elapsed: 0.407 s
% 28.20/5.26 % (12693)Instructions burned: 1213 (million)
% 28.20/5.26 % (12693)------------------------------
% 28.20/5.26 % (12693)------------------------------
% 28.20/5.27 % (12696)Instruction limit reached!
% 28.20/5.27 % (12696)------------------------------
% 28.20/5.27 % (12696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.20/5.27 % (12696)Termination reason: Unknown
% 28.20/5.27 % (12696)Termination phase: Saturation
% 28.20/5.27
% 28.20/5.27 % (12696)Memory used [KB]: 8059
% 28.20/5.27 % (12696)Time elapsed: 0.246 s
% 28.20/5.27 % (12696)Instructions burned: 785 (million)
% 28.20/5.27 % (12696)------------------------------
% 28.20/5.27 % (12696)------------------------------
% 28.20/5.27 % (12699)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_12084 for (2962ds/90Mi)
% 28.20/5.28 % (12700)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_12084 for (2962ds/346Mi)
% 28.20/5.28 % (12697)Instruction limit reached!
% 28.20/5.28 % (12697)------------------------------
% 28.20/5.28 % (12697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.20/5.28 % (12697)Termination reason: Unknown
% 28.20/5.28 % (12697)Termination phase: Saturation
% 28.20/5.28
% 28.20/5.28 % (12697)Memory used [KB]: 8187
% 28.20/5.28 % (12697)Time elapsed: 0.143 s
% 28.20/5.28 % (12697)Instructions burned: 434 (million)
% 28.20/5.28 % (12697)------------------------------
% 28.20/5.28 % (12697)------------------------------
% 28.20/5.29 % (12701)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_12084 for (2962ds/401Mi)
% 28.98/5.30 % (12699)Instruction limit reached!
% 28.98/5.30 % (12699)------------------------------
% 28.98/5.30 % (12699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.98/5.30 % (12699)Termination reason: Unknown
% 28.98/5.30 % (12699)Termination phase: Property scanning
% 28.98/5.30
% 28.98/5.30 % (12699)Memory used [KB]: 2302
% 28.98/5.30 % (12699)Time elapsed: 0.029 s
% 28.98/5.30 % (12699)Instructions burned: 93 (million)
% 28.98/5.30 % (12699)------------------------------
% 28.98/5.30 % (12699)------------------------------
% 28.98/5.31 % (12702)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_12084 for (2962ds/6454Mi)
% 28.98/5.38 % (12700)Instruction limit reached!
% 28.98/5.38 % (12700)------------------------------
% 28.98/5.38 % (12700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.98/5.38 % (12700)Termination reason: Unknown
% 28.98/5.38 % (12700)Termination phase: Saturation
% 28.98/5.38
% 28.98/5.38 % (12700)Memory used [KB]: 8059
% 28.98/5.38 % (12700)Time elapsed: 0.104 s
% 28.98/5.38 % (12700)Instructions burned: 347 (million)
% 28.98/5.38 % (12700)------------------------------
% 28.98/5.38 % (12700)------------------------------
% 28.98/5.39 % (12703)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_12084 for (2961ds/283Mi)
% 29.44/5.41 % (12701)Instruction limit reached!
% 29.44/5.41 % (12701)------------------------------
% 29.44/5.41 % (12701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.44/5.41 % (12701)Termination reason: Unknown
% 29.44/5.41 % (12701)Termination phase: Saturation
% 29.44/5.41
% 29.44/5.41 % (12701)Memory used [KB]: 8827
% 29.44/5.41 % (12701)Time elapsed: 0.118 s
% 29.44/5.41 % (12701)Instructions burned: 402 (million)
% 29.44/5.41 % (12701)------------------------------
% 29.44/5.41 % (12701)------------------------------
% 29.44/5.42 % (12704)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_12084 for (2961ds/865Mi)
% 29.44/5.48 % (12703)Instruction limit reached!
% 29.44/5.48 % (12703)------------------------------
% 29.44/5.48 % (12703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.44/5.48 % (12703)Termination reason: Unknown
% 29.44/5.48 % (12703)Termination phase: Saturation
% 29.44/5.48
% 29.44/5.48 % (12703)Memory used [KB]: 7803
% 29.44/5.48 % (12703)Time elapsed: 0.094 s
% 29.44/5.48 % (12703)Instructions burned: 283 (million)
% 29.44/5.48 % (12703)------------------------------
% 29.44/5.48 % (12703)------------------------------
% 29.44/5.49 % (12705)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_12084 for (2960ds/4528Mi)
% 29.97/5.51 % (12705)Refutation not found, incomplete strategy
% 29.97/5.51 % (12705)------------------------------
% 29.97/5.51 % (12705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.97/5.51 % (12705)Termination reason: Refutation not found, incomplete strategy
% 29.97/5.51
% 29.97/5.51
% 29.97/5.51 % (12705)Memory used [KB]: 2430
% 29.97/5.51 % (12705)Time elapsed: 0.022 s
% 29.97/5.51 % (12705)Instructions burned: 67 (million)
% 29.97/5.51 % (12705)------------------------------
% 29.97/5.51 % (12705)------------------------------
% 29.97/5.52 % (12694)Instruction limit reached!
% 29.97/5.52 % (12694)------------------------------
% 29.97/5.52 % (12694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.97/5.52 % (12694)Termination reason: Unknown
% 29.97/5.52 % (12694)Termination phase: Saturation
% 29.97/5.52
% 29.97/5.52 % (12694)Memory used [KB]: 8059
% 29.97/5.52 % (12694)Time elapsed: 0.642 s
% 29.97/5.52 % (12694)Instructions burned: 1981 (million)
% 29.97/5.52 % (12694)------------------------------
% 29.97/5.52 % (12694)------------------------------
% 29.97/5.52 % (12706)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_12084 for (2960ds/1001Mi)
% 29.97/5.53 % (12707)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_12084 for (2960ds/102Mi)
% 29.97/5.55 % (12707)Instruction limit reached!
% 29.97/5.55 % (12707)------------------------------
% 29.97/5.55 % (12707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.97/5.55 % (12707)Termination reason: Unknown
% 29.97/5.55 % (12707)Termination phase: Property scanning
% 29.97/5.55
% 29.97/5.55 % (12707)Memory used [KB]: 2814
% 29.97/5.55 % (12707)Time elapsed: 0.030 s
% 29.97/5.55 % (12707)Instructions burned: 105 (million)
% 29.97/5.55 % (12707)------------------------------
% 29.97/5.55 % (12707)------------------------------
% 29.97/5.56 % (12708)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_12084 for (2959ds/952Mi)
% 30.27/5.64 % (12698)Instruction limit reached!
% 30.27/5.64 % (12698)------------------------------
% 30.27/5.64 % (12698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.27/5.64 % (12698)Termination reason: Unknown
% 30.27/5.64 % (12698)Termination phase: Saturation
% 30.27/5.64
% 30.27/5.64 % (12698)Memory used [KB]: 10106
% 30.27/5.64 % (12698)Time elapsed: 0.507 s
% 30.27/5.64 % (12698)Instructions burned: 1671 (million)
% 30.27/5.64 % (12698)------------------------------
% 30.27/5.64 % (12698)------------------------------
% 30.27/5.65 % (12709)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_12084 for (2959ds/578Mi)
% 30.27/5.69 % (12685)Instruction limit reached!
% 30.27/5.69 % (12685)------------------------------
% 30.27/5.69 % (12685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.27/5.69 % (12685)Termination reason: Unknown
% 30.27/5.69 % (12685)Termination phase: Saturation
% 30.27/5.69
% 30.27/5.69 % (12685)Memory used [KB]: 11129
% 30.27/5.69 % (12685)Time elapsed: 1.025 s
% 30.27/5.69 % (12685)Instructions burned: 3375 (million)
% 30.27/5.69 % (12685)------------------------------
% 30.27/5.69 % (12685)------------------------------
% 30.27/5.69 % (12704)Instruction limit reached!
% 30.27/5.69 % (12704)------------------------------
% 30.27/5.69 % (12704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.27/5.69 % (12704)Termination reason: Unknown
% 30.27/5.69 % (12704)Termination phase: Saturation
% 30.27/5.69
% 30.27/5.69 % (12704)Memory used [KB]: 9338
% 30.27/5.69 % (12704)Time elapsed: 0.277 s
% 30.27/5.69 % (12704)Instructions burned: 866 (million)
% 30.27/5.69 % (12704)------------------------------
% 30.27/5.69 % (12704)------------------------------
% 31.28/5.70 % (12710)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_12084 for (2958ds/643Mi)
% 31.28/5.70 % (12711)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_12084 for (2958ds/865Mi)
% 31.28/5.79 % (12706)Instruction limit reached!
% 31.28/5.79 % (12706)------------------------------
% 31.28/5.79 % (12706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.28/5.79 % (12706)Termination reason: Unknown
% 31.28/5.79 % (12706)Termination phase: Saturation
% 31.28/5.79
% 31.28/5.79 % (12706)Memory used [KB]: 8187
% 31.28/5.79 % (12706)Time elapsed: 0.266 s
% 31.28/5.79 % (12706)Instructions burned: 1003 (million)
% 31.28/5.79 % (12706)------------------------------
% 31.28/5.79 % (12706)------------------------------
% 31.66/5.80 % (12712)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_12084 for (2957ds/1174Mi)
% 31.66/5.82 % (12709)Instruction limit reached!
% 31.66/5.82 % (12709)------------------------------
% 31.66/5.82 % (12709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.66/5.82 % (12709)Termination reason: Unknown
% 31.66/5.82 % (12709)Termination phase: Saturation
% 31.66/5.82
% 31.66/5.82 % (12709)Memory used [KB]: 9210
% 31.66/5.82 % (12709)Time elapsed: 0.170 s
% 31.66/5.82 % (12709)Instructions burned: 579 (million)
% 31.66/5.82 % (12709)------------------------------
% 31.66/5.82 % (12709)------------------------------
% 31.66/5.83 % (12713)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_12084 for (2957ds/644Mi)
% 31.66/5.86 % (12658)Instruction limit reached!
% 31.66/5.86 % (12658)------------------------------
% 31.66/5.86 % (12658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.66/5.86 % (12658)Termination reason: Unknown
% 31.66/5.86 % (12658)Termination phase: Saturation
% 31.66/5.86
% 31.66/5.86 % (12658)Memory used [KB]: 15607
% 31.66/5.86 % (12658)Time elapsed: 2.539 s
% 31.66/5.86 % (12658)Instructions burned: 8252 (million)
% 31.66/5.86 % (12658)------------------------------
% 31.66/5.86 % (12658)------------------------------
% 31.66/5.86 % (12708)Instruction limit reached!
% 31.66/5.86 % (12708)------------------------------
% 31.66/5.86 % (12708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.66/5.86 % (12708)Termination reason: Unknown
% 31.66/5.86 % (12708)Termination phase: Saturation
% 31.66/5.86
% 31.66/5.86 % (12708)Memory used [KB]: 9083
% 31.66/5.86 % (12708)Time elapsed: 0.302 s
% 31.66/5.86 % (12708)Instructions burned: 954 (million)
% 31.66/5.86 % (12708)------------------------------
% 31.66/5.86 % (12708)------------------------------
% 31.66/5.87 % (12714)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_12084 for (2956ds/1201Mi)
% 31.66/5.87 % (12715)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_12084 for (2956ds/1046Mi)
% 31.66/5.89 % (12710)Instruction limit reached!
% 31.66/5.89 % (12710)------------------------------
% 31.66/5.89 % (12710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.66/5.89 % (12710)Termination reason: Unknown
% 31.66/5.89 % (12710)Termination phase: Saturation
% 31.66/5.89
% 31.66/5.89 % (12710)Memory used [KB]: 9594
% 31.66/5.89 % (12710)Time elapsed: 0.190 s
% 31.66/5.89 % (12710)Instructions burned: 643 (million)
% 31.66/5.89 % (12710)------------------------------
% 31.66/5.89 % (12710)------------------------------
% 31.66/5.89 % (12711)Refutation not found, non-redundant clauses discarded% (12711)------------------------------
% 31.66/5.89 % (12711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.66/5.89 % (12711)Termination reason: Refutation not found, non-redundant clauses discarded
% 31.66/5.89
% 31.66/5.89 % (12711)Memory used [KB]: 8315
% 31.66/5.89 % (12711)Time elapsed: 0.189 s
% 31.66/5.89 % (12711)Instructions burned: 605 (million)
% 31.66/5.89 % (12711)------------------------------
% 31.66/5.89 % (12711)------------------------------
% 32.62/5.90 % (12716)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_12084 for (2956ds/222Mi)
% 32.62/5.90 % (12717)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_12084 for (2956ds/68Mi)
% 32.62/5.92 % (12717)Instruction limit reached!
% 32.62/5.92 % (12717)------------------------------
% 32.62/5.92 % (12717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.62/5.92 % (12717)Termination reason: Unknown
% 32.62/5.92 % (12717)Termination phase: Property scanning
% 32.62/5.92
% 32.62/5.92 % (12717)Memory used [KB]: 2302
% 32.62/5.92 % (12717)Time elapsed: 0.023 s
% 32.62/5.92 % (12717)Instructions burned: 70 (million)
% 32.62/5.92 % (12717)------------------------------
% 32.62/5.92 % (12717)------------------------------
% 32.62/5.93 % (12718)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_12084 for (2956ds/454Mi)
% 32.62/5.96 % (12716)Instruction limit reached!
% 32.62/5.96 % (12716)------------------------------
% 32.62/5.96 % (12716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.62/5.96 % (12716)Termination reason: Unknown
% 32.62/5.96 % (12716)Termination phase: Saturation
% 32.62/5.96
% 32.62/5.96 % (12716)Memory used [KB]: 7419
% 32.62/5.96 % (12716)Time elapsed: 0.063 s
% 32.62/5.96 % (12716)Instructions burned: 224 (million)
% 32.62/5.96 % (12716)------------------------------
% 32.62/5.96 % (12716)------------------------------
% 32.62/5.97 % (12719)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_12084 for (2955ds/360Mi)
% 34.29/6.04 % (12713)Instruction limit reached!
% 34.29/6.04 % (12713)------------------------------
% 34.29/6.04 % (12713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.29/6.04 % (12713)Termination reason: Unknown
% 34.29/6.04 % (12713)Termination phase: Saturation
% 34.29/6.04
% 34.29/6.04 % (12713)Memory used [KB]: 11001
% 34.29/6.04 % (12713)Time elapsed: 0.207 s
% 34.29/6.04 % (12713)Instructions burned: 644 (million)
% 34.29/6.04 % (12713)------------------------------
% 34.29/6.04 % (12713)------------------------------
% 34.29/6.05 % (12720)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_12084 for (2955ds/157Mi)
% 34.29/6.06 % (12718)Instruction limit reached!
% 34.29/6.06 % (12718)------------------------------
% 34.29/6.06 % (12718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.29/6.06 % (12718)Termination reason: Unknown
% 34.29/6.06 % (12718)Termination phase: Saturation
% 34.29/6.06
% 34.29/6.06 % (12718)Memory used [KB]: 13304
% 34.29/6.06 % (12718)Time elapsed: 0.133 s
% 34.29/6.06 % (12718)Instructions burned: 455 (million)
% 34.29/6.06 % (12718)------------------------------
% 34.29/6.06 % (12718)------------------------------
% 34.29/6.07 % (12721)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_12084 for (2954ds/5061Mi)
% 34.29/6.07 % (12719)Instruction limit reached!
% 34.29/6.07 % (12719)------------------------------
% 34.29/6.07 % (12719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.29/6.07 % (12719)Termination reason: Unknown
% 34.29/6.07 % (12719)Termination phase: Saturation
% 34.29/6.07
% 34.29/6.07 % (12719)Memory used [KB]: 8187
% 34.29/6.07 % (12719)Time elapsed: 0.104 s
% 34.29/6.07 % (12719)Instructions burned: 362 (million)
% 34.29/6.07 % (12719)------------------------------
% 34.29/6.07 % (12719)------------------------------
% 34.29/6.08 % (12722)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_12084 for (2954ds/2401Mi)
% 34.29/6.09 % (12720)Instruction limit reached!
% 34.29/6.09 % (12720)------------------------------
% 34.29/6.09 % (12720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.29/6.09 % (12720)Termination reason: Unknown
% 34.29/6.09 % (12720)Termination phase: Property scanning
% 34.29/6.09
% 34.29/6.09 % (12720)Memory used [KB]: 2814
% 34.29/6.09 % (12720)Time elapsed: 0.044 s
% 34.29/6.09 % (12720)Instructions burned: 158 (million)
% 34.29/6.09 % (12720)------------------------------
% 34.29/6.09 % (12720)------------------------------
% 34.29/6.10 % (12723)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_12084 for (2954ds/5798Mi)
% 34.88/6.16 % (12712)Instruction limit reached!
% 34.88/6.16 % (12712)------------------------------
% 34.88/6.16 % (12712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.88/6.16 % (12712)Termination reason: Unknown
% 34.88/6.16 % (12712)Termination phase: Saturation
% 34.88/6.16
% 34.88/6.16 % (12712)Memory used [KB]: 9978
% 34.88/6.16 % (12712)Time elapsed: 0.365 s
% 34.88/6.16 % (12712)Instructions burned: 1175 (million)
% 34.88/6.16 % (12712)------------------------------
% 34.88/6.16 % (12712)------------------------------
% 34.88/6.17 % (12724)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_12084 for (2953ds/346Mi)
% 34.88/6.19 % (12715)Instruction limit reached!
% 34.88/6.19 % (12715)------------------------------
% 34.88/6.19 % (12715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.88/6.19 % (12715)Termination reason: Unknown
% 34.88/6.19 % (12715)Termination phase: Saturation
% 34.88/6.19
% 34.88/6.19 % (12715)Memory used [KB]: 9850
% 34.88/6.19 % (12715)Time elapsed: 0.316 s
% 34.88/6.19 % (12715)Instructions burned: 1047 (million)
% 34.88/6.19 % (12715)------------------------------
% 34.88/6.19 % (12715)------------------------------
% 35.16/6.20 % (12725)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_12084 for (2953ds/1321Mi)
% 35.16/6.23 % (12714)Refutation not found, non-redundant clauses discarded% (12714)------------------------------
% 35.16/6.23 % (12714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.16/6.23 % (12714)Termination reason: Refutation not found, non-redundant clauses discarded
% 35.16/6.23
% 35.16/6.23 % (12714)Memory used [KB]: 9594
% 35.16/6.23 % (12714)Time elapsed: 0.369 s
% 35.16/6.23 % (12714)Instructions burned: 1154 (million)
% 35.16/6.23 % (12714)------------------------------
% 35.16/6.23 % (12714)------------------------------
% 35.16/6.25 % (12726)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_12084 for (2953ds/1312Mi)
% 35.16/6.27 % (12724)Instruction limit reached!
% 35.16/6.27 % (12724)------------------------------
% 35.16/6.27 % (12724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.16/6.27 % (12724)Termination reason: Unknown
% 35.16/6.27 % (12724)Termination phase: Saturation
% 35.16/6.27
% 35.16/6.27 % (12724)Memory used [KB]: 8059
% 35.16/6.27 % (12724)Time elapsed: 0.104 s
% 35.16/6.27 % (12724)Instructions burned: 348 (million)
% 35.16/6.27 % (12724)------------------------------
% 35.16/6.27 % (12724)------------------------------
% 35.16/6.28 % (12727)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_12084 for (2952ds/672Mi)
% 35.53/6.47 % (12702)Refutation not found, non-redundant clauses discarded% (12702)------------------------------
% 35.53/6.47 % (12702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.53/6.47 % (12702)Termination reason: Refutation not found, non-redundant clauses discarded
% 35.53/6.47
% 35.53/6.47 % (12702)Memory used [KB]: 10746
% 35.53/6.47 % (12702)Time elapsed: 1.160 s
% 35.53/6.47 % (12702)Instructions burned: 3886 (million)
% 35.53/6.47 % (12702)------------------------------
% 35.53/6.47 % (12702)------------------------------
% 35.53/6.48 % (12728)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_12084 for (2950ds/1897Mi)
% 35.62/6.51 % (12727)Instruction limit reached!
% 35.62/6.51 % (12727)------------------------------
% 35.62/6.51 % (12727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.62/6.51 % (12727)Termination reason: Unknown
% 35.62/6.51 % (12727)Termination phase: Saturation
% 35.62/6.51
% 35.62/6.51 % (12727)Memory used [KB]: 8443
% 35.62/6.51 % (12727)Time elapsed: 0.226 s
% 35.62/6.51 % (12727)Instructions burned: 672 (million)
% 35.62/6.51 % (12727)------------------------------
% 35.62/6.51 % (12727)------------------------------
% 35.62/6.52 % (12729)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_12084 for (2950ds/1202Mi)
% 35.62/6.59 % (12725)Instruction limit reached!
% 35.62/6.59 % (12725)------------------------------
% 35.62/6.59 % (12725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.62/6.59 % (12725)Termination reason: Unknown
% 35.62/6.59 % (12725)Termination phase: Saturation
% 35.62/6.59
% 35.62/6.59 % (12725)Memory used [KB]: 4221
% 35.62/6.59 % (12725)Time elapsed: 0.396 s
% 35.62/6.59 % (12725)Instructions burned: 1321 (million)
% 35.62/6.59 % (12725)------------------------------
% 35.62/6.59 % (12725)------------------------------
% 36.25/6.60 % (12730)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_12084 for (2949ds/1493Mi)
% 36.25/6.64 % (12726)Instruction limit reached!
% 36.25/6.64 % (12726)------------------------------
% 36.25/6.64 % (12726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.25/6.64 % (12726)Termination reason: Unknown
% 36.25/6.64 % (12726)Termination phase: Saturation
% 36.25/6.64
% 36.25/6.64 % (12726)Memory used [KB]: 9978
% 36.25/6.64 % (12726)Time elapsed: 0.398 s
% 36.25/6.64 % (12726)Instructions burned: 1314 (million)
% 36.25/6.64 % (12726)------------------------------
% 36.25/6.64 % (12726)------------------------------
% 36.25/6.65 % (12731)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_12084 for (2949ds/7679Mi)
% 36.67/6.84 % (12722)Instruction limit reached!
% 36.67/6.84 % (12722)------------------------------
% 36.67/6.84 % (12722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.67/6.84 % (12722)Termination reason: Unknown
% 36.67/6.84 % (12722)Termination phase: Saturation
% 36.67/6.84
% 36.67/6.84 % (12722)Memory used [KB]: 7547
% 36.67/6.84 % (12722)Time elapsed: 0.755 s
% 36.67/6.84 % (12722)Instructions burned: 2401 (million)
% 36.67/6.84 % (12722)------------------------------
% 36.67/6.84 % (12722)------------------------------
% 36.67/6.85 % (12732)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_12084 for (2947ds/340Mi)
% 36.67/6.88 % (12729)Instruction limit reached!
% 36.67/6.88 % (12729)------------------------------
% 36.67/6.88 % (12729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.67/6.88 % (12729)Termination reason: Unknown
% 36.67/6.88 % (12729)Termination phase: Saturation
% 36.67/6.88
% 36.67/6.88 % (12729)Memory used [KB]: 4733
% 36.67/6.88 % (12729)Time elapsed: 0.365 s
% 36.67/6.88 % (12729)Instructions burned: 1203 (million)
% 36.67/6.88 % (12729)------------------------------
% 36.67/6.88 % (12729)------------------------------
% 36.67/6.89 % (12733)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_12084 for (2946ds/3672Mi)
% 37.82/6.95 % (12732)Instruction limit reached!
% 37.82/6.95 % (12732)------------------------------
% 37.82/6.95 % (12732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.82/6.95 % (12732)Termination reason: Unknown
% 37.82/6.95 % (12732)Termination phase: Saturation
% 37.82/6.95
% 37.82/6.95 % (12732)Memory used [KB]: 8827
% 37.82/6.95 % (12732)Time elapsed: 0.106 s
% 37.82/6.95 % (12732)Instructions burned: 340 (million)
% 37.82/6.95 % (12732)------------------------------
% 37.82/6.95 % (12732)------------------------------
% 37.82/6.96 % (12734)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_12084 for (2945ds/1535Mi)
% 41.31/7.05 % (12728)Instruction limit reached!
% 41.31/7.05 % (12728)------------------------------
% 41.31/7.05 % (12728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.31/7.05 % (12728)Termination reason: Unknown
% 41.31/7.05 % (12728)Termination phase: Saturation
% 41.31/7.05
% 41.31/7.05 % (12728)Memory used [KB]: 11385
% 41.31/7.05 % (12728)Time elapsed: 0.572 s
% 41.31/7.05 % (12728)Instructions burned: 1897 (million)
% 41.31/7.05 % (12728)------------------------------
% 41.31/7.05 % (12728)------------------------------
% 41.31/7.06 % (12730)Instruction limit reached!
% 41.31/7.06 % (12730)------------------------------
% 41.31/7.06 % (12730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.31/7.06 % (12730)Termination reason: Unknown
% 41.31/7.06 % (12730)Termination phase: Saturation
% 41.31/7.06
% 41.31/7.06 % (12730)Memory used [KB]: 12281
% 41.31/7.06 % (12730)Time elapsed: 0.456 s
% 41.31/7.06 % (12730)Instructions burned: 1495 (million)
% 41.31/7.06 % (12730)------------------------------
% 41.31/7.06 % (12730)------------------------------
% 41.31/7.06 % (12735)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_12084 for (2945ds/4637Mi)
% 41.31/7.07 % (12736)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_12084 for (2944ds/3174Mi)
% 43.29/7.42 % (12734)Instruction limit reached!
% 43.29/7.42 % (12734)------------------------------
% 43.29/7.42 % (12734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.29/7.42 % (12734)Termination reason: Unknown
% 43.29/7.42 % (12734)Termination phase: Saturation
% 43.29/7.42
% 43.29/7.42 % (12734)Memory used [KB]: 12537
% 43.29/7.42 % (12734)Time elapsed: 0.459 s
% 43.29/7.42 % (12734)Instructions burned: 1536 (million)
% 43.29/7.42 % (12734)------------------------------
% 43.29/7.42 % (12734)------------------------------
% 43.29/7.43 % (12737)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_12084 for (2941ds/307Mi)
% 43.73/7.52 % (12737)Instruction limit reached!
% 43.73/7.52 % (12737)------------------------------
% 43.73/7.52 % (12737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.73/7.52 % (12737)Termination reason: Unknown
% 43.73/7.52 % (12737)Termination phase: Saturation
% 43.73/7.52
% 43.73/7.52 % (12737)Memory used [KB]: 7547
% 43.73/7.52 % (12737)Time elapsed: 0.087 s
% 43.73/7.52 % (12737)Instructions burned: 307 (million)
% 43.73/7.52 % (12737)------------------------------
% 43.73/7.52 % (12737)------------------------------
% 43.73/7.53 % (12738)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_12084 for (2940ds/3619Mi)
% 43.73/7.57 % (12738)Refutation not found, incomplete strategy
% 43.73/7.57 % (12738)------------------------------
% 43.73/7.57 % (12738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.73/7.57 % (12738)Termination reason: Refutation not found, incomplete strategy
% 43.73/7.57
% 43.73/7.57
% 43.73/7.57 % (12738)Memory used [KB]: 7419
% 43.73/7.57 % (12738)Time elapsed: 0.048 s
% 43.73/7.57 % (12738)Instructions burned: 156 (million)
% 43.73/7.57 % (12738)------------------------------
% 43.73/7.57 % (12738)------------------------------
% 43.73/7.58 % (12739)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_12084 for (2939ds/2325Mi)
% 44.27/7.69 % (12721)Instruction limit reached!
% 44.27/7.69 % (12721)------------------------------
% 44.27/7.69 % (12721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.27/7.69 % (12721)Termination reason: Unknown
% 44.27/7.69 % (12721)Termination phase: Saturation
% 44.27/7.69
% 44.27/7.69 % (12721)Memory used [KB]: 24306
% 44.27/7.69 % (12721)Time elapsed: 1.617 s
% 44.27/7.69 % (12721)Instructions burned: 5062 (million)
% 44.27/7.69 % (12721)------------------------------
% 44.27/7.69 % (12721)------------------------------
% 44.67/7.70 % (12740)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_12084 for (2938ds/2341Mi)
% 44.97/7.85 % (12723)Instruction limit reached!
% 44.97/7.85 % (12723)------------------------------
% 44.97/7.85 % (12723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.97/7.85 % (12723)Termination reason: Unknown
% 44.97/7.85 % (12723)Termination phase: Saturation
% 44.97/7.85
% 44.97/7.85 % (12723)Memory used [KB]: 12792
% 44.97/7.85 % (12723)Time elapsed: 1.753 s
% 44.97/7.85 % (12723)Instructions burned: 5800 (million)
% 44.97/7.85 % (12723)------------------------------
% 44.97/7.85 % (12723)------------------------------
% 44.97/7.86 % (12741)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_12084 for (2936ds/7257Mi)
% 45.25/8.02 % (12733)Instruction limit reached!
% 45.25/8.02 % (12733)------------------------------
% 45.25/8.02 % (12733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.25/8.02 % (12733)Termination reason: Unknown
% 45.25/8.02 % (12733)Termination phase: Saturation
% 45.25/8.02
% 45.25/8.02 % (12733)Memory used [KB]: 10490
% 45.25/8.02 % (12733)Time elapsed: 1.128 s
% 45.25/8.02 % (12733)Instructions burned: 3673 (million)
% 45.25/8.02 % (12733)------------------------------
% 45.25/8.02 % (12733)------------------------------
% 48.34/8.03 % (12742)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_12084 for (2935ds/3710Mi)
% 48.34/8.04 % (12736)Instruction limit reached!
% 48.34/8.04 % (12736)------------------------------
% 48.34/8.04 % (12736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.34/8.04 % (12736)Termination reason: Unknown
% 48.34/8.04 % (12736)Termination phase: Saturation
% 48.34/8.04
% 48.34/8.04 % (12736)Memory used [KB]: 13432
% 48.34/8.04 % (12736)Time elapsed: 0.974 s
% 48.34/8.04 % (12736)Instructions burned: 3175 (million)
% 48.34/8.04 % (12736)------------------------------
% 48.34/8.04 % (12736)------------------------------
% 48.34/8.05 % (12743)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_12084 for (2935ds/326Mi)
% 48.89/8.15 % (12743)Instruction limit reached!
% 48.89/8.15 % (12743)------------------------------
% 48.89/8.15 % (12743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.89/8.15 % (12743)Termination reason: Unknown
% 48.89/8.15 % (12743)Termination phase: Saturation
% 48.89/8.15
% 48.89/8.15 % (12743)Memory used [KB]: 7803
% 48.89/8.15 % (12743)Time elapsed: 0.127 s
% 48.89/8.15 % (12743)Instructions burned: 328 (million)
% 48.89/8.15 % (12743)------------------------------
% 48.89/8.15 % (12743)------------------------------
% 48.89/8.17 % (12744)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_12084 for (2933ds/1100Mi)
% 49.86/8.31 % (12739)Instruction limit reached!
% 49.86/8.31 % (12739)------------------------------
% 49.86/8.31 % (12739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.86/8.31 % (12739)Termination reason: Unknown
% 49.86/8.31 % (12739)Termination phase: Saturation
% 49.86/8.31
% 49.86/8.31 % (12739)Memory used [KB]: 10618
% 49.86/8.31 % (12739)Time elapsed: 0.727 s
% 49.86/8.31 % (12739)Instructions burned: 2325 (million)
% 49.86/8.31 % (12739)------------------------------
% 49.86/8.31 % (12739)------------------------------
% 49.86/8.32 % (12745)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_12084 for (2932ds/406Mi)
% 50.30/8.43 % (12740)Instruction limit reached!
% 50.30/8.43 % (12740)------------------------------
% 50.30/8.43 % (12740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.30/8.43 % (12740)Termination reason: Unknown
% 50.30/8.43 % (12740)Termination phase: Saturation
% 50.30/8.43
% 50.30/8.43 % (12740)Memory used [KB]: 9083
% 50.30/8.43 % (12740)Time elapsed: 0.728 s
% 50.30/8.43 % (12740)Instructions burned: 2341 (million)
% 50.30/8.43 % (12740)------------------------------
% 50.30/8.43 % (12740)------------------------------
% 50.30/8.44 % (12746)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_12084 for (2931ds/1871Mi)
% 50.30/8.45 % (12745)Instruction limit reached!
% 50.30/8.45 % (12745)------------------------------
% 50.30/8.45 % (12745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.30/8.45 % (12745)Termination reason: Unknown
% 50.30/8.45 % (12745)Termination phase: Saturation
% 50.30/8.45
% 50.30/8.45 % (12745)Memory used [KB]: 7931
% 50.30/8.45 % (12745)Time elapsed: 0.128 s
% 50.30/8.45 % (12745)Instructions burned: 407 (million)
% 50.30/8.45 % (12745)------------------------------
% 50.30/8.45 % (12745)------------------------------
% 50.30/8.46 % (12747)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_12084 for (2930ds/1194Mi)
% 50.30/8.49 % (12735)Instruction limit reached!
% 50.30/8.49 % (12735)------------------------------
% 50.30/8.49 % (12735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.30/8.49 % (12735)Termination reason: Unknown
% 50.30/8.49 % (12735)Termination phase: Saturation
% 50.30/8.49
% 50.30/8.49 % (12735)Memory used [KB]: 14328
% 50.30/8.49 % (12735)Time elapsed: 1.450 s
% 50.30/8.49 % (12735)Instructions burned: 4637 (million)
% 50.30/8.49 % (12735)------------------------------
% 50.30/8.49 % (12735)------------------------------
% 50.30/8.50 % (12748)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_12084 for (2930ds/474Mi)
% 50.76/8.51 % (12744)Instruction limit reached!
% 50.76/8.51 % (12744)------------------------------
% 50.76/8.51 % (12744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.76/8.51 % (12744)Termination reason: Unknown
% 50.76/8.51 % (12744)Termination phase: Saturation
% 50.76/8.51
% 50.76/8.51 % (12744)Memory used [KB]: 10106
% 50.76/8.51 % (12744)Time elapsed: 0.346 s
% 50.76/8.51 % (12744)Instructions burned: 1101 (million)
% 50.76/8.51 % (12744)------------------------------
% 50.76/8.51 % (12744)------------------------------
% 50.76/8.52 % (12749)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_12084 for (2930ds/3115Mi)
% 51.32/8.64 % (12748)Instruction limit reached!
% 51.32/8.64 % (12748)------------------------------
% 51.32/8.64 % (12748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.32/8.64 % (12748)Termination reason: Unknown
% 51.32/8.64 % (12748)Termination phase: Saturation
% 51.32/8.64
% 51.32/8.64 % (12748)Memory used [KB]: 8571
% 51.32/8.64 % (12748)Time elapsed: 0.149 s
% 51.32/8.64 % (12748)Instructions burned: 475 (million)
% 51.32/8.64 % (12748)------------------------------
% 51.32/8.64 % (12748)------------------------------
% 51.32/8.65 % (12750)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_12084 for (2928ds/831Mi)
% 51.87/8.82 % (12747)Instruction limit reached!
% 51.87/8.82 % (12747)------------------------------
% 51.87/8.82 % (12747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.87/8.82 % (12747)Termination reason: Unknown
% 51.87/8.82 % (12747)Termination phase: Saturation
% 51.87/8.82
% 51.87/8.82 % (12747)Memory used [KB]: 8699
% 51.87/8.82 % (12747)Time elapsed: 0.368 s
% 51.87/8.82 % (12747)Instructions burned: 1197 (million)
% 51.87/8.82 % (12747)------------------------------
% 51.87/8.82 % (12747)------------------------------
% 51.87/8.83 % (12751)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_12084 for (2927ds/1188Mi)
% 52.47/8.92 % (12731)Instruction limit reached!
% 52.47/8.92 % (12731)------------------------------
% 52.47/8.92 % (12731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.47/8.92 % (12731)Termination reason: Unknown
% 52.47/8.92 % (12731)Termination phase: Saturation
% 52.47/8.92
% 52.47/8.92 % (12731)Memory used [KB]: 12920
% 52.47/8.92 % (12731)Time elapsed: 2.269 s
% 52.47/8.92 % (12731)Instructions burned: 7680 (million)
% 52.47/8.92 % (12731)------------------------------
% 52.47/8.92 % (12731)------------------------------
% 52.47/8.93 % (12750)Instruction limit reached!
% 52.47/8.93 % (12750)------------------------------
% 52.47/8.93 % (12750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.47/8.93 % (12750)Termination reason: Unknown
% 52.47/8.93 % (12750)Termination phase: Saturation
% 52.47/8.93
% 52.47/8.93 % (12750)Memory used [KB]: 8955
% 52.47/8.93 % (12750)Time elapsed: 0.274 s
% 52.47/8.93 % (12750)Instructions burned: 831 (million)
% 52.47/8.93 % (12750)------------------------------
% 52.47/8.93 % (12750)------------------------------
% 52.47/8.93 % (12752)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_12084 for (2926ds/2868Mi)
% 52.47/8.94 % (12753)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_12084 for (2926ds/1516Mi)
% 55.36/9.04 % (12746)Instruction limit reached!
% 55.36/9.04 % (12746)------------------------------
% 55.36/9.04 % (12746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.36/9.04 % (12746)Termination reason: Unknown
% 55.36/9.04 % (12746)Termination phase: Saturation
% 55.36/9.04
% 55.36/9.04 % (12746)Memory used [KB]: 13560
% 55.36/9.04 % (12746)Time elapsed: 0.604 s
% 55.36/9.04 % (12746)Instructions burned: 1873 (million)
% 55.36/9.04 % (12746)------------------------------
% 55.36/9.04 % (12746)------------------------------
% 55.36/9.05 % (12754)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_12084 for (2925ds/2321Mi)
% 56.44/9.21 % (12751)Instruction limit reached!
% 56.44/9.21 % (12751)------------------------------
% 56.44/9.21 % (12751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.44/9.21 % (12751)Termination reason: Unknown
% 56.44/9.21 % (12751)Termination phase: Saturation
% 56.44/9.21
% 56.44/9.21 % (12751)Memory used [KB]: 10106
% 56.44/9.21 % (12751)Time elapsed: 0.376 s
% 56.44/9.21 % (12751)Instructions burned: 1190 (million)
% 56.44/9.21 % (12751)------------------------------
% 56.44/9.21 % (12751)------------------------------
% 56.44/9.21 % (12742)Instruction limit reached!
% 56.44/9.21 % (12742)------------------------------
% 56.44/9.21 % (12742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.44/9.21 % (12742)Termination reason: Unknown
% 56.44/9.21 % (12742)Termination phase: Saturation
% 56.44/9.21
% 56.44/9.21 % (12742)Memory used [KB]: 17910
% 56.44/9.21 % (12742)Time elapsed: 1.207 s
% 56.44/9.21 % (12742)Instructions burned: 3711 (million)
% 56.44/9.21 % (12742)------------------------------
% 56.44/9.21 % (12742)------------------------------
% 56.44/9.22 % (12755)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_12084 for (2923ds/2812Mi)
% 56.44/9.22 % (12756)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_12084 for (2923ds/4604Mi)
% 57.29/9.40 % (12753)Instruction limit reached!
% 57.29/9.40 % (12753)------------------------------
% 57.29/9.40 % (12753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.29/9.40 % (12753)Termination reason: Unknown
% 57.29/9.40 % (12753)Termination phase: Saturation
% 57.29/9.40
% 57.29/9.40 % (12753)Memory used [KB]: 10618
% 57.29/9.40 % (12753)Time elapsed: 0.469 s
% 57.29/9.40 % (12753)Instructions burned: 1516 (million)
% 57.29/9.40 % (12753)------------------------------
% 57.29/9.40 % (12753)------------------------------
% 57.29/9.41 % (12757)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_12084 for (2921ds/2678Mi)
% 57.29/9.47 % (12749)Instruction limit reached!
% 57.29/9.47 % (12749)------------------------------
% 57.29/9.47 % (12749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.29/9.47 % (12749)Termination reason: Unknown
% 57.29/9.47 % (12749)Termination phase: Saturation
% 57.29/9.47
% 57.29/9.47 % (12749)Memory used [KB]: 13816
% 57.29/9.47 % (12749)Time elapsed: 0.950 s
% 57.29/9.47 % (12749)Instructions burned: 3117 (million)
% 57.29/9.47 % (12749)------------------------------
% 57.29/9.47 % (12749)------------------------------
% 57.29/9.48 % (12758)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_12084 for (2920ds/643Mi)
% 57.61/9.58 % (12754)Refutation not found, non-redundant clauses discarded% (12754)------------------------------
% 57.61/9.58 % (12754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.61/9.58 % (12754)Termination reason: Refutation not found, non-redundant clauses discarded
% 57.61/9.58
% 57.61/9.58 % (12754)Memory used [KB]: 12665
% 57.61/9.58 % (12754)Time elapsed: 0.556 s
% 57.61/9.58 % (12754)Instructions burned: 1784 (million)
% 57.61/9.58 % (12754)------------------------------
% 57.61/9.58 % (12754)------------------------------
% 57.61/9.59 % (12759)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_12084 for (2919ds/458Mi)
% 58.33/9.67 % (12758)Instruction limit reached!
% 58.33/9.67 % (12758)------------------------------
% 58.33/9.67 % (12758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.33/9.67 % (12758)Termination reason: Unknown
% 58.33/9.67 % (12758)Termination phase: Saturation
% 58.33/9.67
% 58.33/9.67 % (12758)Memory used [KB]: 9466
% 58.33/9.67 % (12758)Time elapsed: 0.196 s
% 58.33/9.67 % (12758)Instructions burned: 645 (million)
% 58.33/9.67 % (12758)------------------------------
% 58.33/9.67 % (12758)------------------------------
% 58.33/9.68 % (12760)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_12084 for (2918ds/2546Mi)
% 58.74/9.72 % (12759)Instruction limit reached!
% 58.74/9.72 % (12759)------------------------------
% 58.74/9.72 % (12759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.74/9.72 % (12759)Termination reason: Unknown
% 58.74/9.72 % (12759)Termination phase: Saturation
% 58.74/9.72
% 58.74/9.72 % (12759)Memory used [KB]: 8571
% 58.74/9.72 % (12759)Time elapsed: 0.135 s
% 58.74/9.72 % (12759)Instructions burned: 459 (million)
% 58.74/9.72 % (12759)------------------------------
% 58.74/9.72 % (12759)------------------------------
% 58.74/9.74 % (12761)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_12084 for (2918ds/1432Mi)
% 58.74/9.79 % (12752)Instruction limit reached!
% 58.74/9.79 % (12752)------------------------------
% 58.74/9.79 % (12752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.74/9.79 % (12752)Termination reason: Unknown
% 58.74/9.79 % (12752)Termination phase: Saturation
% 58.74/9.79
% 58.74/9.79 % (12752)Memory used [KB]: 18677
% 58.74/9.79 % (12752)Time elapsed: 0.858 s
% 58.74/9.79 % (12752)Instructions burned: 2868 (million)
% 58.74/9.79 % (12752)------------------------------
% 58.74/9.79 % (12752)------------------------------
% 59.09/9.80 % (12762)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_12084 for (2917ds/386Mi)
% 59.20/9.91 % (12762)Instruction limit reached!
% 59.20/9.91 % (12762)------------------------------
% 59.20/9.91 % (12762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.20/9.91 % (12762)Termination reason: Unknown
% 59.20/9.91 % (12762)Termination phase: Saturation
% 59.20/9.91
% 59.20/9.91 % (12762)Memory used [KB]: 8827
% 59.20/9.91 % (12762)Time elapsed: 0.112 s
% 59.20/9.91 % (12762)Instructions burned: 387 (million)
% 59.20/9.91 % (12762)------------------------------
% 59.20/9.91 % (12762)------------------------------
% 59.20/9.92 % (12763)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_12084 for (2916ds/360Mi)
% 59.20/9.98 % (12741)Refutation not found, non-redundant clauses discarded% (12741)------------------------------
% 59.20/9.98 % (12741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.20/9.98 % (12741)Termination reason: Refutation not found, non-redundant clauses discarded
% 59.20/9.98
% 59.20/9.98 % (12741)Memory used [KB]: 19701
% 59.20/9.98 % (12741)Time elapsed: 2.117 s
% 59.20/9.98 % (12741)Instructions burned: 6771 (million)
% 59.20/9.98 % (12741)------------------------------
% 59.20/9.98 % (12741)------------------------------
% 59.20/9.99 % (12764)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_12084 for (2915ds/5446Mi)
% 59.20/10.02 % (12763)Instruction limit reached!
% 59.20/10.02 % (12763)------------------------------
% 59.20/10.02 % (12763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.20/10.02 % (12763)Termination reason: Unknown
% 59.20/10.02 % (12763)Termination phase: Saturation
% 59.20/10.02
% 59.20/10.02 % (12763)Memory used [KB]: 8187
% 59.20/10.02 % (12763)Time elapsed: 0.103 s
% 59.20/10.02 % (12763)Instructions burned: 360 (million)
% 59.20/10.02 % (12763)------------------------------
% 59.20/10.02 % (12763)------------------------------
% 62.39/10.03 % (12765)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_12084 for (2915ds/2573Mi)
% 62.39/10.11 % (12755)Instruction limit reached!
% 62.39/10.11 % (12755)------------------------------
% 62.39/10.11 % (12755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.39/10.11 % (12755)Termination reason: Unknown
% 62.39/10.11 % (12755)Termination phase: Saturation
% 62.39/10.11
% 62.39/10.11 % (12755)Memory used [KB]: 13304
% 62.39/10.11 % (12755)Time elapsed: 0.898 s
% 62.39/10.11 % (12755)Instructions burned: 2812 (million)
% 62.39/10.11 % (12755)------------------------------
% 62.39/10.11 % (12755)------------------------------
% 63.01/10.13 % (12766)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_12084 for (2914ds/2655Mi)
% 63.01/10.13 % (12761)Instruction limit reached!
% 63.01/10.13 % (12761)------------------------------
% 63.01/10.13 % (12761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.01/10.13 % (12761)Termination reason: Unknown
% 63.01/10.13 % (12761)Termination phase: Saturation
% 63.01/10.13
% 63.01/10.13 % (12761)Memory used [KB]: 12153
% 63.01/10.13 % (12761)Time elapsed: 0.398 s
% 63.01/10.13 % (12761)Instructions burned: 1433 (million)
% 63.01/10.13 % (12761)------------------------------
% 63.01/10.13 % (12761)------------------------------
% 63.01/10.14 % (12767)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_12084 for (2914ds/2781Mi)
% 63.32/10.23 % (12757)Instruction limit reached!
% 63.32/10.23 % (12757)------------------------------
% 63.32/10.23 % (12757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.32/10.23 % (12757)Termination reason: Unknown
% 63.32/10.23 % (12757)Termination phase: Saturation
% 63.32/10.23
% 63.32/10.23 % (12757)Memory used [KB]: 10746
% 63.32/10.23 % (12757)Time elapsed: 0.812 s
% 63.32/10.23 % (12757)Instructions burned: 2679 (million)
% 63.32/10.23 % (12757)------------------------------
% 63.32/10.23 % (12757)------------------------------
% 63.32/10.24 % (12768)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_12084 for (2913ds/307Mi)
% 63.65/10.32 % (12768)Instruction limit reached!
% 63.65/10.32 % (12768)------------------------------
% 63.65/10.32 % (12768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.65/10.32 % (12768)Termination reason: Unknown
% 63.65/10.32 % (12768)Termination phase: Saturation
% 63.65/10.32
% 63.65/10.32 % (12768)Memory used [KB]: 7675
% 63.65/10.32 % (12768)Time elapsed: 0.087 s
% 63.65/10.32 % (12768)Instructions burned: 309 (million)
% 63.65/10.32 % (12768)------------------------------
% 63.65/10.32 % (12768)------------------------------
% 63.65/10.33 % (12769)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_12084 for (2912ds/1548Mi)
% 64.36/10.50 % (12760)Instruction limit reached!
% 64.36/10.50 % (12760)------------------------------
% 64.36/10.50 % (12760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.36/10.50 % (12760)Termination reason: Unknown
% 64.36/10.50 % (12760)Termination phase: Saturation
% 64.36/10.50
% 64.36/10.50 % (12760)Memory used [KB]: 11385
% 64.36/10.50 % (12760)Time elapsed: 0.816 s
% 64.36/10.50 % (12760)Instructions burned: 2548 (million)
% 64.36/10.50 % (12760)------------------------------
% 64.36/10.50 % (12760)------------------------------
% 64.36/10.51 % (12770)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_12084 for (2910ds/5214Mi)
% 64.57/10.60 % (12756)Instruction limit reached!
% 64.57/10.60 % (12756)------------------------------
% 64.57/10.60 % (12756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.57/10.60 % (12756)Termination reason: Unknown
% 64.57/10.60 % (12756)Termination phase: Saturation
% 64.57/10.60
% 64.57/10.60 % (12756)Memory used [KB]: 12281
% 64.57/10.60 % (12756)Time elapsed: 1.377 s
% 64.57/10.60 % (12756)Instructions burned: 4604 (million)
% 64.57/10.60 % (12756)------------------------------
% 64.57/10.60 % (12756)------------------------------
% 64.57/10.61 % (12771)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_12084 for (2909ds/3201Mi)
% 64.78/10.81 % (12765)Instruction limit reached!
% 64.78/10.81 % (12765)------------------------------
% 64.78/10.81 % (12765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.78/10.81 % (12765)Termination reason: Unknown
% 64.78/10.81 % (12765)Termination phase: Saturation
% 64.78/10.81
% 64.78/10.81 % (12765)Memory used [KB]: 16119
% 64.78/10.81 % (12765)Time elapsed: 0.780 s
% 64.78/10.81 % (12765)Instructions burned: 2574 (million)
% 64.78/10.81 % (12765)------------------------------
% 64.78/10.81 % (12765)------------------------------
% 64.78/10.81 % (12769)Instruction limit reached!
% 64.78/10.81 % (12769)------------------------------
% 64.78/10.81 % (12769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.78/10.81 % (12769)Termination reason: Unknown
% 64.78/10.81 % (12769)Termination phase: Saturation
% 64.78/10.81
% 64.78/10.81 % (12769)Memory used [KB]: 11513
% 64.78/10.81 % (12769)Time elapsed: 0.503 s
% 64.78/10.81 % (12769)Instructions burned: 1550 (million)
% 64.78/10.81 % (12769)------------------------------
% 64.78/10.81 % (12769)------------------------------
% 64.78/10.82 % (12773)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_12084 for (2907ds/3049Mi)
% 64.78/10.82 % (12772)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_12084 for (2907ds/454Mi)
% 66.16/10.91 % (12766)Instruction limit reached!
% 66.16/10.91 % (12766)------------------------------
% 66.16/10.91 % (12766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.16/10.91 % (12766)Termination reason: Unknown
% 66.16/10.91 % (12766)Termination phase: Saturation
% 66.16/10.91
% 66.16/10.91 % (12766)Memory used [KB]: 16630
% 66.16/10.91 % (12766)Time elapsed: 0.811 s
% 66.16/10.91 % (12766)Instructions burned: 2658 (million)
% 66.16/10.91 % (12766)------------------------------
% 66.16/10.91 % (12766)------------------------------
% 66.16/10.92 % (12774)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_12084 for (2906ds/7311Mi)
% 66.16/10.95 % (12772)Instruction limit reached!
% 66.16/10.95 % (12772)------------------------------
% 66.16/10.95 % (12772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.16/10.95 % (12772)Termination reason: Unknown
% 66.16/10.95 % (12772)Termination phase: Saturation
% 66.16/10.95
% 66.16/10.95 % (12772)Memory used [KB]: 13304
% 66.16/10.95 % (12772)Time elapsed: 0.133 s
% 66.16/10.95 % (12772)Instructions burned: 455 (million)
% 66.16/10.95 % (12772)------------------------------
% 66.16/10.95 % (12772)------------------------------
% 66.16/10.96 % (12775)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_12084 for (2905ds/6804Mi)
% 66.16/11.00 % (12767)Instruction limit reached!
% 66.16/11.00 % (12767)------------------------------
% 66.16/11.00 % (12767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.16/11.00 % (12767)Termination reason: Unknown
% 66.16/11.00 % (12767)Termination phase: Saturation
% 66.16/11.00
% 66.16/11.00 % (12767)Memory used [KB]: 4861
% 66.16/11.00 % (12767)Time elapsed: 0.882 s
% 66.16/11.00 % (12767)Instructions burned: 2783 (million)
% 66.16/11.00 % (12767)------------------------------
% 66.16/11.00 % (12767)------------------------------
% 66.16/11.01 % (12776)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_12084 for (2905ds/1683Mi)
% 66.16/11.02 % (12775)Refutation not found, incomplete strategy
% 66.16/11.02 % (12775)------------------------------
% 66.16/11.02 % (12775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.16/11.02 % (12775)Termination reason: Refutation not found, incomplete strategy
% 66.16/11.02
% 66.16/11.02
% 66.16/11.02 % (12775)Memory used [KB]: 7675
% 66.16/11.02 % (12775)Time elapsed: 0.055 s
% 66.16/11.02 % (12775)Instructions burned: 171 (million)
% 66.16/11.02 % (12775)------------------------------
% 66.16/11.02 % (12775)------------------------------
% 69.40/11.03 % (12777)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_12084 for (2905ds/4688Mi)
% 71.78/11.51 % (12774)Refutation not found, non-redundant clauses discarded% (12774)------------------------------
% 71.78/11.51 % (12774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.78/11.51 % (12774)Termination reason: Refutation not found, non-redundant clauses discarded
% 71.78/11.51
% 71.78/11.51 % (12774)Memory used [KB]: 10490
% 71.78/11.51 % (12774)Time elapsed: 0.589 s
% 71.78/11.51 % (12774)Instructions burned: 1871 (million)
% 71.78/11.51 % (12774)------------------------------
% 71.78/11.51 % (12774)------------------------------
% 71.78/11.52 % (12778)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_12084 for (2900ds/2207Mi)
% 71.78/11.54 % (12776)Instruction limit reached!
% 71.78/11.54 % (12776)------------------------------
% 71.78/11.54 % (12776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.78/11.54 % (12776)Termination reason: Unknown
% 71.78/11.54 % (12776)Termination phase: Saturation
% 71.78/11.54
% 71.78/11.54 % (12776)Memory used [KB]: 10490
% 71.78/11.54 % (12776)Time elapsed: 0.526 s
% 71.78/11.54 % (12776)Instructions burned: 1686 (million)
% 71.78/11.54 % (12776)------------------------------
% 71.78/11.54 % (12776)------------------------------
% 71.78/11.55 % (12779)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_12084 for (2900ds/8216Mi)
% 71.78/11.56 % (12771)Instruction limit reached!
% 71.78/11.56 % (12771)------------------------------
% 71.78/11.56 % (12771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.78/11.56 % (12771)Termination reason: Unknown
% 71.78/11.56 % (12771)Termination phase: Saturation
% 71.78/11.56
% 71.78/11.56 % (12771)Memory used [KB]: 12281
% 71.78/11.56 % (12771)Time elapsed: 0.975 s
% 71.78/11.56 % (12771)Instructions burned: 3201 (million)
% 71.78/11.56 % (12771)------------------------------
% 71.78/11.56 % (12771)------------------------------
% 71.78/11.57 % (12780)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_12084 for (2899ds/430Mi)
% 72.71/11.69 % (12773)Instruction limit reached!
% 72.71/11.69 % (12773)------------------------------
% 72.71/11.69 % (12773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.71/11.69 % (12773)Termination reason: Unknown
% 72.71/11.69 % (12773)Termination phase: Saturation
% 72.71/11.69
% 72.71/11.69 % (12773)Memory used [KB]: 8443
% 72.71/11.69 % (12773)Time elapsed: 0.897 s
% 72.71/11.69 % (12773)Instructions burned: 3051 (million)
% 72.71/11.69 % (12773)------------------------------
% 72.71/11.69 % (12773)------------------------------
% 72.71/11.69 % (12780)Instruction limit reached!
% 72.71/11.69 % (12780)------------------------------
% 72.71/11.69 % (12780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.71/11.69 % (12780)Termination reason: Unknown
% 72.71/11.69 % (12780)Termination phase: Saturation
% 72.71/11.69
% 72.71/11.69 % (12780)Memory used [KB]: 8059
% 72.71/11.69 % (12780)Time elapsed: 0.125 s
% 72.71/11.69 % (12780)Instructions burned: 432 (million)
% 72.71/11.69 % (12780)------------------------------
% 72.71/11.69 % (12780)------------------------------
% 73.16/11.70 % (12781)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_12084 for (2898ds/2012Mi)
% 73.16/11.70 % (12782)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_12084 for (2898ds/631Mi)
% 73.16/11.74 % (12764)Instruction limit reached!
% 73.16/11.74 % (12764)------------------------------
% 73.16/11.74 % (12764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.16/11.74 % (12764)Termination reason: Unknown
% 73.16/11.74 % (12764)Termination phase: Saturation
% 73.16/11.74
% 73.16/11.74 % (12764)Memory used [KB]: 18933
% 73.16/11.74 % (12764)Time elapsed: 1.748 s
% 73.16/11.74 % (12764)Instructions burned: 5448 (million)
% 73.16/11.74 % (12764)------------------------------
% 73.16/11.74 % (12764)------------------------------
% 73.16/11.75 % (12783)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_12084 for (2898ds/8785Mi)
% 73.42/11.91 % (12782)Instruction limit reached!
% 73.42/11.91 % (12782)------------------------------
% 73.42/11.91 % (12782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.42/11.91 % (12782)Termination reason: Unknown
% 73.42/11.91 % (12782)Termination phase: Saturation
% 73.42/11.91
% 73.42/11.91 % (12782)Memory used [KB]: 10874
% 73.42/11.91 % (12782)Time elapsed: 0.210 s
% 73.42/11.91 % (12782)Instructions burned: 633 (million)
% 73.42/11.91 % (12782)------------------------------
% 73.42/11.91 % (12782)------------------------------
% 73.42/11.92 % (12784)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_12084 for (2896ds/739Mi)
% 76.41/12.11 % (12770)Instruction limit reached!
% 76.41/12.11 % (12770)------------------------------
% 76.41/12.11 % (12770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.41/12.11 % (12770)Termination reason: Unknown
% 76.41/12.11 % (12770)Termination phase: Saturation
% 76.41/12.11
% 76.41/12.11 % (12770)Memory used [KB]: 14967
% 76.41/12.11 % (12770)Time elapsed: 1.622 s
% 76.41/12.11 % (12770)Instructions burned: 5215 (million)
% 76.41/12.11 % (12770)------------------------------
% 76.41/12.11 % (12770)------------------------------
% 76.41/12.12 % (12785)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_12084 for (2894ds/5473Mi)
% 77.14/12.15 % (12784)Instruction limit reached!
% 77.14/12.15 % (12784)------------------------------
% 77.14/12.15 % (12784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.14/12.15 % (12784)Termination reason: Unknown
% 77.14/12.15 % (12784)Termination phase: Saturation
% 77.14/12.15
% 77.14/12.15 % (12784)Memory used [KB]: 8571
% 77.14/12.15 % (12784)Time elapsed: 0.234 s
% 77.14/12.15 % (12784)Instructions burned: 739 (million)
% 77.14/12.15 % (12784)------------------------------
% 77.14/12.15 % (12784)------------------------------
% 77.14/12.16 % (12786)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_12084 for (2893ds/43570Mi)
% 77.14/12.19 % (12786)Refutation not found, incomplete strategy
% 77.14/12.19 % (12786)------------------------------
% 77.14/12.19 % (12786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.14/12.19 % (12786)Termination reason: Refutation not found, incomplete strategy
% 77.14/12.19
% 77.14/12.19
% 77.14/12.19 % (12786)Memory used [KB]: 6780
% 77.14/12.19 % (12786)Time elapsed: 0.026 s
% 77.14/12.19 % (12786)Instructions burned: 76 (million)
% 77.14/12.19 % (12786)------------------------------
% 77.14/12.19 % (12786)------------------------------
% 77.58/12.20 % (12787)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_12084 for (2893ds/8382Mi)
% 77.58/12.22 % (12778)Instruction limit reached!
% 77.58/12.22 % (12778)------------------------------
% 77.58/12.22 % (12778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.58/12.22 % (12778)Termination reason: Unknown
% 77.58/12.22 % (12778)Termination phase: Saturation
% 77.58/12.22
% 77.58/12.22 % (12778)Memory used [KB]: 10746
% 77.58/12.22 % (12778)Time elapsed: 0.693 s
% 77.58/12.22 % (12778)Instructions burned: 2207 (million)
% 77.58/12.22 % (12778)------------------------------
% 77.58/12.22 % (12778)------------------------------
% 77.58/12.23 % (12788)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_12084 for (2893ds/407Mi)
% 78.01/12.34 % (12781)Instruction limit reached!
% 78.01/12.34 % (12781)------------------------------
% 78.01/12.34 % (12781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.01/12.34 % (12781)Termination reason: Unknown
% 78.01/12.34 % (12781)Termination phase: Saturation
% 78.01/12.34
% 78.01/12.34 % (12781)Memory used [KB]: 20468
% 78.01/12.34 % (12781)Time elapsed: 0.638 s
% 78.01/12.34 % (12781)Instructions burned: 2015 (million)
% 78.01/12.34 % (12781)------------------------------
% 78.01/12.34 % (12781)------------------------------
% 78.01/12.35 % (12789)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_12084 for (2892ds/2971Mi)
% 78.01/12.35 % (12788)Instruction limit reached!
% 78.01/12.35 % (12788)------------------------------
% 78.01/12.35 % (12788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.01/12.35 % (12788)Termination reason: Unknown
% 78.01/12.35 % (12788)Termination phase: Saturation
% 78.01/12.35
% 78.01/12.35 % (12788)Memory used [KB]: 9338
% 78.01/12.35 % (12788)Time elapsed: 0.128 s
% 78.01/12.35 % (12788)Instructions burned: 409 (million)
% 78.01/12.35 % (12788)------------------------------
% 78.01/12.35 % (12788)------------------------------
% 78.01/12.36 % (12790)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_12084 for (2891ds/9822Mi)
% 78.50/12.48 % (12777)Instruction limit reached!
% 78.50/12.48 % (12777)------------------------------
% 78.50/12.48 % (12777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.50/12.48 % (12777)Termination reason: Unknown
% 78.50/12.48 % (12777)Termination phase: Saturation
% 78.50/12.48
% 78.50/12.48 % (12777)Memory used [KB]: 10234
% 78.50/12.48 % (12777)Time elapsed: 1.457 s
% 78.50/12.48 % (12777)Instructions burned: 4690 (million)
% 78.50/12.48 % (12777)------------------------------
% 78.50/12.48 % (12777)------------------------------
% 78.50/12.49 % (12791)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_12084 for (2890ds/8425Mi)
% 84.68/13.21 % (12789)Instruction limit reached!
% 84.68/13.21 % (12789)------------------------------
% 84.68/13.21 % (12789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.68/13.21 % (12789)Termination reason: Unknown
% 84.68/13.21 % (12789)Termination phase: Saturation
% 84.68/13.21
% 84.68/13.21 % (12789)Memory used [KB]: 14711
% 84.68/13.21 % (12789)Time elapsed: 0.862 s
% 84.68/13.21 % (12789)Instructions burned: 2974 (million)
% 84.68/13.21 % (12789)------------------------------
% 84.68/13.21 % (12789)------------------------------
% 84.68/13.22 % (12792)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_12084 for (2883ds/3107Mi)
% 87.69/13.76 % (12785)Instruction limit reached!
% 87.69/13.76 % (12785)------------------------------
% 87.69/13.76 % (12785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.69/13.76 % (12785)Termination reason: Unknown
% 87.69/13.76 % (12785)Termination phase: Saturation
% 87.69/13.76
% 87.69/13.76 % (12785)Memory used [KB]: 8699
% 87.69/13.76 % (12785)Time elapsed: 1.649 s
% 87.69/13.76 % (12785)Instructions burned: 5476 (million)
% 87.69/13.76 % (12785)------------------------------
% 87.69/13.76 % (12785)------------------------------
% 87.69/13.78 % (12793)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_12084 for (2877ds/7967Mi)
% 90.43/14.11 % (12779)Instruction limit reached!
% 90.43/14.11 % (12779)------------------------------
% 90.43/14.11 % (12779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.43/14.11 % (12779)Termination reason: Unknown
% 90.43/14.11 % (12779)Termination phase: Saturation
% 90.43/14.11
% 90.43/14.11 % (12779)Memory used [KB]: 17398
% 90.43/14.11 % (12779)Time elapsed: 2.560 s
% 90.43/14.11 % (12779)Instructions burned: 8216 (million)
% 90.43/14.11 % (12779)------------------------------
% 90.43/14.11 % (12779)------------------------------
% 90.43/14.12 % (12795)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_12084 for (2874ds/3629Mi)
% 91.17/14.19 % (12792)Instruction limit reached!
% 91.17/14.19 % (12792)------------------------------
% 91.17/14.19 % (12792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.17/14.19 % (12792)Termination reason: Unknown
% 91.17/14.19 % (12792)Termination phase: Saturation
% 91.17/14.19
% 91.17/14.19 % (12792)Memory used [KB]: 13048
% 91.17/14.19 % (12792)Time elapsed: 0.997 s
% 91.17/14.19 % (12792)Instructions burned: 3107 (million)
% 91.17/14.19 % (12792)------------------------------
% 91.17/14.19 % (12792)------------------------------
% 91.62/14.21 % (12797)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_12084 for (2873ds/939Mi)
% 92.63/14.41 % (12783)Instruction limit reached!
% 92.63/14.41 % (12783)------------------------------
% 92.63/14.41 % (12783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.63/14.41 % (12783)Termination reason: Unknown
% 92.63/14.41 % (12783)Termination phase: Saturation
% 92.63/14.41
% 92.63/14.41 % (12783)Memory used [KB]: 15863
% 92.63/14.41 % (12783)Time elapsed: 2.660 s
% 92.63/14.41 % (12783)Instructions burned: 8786 (million)
% 92.63/14.41 % (12783)------------------------------
% 92.63/14.41 % (12783)------------------------------
% 92.63/14.42 % (12878)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_12084 for (2871ds/1188Mi)
% 93.06/14.51 % (12797)Instruction limit reached!
% 93.06/14.51 % (12797)------------------------------
% 93.06/14.51 % (12797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.06/14.51 % (12797)Termination reason: Unknown
% 93.06/14.51 % (12797)Termination phase: Saturation
% 93.06/14.51
% 93.06/14.51 % (12797)Memory used [KB]: 10106
% 93.06/14.51 % (12797)Time elapsed: 0.311 s
% 93.06/14.51 % (12797)Instructions burned: 941 (million)
% 93.06/14.51 % (12797)------------------------------
% 93.06/14.51 % (12797)------------------------------
% 93.06/14.52 % (12917)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_12084 for (2870ds/3205Mi)
% 94.16/14.79 % (12878)Instruction limit reached!
% 94.16/14.79 % (12878)------------------------------
% 94.16/14.79 % (12878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.16/14.79 % (12878)Termination reason: Unknown
% 94.16/14.79 % (12878)Termination phase: Saturation
% 94.16/14.79
% 94.16/14.79 % (12878)Memory used [KB]: 10106
% 94.16/14.79 % (12878)Time elapsed: 0.374 s
% 94.16/14.79 % (12878)Instructions burned: 1189 (million)
% 94.16/14.79 % (12878)------------------------------
% 94.16/14.79 % (12878)------------------------------
% 94.96/14.80 % (13022)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_12084 for (2867ds/865Mi)
% 95.36/14.90 % (12787)Instruction limit reached!
% 95.36/14.90 % (12787)------------------------------
% 95.36/14.90 % (12787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.36/14.90 % (12787)Termination reason: Unknown
% 95.36/14.90 % (12787)Termination phase: Saturation
% 95.36/14.90
% 95.36/14.90 % (12787)Memory used [KB]: 24178
% 95.36/14.90 % (12787)Time elapsed: 2.703 s
% 95.36/14.90 % (12787)Instructions burned: 8382 (million)
% 95.36/14.90 % (12787)------------------------------
% 95.36/14.90 % (12787)------------------------------
% 95.36/14.91 % (13049)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_12084 for (2866ds/7469Mi)
% 95.36/14.97 % (12793)Refutation not found, non-redundant clauses discarded% (12793)------------------------------
% 95.36/14.97 % (12793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.36/14.97 % (12793)Termination reason: Refutation not found, non-redundant clauses discarded
% 95.36/14.97
% 95.36/14.97 % (12793)Memory used [KB]: 18293
% 95.36/14.97 % (12793)Time elapsed: 1.220 s
% 95.36/14.97 % (12793)Instructions burned: 4061 (million)
% 95.36/14.97 % (12793)------------------------------
% 95.36/14.97 % (12793)------------------------------
% 95.36/14.98 % (13084)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_12084 for (2865ds/4165Mi)
% 95.36/15.00 % (13022)Refutation not found, non-redundant clauses discarded% (13022)------------------------------
% 95.36/15.00 % (13022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.36/15.00 % (13022)Termination reason: Refutation not found, non-redundant clauses discarded
% 95.36/15.00
% 95.36/15.00 % (13022)Memory used [KB]: 8315
% 95.36/15.00 % (13022)Time elapsed: 0.201 s
% 95.36/15.00 % (13022)Instructions burned: 620 (million)
% 95.36/15.00 % (13022)------------------------------
% 95.36/15.00 % (13022)------------------------------
% 95.36/15.02 % (13099)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_12084 for (2865ds/13468Mi)
% 97.48/15.08 % (12791)Instruction limit reached!
% 97.48/15.08 % (12791)------------------------------
% 97.48/15.08 % (12791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.48/15.08 % (12791)Termination reason: Unknown
% 97.48/15.08 % (12791)Termination phase: Saturation
% 97.48/15.08
% 97.48/15.08 % (12791)Memory used [KB]: 13816
% 97.48/15.08 % (12791)Time elapsed: 2.591 s
% 97.48/15.08 % (12791)Instructions burned: 8425 (million)
% 97.48/15.08 % (12791)------------------------------
% 97.48/15.08 % (12791)------------------------------
% 97.48/15.09 % (13163)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_12084 for (2864ds/2635Mi)
% 98.43/15.27 % (12795)Instruction limit reached!
% 98.43/15.27 % (12795)------------------------------
% 98.43/15.27 % (12795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.43/15.27 % (12795)Termination reason: Unknown
% 98.43/15.27 % (12795)Termination phase: Saturation
% 98.43/15.27
% 98.43/15.27 % (12795)Memory used [KB]: 14328
% 98.43/15.27 % (12795)Time elapsed: 1.154 s
% 98.43/15.27 % (12795)Instructions burned: 3630 (million)
% 98.43/15.27 % (12795)------------------------------
% 98.43/15.27 % (12795)------------------------------
% 98.43/15.28 % (13193)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_12084 for (2862ds/631Mi)
% 99.32/15.46 % (12790)Instruction limit reached!
% 99.32/15.46 % (12790)------------------------------
% 99.32/15.46 % (12790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.32/15.46 % (12790)Termination reason: Unknown
% 99.32/15.46 % (12790)Termination phase: Saturation
% 99.32/15.46
% 99.32/15.46 % (12790)Memory used [KB]: 19445
% 99.32/15.46 % (12790)Time elapsed: 3.095 s
% 99.32/15.46 % (12790)Instructions burned: 9823 (million)
% 99.32/15.46 % (12790)------------------------------
% 99.32/15.46 % (12790)------------------------------
% 99.32/15.47 % (13277)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_12084 for (2860ds/15557Mi)
% 99.32/15.47 % (13193)Instruction limit reached!
% 99.32/15.47 % (13193)------------------------------
% 99.32/15.47 % (13193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.32/15.47 % (13193)Termination reason: Unknown
% 99.32/15.47 % (13193)Termination phase: Saturation
% 99.32/15.47
% 99.32/15.47 % (13193)Memory used [KB]: 9466
% 99.32/15.47 % (13193)Time elapsed: 0.192 s
% 99.32/15.47 % (13193)Instructions burned: 633 (million)
% 99.32/15.47 % (13193)------------------------------
% 99.32/15.47 % (13193)------------------------------
% 99.32/15.48 % (13280)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_12084 for (2860ds/2142Mi)
% 99.89/15.59 % (12917)Instruction limit reached!
% 99.89/15.59 % (12917)------------------------------
% 99.89/15.59 % (12917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.89/15.59 % (12917)Termination reason: Unknown
% 99.89/15.59 % (12917)Termination phase: Saturation
% 99.89/15.59
% 99.89/15.59 % (12917)Memory used [KB]: 10490
% 99.89/15.59 % (12917)Time elapsed: 1.069 s
% 99.89/15.59 % (12917)Instructions burned: 3205 (million)
% 99.89/15.59 % (12917)------------------------------
% 99.89/15.59 % (12917)------------------------------
% 100.20/15.60 % (13288)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_12084 for (2859ds/5624Mi)
% 100.80/15.92 % (13163)Instruction limit reached!
% 100.80/15.92 % (13163)------------------------------
% 100.80/15.92 % (13163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.80/15.92 % (13163)Termination reason: Unknown
% 100.80/15.92 % (13163)Termination phase: Saturation
% 100.80/15.92
% 100.80/15.92 % (13163)Memory used [KB]: 11897
% 100.80/15.92 % (13163)Time elapsed: 0.830 s
% 100.80/15.92 % (13163)Instructions burned: 2636 (million)
% 100.80/15.92 % (13163)------------------------------
% 100.80/15.92 % (13163)------------------------------
% 100.80/15.93 % (13289)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_12084 for (2856ds/1665Mi)
% 105.22/16.19 % (13280)Instruction limit reached!
% 105.22/16.19 % (13280)------------------------------
% 105.22/16.19 % (13280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.22/16.19 % (13280)Termination reason: Unknown
% 105.22/16.19 % (13280)Termination phase: Saturation
% 105.22/16.19
% 105.22/16.19 % (13280)Memory used [KB]: 8955
% 105.22/16.19 % (13280)Time elapsed: 0.711 s
% 105.22/16.19 % (13280)Instructions burned: 2143 (million)
% 105.22/16.19 % (13280)------------------------------
% 105.22/16.19 % (13280)------------------------------
% 105.74/16.20 % (13291)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_12084 for (2853ds/64912Mi)
% 106.33/16.36 % (13084)Instruction limit reached!
% 106.33/16.36 % (13084)------------------------------
% 106.33/16.36 % (13084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.33/16.36 % (13084)Termination reason: Unknown
% 106.33/16.36 % (13084)Termination phase: Saturation
% 106.33/16.36
% 106.33/16.36 % (13084)Memory used [KB]: 25458
% 106.33/16.36 % (13084)Time elapsed: 1.378 s
% 106.33/16.36 % (13084)Instructions burned: 4166 (million)
% 106.33/16.36 % (13084)------------------------------
% 106.33/16.36 % (13084)------------------------------
% 106.33/16.38 % (13292)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_12084 for (2851ds/7801Mi)
% 107.41/16.56 % (13289)Instruction limit reached!
% 107.41/16.56 % (13289)------------------------------
% 107.41/16.56 % (13289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 107.41/16.56 % (13289)Termination reason: Unknown
% 107.41/16.56 % (13289)Termination phase: Saturation
% 107.41/16.56
% 107.41/16.56 % (13289)Memory used [KB]: 10362
% 107.41/16.56 % (13289)Time elapsed: 0.654 s
% 107.41/16.56 % (13289)Instructions burned: 1666 (million)
% 107.41/16.56 % (13289)------------------------------
% 107.41/16.56 % (13289)------------------------------
% 107.41/16.57 % (13329)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_12084 for (2849ds/15194Mi)
% 114.12/17.46 % (13099)First to succeed.
% 114.12/17.46 % (13099)Refutation found. Thanks to Tanya!
% 114.12/17.46 % SZS status Theorem for DTF2THF_12084
% 114.12/17.46 % SZS output start Proof for DTF2THF_12084
% 114.12/17.46 thf(type_def_6, type, sigma_measure: ($tType) > $tType).
% 114.12/17.46 thf(type_def_7, type, set: ($tType) > $tType).
% 114.12/17.46 thf(type_def_8, type, int: $tType).
% 114.12/17.46 thf(type_def_9, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 114.12/17.46 thf(type_def_10, type, n: $tType).
% 114.12/17.46 thf(type_def_11, type, real: $tType).
% 114.12/17.46 thf(type_def_12, type, nat: $tType).
% 114.12/17.46 thf(func_def_0, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 114.12/17.46 thf(func_def_1, type, sigma_measure: ($tType) > $tType).
% 114.12/17.46 thf(func_def_2, type, real: $tType).
% 114.12/17.46 thf(func_def_3, type, set: ($tType) > $tType).
% 114.12/17.46 thf(func_def_4, type, nat: $tType).
% 114.12/17.46 thf(func_def_5, type, int: $tType).
% 114.12/17.46 thf(func_def_6, type, n: $tType).
% 114.12/17.46 thf(func_def_7, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_8, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_9, type, type: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_10, type, plus: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_11, type, zero: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_12, type, minus: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_13, type, ring_char_0: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_14, type, group_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_15, type, lattice: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_16, type, finite_finite: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_17, type, monoid_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_18, type, countable: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_19, type, ab_group_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_20, type, semigroup_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_21, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_22, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_23, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_24, type, semilattice_inf: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_25, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_26, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_27, type, topological_t2_space: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_28, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_29, type, topolo1314133330id_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_30, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_31, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_32, type, real_V1076094709vector: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_33, type, euclid925273238_space: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_34, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_35, type, topolo2117631714pology: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_36, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_37, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_38, type, real_V55928688vector: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_39, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_40, type, elemen1026692323pology: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_41, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 114.12/17.46 thf(func_def_42, type, borel_is_borel: !>[X0: $tType, X1: $tType]:((X0 > X1) > sigma_measure @ X0 > $o)).
% 114.12/17.46 thf(func_def_43, type, borel_1404511681_borel: !>[X0: $tType]:(sigma_measure @ X0)).
% 114.12/17.46 thf(func_def_44, type, complete_completion: !>[X0: $tType]:(sigma_measure @ X0 > sigma_measure @ X0)).
% 114.12/17.46 thf(func_def_45, type, complete_main_part: !>[X0: $tType]:(sigma_measure @ X0 > set @ X0 > set @ X0)).
% 114.12/17.46 thf(func_def_46, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 114.12/17.46 thf(func_def_47, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 114.12/17.46 thf(func_def_48, type, zero_zero: !>[X0: $tType]:(X0)).
% 114.12/17.46 thf(func_def_49, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 114.12/17.46 thf(func_def_50, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 114.12/17.46 thf(func_def_51, type, lebesgue_lborel: !>[X0: $tType]:(sigma_measure @ X0)).
% 114.12/17.46 thf(func_def_52, type, minkow1937162798nt_vec: !>[X0: $tType, X1: $tType]:(finite_Cartesian_vec @ int @ X0 > finite_Cartesian_vec @ X1 @ X0)).
% 114.12/17.46 thf(func_def_53, type, ord_Least: !>[X0: $tType]:((X0 > $o) > X0)).
% 114.12/17.46 thf(func_def_54, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 114.12/17.46 thf(func_def_55, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 114.12/17.46 thf(func_def_56, type, image: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > set @ X1)).
% 114.12/17.46 thf(func_def_57, type, vimage: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X1 > set @ X0)).
% 114.12/17.46 thf(func_def_58, type, sigma_measurable: !>[X0: $tType, X1: $tType]:(sigma_measure @ X0 > sigma_measure @ X1 > set @ (X0 > X1))).
% 114.12/17.46 thf(func_def_59, type, sigma_restrict_space: !>[X0: $tType]:(sigma_measure @ X0 > set @ X0 > sigma_measure @ X0)).
% 114.12/17.46 thf(func_def_60, type, sigma_sets: !>[X0: $tType]:(sigma_measure @ X0 > set @ set @ X0)).
% 114.12/17.46 thf(func_def_61, type, sigma_space: !>[X0: $tType]:(sigma_measure @ X0 > set @ X0)).
% 114.12/17.46 thf(func_def_62, type, sigma_vimage_algebra: !>[X0: $tType, X1: $tType]:(set @ X0 > (X0 > X1) > sigma_measure @ X1 > sigma_measure @ X0)).
% 114.12/17.46 thf(func_def_63, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 114.12/17.46 thf(func_def_64, type, r: finite_Cartesian_vec @ int @ n > set @ finite_Cartesian_vec @ real @ n).
% 114.12/17.46 thf(func_def_65, type, s: set @ finite_Cartesian_vec @ real @ n).
% 114.12/17.46 thf(func_def_66, type, t: finite_Cartesian_vec @ int @ n > set @ finite_Cartesian_vec @ real @ n).
% 114.12/17.46 thf(func_def_67, type, t2: finite_Cartesian_vec @ int @ n > set @ finite_Cartesian_vec @ real @ n).
% 114.12/17.46 thf(func_def_68, type, a: finite_Cartesian_vec @ int @ n).
% 114.12/17.46 thf(func_def_88, type, sK1: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > $o) > (X1 > $o) > X1)).
% 114.12/17.46 thf(func_def_89, type, sK2: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 114.12/17.46 thf(func_def_90, type, sK3: !>[X0: $tType, X1: $tType]:((X1 > X0) > X0 > set @ X1 > X1)).
% 114.12/17.46 thf(func_def_91, type, sK4: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > set @ X1)).
% 114.12/17.46 thf(func_def_92, type, sK5: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ X1 > (X1 > X0) > X1)).
% 114.12/17.46 thf(func_def_93, type, sK6: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 114.12/17.46 thf(func_def_94, type, sK7: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X1)).
% 114.12/17.46 thf(func_def_95, type, sK8: !>[X0: $tType, X1: $tType]:((X0 > X1) > sigma_measure @ X0 > sigma_measure @ X1 > set @ X1)).
% 114.12/17.46 thf(func_def_96, type, sK9: !>[X0: $tType, X1: $tType]:((X0 > X1) > sigma_measure @ X0 > sigma_measure @ X1 > X0)).
% 114.12/17.46 thf(func_def_97, type, sK10: !>[X0: $tType, X1: $tType]:(set @ X0 > (X0 > X1) > (X1 > $o) > X1)).
% 114.12/17.46 thf(func_def_98, type, sK11: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 114.12/17.46 thf(func_def_99, type, sK12: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0)).
% 114.12/17.46 thf(func_def_100, type, sK13: !>[X0: $tType]:(set @ X0 > X0 > set @ X0 > X0)).
% 114.12/17.46 thf(func_def_101, type, ph14: !>[X0: $tType]:(X0)).
% 114.12/17.46 thf(f11885,plain,(
% 114.12/17.46 $false),
% 114.12/17.46 inference(avatar_sat_refutation,[status(thm)],[f4825,f11851,f11879])).
% 114.12/17.46 thf(f11879,plain,(
% 114.12/17.46 ~spl0_193),
% 114.12/17.46 inference(avatar_contradiction_clause,[status(thm)],[f11878])).
% 114.12/17.46 thf(f11878,plain,(
% 114.12/17.46 $false | ~spl0_193),
% 114.12/17.46 inference(trivial_inequality_removal,[status(thm)],[f11856])).
% 114.12/17.46 thf(f11856,plain,(
% 114.12/17.46 ($true = $false) | ~spl0_193),
% 114.12/17.46 inference(superposition,[status(thm)],[f11850,f2571])).
% 114.12/17.46 thf(f2571,plain,(
% 114.12/17.46 ((member @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ a))) @ (t2 @ a)) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) = $false)),
% 114.12/17.46 inference(not_proxy_clausification,[status(thm)],[f1578])).
% 114.12/17.46 thf(f1578,plain,(
% 114.12/17.46 ((~ (member @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ a))) @ (t2 @ a)) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))) = $true)),
% 114.12/17.46 inference(cnf_transformation,[status(thm)],[f578])).
% 114.12/17.46 thf(f578,plain,(
% 114.12/17.46 ((~ (member @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ a))) @ (t2 @ a)) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))) = $true)),
% 114.12/17.46 inference(fool_elimination,[status(thm)],[f577])).
% 114.12/17.46 thf(f577,plain,(
% 114.12/17.46 ~(member @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[X0 : finite_Cartesian_vec @ real @ n] : (plus_plus @ finite_Cartesian_vec @ real @ n @ X0 @ (minkow1937162798nt_vec @ n @ real @ a))) @ (t2 @ a)) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))),
% 114.12/17.46 inference(rectify,[status(thm)],[f399])).
% 114.12/17.46 thf(f399,negated_conjecture,(
% 114.12/17.46 ~(member @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[X6 : finite_Cartesian_vec @ real @ n] : (plus_plus @ finite_Cartesian_vec @ real @ n @ X6 @ (minkow1937162798nt_vec @ n @ real @ a))) @ (t2 @ a)) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))),
% 114.12/17.46 inference(negated_conjecture,[status(cth)],[f398])).
% 114.12/17.46 thf(f398,conjecture,(
% 114.12/17.46 (member @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[X6 : finite_Cartesian_vec @ real @ n] : (plus_plus @ finite_Cartesian_vec @ real @ n @ X6 @ (minkow1937162798nt_vec @ n @ real @ a))) @ (t2 @ a)) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))),
% 114.12/17.46 file('/export/starexec/sandbox/tmp/tmp.3Wo9oJ6aQl/DTF2THF_12084.p',conj_0)).
% 114.12/17.46 thf(f11850,plain,(
% 114.12/17.46 ( ! [X0 : finite_Cartesian_vec @ int @ n] : (($true = (member @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ (t2 @ X0)) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))))) ) | ~spl0_193),
% 114.12/17.46 inference(avatar_component_clause,[status(thm)],[f11849])).
% 114.12/17.46 thf(f11849,definition,(
% 114.12/17.46 spl0_193 <=> ! [X0 : finite_Cartesian_vec @ int @ n] : ($true = (member @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ (t2 @ X0)) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))))),
% 114.12/17.46 introduced(definition,[new_symbols(naming,[spl0_193])],[avatar_definition])).
% 114.12/17.46 thf(f11851,plain,(
% 114.12/17.46 spl0_69 | spl0_193),
% 114.12/17.46 inference(avatar_split_clause,[status(thm)],[f11834,f11849,f4773])).
% 114.12/17.46 thf(f4773,definition,(
% 114.12/17.46 spl0_69 <=> ($false = euclid925273238_space @ finite_Cartesian_vec @ real @ n)),
% 114.12/17.46 introduced(definition,[new_symbols(naming,[spl0_69])],[avatar_definition])).
% 114.12/17.46 thf(f11834,plain,(
% 114.12/17.46 ( ! [X0 : finite_Cartesian_vec @ int @ n] : (($true = (member @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ (t2 @ X0)) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))) | ($false = euclid925273238_space @ finite_Cartesian_vec @ real @ n)) )),
% 114.12/17.46 inference(superposition,[status(thm)],[f11740,f1986])).
% 114.12/17.46 thf(f1986,plain,(
% 114.12/17.46 ( ! [X0 : $tType,X1 : set @ X0] : (((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ (complete_completion @ X0 @ lebesgue_lborel @ X0) @ X1)) = X1) | (euclid925273238_space @ X0 = $false)) )),
% 114.12/17.46 inference(equality_proxy_clausification,[status(thm)],[f1985])).
% 114.12/17.46 thf(f1985,plain,(
% 114.12/17.46 ( ! [X0 : $tType,X1 : set @ X0] : ((euclid925273238_space @ X0 = $false) | (((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ (complete_completion @ X0 @ lebesgue_lborel @ X0) @ X1)) = X1) = $true)) )),
% 114.12/17.46 inference(beta_eta_normalization,[status(thm)],[f1984])).
% 114.12/17.46 thf(f1984,plain,(
% 114.12/17.46 ( ! [X0 : $tType,X1 : set @ X0] : ((euclid925273238_space @ X0 = $false) | (((^[Y0 : set @ X0]: ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ (complete_completion @ X0 @ lebesgue_lborel @ X0) @ Y0)) = Y0)) @ X1) = $true)) )),
% 114.12/17.46 inference(pi_clausification,[status(thm)],[f1983])).
% 114.12/17.46 thf(f1983,plain,(
% 114.12/17.46 ( ! [X0 : $tType] : ((euclid925273238_space @ X0 = $false) | ((!! @ set @ X0 @ (^[Y0 : set @ X0]: ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ (complete_completion @ X0 @ lebesgue_lborel @ X0) @ Y0)) = Y0))) = $true)) )),
% 114.12/17.46 inference(binary_proxy_clausification,[status(thm)],[f1557])).
% 114.12/17.46 thf(f1557,plain,(
% 114.12/17.46 ( ! [X0 : $tType] : (((euclid925273238_space @ X0 => (!! @ set @ X0 @ (^[Y0 : set @ X0]: ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ (complete_completion @ X0 @ lebesgue_lborel @ X0) @ Y0)) = Y0)))) = $true)) )),
% 114.12/17.46 inference(cnf_transformation,[status(thm)],[f1209])).
% 114.12/17.46 thf(f1209,plain,(
% 114.12/17.46 ! [X0 : $tType] : ((euclid925273238_space @ X0 => (!! @ set @ X0 @ (^[Y0 : set @ X0]: ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ (complete_completion @ X0 @ lebesgue_lborel @ X0) @ Y0)) = Y0)))) = $true)),
% 114.12/17.46 inference(closure,[status(thm)],[f594])).
% 114.12/17.46 thf(f594,plain,(
% 114.12/17.46 ( ! [X0 : $tType] : (((euclid925273238_space @ X0 => (!! @ set @ X0 @ (^[Y0 : set @ X0]: ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ (complete_completion @ X0 @ lebesgue_lborel @ X0) @ Y0)) = Y0)))) = $true)) )),
% 114.12/17.46 inference(fool_elimination,[status(thm)],[f593])).
% 114.12/17.46 thf(f593,plain,(
% 114.12/17.46 ! [X0 : $tType] : (euclid925273238_space @ X0 => ! [X1 : set @ X0] : ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ (complete_completion @ X0 @ lebesgue_lborel @ X0) @ X1)) = X1))),
% 114.12/17.46 inference(rectify,[status(thm)],[f163])).
% 114.12/17.46 thf(f163,axiom,(
% 114.12/17.46 ! [X0 : $tType] : (euclid925273238_space @ X0 => ! [X24 : set @ X0] : ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ (complete_completion @ X0 @ lebesgue_lborel @ X0) @ X24)) = X24))),
% 114.12/17.46 file('/export/starexec/sandbox/tmp/tmp.3Wo9oJ6aQl/DTF2THF_12084.p',fact_162_space__lebesgue__on)).
% 114.12/17.46 thf(f11740,plain,(
% 114.12/17.46 ( ! [X1 : finite_Cartesian_vec @ int @ n] : (((member @ set @ finite_Cartesian_vec @ real @ n @ (sigma_space @ finite_Cartesian_vec @ real @ n @ (sigma_restrict_space @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X1))) @ (t2 @ X1)))) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) = $true)) )),
% 114.12/17.46 inference(forward_demodulation,[status(thm)],[f11739,f2008])).
% 114.12/17.46 thf(f2008,plain,(
% 114.12/17.46 ( ! [X0 : $tType,X2 : sigma_measure @ X0,X1 : set @ X0] : (((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ X2 @ X1)) = (inf_inf @ set @ X0 @ X1 @ (sigma_space @ X0 @ X2)))) )),
% 114.12/17.46 inference(equality_proxy_clausification,[status(thm)],[f2007])).
% 114.12/17.46 thf(f2007,plain,(
% 114.12/17.46 ( ! [X0 : $tType,X2 : sigma_measure @ X0,X1 : set @ X0] : ((((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ X2 @ X1)) = (inf_inf @ set @ X0 @ X1 @ (sigma_space @ X0 @ X2))) = $true)) )),
% 114.12/17.46 inference(beta_eta_normalization,[status(thm)],[f2006])).
% 114.12/17.46 thf(f2006,plain,(
% 114.12/17.46 ( ! [X0 : $tType,X2 : sigma_measure @ X0,X1 : set @ X0] : (($true = ((^[Y0 : sigma_measure @ X0]: ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ Y0 @ X1)) = (inf_inf @ set @ X0 @ X1 @ (sigma_space @ X0 @ Y0)))) @ X2))) )),
% 114.12/17.46 inference(pi_clausification,[status(thm)],[f2005])).
% 114.12/17.46 thf(f2005,plain,(
% 114.12/17.46 ( ! [X0 : $tType,X1 : set @ X0] : (((!! @ sigma_measure @ X0 @ (^[Y0 : sigma_measure @ X0]: ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ Y0 @ X1)) = (inf_inf @ set @ X0 @ X1 @ (sigma_space @ X0 @ Y0))))) = $true)) )),
% 114.12/17.46 inference(beta_eta_normalization,[status(thm)],[f2004])).
% 114.12/17.46 thf(f2004,plain,(
% 114.12/17.46 ( ! [X0 : $tType,X1 : set @ X0] : (($true = ((^[Y0 : set @ X0]: (!! @ sigma_measure @ X0 @ (^[Y1 : sigma_measure @ X0]: ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ Y1 @ Y0)) = (inf_inf @ set @ X0 @ Y0 @ (sigma_space @ X0 @ Y1)))))) @ X1))) )),
% 114.12/17.46 inference(pi_clausification,[status(thm)],[f1581])).
% 114.12/17.46 thf(f1581,plain,(
% 114.12/17.46 ( ! [X0 : $tType] : (($true = (!! @ set @ X0 @ (^[Y0 : set @ X0]: (!! @ sigma_measure @ X0 @ (^[Y1 : sigma_measure @ X0]: ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ Y1 @ Y0)) = (inf_inf @ set @ X0 @ Y0 @ (sigma_space @ X0 @ Y1))))))))) )),
% 114.12/17.46 inference(cnf_transformation,[status(thm)],[f1327])).
% 114.12/17.46 thf(f1327,plain,(
% 114.12/17.46 ! [X0 : $tType] : ($true = (!! @ set @ X0 @ (^[Y0 : set @ X0]: (!! @ sigma_measure @ X0 @ (^[Y1 : sigma_measure @ X0]: ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ Y1 @ Y0)) = (inf_inf @ set @ X0 @ Y0 @ (sigma_space @ X0 @ Y1))))))))),
% 114.12/17.46 inference(closure,[status(thm)],[f452])).
% 114.12/17.46 thf(f452,plain,(
% 114.12/17.46 ( ! [X0 : $tType] : (($true = (!! @ set @ X0 @ (^[Y0 : set @ X0]: (!! @ sigma_measure @ X0 @ (^[Y1 : sigma_measure @ X0]: ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ Y1 @ Y0)) = (inf_inf @ set @ X0 @ Y0 @ (sigma_space @ X0 @ Y1))))))))) )),
% 114.12/17.46 inference(fool_elimination,[status(thm)],[f451])).
% 114.12/17.46 thf(f451,plain,(
% 114.12/17.46 ! [X0 : $tType,X1 : sigma_measure @ X0,X2 : set @ X0] : ((sigma_space @ X0 @ (sigma_restrict_space @ X0 @ X1 @ X2)) = (inf_inf @ set @ X0 @ X2 @ (sigma_space @ X0 @ X1)))),
% 114.12/17.46 inference(rectify,[status(thm)],[f156])).
% 114.12/17.46 thf(f156,axiom,(
% 114.12/17.46 ! [X0 : $tType,X8 : sigma_measure @ X0,X45 : set @ X0] : ((inf_inf @ set @ X0 @ X45 @ (sigma_space @ X0 @ X8)) = (sigma_space @ X0 @ (sigma_restrict_space @ X0 @ X8 @ X45)))),
% 114.12/17.46 file('/export/starexec/sandbox/tmp/tmp.3Wo9oJ6aQl/DTF2THF_12084.p',fact_155_space__restrict__space)).
% 114.12/17.46 thf(f11739,plain,(
% 114.12/17.46 ( ! [X1 : finite_Cartesian_vec @ int @ n] : (($true = (member @ set @ finite_Cartesian_vec @ real @ n @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X1))) @ (t2 @ X1)) @ (sigma_space @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))))) )),
% 114.12/17.46 inference(trivial_inequality_removal,[status(thm)],[f11738])).
% 114.12/17.46 thf(f11738,plain,(
% 114.12/17.46 ( ! [X1 : finite_Cartesian_vec @ int @ n] : (($true = (member @ set @ finite_Cartesian_vec @ real @ n @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X1))) @ (t2 @ X1)) @ (sigma_space @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))) | ($true = $false)) )),
% 114.12/17.46 inference(forward_demodulation,[status(thm)],[f2201,f2614])).
% 114.12/17.46 thf(f2614,plain,(
% 114.12/17.46 ( ! [X1 : finite_Cartesian_vec @ int @ n] : (($true = (member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ X1) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))))) )),
% 114.12/17.46 inference(beta_eta_normalization,[status(thm)],[f2613])).
% 114.12/17.46 thf(f2613,plain,(
% 114.12/17.46 ( ! [X1 : finite_Cartesian_vec @ int @ n] : ((((^[Y0 : finite_Cartesian_vec @ int @ n]: (member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ Y0) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))) @ X1) = $true)) )),
% 114.12/17.46 inference(pi_clausification,[status(thm)],[f1551])).
% 114.12/17.46 thf(f1551,plain,(
% 114.12/17.46 ((!! @ finite_Cartesian_vec @ int @ n @ (^[Y0 : finite_Cartesian_vec @ int @ n]: (member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ Y0) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))))) = $true)),
% 114.12/17.46 inference(cnf_transformation,[status(thm)],[f682])).
% 114.12/17.46 thf(f682,plain,(
% 114.12/17.46 ((!! @ finite_Cartesian_vec @ int @ n @ (^[Y0 : finite_Cartesian_vec @ int @ n]: (member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ Y0) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))))) = $true)),
% 114.12/17.46 inference(fool_elimination,[status(thm)],[f681])).
% 114.12/17.46 thf(f681,plain,(
% 114.12/17.46 ! [X0 : finite_Cartesian_vec @ int @ n] : (member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ X0) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))),
% 114.12/17.46 inference(rectify,[status(thm)],[f4])).
% 114.12/17.46 thf(f4,axiom,(
% 114.12/17.46 ! [X3 : finite_Cartesian_vec @ int @ n] : (member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ X3) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))),
% 114.12/17.46 file('/export/starexec/sandbox/tmp/tmp.3Wo9oJ6aQl/DTF2THF_12084.p',fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062)).
% 114.12/17.46 thf(f2201,plain,(
% 114.12/17.46 ( ! [X1 : finite_Cartesian_vec @ int @ n] : (($false = (member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ X1) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))) | ($true = (member @ set @ finite_Cartesian_vec @ real @ n @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X1))) @ (t2 @ X1)) @ (sigma_space @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))))) )),
% 114.12/17.46 inference(binary_proxy_clausification,[status(thm)],[f2200])).
% 114.12/17.46 thf(f2200,plain,(
% 114.12/17.46 ( ! [X1 : finite_Cartesian_vec @ int @ n] : ((((member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ X1) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) => (member @ set @ finite_Cartesian_vec @ real @ n @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X1))) @ (t2 @ X1)) @ (sigma_space @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))) = $true)) )),
% 114.12/17.46 inference(beta_eta_normalization,[status(thm)],[f2199])).
% 114.12/17.46 thf(f2199,plain,(
% 114.12/17.46 ( ! [X1 : finite_Cartesian_vec @ int @ n] : (($true = ((^[Y0 : finite_Cartesian_vec @ int @ n]: ((member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ Y0) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) => (member @ set @ finite_Cartesian_vec @ real @ n @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y1 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y1 @ (minkow1937162798nt_vec @ n @ real @ Y0))) @ (t2 @ Y0)) @ (sigma_space @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))))) @ X1))) )),
% 114.12/17.46 inference(pi_clausification,[status(thm)],[f1465])).
% 114.12/17.46 thf(f1465,plain,(
% 114.12/17.46 ($true = (!! @ finite_Cartesian_vec @ int @ n @ (^[Y0 : finite_Cartesian_vec @ int @ n]: ((member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ Y0) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) => (member @ set @ finite_Cartesian_vec @ real @ n @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y1 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y1 @ (minkow1937162798nt_vec @ n @ real @ Y0))) @ (t2 @ Y0)) @ (sigma_space @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))))))),
% 114.12/17.46 inference(cnf_transformation,[status(thm)],[f422])).
% 114.12/17.46 thf(f422,plain,(
% 114.12/17.46 ($true = (!! @ finite_Cartesian_vec @ int @ n @ (^[Y0 : finite_Cartesian_vec @ int @ n]: ((member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ Y0) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) => (member @ set @ finite_Cartesian_vec @ real @ n @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y1 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y1 @ (minkow1937162798nt_vec @ n @ real @ Y0))) @ (t2 @ Y0)) @ (sigma_space @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n)))))))),
% 114.12/17.46 inference(fool_elimination,[status(thm)],[f421])).
% 114.12/17.46 thf(f421,plain,(
% 114.12/17.46 ! [X0 : finite_Cartesian_vec @ int @ n] : ((member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ X0) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) => (member @ set @ finite_Cartesian_vec @ real @ n @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[X1 : finite_Cartesian_vec @ real @ n] : (plus_plus @ finite_Cartesian_vec @ real @ n @ X1 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ (t2 @ X0)) @ (sigma_space @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))))),
% 114.12/17.46 inference(rectify,[status(thm)],[f3])).
% 114.12/17.46 thf(f3,axiom,(
% 114.12/17.46 ! [X5 : finite_Cartesian_vec @ int @ n] : ((member @ set @ finite_Cartesian_vec @ real @ n @ (t2 @ X5) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) => (member @ set @ finite_Cartesian_vec @ real @ n @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ (vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[X6 : finite_Cartesian_vec @ real @ n] : (plus_plus @ finite_Cartesian_vec @ real @ n @ X6 @ (minkow1937162798nt_vec @ n @ real @ X5))) @ (t2 @ X5)) @ (sigma_space @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))) @ (sigma_sets @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n))))),
% 114.12/17.46 file('/export/starexec/sandbox/tmp/tmp.3Wo9oJ6aQl/DTF2THF_12084.p',fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062)).
% 114.12/17.46 thf(f4825,plain,(
% 114.12/17.46 ~spl0_69),
% 114.12/17.46 inference(avatar_contradiction_clause,[status(thm)],[f4824])).
% 114.12/17.46 thf(f4824,plain,(
% 114.12/17.46 $false | ~spl0_69),
% 114.12/17.46 inference(trivial_inequality_removal,[status(thm)],[f4823])).
% 114.12/17.46 thf(f4823,plain,(
% 114.12/17.46 ($true = $false) | ~spl0_69),
% 114.12/17.46 inference(backward_demodulation,[status(thm)],[f1514,f4788])).
% 114.12/17.46 thf(f4788,plain,(
% 114.12/17.46 (euclid925273238_space @ real = $false) | ~spl0_69),
% 114.12/17.46 inference(trivial_inequality_removal,[status(thm)],[f4787])).
% 114.12/17.46 thf(f4787,plain,(
% 114.12/17.46 ($true = $false) | (euclid925273238_space @ real = $false) | ~spl0_69),
% 114.12/17.46 inference(forward_demodulation,[status(thm)],[f4786,f1546])).
% 114.12/17.46 thf(f1546,plain,(
% 114.12/17.46 (finite_finite @ n = $true)),
% 114.12/17.46 inference(cnf_transformation,[status(thm)],[f1082])).
% 114.12/17.46 thf(f1082,plain,(
% 114.12/17.46 (finite_finite @ n = $true)),
% 114.12/17.46 inference(fool_elimination,[status(thm)],[f1081])).
% 114.12/17.46 thf(f1081,plain,(
% 114.12/17.46 finite_finite @ n),
% 114.12/17.46 inference(rectify,[status(thm)],[f397])).
% 114.12/17.46 thf(f397,axiom,(
% 114.12/17.46 finite_finite @ n),
% 114.12/17.46 file('/export/starexec/sandbox/tmp/tmp.3Wo9oJ6aQl/DTF2THF_12084.p',tfree_0)).
% 114.12/17.46 thf(f4786,plain,(
% 114.12/17.46 (finite_finite @ n = $false) | (euclid925273238_space @ real = $false) | ~spl0_69),
% 114.12/17.46 inference(trivial_inequality_removal,[status(thm)],[f4784])).
% 114.12/17.46 thf(f4784,plain,(
% 114.12/17.46 ($true = $false) | (finite_finite @ n = $false) | (euclid925273238_space @ real = $false) | ~spl0_69),
% 114.12/17.46 inference(superposition,[status(thm)],[f1809,f4775])).
% 114.12/17.46 thf(f4775,plain,(
% 114.12/17.46 ($false = euclid925273238_space @ finite_Cartesian_vec @ real @ n) | ~spl0_69),
% 114.12/17.46 inference(avatar_component_clause,[status(thm)],[f4773])).
% 114.12/17.46 thf(f1809,plain,(
% 114.12/17.46 ( ! [X1 : $tType,X0 : $tType] : ((euclid925273238_space @ finite_Cartesian_vec @ X0 @ X1 = $true) | (finite_finite @ X1 = $false) | (euclid925273238_space @ X0 = $false)) )),
% 114.12/17.46 inference(binary_proxy_clausification,[status(thm)],[f1808])).
% 114.12/17.46 thf(f1808,plain,(
% 114.12/17.46 ( ! [X1 : $tType,X0 : $tType] : ((euclid925273238_space @ finite_Cartesian_vec @ X0 @ X1 = $true) | ((finite_finite @ X1 & euclid925273238_space @ X0) = $false)) )),
% 114.12/17.46 inference(binary_proxy_clausification,[status(thm)],[f1583])).
% 114.12/17.46 thf(f1583,plain,(
% 114.12/17.46 ( ! [X1 : $tType,X0 : $tType] : ((((finite_finite @ X1 & euclid925273238_space @ X0) => euclid925273238_space @ finite_Cartesian_vec @ X0 @ X1) = $true)) )),
% 114.12/17.46 inference(cnf_transformation,[status(thm)],[f1425])).
% 114.12/17.46 thf(f1425,plain,(
% 114.12/17.46 ! [X0 : $tType,X1 : $tType] : (((finite_finite @ X1 & euclid925273238_space @ X0) => euclid925273238_space @ finite_Cartesian_vec @ X0 @ X1) = $true)),
% 114.12/17.46 inference(rectify,[status(thm)],[f1288])).
% 114.12/17.46 thf(f1288,plain,(
% 114.12/17.46 ! [X1 : $tType,X0 : $tType] : ($true = ((finite_finite @ X0 & euclid925273238_space @ X1) => euclid925273238_space @ finite_Cartesian_vec @ X1 @ X0))),
% 114.12/17.46 inference(closure,[status(thm)],[f1287])).
% 114.12/17.46 thf(f1287,plain,(
% 114.12/17.46 ( ! [X1 : $tType,X0 : $tType] : (($true = ((finite_finite @ X0 & euclid925273238_space @ X1) => euclid925273238_space @ finite_Cartesian_vec @ X1 @ X0))) )),
% 114.12/17.46 inference(rectify,[status(thm)],[f1012])).
% 114.12/17.46 thf(f1012,plain,(
% 114.12/17.46 ( ! [X1 : $tType,X0 : $tType] : ((((finite_finite @ X1 & euclid925273238_space @ X0) => euclid925273238_space @ finite_Cartesian_vec @ X0 @ X1) = $true)) )),
% 114.12/17.46 inference(fool_elimination,[status(thm)],[f1011])).
% 114.12/17.46 thf(f1011,plain,(
% 114.12/17.46 ! [X0 : $tType,X1 : $tType] : ((euclid925273238_space @ X0 & finite_finite @ X1) => euclid925273238_space @ finite_Cartesian_vec @ X0 @ X1)),
% 114.12/17.46 inference(rectify,[status(thm)],[f372])).
% 114.12/17.46 thf(f372,axiom,(
% 114.12/17.46 ! [X65 : $tType,X66 : $tType] : ((euclid925273238_space @ X65 & finite_finite @ X66) => euclid925273238_space @ finite_Cartesian_vec @ X65 @ X66)),
% 114.12/17.46 file('/export/starexec/sandbox/tmp/tmp.3Wo9oJ6aQl/DTF2THF_12084.p',tcon_Finite__Cartesian__Product_Ovec___Euclidean__Space_Oeuclidean__space_81)).
% 114.12/17.46 thf(f1514,plain,(
% 114.12/17.46 (euclid925273238_space @ real = $true)),
% 114.12/17.46 inference(cnf_transformation,[status(thm)],[f548])).
% 114.12/17.46 thf(f548,plain,(
% 114.12/17.46 (euclid925273238_space @ real = $true)),
% 114.12/17.46 inference(fool_elimination,[status(thm)],[f547])).
% 114.12/17.46 thf(f547,plain,(
% 114.12/17.46 euclid925273238_space @ real),
% 114.12/17.46 inference(rectify,[status(thm)],[f343])).
% 114.12/17.46 thf(f343,axiom,(
% 114.12/17.46 euclid925273238_space @ real),
% 114.12/17.46 file('/export/starexec/sandbox/tmp/tmp.3Wo9oJ6aQl/DTF2THF_12084.p',tcon_Real_Oreal___Euclidean__Space_Oeuclidean__space)).
% 114.12/17.46 % SZS output end Proof for DTF2THF_12084
% 114.12/17.46 % (13099)------------------------------
% 114.12/17.46 % (13099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.12/17.46 % (13099)Termination reason: Refutation
% 114.12/17.46
% 114.12/17.46 % (13099)Memory used [KB]: 14072
% 114.12/17.46 % (13099)Time elapsed: 2.447 s
% 114.12/17.46 % (13099)Instructions burned: 7570 (million)
% 114.12/17.46 % (13099)------------------------------
% 114.12/17.46 % (13099)------------------------------
% 114.12/17.46 % (12281)Success in time 15.923 s
%------------------------------------------------------------------------------