%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP116^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:49 AM UTC 2026
% Result : Theorem 42.64s 21.83s
% Output : Refutation 44.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 397
% Syntax : Number of formulae : 796 ( 274 unt; 0 typ; 0 def)
% Number of atoms : 2475 ( 530 equ; 2 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 9907 ( 34 ~; 3 |; 190 &;8986 @)
% ( 0 <=>; 694 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 446 ( 446 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 65 usr; 8 con; 0-5 aty)
% Number of variables : 2310 ( 241 ^;2063 !; 6 ?;2310 :)
% Comments :
%------------------------------------------------------------------------------
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(n_type,type,
n: $tType ).
thf(real_V2090557954_space_decl,type,
real_V2090557954_space:
!>[TA: $tType] : $o ).
thf(ordere890947078_space_decl,type,
ordere890947078_space:
!>[TA: $tType] : $o ).
thf(type_decl,type,
type:
!>[TA: $tType] : $o ).
thf(plus_decl,type,
plus:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(minus_decl,type,
minus:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(lattice_decl,type,
lattice:
!>[TA: $tType] : $o ).
thf(finite_finite_decl,type,
finite_finite:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(countable_decl,type,
countable:
!>[TA: $tType] : $o ).
thf(ab_group_add_decl,type,
ab_group_add:
!>[TA: $tType] : $o ).
thf(semigroup_add_decl,type,
semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_diff_decl,type,
comm_monoid_diff:
!>[TA: $tType] : $o ).
thf(semilattice_inf_decl,type,
semilattice_inf:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(topological_t2_space_decl,type,
topological_t2_space:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_decl,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(topolo1314133330id_add_decl,type,
topolo1314133330id_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(real_V1076094709vector_decl,type,
real_V1076094709vector:
!>[TA: $tType] : $o ).
thf(euclid925273238_space_decl,type,
euclid925273238_space:
!>[TA: $tType] : $o ).
thf(ordere779506340up_add_decl,type,
ordere779506340up_add:
!>[TA: $tType] : $o ).
thf(topolo2117631714pology_decl,type,
topolo2117631714pology:
!>[TA: $tType] : $o ).
thf(topolo503727757_space_decl,type,
topolo503727757_space:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_decl,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(real_V55928688vector_decl,type,
real_V55928688vector:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(elemen1026692323pology_decl,type,
elemen1026692323pology:
!>[TA: $tType] : $o ).
thf(ordere516151231imp_le_decl,type,
ordere516151231imp_le:
!>[TA: $tType] : $o ).
thf(borel_is_borel_decl,type,
borel_is_borel:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( sigma_measure @ TB ) > $o ) ).
thf(borel_1404511681_borel_decl,type,
borel_1404511681_borel:
!>[TA: $tType] : ( sigma_measure @ TA ) ).
thf(complete_completion_decl,type,
complete_completion:
!>[TA: $tType] : ( ( sigma_measure @ TA ) > ( sigma_measure @ TA ) ) ).
thf(complete_main_part_decl,type,
complete_main_part:
!>[TA: $tType] : ( ( sigma_measure @ TA ) > ( set @ TA ) > ( set @ TA ) ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(inf_inf_decl,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(lebesgue_lborel_decl,type,
lebesgue_lborel:
!>[TA: $tType] : ( sigma_measure @ TA ) ).
thf(minkow1937162798nt_vec_decl,type,
minkow1937162798nt_vec:
!>[TA: $tType,TB: $tType] : ( ( finite_Cartesian_vec @ int @ TB ) > ( finite_Cartesian_vec @ TA @ TB ) ) ).
thf(ord_Least_decl,type,
ord_Least:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(image_decl,type,
image:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(vimage_decl,type,
vimage:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TA ) > ( set @ TB ) ) ).
thf(sigma_measurable_decl,type,
sigma_measurable:
!>[TA: $tType,TB: $tType] : ( ( sigma_measure @ TB ) > ( sigma_measure @ TA ) > ( set @ ( TB > TA ) ) ) ).
thf(sigma_restrict_space_decl,type,
sigma_restrict_space:
!>[TA: $tType] : ( ( sigma_measure @ TA ) > ( set @ TA ) > ( sigma_measure @ TA ) ) ).
thf(sigma_sets_decl,type,
sigma_sets:
!>[TA: $tType] : ( ( sigma_measure @ TA ) > ( set @ ( set @ TA ) ) ) ).
thf(sigma_space_decl,type,
sigma_space:
!>[TA: $tType] : ( ( sigma_measure @ TA ) > ( set @ TA ) ) ).
thf(sigma_vimage_algebra_decl,type,
sigma_vimage_algebra:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > TA ) > ( sigma_measure @ TA ) > ( sigma_measure @ TB ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(r_decl,type,
r: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).
thf(s_decl,type,
s: set @ ( finite_Cartesian_vec @ real @ n ) ).
thf(t_decl,type,
t: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).
thf(t2_decl,type,
t2: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).
thf(a_decl,type,
a: finite_Cartesian_vec @ int @ n ).
thf(127,axiom,
plus @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oplus_72) ).
thf(645,plain,
plus @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(121,axiom,
topolo2117631714pology @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Olinorder__topology_52) ).
thf(629,plain,
topolo2117631714pology @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(278,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_diff__add__eq) ).
thf(1024,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(336,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_add__diff__cancel) ).
thf(1168,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(51,axiom,
cancel1352612707id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_16) ).
thf(479,plain,
cancel1352612707id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(210,axiom,
ordere779506340up_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_53) ).
thf(846,plain,
ordere779506340up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(236,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: sigma_measure @ TC,C: sigma_measure @ TA,D: TB > TC,E: sigma_measure @ TB] :
( ( member @ ( TC > TA ) @ A @ ( sigma_measurable @ TC @ TA @ B @ C ) )
=> ( ( member @ ( TB > TC ) @ D @ ( sigma_measurable @ TB @ TC @ E @ B ) )
=> ( member @ ( TB > TA )
@ ^ [F: TB] : ( A @ ( D @ F ) )
@ ( sigma_measurable @ TB @ TA @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_measurable__compose__rev) ).
thf(909,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: sigma_measure @ TC,C: sigma_measure @ TA,D: TB > TC,E: sigma_measure @ TB] :
( ( member @ ( TC > TA ) @ A @ ( sigma_measurable @ TC @ TA @ B @ C ) )
=> ( ( member @ ( TB > TC ) @ D @ ( sigma_measurable @ TB @ TC @ E @ B ) )
=> ( member @ ( TB > TA )
@ ^ [F: TB] : ( A @ ( D @ F ) )
@ ( sigma_measurable @ TB @ TA @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(230,axiom,
topolo1314133330id_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Limits_Otopological__monoid__add_56) ).
thf(893,plain,
topolo1314133330id_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(255,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TB )
& ( finite_finite @ TA ) )
=> ( topolo1314133330id_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Limits_Otopological__monoid__add_84) ).
thf(962,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TB )
& ( finite_finite @ TA ) )
=> ( topolo1314133330id_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).
thf(555,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(272,axiom,
! [TA: $tType,TB: $tType] :
( ( ( elemen1026692323pology @ TA )
& ( real_V55928688vector @ TA ) )
=> ! [A: TB > TA,B: sigma_measure @ TB,C: TB > TA] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( TB > TA )
@ ^ [D: TB] : ( minus_minus @ TA @ ( A @ D ) @ ( C @ D ) )
@ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_borel__measurable__diff) ).
thf(1005,plain,
! [TA: $tType,TB: $tType] :
( ( ( elemen1026692323pology @ TA )
& ( real_V55928688vector @ TA ) )
=> ! [A: TB > TA,B: sigma_measure @ TB,C: TB > TA] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( TB > TA )
@ ^ [D: TB] : ( minus_minus @ TA @ ( A @ D ) @ ( C @ D ) )
@ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(160,axiom,
cancel1352612707id_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_57) ).
thf(730,plain,
cancel1352612707id_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(294,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ( ( sigma_sets @ TA @ ( lebesgue_lborel @ TA ) )
= ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_sets__lborel) ).
thf(1068,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ( ( sigma_sets @ TA @ ( lebesgue_lborel @ TA ) )
= ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: set @ TB,B: set @ TB,C: TB > TA] :
( ( member @ ( set @ TB ) @ A @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
=> ( ( member @ ( set @ TB ) @ B @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
=> ( ( ord_less_eq @ ( set @ TB ) @ A @ B )
=> ( ( member @ ( TB > TA )
@ ^ [D: TB] : ( if @ TA @ ( member @ TB @ D @ A ) @ ( C @ D ) @ ( zero_zero @ TA ) )
@ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) @ ( borel_1404511681_borel @ TA ) ) )
= ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ ( borel_1404511681_borel @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_borel__measurable__if__lebesgue__on) ).
thf(741,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: set @ TB,B: set @ TB,C: TB > TA] :
( ( member @ ( set @ TB ) @ A @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
=> ( ( member @ ( set @ TB ) @ B @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
=> ( ( ord_less_eq @ ( set @ TB ) @ A @ B )
=> ( ( member @ ( TB > TA )
@ ^ [D: TB] : ( if @ TA @ ( member @ TB @ D @ A ) @ ( C @ D ) @ ( zero_zero @ TA ) )
@ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) @ ( borel_1404511681_borel @ TA ) ) )
= ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ ( borel_1404511681_borel @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(371,axiom,
! [A: finite_Cartesian_vec @ int @ n] :
( member @ ( ( finite_Cartesian_vec @ real @ n ) > ( finite_Cartesian_vec @ real @ n ) )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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) ).
thf(1269,plain,
! [A: finite_Cartesian_vec @ int @ n] :
( member @ ( ( finite_Cartesian_vec @ real @ n ) > ( finite_Cartesian_vec @ real @ n ) )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(112,axiom,
finite_finite @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_45) ).
thf(614,plain,
finite_finite @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(216,axiom,
! [TA: $tType,TB: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: sigma_measure @ TB] :
( ( sigma_measurable @ TB @ TA @ A @ ( lebesgue_lborel @ TA ) )
= ( sigma_measurable @ TB @ TA @ A @ ( borel_1404511681_borel @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_measurable__lborel1) ).
thf(861,plain,
! [TA: $tType,TB: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: sigma_measure @ TB] :
( ( sigma_measurable @ TB @ TA @ A @ ( lebesgue_lborel @ TA ) )
= ( sigma_measurable @ TB @ TA @ A @ ( borel_1404511681_borel @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(11,axiom,
comm_monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(408,plain,
comm_monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(262,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B )
= ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_translation__invert) ).
thf(977,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B )
= ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(221,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_add__left__cancel) ).
thf(873,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(349,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ C @ D )
=> ( member @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ ( set @ TA ) @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_set__plus__intro) ).
thf(1205,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ C @ D )
=> ( member @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ ( set @ TA ) @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(36,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add_20) ).
thf(449,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(223,axiom,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TB )
& ( finite_finite @ TA ) )
=> ( topolo503727757_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_79) ).
thf(878,plain,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TB )
& ( finite_finite @ TA ) )
=> ( topolo503727757_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TB )
=> ( ( borel_is_borel @ TA @ TB )
= ( ^ [A: TA > TB,B: sigma_measure @ TA] : ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_is__borel__def) ).
thf(655,plain,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TB )
=> ( ( borel_is_borel @ TA @ TB )
= ( ^ [A: TA > TB,B: sigma_measure @ TA] : ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(67,axiom,
! [A: nat] :
( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_minus__nat_Odiff__0) ).
thf(511,plain,
! [A: nat] :
( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(76,axiom,
minus @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ominus_47) ).
thf(533,plain,
minus @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(62,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_diff__zero) ).
thf(500,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(47,axiom,
ordere779506340up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_13) ).
thf(472,plain,
ordere779506340up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(194,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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(814,plain,
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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(292,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( minus_minus @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_add__diff__cancel__left) ).
thf(1063,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( minus_minus @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(79,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_eq__iff__diff__eq__0) ).
thf(538,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ring_char_0 @ TB )
& ( finite_finite @ TA ) )
=> ( ring_char_0 @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Nat_Oring__char__0_99) ).
thf(670,plain,
! [TA: $tType,TB: $tType] :
( ( ( ring_char_0 @ TB )
& ( finite_finite @ TA ) )
=> ( ring_char_0 @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(335,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_subsetI) ).
thf(1164,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(188,axiom,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_set__diff__eq) ).
thf(797,plain,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(270,axiom,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TA,B: sigma_measure @ TB] :
( member @ ( TB > TA )
@ ^ [C: TB] : A
@ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_borel__measurable__const) ).
thf(1001,plain,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TA,B: sigma_measure @ TB] :
( member @ ( TB > TA )
@ ^ [C: TB] : A
@ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(181,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_add__cancel__left__right) ).
thf(782,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(29,axiom,
! [A: nat] :
( ( minus_minus @ nat @ A @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_diff__self__eq__0) ).
thf(436,plain,
! [A: nat] :
( ( minus_minus @ nat @ A @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V2090557954_space @ TB )
& ( finite_finite @ TA ) )
=> ( real_V2090557954_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Ometric__space) ).
thf(651,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V2090557954_space @ TB )
& ( finite_finite @ TA ) )
=> ( real_V2090557954_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(202,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: set @ TA,B: TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) ) )
=> ( member @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) @ ( sigma_sets @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_lebesgue__sets__translation) ).
thf(829,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: set @ TA,B: TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) ) )
=> ( member @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) @ ( sigma_sets @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(7,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(404,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(362,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_image__eqI) ).
thf(1243,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(318,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_DiffD2) ).
thf(1127,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(208,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ozero_38) ).
thf(841,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(20,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_diff__0__right) ).
thf(417,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(227,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_add__right__cancel) ).
thf(885,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(285,axiom,
comm_monoid_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocomm__monoid__add_63) ).
thf(1046,plain,
comm_monoid_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(378,axiom,
( t2
= ( ^ [A: finite_Cartesian_vec @ int @ n] : ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( r @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_T__def) ).
thf(1287,plain,
( t2
= ( ^ [A: finite_Cartesian_vec @ int @ n] : ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( r @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(93,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_zero__reorient) ).
thf(570,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(383,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( B @ D ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( ( C @ D )
| ( B @ D ) ) ) )
@ ( sigma_sets @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_sets_Osets__Collect__disj) ).
thf(1298,plain,
! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( B @ D ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( ( C @ D )
| ( B @ D ) ) ) )
@ ( sigma_sets @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType] :
( ( ( elemen1026692323pology @ TB )
& ( topolo2117631714pology @ TB ) )
=> ! [A: TA > TB,B: sigma_measure @ TA,C: TA > TB] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( ( member @ ( TA > TB ) @ C @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
& ( ( A @ D )
!= ( C @ D ) ) ) )
@ ( sigma_sets @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_borel__measurable__neq) ).
thf(719,plain,
! [TA: $tType,TB: $tType] :
( ( ( elemen1026692323pology @ TB )
& ( topolo2117631714pology @ TB ) )
=> ! [A: TA > TB,B: sigma_measure @ TA,C: TA > TB] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( ( member @ ( TA > TB ) @ C @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
& ( ( A @ D )
!= ( C @ D ) ) ) )
@ ( sigma_sets @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(182,axiom,
! [TA: $tType,TB: $tType] :
( ( ( monoid_add @ TB )
& ( finite_finite @ TA ) )
=> ( monoid_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Omonoid__add_95) ).
thf(785,plain,
! [TA: $tType,TB: $tType] :
( ( ( monoid_add @ TB )
& ( finite_finite @ TA ) )
=> ( monoid_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(64,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_diff__self) ).
thf(504,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(369,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ B )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_translation__subtract__diff) ).
thf(1264,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ B )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(246,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_group__cancel_Oadd1) ).
thf(934,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(320,axiom,
( t
= ( ^ [A: finite_Cartesian_vec @ int @ n] :
( image @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( minus_minus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( t2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_T_H__def) ).
thf(1132,plain,
( t
= ( ^ [A: finite_Cartesian_vec @ int @ n] :
( image @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( minus_minus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( t2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(250,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_measurable__completion) ).
thf(949,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(289,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Oring__char__0_69) ).
thf(1055,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(158,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Int__assoc) ).
thf(724,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(100,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( type @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Finite__Set_Ofinite___HOL_Otype) ).
thf(587,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( type @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(390,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_add_Oleft__commute) ).
thf(1323,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( countable @ TA ) )
=> ( countable @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Countable_Ocountable) ).
thf(619,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( countable @ TA ) )
=> ( countable @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(207,axiom,
! [TA: $tType,A: set @ TA] :
( ( vimage @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_vimage__ident) ).
thf(838,plain,
! [TA: $tType,A: set @ TA] :
( ( vimage @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(149,axiom,
cancel_semigroup_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__semigroup__add_60) ).
thf(702,plain,
cancel_semigroup_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(170,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_add__diff__eq) ).
thf(751,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(196,axiom,
zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_71) ).
thf(817,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(213,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
= ( member @ TA @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_vimage__eq) ).
thf(853,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
= ( member @ TA @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(327,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TB )
& ( finite_finite @ TA ) )
=> ( elemen1026692323pology @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Elementary__Topology_Osecond__countable__topology_76) ).
thf(1147,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TB )
& ( finite_finite @ TA ) )
=> ( elemen1026692323pology @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(363,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: nat > TA > $o,C: set @ nat] :
( ! [D: nat] :
( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ ( sigma_space @ TA @ A ) )
& ( B @ D @ E ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( inf_inf @ ( set @ TA )
@ ( vimage @ TA @ nat
@ ^ [D: TA] :
( ord_Least @ nat
@ ^ [E: nat] : ( B @ E @ D ) )
@ C )
@ ( sigma_space @ TA @ A ) )
@ ( sigma_sets @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_sets__Least) ).
thf(1247,plain,
! [TA: $tType,A: sigma_measure @ TA,B: nat > TA > $o,C: set @ nat] :
( ! [D: nat] :
( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ ( sigma_space @ TA @ A ) )
& ( B @ D @ E ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( inf_inf @ ( set @ TA )
@ ( vimage @ TA @ nat
@ ^ [D: TA] :
( ord_Least @ nat
@ ^ [E: nat] : ( B @ E @ D ) )
@ C )
@ ( sigma_space @ TA @ A ) )
@ ( sigma_sets @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(258,axiom,
real_V55928688vector @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector) ).
thf(969,plain,
real_V55928688vector @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(19,axiom,
lattice @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Lattices_Olattice_6) ).
thf(416,plain,
lattice @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(313,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: sigma_measure @ TA] : ( member @ ( set @ TB ) @ A @ ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_sets__vimage__algebra__space) ).
thf(1115,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: sigma_measure @ TA] : ( member @ ( set @ TB ) @ A @ ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(35,axiom,
minus @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ominus_26) ).
thf(448,plain,
minus @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(306,axiom,
! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( r @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).
thf(1100,plain,
! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( r @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(358,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_IntE) ).
thf(1232,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(22,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_inf1D1) ).
thf(421,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(219,axiom,
finite_finite @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
thf(870,plain,
finite_finite @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(58,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(492,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(172,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( B @ D ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( ( C @ D )
=> ( B @ D ) ) ) )
@ ( sigma_sets @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_sets_Osets__Collect__imp) ).
thf(756,plain,
! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( B @ D ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( ( C @ D )
=> ( B @ D ) ) ) )
@ ( sigma_sets @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(102,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_le__inf__iff) ).
thf(591,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TB )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_fun__diff__def) ).
thf(514,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TB )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(329,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_double__zero__sym) ).
thf(1151,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(343,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_DiffE) ).
thf(1183,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(287,axiom,
ordere890947078_space @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_1) ).
thf(1051,plain,
ordere890947078_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(52,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_inf_Oleft__commute) ).
thf(480,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(283,axiom,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TB > TA,B: sigma_measure @ TB] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
= ( ! [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ C ) @ ( sigma_space @ TB @ B ) ) @ ( sigma_sets @ TB @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_in__borel__measurable__borel) ).
thf(1040,plain,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TB > TA,B: sigma_measure @ TB] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
= ( ! [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ C ) @ ( sigma_space @ TB @ B ) ) @ ( sigma_sets @ TB @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(310,axiom,
! [TA: $tType,TB: $tType] :
( ( real_V55928688vector @ TA )
=> ! [A: TB > TA,B: sigma_measure @ TB,C: TA] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( TB > TA )
@ ^ [D: TB] : ( plus_plus @ TA @ C @ ( A @ D ) )
@ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_borel__measurable__const__add) ).
thf(1109,plain,
! [TA: $tType,TB: $tType] :
( ( real_V55928688vector @ TA )
=> ! [A: TB > TA,B: sigma_measure @ TB,C: TA] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( TB > TA )
@ ^ [D: TB] : ( plus_plus @ TA @ C @ ( A @ D ) )
@ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(394,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_35) ).
thf(1334,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType] :
( ( ( elemen1026692323pology @ TB )
& ( topolo2117631714pology @ TB ) )
=> ! [A: TA > TB,B: sigma_measure @ TA,C: TA > TB] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( ( member @ ( TA > TB ) @ C @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
& ( ( A @ D )
= ( C @ D ) ) ) )
@ ( sigma_sets @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_borel__measurable__eq) ).
thf(646,plain,
! [TA: $tType,TB: $tType] :
( ( ( elemen1026692323pology @ TB )
& ( topolo2117631714pology @ TB ) )
=> ! [A: TA > TB,B: sigma_measure @ TA,C: TA > TB] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( ( member @ ( TA > TB ) @ C @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
& ( ( A @ D )
= ( C @ D ) ) ) )
@ ( sigma_sets @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(322,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( B @ D ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D )
& ( B @ D ) ) )
@ ( sigma_sets @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_sets_Osets__Collect__conj) ).
thf(1136,plain,
! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( B @ D ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D )
& ( B @ D ) ) )
@ ( sigma_sets @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(204,axiom,
euclid925273238_space @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Euclidean__Space_Oeuclidean__space) ).
thf(834,plain,
euclid925273238_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(351,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere890947078_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space) ).
thf(1215,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere890947078_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(253,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_add__left__imp__eq) ).
thf(956,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(39,axiom,
plus @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oplus_28) ).
thf(453,plain,
plus @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ab_group_add @ TB )
& ( finite_finite @ TA ) )
=> ( ab_group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__group__add_93) ).
thf(660,plain,
! [TA: $tType,TB: $tType] :
( ( ( ab_group_add @ TB )
& ( finite_finite @ TA ) )
=> ( ab_group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(269,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_add_Ogroup__left__neutral) ).
thf(998,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(308,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: sigma_measure @ TA,C: TB > TA,D: set @ TB] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ C @ A ) @ D ) @ ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_in__vimage__algebra) ).
thf(1104,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: sigma_measure @ TA,C: TB > TA,D: set @ TB] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ C @ A ) @ D ) @ ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_inf__fun__def) ).
thf(507,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(107,axiom,
! [A: nat] :
( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_diff__0__eq__0) ).
thf(602,plain,
! [A: nat] :
( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(176,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: set @ TB,B: TB > TA] :
( ( member @ ( set @ TB ) @ A @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
=> ( ( member @ ( TB > TA )
@ ^ [C: TB] : ( if @ TA @ ( member @ TB @ C @ A ) @ ( B @ C ) @ ( zero_zero @ TA ) )
@ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) )
= ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_borel__measurable__if) ).
thf(766,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: set @ TB,B: TB > TA] :
( ( member @ ( set @ TB ) @ A @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
=> ( ( member @ ( TB > TA )
@ ^ [C: TB] : ( if @ TA @ ( member @ TB @ C @ A ) @ ( B @ C ) @ ( zero_zero @ TA ) )
@ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) )
= ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(14,axiom,
ab_group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__group__add) ).
thf(411,plain,
ab_group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(266,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_translation__diff) ).
thf(988,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
= ( image @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_image__image) ).
thf(428,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
= ( image @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(348,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ D @ A )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_group__cancel_Oadd2) ).
thf(1201,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ D @ A )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(296,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: set @ TA] : ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_sets__lebesgue__on__refl) ).
thf(1074,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: set @ TA] : ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(38,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add_18) ).
thf(452,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(30,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(439,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(74,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add_21) ).
thf(529,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(243,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_zero__le__double__add__iff__zero__le__single__add) ).
thf(925,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(174,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TB )
& ( finite_finite @ TA ) )
=> ( euclid925273238_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Euclidean__Space_Oeuclidean__space_81) ).
thf(761,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TB )
& ( finite_finite @ TA ) )
=> ( euclid925273238_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(396,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordered_ab_group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add_87) ).
thf(1338,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordered_ab_group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(286,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: sigma_measure @ TA,D: sigma_measure @ TA] :
( ( A = B )
=> ( ( ( sigma_sets @ TA @ C )
= ( sigma_sets @ TA @ D ) )
=> ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ C @ A ) )
= ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_restrict__space__sets__cong) ).
thf(1047,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: sigma_measure @ TA,D: sigma_measure @ TA] :
( ( A = B )
=> ( ( ( sigma_sets @ TA @ C )
= ( sigma_sets @ TA @ D ) )
=> ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ C @ A ) )
= ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(386,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_add_Oleft__cancel) ).
thf(1311,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(77,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_inf__left__commute) ).
thf(534,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(373,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( plus_plus @ ( set @ TA ) @ A @ C ) @ ( plus_plus @ ( set @ TA ) @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_set__plus__mono2) ).
thf(1274,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( plus_plus @ ( set @ TA ) @ A @ C ) @ ( plus_plus @ ( set @ TA ) @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(277,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ B ) )
= ( image @ ( set @ TA ) @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ B ) @ ( sigma_sets @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_sets__restrict__space) ).
thf(1021,plain,
! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ B ) )
= ( image @ ( set @ TA ) @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ B ) @ ( sigma_sets @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(316,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_inf @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Collect__conj__eq) ).
thf(1123,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_inf @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(339,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( sigma_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_sets_OInt) ).
thf(1174,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( sigma_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(352,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: sigma_measure @ TB,C: sigma_measure @ TC,D: TC > TA,E: sigma_measure @ TA] :
( ( member @ ( TB > TC ) @ A @ ( sigma_measurable @ TB @ TC @ B @ C ) )
=> ( ( member @ ( TC > TA ) @ D @ ( sigma_measurable @ TC @ TA @ C @ E ) )
=> ( member @ ( TB > TA )
@ ^ [F: TB] : ( D @ ( A @ F ) )
@ ( sigma_measurable @ TB @ TA @ B @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_measurable__compose) ).
thf(1217,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: sigma_measure @ TB,C: sigma_measure @ TC,D: TC > TA,E: sigma_measure @ TA] :
( ( member @ ( TB > TC ) @ A @ ( sigma_measurable @ TB @ TC @ B @ C ) )
=> ( ( member @ ( TC > TA ) @ D @ ( sigma_measurable @ TC @ TA @ C @ E ) )
=> ( member @ ( TB > TA )
@ ^ [F: TB] : ( D @ ( A @ F ) )
@ ( sigma_measurable @ TB @ TA @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(24,axiom,
ordere236663937imp_le @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_10) ).
thf(424,plain,
ordere236663937imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(184,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_inf__set__def) ).
thf(788,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(195,axiom,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TB] :
( member @ ( ( TB > TA ) > TA )
@ ^ [B: TB > TA] : ( B @ A )
@ ( sigma_measurable @ ( TB > TA ) @ TA @ ( borel_1404511681_borel @ ( TB > TA ) ) @ ( borel_1404511681_borel @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_measurable__product__coordinates) ).
thf(815,plain,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TB] :
( member @ ( ( TB > TA ) > TA )
@ ^ [B: TB > TA] : ( B @ A )
@ ( sigma_measurable @ ( TB > TA ) @ TA @ ( borel_1404511681_borel @ ( TB > TA ) ) @ ( borel_1404511681_borel @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(354,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Int__def) ).
thf(1223,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(231,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_diff__diff__add) ).
thf(894,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(167,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: $o] :
( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
& B ) )
@ ( sigma_sets @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_sets_Osets__Collect__const) ).
thf(746,plain,
! [TA: $tType,A: sigma_measure @ TA,B: $o] :
( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
& B ) )
@ ( sigma_sets @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(302,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ( ( sigma_space @ TA @ ( lebesgue_lborel @ TA ) )
= ( sigma_space @ TA @ ( borel_1404511681_borel @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_space__lborel) ).
thf(1091,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ( ( sigma_space @ TA @ ( lebesgue_lborel @ TA ) )
= ( sigma_space @ TA @ ( borel_1404511681_borel @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(200,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( countable @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Countable_Ocountable_33) ).
thf(825,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( countable @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(398,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(1343,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(10,axiom,
topolo2117631714pology @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Topological__Spaces_Olinorder__topology) ).
thf(407,plain,
topolo2117631714pology @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere516151231imp_le @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__monoid__add__imp__le_75) ).
thf(630,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere516151231imp_le @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(211,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_image__add__0) ).
thf(847,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(281,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ( plus @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Oplus_39) ).
thf(1032,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ( plus @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(119,axiom,
topolo503727757_space @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Otopological__space_11) ).
thf(625,plain,
topolo503727757_space @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(341,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: TB > TA,E: set @ TB] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( ( member @ ( TB > TA ) @ D @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ E @ ( sigma_space @ TB @ B ) ) @ ( sigma_sets @ TB @ B ) )
=> ( member @ ( TB > TA )
@ ^ [F: TB] : ( if @ TA @ ( member @ TB @ F @ E ) @ ( A @ F ) @ ( D @ F ) )
@ ( sigma_measurable @ TB @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_measurable__If__set) ).
thf(1178,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: TB > TA,E: set @ TB] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( ( member @ ( TB > TA ) @ D @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ E @ ( sigma_space @ TB @ B ) ) @ ( sigma_sets @ TB @ B ) )
=> ( member @ ( TB > TA )
@ ^ [F: TB] : ( if @ TA @ ( member @ TB @ F @ E ) @ ( A @ F ) @ ( D @ F ) )
@ ( sigma_measurable @ TB @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(332,axiom,
real_V1076094709vector @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector) ).
thf(1159,plain,
real_V1076094709vector @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: sigma_measure @ TB] :
( ( sigma_space @ TA @ ( sigma_vimage_algebra @ TA @ TB @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_space__vimage__algebra) ).
thf(493,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: sigma_measure @ TB] :
( ( sigma_space @ TA @ ( sigma_vimage_algebra @ TA @ TB @ A @ B @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_imageI) ).
thf(682,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(83,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_inf_Oassoc) ).
thf(551,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(376,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > $o] :
( ( vimage @ TA @ TB @ A @ ( collect @ TB @ B ) )
= ( collect @ TA
@ ^ [C: TA] : ( B @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_vimage__Collect__eq) ).
thf(1281,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > $o] :
( ( vimage @ TA @ TB @ A @ ( collect @ TB @ B ) )
= ( collect @ TA
@ ^ [C: TA] : ( B @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: set @ TA] :
( ( member @ TA @ ( A @ B ) @ C )
=> ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_vimageI2) ).
thf(710,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: set @ TA] :
( ( member @ TA @ ( A @ B ) @ C )
=> ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(275,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_Int__subset__iff) ).
thf(1012,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(309,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_comm__monoid__add__class_Oadd__0) ).
thf(1106,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(382,axiom,
! [TA: $tType,TB: $tType] :
( ( ( semigroup_add @ TB )
& ( finite_finite @ TA ) )
=> ( semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Osemigroup__add_92) ).
thf(1296,plain,
! [TA: $tType,TB: $tType] :
( ( ( semigroup_add @ TB )
& ( finite_finite @ TA ) )
=> ( semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
=> ( member @ TA @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_vimageD) ).
thf(665,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
=> ( member @ TA @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(98,axiom,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_image__ident) ).
thf(583,plain,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(72,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_inf__sup__aci_I1_J) ).
thf(522,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(298,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_diff__add__eq__diff__diff__swap) ).
thf(1079,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(279,axiom,
! [TA: $tType,TB: $tType] :
( ( ( minus @ TB )
& ( finite_finite @ TA ) )
=> ( minus @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ominus_100) ).
thf(1027,plain,
! [TA: $tType,TB: $tType] :
( ( ( minus @ TB )
& ( finite_finite @ TA ) )
=> ( minus @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(325,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: set @ TB,B: TB > TA] :
( ( member @ ( TB > TA )
@ ^ [C: TB] : ( if @ TA @ ( member @ TB @ C @ A ) @ ( B @ C ) @ ( zero_zero @ TA ) )
@ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ ( borel_1404511681_borel @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_borel__measurable__if__D) ).
thf(1143,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: set @ TB,B: TB > TA] :
( ( member @ ( TB > TA )
@ ^ [C: TB] : ( if @ TA @ ( member @ TB @ C @ A ) @ ( B @ C ) @ ( zero_zero @ TA ) )
@ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ ( borel_1404511681_borel @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(113,axiom,
ordere779506340up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add) ).
thf(615,plain,
ordere779506340up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(392,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_add_Ocomm__neutral) ).
thf(1328,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(304,axiom,
! [TA: $tType,TB: $tType] :
( ( ( group_add @ TB )
& ( finite_finite @ TA ) )
=> ( group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ogroup__add_98) ).
thf(1096,plain,
! [TA: $tType,TB: $tType] :
( ( ( group_add @ TB )
& ( finite_finite @ TA ) )
=> ( group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(323,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( image @ TA @ TB @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Compr__image__eq) ).
thf(1138,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( image @ TA @ TB @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(21,axiom,
topolo503727757_space @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Otopological__space_40) ).
thf(420,plain,
topolo503727757_space @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(61,axiom,
topological_t2_space @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Topological__Spaces_Ot2__space) ).
thf(499,plain,
topological_t2_space @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(311,axiom,
group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add_68) ).
thf(1111,plain,
group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(356,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: set @ TA] :
( ( vimage @ TB @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ B ) @ ( vimage @ TB @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_vimage__Int) ).
thf(1227,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: set @ TA] :
( ( vimage @ TB @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ B ) @ ( vimage @ TB @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(263,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ ( sigma_space @ TA @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_sets_OInt__space__eq2) ).
thf(980,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ ( sigma_space @ TA @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(6,axiom,
countable @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Countable_Ocountable_5) ).
thf(403,plain,
countable @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(333,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: $o] :
( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
& B ) )
@ ( sigma_sets @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_sets_Osets__Collect_I5_J) ).
thf(1160,plain,
! [TA: $tType,A: sigma_measure @ TA,B: $o] :
( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
& B ) )
@ ( sigma_sets @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(299,axiom,
! [TA: $tType] :
( ( real_V1076094709vector @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_subset__translation__eq) ).
thf(1082,plain,
! [TA: $tType] :
( ( real_V1076094709vector @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(56,axiom,
semilattice_inf @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_43) ).
thf(488,plain,
semilattice_inf @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(380,axiom,
ordered_ab_group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add_59) ).
thf(1292,plain,
ordered_ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(84,axiom,
topological_t2_space @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Ot2__space_42) ).
thf(554,plain,
topological_t2_space @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(78,axiom,
topolo2117631714pology @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Olinorder__topology_41) ).
thf(537,plain,
topolo2117631714pology @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(57,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_inf__sup__aci_I4_J) ).
thf(489,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(350,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TB,C: TB > TA,D: TB > TA,E: sigma_measure @ TA,F: sigma_measure @ TA] :
( ( A = B )
=> ( ! [G: TB] :
( ( member @ TB @ G @ B )
=> ( ( C @ G )
= ( D @ G ) ) )
=> ( ( ( sigma_sets @ TA @ E )
= ( sigma_sets @ TA @ F ) )
=> ( ( sigma_vimage_algebra @ TB @ TA @ A @ C @ E )
= ( sigma_vimage_algebra @ TB @ TA @ B @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_vimage__algebra__cong) ).
thf(1207,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TB,C: TB > TA,D: TB > TA,E: sigma_measure @ TA,F: sigma_measure @ TA] :
( ( A = B )
=> ( ! [G: TB] :
( ( member @ TB @ G @ B )
=> ( ( C @ G )
= ( D @ G ) ) )
=> ( ( ( sigma_sets @ TA @ E )
= ( sigma_sets @ TA @ F ) )
=> ( ( sigma_vimage_algebra @ TB @ TA @ A @ C @ E )
= ( sigma_vimage_algebra @ TB @ TA @ B @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: sigma_measure @ TB,C: sigma_measure @ TA,D: sigma_measure @ TA] :
( ( ( sigma_sets @ TB @ A )
= ( sigma_sets @ TB @ B ) )
=> ( ( ( sigma_sets @ TA @ C )
= ( sigma_sets @ TA @ D ) )
=> ( ( sigma_measurable @ TB @ TA @ A @ C )
= ( sigma_measurable @ TB @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_measurable__cong__sets) ).
thf(686,plain,
! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: sigma_measure @ TB,C: sigma_measure @ TA,D: sigma_measure @ TA] :
( ( ( sigma_sets @ TB @ A )
= ( sigma_sets @ TB @ B ) )
=> ( ( ( sigma_sets @ TA @ C )
= ( sigma_sets @ TA @ D ) )
=> ( ( sigma_measurable @ TB @ TA @ A @ C )
= ( sigma_measurable @ TB @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(50,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_inf_Obounded__iff) ).
thf(476,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(142,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA] :
( ( ( sigma_sets @ TA @ A )
= ( sigma_sets @ TA @ B ) )
=> ( member @ ( TA > TA )
@ ^ [C: TA] : C
@ ( sigma_measurable @ TA @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_measurable__ident__sets) ).
thf(679,plain,
! [TA: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA] :
( ( ( sigma_sets @ TA @ A )
= ( sigma_sets @ TA @ B ) )
=> ( member @ ( TA > TA )
@ ^ [C: TA] : C
@ ( sigma_measurable @ TA @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(259,axiom,
! [TA: $tType,TB: $tType] :
( ( ( cancel146912293up_add @ TB )
& ( finite_finite @ TA ) )
=> ( cancel146912293up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__ab__semigroup__add_83) ).
thf(970,plain,
! [TA: $tType,TB: $tType] :
( ( ( cancel146912293up_add @ TB )
& ( finite_finite @ TA ) )
=> ( cancel146912293up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(206,axiom,
ab_semigroup_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oab__semigroup__add_62) ).
thf(837,plain,
ab_semigroup_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(268,axiom,
linord219039673up_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Olinordered__ab__group__add_54) ).
thf(997,plain,
linord219039673up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(364,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_add__mono__thms__linordered__semiring_I4_J) ).
thf(1249,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(164,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_add__right__imp__eq) ).
thf(738,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(346,axiom,
! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: TB > TA,C: sigma_measure @ TA] :
( ! [D: TB] :
( ( member @ TB @ D @ ( sigma_space @ TB @ A ) )
=> ( member @ TA @ ( B @ D ) @ ( sigma_space @ TA @ C ) ) )
=> ( ! [D: set @ TA] :
( ( member @ ( set @ TA ) @ D @ ( sigma_sets @ TA @ C ) )
=> ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ B @ D ) @ ( sigma_space @ TB @ A ) ) @ ( sigma_sets @ TB @ A ) ) )
=> ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_measurableI) ).
thf(1192,plain,
! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: TB > TA,C: sigma_measure @ TA] :
( ! [D: TB] :
( ( member @ TB @ D @ ( sigma_space @ TB @ A ) )
=> ( member @ TA @ ( B @ D ) @ ( sigma_space @ TA @ C ) ) )
=> ( ! [D: set @ TA] :
( ( member @ ( set @ TA ) @ D @ ( sigma_sets @ TA @ C ) )
=> ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ B @ D ) @ ( sigma_space @ TB @ A ) ) @ ( sigma_sets @ TB @ A ) ) )
=> ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(291,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_add__cancel__right__left) ).
thf(1060,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(237,axiom,
topolo503727757_space @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Otopological__space_51) ).
thf(911,plain,
topolo503727757_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(157,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ B )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_translation__subtract__Int) ).
thf(721,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ B )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(92,axiom,
comm_monoid_diff @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff) ).
thf(569,plain,
comm_monoid_diff @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(63,axiom,
countable @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Countable_Ocountable_44) ).
thf(503,plain,
countable @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(108,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_inf_Oleft__idem) ).
thf(605,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(186,axiom,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_29) ).
thf(792,plain,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(247,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( plus_plus @ ( set @ TA ) @ B @ C ) )
=> ~ ! [D: TA,E: TA] :
( ( A
= ( plus_plus @ TA @ D @ E ) )
=> ( ( member @ TA @ D @ B )
=> ~ ( member @ TA @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_set__plus__elim) ).
thf(938,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( plus_plus @ ( set @ TA ) @ B @ C ) )
=> ~ ! [D: TA,E: TA] :
( ( A
= ( plus_plus @ TA @ D @ E ) )
=> ( ( member @ TA @ D @ B )
=> ~ ( member @ TA @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(361,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TB > TA,B: set @ TB] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) @ ( borel_1404511681_borel @ TA ) ) )
=> ( ( member @ ( set @ TB ) @ B @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
=> ( member @ ( TB > TA )
@ ^ [C: TB] : ( if @ TA @ ( member @ TB @ C @ B ) @ ( A @ C ) @ ( zero_zero @ TA ) )
@ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_borel__measurable__if__I) ).
thf(1241,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TB > TA,B: set @ TB] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) @ ( borel_1404511681_borel @ TA ) ) )
=> ( ( member @ ( set @ TB ) @ B @ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) )
=> ( member @ ( TB > TA )
@ ^ [C: TB] : ( if @ TA @ ( member @ TB @ C @ B ) @ ( A @ C ) @ ( zero_zero @ TA ) )
@ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(191,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_Diff__iff) ).
thf(805,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(241,axiom,
! [TA: $tType] : ( minus @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ominus_37) ).
thf(921,plain,
! [TA: $tType] : ( minus @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(80,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(541,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(295,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: TA > $o] :
( ! [D: TA] :
( ( A @ ( B @ D ) )
= ( C @ D ) )
=> ( ( vimage @ TA @ TB @ B @ ( collect @ TB @ A ) )
= ( collect @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_vimage__Collect) ).
thf(1071,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: TA > $o] :
( ! [D: TA] :
( ( A @ ( B @ D ) )
= ( C @ D ) )
=> ( ( vimage @ TA @ TB @ B @ ( collect @ TB @ A ) )
= ( collect @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(344,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_IntI) ).
thf(1187,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(75,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_inf__sup__aci_I2_J) ).
thf(530,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(252,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
( ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( sigma_space @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_space__restrict__space) ).
thf(953,plain,
! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
( ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( sigma_space @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: sigma_measure @ TB,C: sigma_measure @ TA,D: sigma_measure @ TA,E: TB > TA,F: TB > TA] :
( ( A = B )
=> ( ( C = D )
=> ( ! [G: TB] :
( ( member @ TB @ G @ ( sigma_space @ TB @ A ) )
=> ( ( E @ G )
= ( F @ G ) ) )
=> ( ( member @ ( TB > TA ) @ E @ ( sigma_measurable @ TB @ TA @ A @ C ) )
= ( member @ ( TB > TA ) @ F @ ( sigma_measurable @ TB @ TA @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_measurable__cong__simp) ).
thf(773,plain,
! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: sigma_measure @ TB,C: sigma_measure @ TA,D: sigma_measure @ TA,E: TB > TA,F: TB > TA] :
( ( A = B )
=> ( ( C = D )
=> ( ! [G: TB] :
( ( member @ TB @ G @ ( sigma_space @ TB @ A ) )
=> ( ( E @ G )
= ( F @ G ) ) )
=> ( ( member @ ( TB > TA ) @ E @ ( sigma_measurable @ TB @ TA @ A @ C ) )
= ( member @ ( TB > TA ) @ F @ ( sigma_measurable @ TB @ TA @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(187,axiom,
! [TA: $tType,TB: $tType] :
( ( vimage @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TB] :
( collect @ TA
@ ^ [C: TA] : ( member @ TB @ ( A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_vimage__def) ).
thf(794,plain,
! [TA: $tType,TB: $tType] :
( ( vimage @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TB] :
( collect @ TA
@ ^ [C: TA] : ( member @ TB @ ( A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(99,axiom,
semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Osemigroup__add) ).
thf(586,plain,
semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(135,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Diff__Int2) ).
thf(662,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(228,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( complete_main_part @ TA @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_main__part) ).
thf(888,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( complete_main_part @ TA @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(375,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ B ) @ C ) )
= ( image @ TA @ TA @ ( plus_plus @ TA @ ( plus_plus @ TA @ B @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_translation__assoc) ).
thf(1278,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ B ) @ C ) )
= ( image @ TA @ TA @ ( plus_plus @ TA @ ( plus_plus @ TA @ B @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(15,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(412,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(169,axiom,
semigroup_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Osemigroup__add_64) ).
thf(750,plain,
semigroup_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(115,axiom,
ordered_ab_group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__group__add) ).
thf(618,plain,
ordered_ab_group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(25,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_inf__sup__aci_I3_J) ).
thf(425,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(353,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA,D: set @ TA] :
( ( ( A @ B )
= C )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_vimageI) ).
thf(1219,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA,D: set @ TA] :
( ( ( A @ B )
= C )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: set @ TB] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_measurable__restrict__space1) ).
thf(856,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: set @ TB] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(94,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_inf__idem) ).
thf(573,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(146,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere236663937imp_le @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add__imp__le_77) ).
thf(689,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere236663937imp_le @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(162,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ( monoid_add @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Omonoid__add_34) ).
thf(733,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ( monoid_add @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(106,axiom,
ordere236663937imp_le @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(601,plain,
ordere236663937imp_le @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(330,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_double__zero) ).
thf(1154,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(198,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: set @ TA] :
( ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_space__lebesgue__on) ).
thf(819,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: set @ TA] :
( ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(261,axiom,
! [TA: $tType,TB: $tType] :
( ( ( countable @ TB )
& ( finite_finite @ TA ) )
=> ( countable @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Countable_Ocountable_94) ).
thf(975,plain,
! [TA: $tType,TB: $tType] :
( ( ( countable @ TB )
& ( finite_finite @ TA ) )
=> ( countable @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(23,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Oring__char__0) ).
thf(423,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(273,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ ( sigma_space @ TA @ B ) ) @ ( sigma_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ C @ ( sigma_space @ TA @ B ) ) @ ( sigma_sets @ TA @ B ) )
=> ( ( sigma_restrict_space @ TA @ ( sigma_restrict_space @ TA @ B @ A ) @ C )
= ( sigma_restrict_space @ TA @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_restrict__restrict__space) ).
thf(1007,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ ( sigma_space @ TA @ B ) ) @ ( sigma_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ C @ ( sigma_space @ TA @ B ) ) @ ( sigma_sets @ TA @ B ) )
=> ( ( sigma_restrict_space @ TA @ ( sigma_restrict_space @ TA @ B @ A ) @ C )
= ( sigma_restrict_space @ TA @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(5,axiom,
group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ogroup__add) ).
thf(402,plain,
group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(209,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: sigma_measure @ TB,C: TA,D: sigma_measure @ TA,E: TB > TA] :
( ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ A @ ( sigma_space @ TB @ B ) ) @ ( sigma_sets @ TB @ B ) )
=> ( ( member @ TA @ C @ ( sigma_space @ TA @ D ) )
=> ( ( member @ ( TB > TA ) @ E @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ B @ A ) @ D ) )
= ( member @ ( TB > TA )
@ ^ [F: TB] : ( if @ TA @ ( member @ TB @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_measurable @ TB @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_measurable__restrict__space__iff) ).
thf(843,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: sigma_measure @ TB,C: TA,D: sigma_measure @ TA,E: TB > TA] :
( ( member @ ( set @ TB ) @ ( inf_inf @ ( set @ TB ) @ A @ ( sigma_space @ TB @ B ) ) @ ( sigma_sets @ TB @ B ) )
=> ( ( member @ TA @ C @ ( sigma_space @ TA @ D ) )
=> ( ( member @ ( TB > TA ) @ E @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ B @ A ) @ D ) )
= ( member @ ( TB > TA )
@ ^ [F: TB] : ( if @ TA @ ( member @ TB @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_measurable @ TB @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(96,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_27) ).
thf(579,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(16,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__semigroup__add) ).
thf(413,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(366,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ab_semigroup_add @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Oab__semigroup__add_30) ).
thf(1256,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ab_semigroup_add @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(355,axiom,
topological_t2_space @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Ot2__space_58) ).
thf(1226,plain,
topological_t2_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TB )
& ( finite_finite @ TA ) )
=> ( real_V1076094709vector @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__vector_82) ).
thf(641,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TB )
& ( finite_finite @ TA ) )
=> ( real_V1076094709vector @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(32,axiom,
lattice @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_46) ).
thf(445,plain,
lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(372,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Diff__Diff__Int) ).
thf(1271,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(183,axiom,
minus @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ominus_70) ).
thf(787,plain,
minus @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(360,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( lattice @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Lattices_Olattice_97) ).
thf(1239,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( lattice @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(45,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_inf_Oright__idem) ).
thf(466,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(249,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( complete_completion @ TA @ B ) ) )
=> ( member @ ( set @ TA ) @ ( complete_main_part @ TA @ B @ A ) @ ( sigma_sets @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_main__part__sets) ).
thf(947,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( complete_completion @ TA @ B ) ) )
=> ( member @ ( set @ TA ) @ ( complete_main_part @ TA @ B @ A ) @ ( sigma_sets @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(139,axiom,
ordere236663937imp_le @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_50) ).
thf(672,plain,
ordere236663937imp_le @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(367,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_add__le__same__cancel1) ).
thf(1258,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(151,axiom,
! [TA: $tType,A: sigma_measure @ TA] :
( ( sigma_space @ TA @ ( complete_completion @ TA @ A ) )
= ( sigma_space @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_space__completion) ).
thf(704,plain,
! [TA: $tType,A: sigma_measure @ TA] :
( ( sigma_space @ TA @ ( complete_completion @ TA @ A ) )
= ( sigma_space @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType] :
( ( euclid925273238_space @ TB )
=> ! [A: sigma_measure @ TA] :
( ( sigma_measurable @ TB @ TA @ ( lebesgue_lborel @ TB ) @ A )
= ( sigma_measurable @ TB @ TA @ ( borel_1404511681_borel @ TB ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_measurable__lborel2) ).
thf(831,plain,
! [TA: $tType,TB: $tType] :
( ( euclid925273238_space @ TB )
=> ! [A: sigma_measure @ TA] :
( ( sigma_measurable @ TB @ TA @ ( lebesgue_lborel @ TB ) @ A )
= ( sigma_measurable @ TB @ TA @ ( borel_1404511681_borel @ TB ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(314,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( ( sigma_sets @ TA @ A )
= ( sigma_sets @ TA @ B ) )
=> ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ C ) )
= ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_sets__restrict__space__cong) ).
thf(1117,plain,
! [TA: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( ( sigma_sets @ TA @ A )
= ( sigma_sets @ TA @ B ) )
=> ( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ C ) )
= ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(90,axiom,
ordere516151231imp_le @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_8) ).
thf(567,plain,
ordere516151231imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(114,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( countable @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Finite__Set_Ofinite___Countable_Ocountable) ).
thf(616,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( countable @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(105,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_inf1D2) ).
thf(599,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(233,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_add_Ocommute) ).
thf(900,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(9,axiom,
cancel1352612707id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__comm__monoid__add) ).
thf(406,plain,
cancel1352612707id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(224,axiom,
! [TA: $tType,A: sigma_measure @ TA] :
( member @ ( TA > TA )
@ ^ [B: TA] : B
@ ( sigma_measurable @ TA @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_measurable__id) ).
thf(880,plain,
! [TA: $tType,A: sigma_measure @ TA] :
( member @ ( TA > TA )
@ ^ [B: TA] : B
@ ( sigma_measurable @ TA @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(284,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( ring_char_0 @ TB ) )
=> ! [A: finite_Cartesian_vec @ int @ TA,B: finite_Cartesian_vec @ int @ TA] :
( ( ( minkow1937162798nt_vec @ TA @ TB @ A )
= ( minkow1937162798nt_vec @ TA @ TB @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_of__int__vec__eq__iff) ).
thf(1043,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( ring_char_0 @ TB ) )
=> ! [A: finite_Cartesian_vec @ int @ TA,B: finite_Cartesian_vec @ int @ TA] :
( ( ( minkow1937162798nt_vec @ TA @ TB @ A )
= ( minkow1937162798nt_vec @ TA @ TB @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(193,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_add__diff__cancel__left_H) ).
thf(811,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(173,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_add_Oright__cancel) ).
thf(758,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(215,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_le__add__same__cancel1) ).
thf(858,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(110,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_diff__eq__diff__eq) ).
thf(609,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType] :
( ( ( countable @ TB )
& ( elemen1026692323pology @ TA ) )
=> ( elemen1026692323pology @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Elementary__Topology_Osecond__countable__topology) ).
thf(594,plain,
! [TA: $tType,TB: $tType] :
( ( ( countable @ TB )
& ( elemen1026692323pology @ TA ) )
=> ( elemen1026692323pology @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(334,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_IntD1) ).
thf(1162,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(117,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_le__zero__eq) ).
thf(621,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_inf__apply) ).
thf(483,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(70,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add_24) ).
thf(520,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(280,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_add_Oassoc) ).
thf(1029,plain,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(177,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_IntD2) ).
thf(769,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(381,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_add_Oleft__neutral) ).
thf(1293,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ( topolo503727757_space @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Topological__Spaces_Otopological__space) ).
thf(462,plain,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ( topolo503727757_space @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(312,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_add__cancel__right__right) ).
thf(1112,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(328,axiom,
! [TA: $tType,TB: $tType] :
( ( ( plus @ TB )
& ( finite_finite @ TA ) )
=> ( plus @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oplus_102) ).
thf(1149,plain,
! [TA: $tType,TB: $tType] :
( ( ( plus @ TB )
& ( finite_finite @ TA ) )
=> ( plus @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(256,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Diff__Int__distrib) ).
thf(964,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(120,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_inf__assoc) ).
thf(626,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(239,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_diff__add__zero) ).
thf(915,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(264,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_double__add__le__zero__iff__single__add__le__zero) ).
thf(983,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(347,axiom,
! [A: finite_Cartesian_vec @ int @ n] :
( ( t @ A )
= ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( t2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_T_H__altdef) ).
thf(1198,plain,
! [A: finite_Cartesian_vec @ int @ n] :
( ( t @ A )
= ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( t2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1,conjecture,
( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [A: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ A @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [A: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ A @ ( 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 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(399,plain,
~ ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [A: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ A @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(254,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_sets_OInt__space__eq1) ).
thf(959,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(201,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_36) ).
thf(827,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(293,axiom,
! [TA: $tType,TB: $tType] :
( ( ( elemen1026692323pology @ TA )
& ( lattice @ TA )
& ( topolo2117631714pology @ TA ) )
=> ! [A: TB > TA,B: sigma_measure @ TB,C: TB > TA] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( TB > TA )
@ ^ [D: TB] : ( inf_inf @ TA @ ( C @ D ) @ ( A @ D ) )
@ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_borel__measurable__inf) ).
thf(1066,plain,
! [TA: $tType,TB: $tType] :
( ( ( elemen1026692323pology @ TA )
& ( lattice @ TA )
& ( topolo2117631714pology @ TA ) )
=> ! [A: TB > TA,B: sigma_measure @ TB,C: TB > TA] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( TB > TA )
@ ^ [D: TB] : ( inf_inf @ TA @ ( C @ D ) @ ( A @ D ) )
@ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(226,axiom,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TA > TB,B: sigma_measure @ TB,C: set @ TB] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ ( borel_1404511681_borel @ TA ) @ B ) )
=> ( ( member @ ( set @ TB ) @ C @ ( sigma_sets @ TB @ B ) )
=> ( member @ ( set @ TA ) @ ( vimage @ TA @ TB @ A @ C ) @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_measurable__sets__borel) ).
thf(883,plain,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TA > TB,B: sigma_measure @ TB,C: set @ TB] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ ( borel_1404511681_borel @ TA ) @ B ) )
=> ( ( member @ ( set @ TB ) @ C @ ( sigma_sets @ TB @ B ) )
=> ( member @ ( set @ TA ) @ ( vimage @ TA @ TB @ A @ C ) @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(276,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_ball__imageD) ).
thf(1015,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(265,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere779506340up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add_80) ).
thf(986,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere779506340up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(88,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(563,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(307,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( countable @ TA )
& ( elemen1026692323pology @ TB ) )
=> ! [A: TC > TA > TB,B: sigma_measure @ TC] :
( ! [C: TA] :
( member @ ( TC > TB )
@ ^ [D: TC] : ( A @ D @ C )
@ ( sigma_measurable @ TC @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( member @ ( TC > TA > TB ) @ A @ ( sigma_measurable @ TC @ ( TA > TB ) @ B @ ( borel_1404511681_borel @ ( TA > TB ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_measurable__coordinatewise__then__product) ).
thf(1102,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( countable @ TA )
& ( elemen1026692323pology @ TB ) )
=> ! [A: TC > TA > TB,B: sigma_measure @ TC] :
( ! [C: TA] :
( member @ ( TC > TB )
@ ^ [D: TC] : ( A @ D @ C )
@ ( sigma_measurable @ TC @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( member @ ( TC > TA > TB ) @ A @ ( sigma_measurable @ TC @ ( TA > TB ) @ B @ ( borel_1404511681_borel @ ( TA > TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(27,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( C @ B )
=> ( inf_inf @ ( TA > $o ) @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_inf1I) ).
thf(431,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( C @ B )
=> ( inf_inf @ ( TA > $o ) @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
=> ( member @ TA @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_vimageE) ).
thf(653,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
=> ( member @ TA @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType] :
( ( ( elemen1026692323pology @ TB )
& ( topological_t2_space @ TB ) )
=> ! [A: TA > TB,B: sigma_measure @ TA,C: TA > TB] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( ( member @ ( TA > TB ) @ C @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
& ( ( A @ D )
= ( C @ D ) ) ) )
@ ( sigma_sets @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_measurable__equality__set) ).
thf(658,plain,
! [TA: $tType,TB: $tType] :
( ( ( elemen1026692323pology @ TB )
& ( topological_t2_space @ TB ) )
=> ! [A: TA > TB,B: sigma_measure @ TA,C: TA > TB] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( ( member @ ( TA > TB ) @ C @ ( sigma_measurable @ TA @ TB @ B @ ( borel_1404511681_borel @ TB ) ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
& ( ( A @ D )
= ( C @ D ) ) ) )
@ ( sigma_sets @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(238,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: TA > $o] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ B @ A ) ) )
& ( C @ D ) ) )
@ ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ B @ A ) ) )
= ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
& ( member @ TA @ D @ A )
& ( C @ D ) ) )
@ ( sigma_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_sets__Collect__restrict__space__iff) ).
thf(912,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: TA > $o] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ B @ A ) ) )
& ( C @ D ) ) )
@ ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ B @ A ) ) )
= ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ B ) )
& ( member @ TA @ D @ A )
& ( C @ D ) ) )
@ ( sigma_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(71,axiom,
semilattice_inf @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__inf_19) ).
thf(521,plain,
semilattice_inf @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(337,axiom,
ordere516151231imp_le @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_48) ).
thf(1171,plain,
ordere516151231imp_le @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(340,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ( semigroup_add @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Osemigroup__add_32) ).
thf(1176,plain,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ( semigroup_add @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(109,axiom,
lattice @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Olattice_25) ).
thf(608,plain,
lattice @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(282,axiom,
! [TA: $tType,TB: $tType] :
( ( euclid925273238_space @ TB )
=> ! [A: set @ TB,B: TB > TA,C: TB > TA,D: sigma_measure @ TA] :
( ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ D ) )
= ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_measurable__lebesgue__cong) ).
thf(1034,plain,
! [TA: $tType,TB: $tType] :
( ( euclid925273238_space @ TB )
=> ! [A: set @ TB,B: TB > TA,C: TB > TA,D: sigma_measure @ TA] :
( ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ D ) )
= ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(385,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_bex__imageD) ).
thf(1304,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(101,axiom,
! [TA: $tType] : ( lattice @ ( sigma_measure @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Sigma__Algebra_Omeasure___Lattices_Olattice_74) ).
thf(589,plain,
! [TA: $tType] : ( lattice @ ( sigma_measure @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(248,axiom,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( minus_minus @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_minus__set__def) ).
thf(944,plain,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( minus_minus @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(82,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_inf__left__idem) ).
thf(548,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(397,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TB > TA,B: set @ TB] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) @ ( borel_1404511681_borel @ TA ) ) )
= ( ! [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( set @ TB )
@ ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ B )
& ( member @ TA @ ( A @ D ) @ C ) ) )
@ ( sigma_sets @ TB @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_borel__measurable__vimage__borel) ).
thf(1340,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TB > TA,B: set @ TB] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) @ ( borel_1404511681_borel @ TA ) ) )
= ( ! [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( set @ TB )
@ ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ B )
& ( member @ TA @ ( A @ D ) @ C ) ) )
@ ( sigma_sets @ TB @ ( sigma_restrict_space @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(326,axiom,
! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).
thf(1145,plain,
! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(171,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_DiffI) ).
thf(754,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(41,axiom,
semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add_22) ).
thf(458,plain,
semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(48,axiom,
topolo2117631714pology @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Olinorder__topology_12) ).
thf(473,plain,
topolo2117631714pology @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(297,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: set @ TA] :
( ( vimage @ TB @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ B ) @ ( vimage @ TB @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_vimage__Diff) ).
thf(1076,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: set @ TA] :
( ( vimage @ TB @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ B ) @ ( vimage @ TB @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(321,axiom,
! [TA: $tType,TB: $tType] :
( ( ( cancel_semigroup_add @ TB )
& ( finite_finite @ TA ) )
=> ( cancel_semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__semigroup__add_88) ).
thf(1134,plain,
! [TA: $tType,TB: $tType] :
( ( ( cancel_semigroup_add @ TB )
& ( finite_finite @ TA ) )
=> ( cancel_semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(129,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(648,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(55,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_14) ).
thf(487,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(73,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ~ ( ( A @ C )
=> ~ ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_inf1E) ).
thf(525,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ~ ( ( A @ C )
=> ~ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(97,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_diff__ge__0__iff__ge) ).
thf(580,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_image__iff) ).
thf(707,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(17,axiom,
semilattice_inf @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Lattices_Osemilattice__inf_4) ).
thf(414,plain,
semilattice_inf @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(370,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( semilattice_inf @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Lattices_Osemilattice__inf_89) ).
thf(1267,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( semilattice_inf @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(305,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [B: TA] :
( ( member @ TA @ B @ ( sigma_space @ TA @ ( borel_1404511681_borel @ TA ) ) )
& ( A @ B ) ) )
@ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [B: TA] :
( ( member @ TA @ B @ ( sigma_space @ TA @ ( lebesgue_lborel @ TA ) ) )
& ( A @ B ) ) )
@ ( sigma_sets @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_lborelD__Collect) ).
thf(1098,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [B: TA] :
( ( member @ TA @ B @ ( sigma_space @ TA @ ( borel_1404511681_borel @ TA ) ) )
& ( A @ B ) ) )
@ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [B: TA] :
( ( member @ TA @ B @ ( sigma_space @ TA @ ( lebesgue_lborel @ TA ) ) )
& ( A @ B ) ) )
@ ( sigma_sets @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(154,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_rev__image__eqI) ).
thf(712,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(86,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_diffs0__imp__equal) ).
thf(557,plain,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(271,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TB )
& ( finite_finite @ TA ) )
=> ( real_V55928688vector @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_78) ).
thf(1003,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TB )
& ( finite_finite @ TA ) )
=> ( real_V55928688vector @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(12,axiom,
minus @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ominus_7) ).
thf(409,plain,
minus @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(357,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: sigma_measure @ TA,C: sigma_measure @ TB,D: set @ TB] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ C ) )
=> ( ( member @ ( set @ TB ) @ D @ ( sigma_sets @ TB @ C ) )
=> ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ A @ D ) @ ( sigma_space @ TA @ B ) ) @ ( sigma_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_measurable__sets) ).
thf(1230,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: sigma_measure @ TA,C: sigma_measure @ TB,D: set @ TB] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ C ) )
=> ( ( member @ ( set @ TB ) @ D @ ( sigma_sets @ TB @ C ) )
=> ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ A @ D ) @ ( sigma_space @ TA @ B ) ) @ ( sigma_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(140,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_eq__add__iff) ).
thf(673,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(384,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= C )
=> ( A
= ( minus_minus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_add__implies__diff) ).
thf(1300,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= C )
=> ( A
= ( minus_minus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(185,axiom,
monoid_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Omonoid__add_66) ).
thf(791,plain,
monoid_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(388,axiom,
! [TA: $tType] :
( ( real_V1076094709vector @ TA )
=> ! [A: set @ TA,B: TA,C: set @ TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
= ( member @ TA @ ( plus_plus @ TA @ B @ D ) @ C ) )
=> ( C
= ( image @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_affine__parallel__expl__aux) ).
thf(1317,plain,
! [TA: $tType] :
( ( real_V1076094709vector @ TA )
=> ! [A: set @ TA,B: TA,C: set @ TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
= ( member @ TA @ ( plus_plus @ TA @ B @ D ) @ C ) )
=> ( C
= ( image @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(81,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ A @ D )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_boolean__algebra__cancel_Oinf1) ).
thf(544,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ A @ D )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(300,axiom,
! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: TB > $o,C: TB > TA,D: TB > TA,E: sigma_measure @ TA] :
( ( member @ ( set @ TB )
@ ( collect @ TB
@ ^ [F: TB] :
( ( member @ TB @ F @ ( sigma_space @ TB @ A ) )
& ( B @ F ) ) )
@ ( sigma_sets @ TB @ A ) )
=> ( ( member @ ( TB > TA )
@ ^ [F: TB] : ( if @ TA @ ( B @ F ) @ ( C @ F ) @ ( D @ F ) )
@ ( sigma_measurable @ TB @ TA @ A @ E ) )
= ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ A @ ( collect @ TB @ B ) ) @ E ) )
& ( member @ ( TB > TA ) @ D
@ ( sigma_measurable @ TB @ TA
@ ( sigma_restrict_space @ TB @ A
@ ( collect @ TB
@ ^ [F: TB] :
~ ( B @ F ) ) )
@ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_measurable__If__restrict__space__iff) ).
thf(1085,plain,
! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: TB > $o,C: TB > TA,D: TB > TA,E: sigma_measure @ TA] :
( ( member @ ( set @ TB )
@ ( collect @ TB
@ ^ [F: TB] :
( ( member @ TB @ F @ ( sigma_space @ TB @ A ) )
& ( B @ F ) ) )
@ ( sigma_sets @ TB @ A ) )
=> ( ( member @ ( TB > TA )
@ ^ [F: TB] : ( if @ TA @ ( B @ F ) @ ( C @ F ) @ ( D @ F ) )
@ ( sigma_measurable @ TB @ TA @ A @ E ) )
= ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ ( sigma_restrict_space @ TB @ A @ ( collect @ TB @ B ) ) @ E ) )
& ( member @ ( TB > TA ) @ D
@ ( sigma_measurable @ TB @ TA
@ ( sigma_restrict_space @ TB @ A
@ ( collect @ TB
@ ^ [F: TB] :
~ ( B @ F ) ) )
@ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TB )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_minus__apply) ).
thf(576,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TB )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(251,axiom,
! [TA: $tType,TB: $tType,A: TA,B: sigma_measure @ TA,C: sigma_measure @ TB] :
( ( member @ TA @ A @ ( sigma_space @ TA @ B ) )
=> ( member @ ( TB > TA )
@ ^ [D: TB] : A
@ ( sigma_measurable @ TB @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_measurable__const) ).
thf(951,plain,
! [TA: $tType,TB: $tType,A: TA,B: sigma_measure @ TA,C: sigma_measure @ TB] :
( ( member @ TA @ A @ ( sigma_space @ TA @ B ) )
=> ( member @ ( TB > TA )
@ ^ [D: TB] : A
@ ( sigma_measurable @ TB @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(192,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Int__absorb) ).
thf(808,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(395,axiom,
! [TA: $tType,TB: $tType] :
( ( ( elemen1026692323pology @ TA )
& ( topolo1314133330id_add @ TA ) )
=> ! [A: TB > TA,B: sigma_measure @ TB,C: TB > TA] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( TB > TA )
@ ^ [D: TB] : ( plus_plus @ TA @ ( A @ D ) @ ( C @ D ) )
@ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_borel__measurable__add) ).
thf(1336,plain,
! [TA: $tType,TB: $tType] :
( ( ( elemen1026692323pology @ TA )
& ( topolo1314133330id_add @ TA ) )
=> ! [A: TB > TA,B: sigma_measure @ TB,C: TB > TA] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( TB > TA )
@ ^ [D: TB] : ( plus_plus @ TA @ ( A @ D ) @ ( C @ D ) )
@ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(126,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( sigma_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_sets_ODiff) ).
thf(643,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( sigma_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(166,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_DiffD1) ).
thf(744,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(150,axiom,
semilattice_inf @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Osemilattice__inf_61) ).
thf(703,plain,
semilattice_inf @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(324,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V2090557954_space @ TB )
& ( finite_finite @ TA ) )
=> ( topological_t2_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Ot2__space_86) ).
thf(1141,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V2090557954_space @ TB )
& ( finite_finite @ TA ) )
=> ( topological_t2_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(377,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ B ) )
= ( sigma_sets @ TA
@ ( sigma_vimage_algebra @ TA @ TA @ ( inf_inf @ ( set @ TA ) @ B @ ( sigma_space @ TA @ A ) )
@ ^ [C: TA] : C
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_restrict__space__eq__vimage__algebra_H) ).
thf(1284,plain,
! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ B ) )
= ( sigma_sets @ TA
@ ( sigma_vimage_algebra @ TA @ TA @ ( inf_inf @ ( set @ TA ) @ B @ ( sigma_space @ TA @ A ) )
@ ^ [C: TA] : C
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(288,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( minus_minus @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_add__diff__cancel__right) ).
thf(1052,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( minus_minus @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(217,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TB > TA] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) )
= ( ! [B: set @ TA] :
( ( member @ ( set @ TA ) @ B @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( set @ TB )
@ ( collect @ TB
@ ^ [C: TB] : ( member @ TA @ ( A @ C ) @ B ) )
@ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_borel__measurable__lebesgue__preimage__borel) ).
thf(864,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TB > TA] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) @ ( borel_1404511681_borel @ TA ) ) )
= ( ! [B: set @ TA] :
( ( member @ ( set @ TA ) @ B @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( set @ TB )
@ ( collect @ TB
@ ^ [C: TB] : ( member @ TA @ ( A @ C ) @ B ) )
@ ( sigma_sets @ TB @ ( complete_completion @ TB @ ( lebesgue_lborel @ TB ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(159,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_zero__eq__add__iff__both__eq__0) ).
thf(727,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(303,axiom,
! [TA: $tType,A: sigma_measure @ TA] : ( member @ ( set @ TA ) @ ( sigma_space @ TA @ A ) @ ( sigma_sets @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_sets_Otop) ).
thf(1094,plain,
! [TA: $tType,A: sigma_measure @ TA] : ( member @ ( set @ TA ) @ ( sigma_space @ TA @ A ) @ ( sigma_sets @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(33,axiom,
topolo1314133330id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Limits_Otopological__monoid__add) ).
thf(446,plain,
topolo1314133330id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( semilattice_inf @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf) ).
thf(612,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( semilattice_inf @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(222,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: TB] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( ( member @ TB @ D @ ( sigma_space @ TB @ B ) )
=> ( member @ TA @ ( A @ D ) @ ( sigma_space @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_measurable__space) ).
thf(876,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: TB] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( ( member @ TB @ D @ ( sigma_space @ TB @ B ) )
=> ( member @ TA @ ( A @ D ) @ ( sigma_space @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(267,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB,D: set @ TB] :
( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ B @ D ) @ A )
= ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_vimage__inter__cong) ).
thf(991,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB,D: set @ TB] :
( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ B @ D ) @ A )
= ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(450,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(342,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1180,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(245,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_Int__iff) ).
thf(931,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(331,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TB > TC > TA,B: sigma_measure @ TB,C: TC] :
( ( member @ ( TB > TC > TA ) @ A @ ( sigma_measurable @ TB @ ( TC > TA ) @ B @ ( borel_1404511681_borel @ ( TC > TA ) ) ) )
=> ( member @ ( TB > TA )
@ ^ [D: TB] : ( A @ D @ C )
@ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_measurable__product__then__coordinatewise) ).
thf(1157,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TB > TC > TA,B: sigma_measure @ TB,C: TC] :
( ( member @ ( TB > TC > TA ) @ A @ ( sigma_measurable @ TB @ ( TC > TA ) @ B @ ( borel_1404511681_borel @ ( TC > TA ) ) ) )
=> ( member @ ( TB > TA )
@ ^ [D: TB] : ( A @ D @ C )
@ ( sigma_measurable @ TB @ TA @ B @ ( borel_1404511681_borel @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(234,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( member @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_imageE) ).
thf(903,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( member @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(229,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( complete_completion @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_sets__completionI__sets) ).
thf(891,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( complete_completion @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(317,axiom,
ab_group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oab__group__add_65) ).
thf(1126,plain,
ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(345,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: set @ TA,C: set @ TA] :
( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ ( sigma_restrict_space @ TA @ A @ B ) @ C ) )
= ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_sets__restrict__restrict__space) ).
thf(1189,plain,
! [TA: $tType,A: sigma_measure @ TA,B: set @ TA,C: set @ TA] :
( ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ ( sigma_restrict_space @ TA @ A @ B ) @ C ) )
= ( sigma_sets @ TA @ ( sigma_restrict_space @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(274,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: TB > TA,E: TB > $o] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( ( member @ ( TB > TA ) @ D @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( ( member @ ( set @ TB )
@ ( collect @ TB
@ ^ [F: TB] :
( ( member @ TB @ F @ ( sigma_space @ TB @ B ) )
& ( E @ F ) ) )
@ ( sigma_sets @ TB @ B ) )
=> ( member @ ( TB > TA )
@ ^ [F: TB] : ( if @ TA @ ( E @ F ) @ ( A @ F ) @ ( D @ F ) )
@ ( sigma_measurable @ TB @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_measurable__If) ).
thf(1010,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: sigma_measure @ TB,C: sigma_measure @ TA,D: TB > TA,E: TB > $o] :
( ( member @ ( TB > TA ) @ A @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( ( member @ ( TB > TA ) @ D @ ( sigma_measurable @ TB @ TA @ B @ C ) )
=> ( ( member @ ( set @ TB )
@ ( collect @ TB
@ ^ [F: TB] :
( ( member @ TB @ F @ ( sigma_space @ TB @ B ) )
& ( E @ F ) ) )
@ ( sigma_sets @ TB @ B ) )
=> ( member @ ( TB > TA )
@ ^ [F: TB] : ( if @ TA @ ( E @ F ) @ ( A @ F ) @ ( D @ F ) )
@ ( sigma_measurable @ TB @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(379,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_add__cancel__left__left) ).
thf(1289,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(178,axiom,
! [TA: $tType,TB: $tType] :
( ( ( comm_monoid_add @ TB )
& ( finite_finite @ TA ) )
=> ( comm_monoid_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ocomm__monoid__add_91) ).
thf(771,plain,
! [TA: $tType,TB: $tType] :
( ( ( comm_monoid_add @ TB )
& ( finite_finite @ TA ) )
=> ( comm_monoid_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(374,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
& ( B @ C ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
& ~ ( B @ C ) ) )
@ ( sigma_sets @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_sets_Osets__Collect__neg) ).
thf(1276,plain,
! [TA: $tType,A: sigma_measure @ TA,B: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
& ( B @ C ) ) )
@ ( sigma_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ ( sigma_space @ TA @ A ) )
& ~ ( B @ C ) ) )
@ ( sigma_sets @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(391,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: sigma_measure @ TA,C: sigma_measure @ TB,D: TB > $o] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ C ) )
=> ( ( member @ ( set @ TB )
@ ( collect @ TB
@ ^ [E: TB] :
( ( member @ TB @ E @ ( sigma_space @ TB @ C ) )
& ( D @ E ) ) )
@ ( sigma_sets @ TB @ C ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ ( sigma_space @ TA @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_measurable__sets__Collect) ).
thf(1326,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: sigma_measure @ TA,C: sigma_measure @ TB,D: TB > $o] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ B @ C ) )
=> ( ( member @ ( set @ TB )
@ ( collect @ TB
@ ^ [E: TB] :
( ( member @ TB @ E @ ( sigma_space @ TB @ C ) )
& ( D @ E ) ) )
@ ( sigma_sets @ TB @ C ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ ( sigma_space @ TA @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(69,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_inf_Oidem) ).
thf(517,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(168,axiom,
! [TA: $tType,TB: $tType] :
( ( ( cancel1352612707id_add @ TB )
& ( finite_finite @ TA ) )
=> ( cancel1352612707id_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__comm__monoid__add_85) ).
thf(748,plain,
! [TA: $tType,TB: $tType] :
( ( ( cancel1352612707id_add @ TB )
& ( finite_finite @ TA ) )
=> ( cancel1352612707id_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA,C: set @ TB,D: TB > TA] :
( ( ( sigma_sets @ TA @ A )
= ( sigma_sets @ TA @ B ) )
=> ( ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ C @ D @ A ) )
= ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ C @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_sets__vimage__algebra__cong) ).
thf(632,plain,
! [TA: $tType,TB: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA,C: set @ TB,D: TB > TA] :
( ( ( sigma_sets @ TA @ A )
= ( sigma_sets @ TA @ B ) )
=> ( ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ C @ D @ A ) )
= ( sigma_sets @ TB @ ( sigma_vimage_algebra @ TB @ TA @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(4,axiom,
topolo503727757_space @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Topological__Spaces_Otopological__space_3) ).
thf(401,plain,
topolo503727757_space @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(161,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( comm_monoid_add @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ocomm__monoid__add_31) ).
thf(731,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( comm_monoid_add @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(180,axiom,
real_V2090557954_space @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space_2) ).
thf(781,plain,
real_V2090557954_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(365,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_add__diff__cancel__right_H) ).
thf(1253,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(148,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_le__add__same__cancel2) ).
thf(699,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(91,axiom,
topolo1314133330id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Limits_Otopological__monoid__add_15) ).
thf(568,plain,
topolo1314133330id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(137,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_add__eq__0__iff__both__eq__0) ).
thf(667,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(175,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_add_Oright__neutral) ).
thf(763,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: set @ TB] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) @ ( borel_1404511681_borel @ TB ) ) )
=> ( ( member @ ( set @ TB ) @ B @ ( sigma_sets @ TB @ ( borel_1404511681_borel @ TB ) ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] : ( member @ TB @ ( A @ C ) @ B ) )
@ ( sigma_sets @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_lebesgue__measurable__vimage__borel) ).
thf(684,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: set @ TB] :
( ( member @ ( TA > TB ) @ A @ ( sigma_measurable @ TA @ TB @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) @ ( borel_1404511681_borel @ TB ) ) )
=> ( ( member @ ( set @ TB ) @ B @ ( sigma_sets @ TB @ ( borel_1404511681_borel @ TB ) ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] : ( member @ TB @ ( A @ C ) @ B ) )
@ ( sigma_sets @ TA @ ( complete_completion @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(433,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(66,axiom,
elemen1026692323pology @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Elementary__Topology_Osecond__countable__topology_9) ).
thf(510,plain,
elemen1026692323pology @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(155,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA] :
( ( ( sigma_sets @ TA @ A )
= ( sigma_sets @ TA @ B ) )
=> ( ( sigma_space @ TA @ A )
= ( sigma_space @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_sets__eq__imp__space__eq) ).
thf(716,plain,
! [TA: $tType,A: sigma_measure @ TA,B: sigma_measure @ TA] :
( ( ( sigma_sets @ TA @ A )
= ( sigma_sets @ TA @ B ) )
=> ( ( sigma_space @ TA @ A )
= ( sigma_space @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(189,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
= ( minus_minus @ TA @ B @ C ) )
= ( ( plus_plus @ TA @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_eq__diff__eq) ).
thf(800,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
= ( minus_minus @ TA @ B @ C ) )
= ( ( plus_plus @ TA @ A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(34,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(447,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(205,axiom,
! [A: finite_Cartesian_vec @ int @ n] :
( ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( 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 )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( t2 @ A ) )
@ ( 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 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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) ).
thf(835,plain,
! [A: finite_Cartesian_vec @ int @ n] :
( ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( 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 )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( t2 @ A ) )
@ ( 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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(197,axiom,
cancel146912293up_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_55) ).
thf(818,plain,
cancel146912293up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(8,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(405,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(218,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Diff__Int__distrib2) ).
thf(867,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(163,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( minus_minus @ TA @ A @ B )
= C )
= ( A
= ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_diff__eq__eq) ).
thf(735,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( minus_minus @ TA @ A @ B )
= C )
= ( A
= ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(13,axiom,
monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Omonoid__add) ).
thf(410,plain,
monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(257,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ab_semigroup_add @ TB )
& ( finite_finite @ TA ) )
=> ( ab_semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__semigroup__add_90) ).
thf(967,plain,
! [TA: $tType,TB: $tType] :
( ( ( ab_semigroup_add @ TB )
& ( finite_finite @ TA ) )
=> ( ab_semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(89,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_zero__diff) ).
thf(564,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(240,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_add__le__same__cancel2) ).
thf(918,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(387,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_translation__Int) ).
thf(1314,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(290,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( minus_minus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( minus_minus @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_group__cancel_Osub1) ).
thf(1056,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( minus_minus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( minus_minus @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(3,axiom,
plus @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oplus) ).
thf(400,plain,
plus @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: TB > TA,C: TB > TA,D: sigma_measure @ TA] :
( ! [E: TB] :
( ( member @ TB @ E @ ( sigma_space @ TB @ A ) )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ A @ D ) )
= ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_measurable__cong) ).
thf(635,plain,
! [TA: $tType,TB: $tType,A: sigma_measure @ TB,B: TB > TA,C: TB > TA,D: sigma_measure @ TA] :
( ! [E: TB] :
( ( member @ TB @ E @ ( sigma_space @ TB @ A ) )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( member @ ( TB > TA ) @ B @ ( sigma_measurable @ TB @ TA @ A @ D ) )
= ( member @ ( TB > TA ) @ C @ ( sigma_measurable @ TB @ TA @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(338,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A ) @ ( sigma_sets @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_sets_Ocompl__sets) ).
thf(1172,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A ) @ ( sigma_sets @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(232,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ C ) ) )
= ( ( member @ TA @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_Int__Collect) ).
thf(897,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ C ) ) )
= ( ( member @ TA @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(49,axiom,
! [TA: $tType] : ( semilattice_inf @ ( sigma_measure @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Sigma__Algebra_Omeasure___Lattices_Osemilattice__inf_73) ).
thf(474,plain,
! [TA: $tType] : ( semilattice_inf @ ( sigma_measure @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(244,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_add__le__cancel__left) ).
thf(928,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(18,axiom,
ordere516151231imp_le @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).
thf(415,plain,
ordere516151231imp_le @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(118,axiom,
countable @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Countable_Ocountable_23) ).
thf(624,plain,
countable @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(359,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_diff__diff__eq2) ).
thf(1236,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TA )
=> ( minus @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ominus) ).
thf(464,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TA )
=> ( minus @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(319,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_space__restrict__space2) ).
thf(1129,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( sigma_space @ TA @ ( sigma_restrict_space @ TA @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(368,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Int__left__absorb) ).
thf(1261,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(104,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(596,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(42,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_inf__commute) ).
thf(459,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(235,axiom,
elemen1026692323pology @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Elementary__Topology_Osecond__countable__topology_49) ).
thf(908,plain,
elemen1026692323pology @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(199,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Int__left__commute) ).
thf(822,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(212,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_subset__antisym) ).
thf(850,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_image__cong) ).
thf(691,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(31,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_inf_Ocommute) ).
thf(442,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(220,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_lborelD) ).
thf(871,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( borel_1404511681_borel @ TA ) ) )
=> ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ ( lebesgue_lborel @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(315,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_diff__add__cancel) ).
thf(1120,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(393,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_Diff__idemp) ).
thf(1331,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(54,axiom,
topological_t2_space @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Ot2__space_17) ).
thf(486,plain,
topological_t2_space @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(190,axiom,
! [TA: $tType,TB: $tType] :
( ( ( zero @ TB )
& ( finite_finite @ TA ) )
=> ( zero @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ozero_101) ).
thf(803,plain,
! [TA: $tType,TB: $tType] :
( ( ( zero @ TB )
& ( finite_finite @ TA ) )
=> ( zero @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(389,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_add__le__cancel__right) ).
thf(1320,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(46,axiom,
! [A: nat > $o] :
( ( A @ ( zero_zero @ nat ) )
=> ( ( ord_Least @ nat @ A )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_Least__eq__0) ).
thf(469,plain,
! [A: nat > $o] :
( ( A @ ( zero_zero @ nat ) )
=> ( ( ord_Least @ nat @ A )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(242,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_96) ).
thf(923,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(87,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_inf__right__idem) ).
thf(560,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(141,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Int__Diff) ).
thf(676,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(301,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ^ [C: TA] : ( member @ TA @ C @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_inf__Int__eq) ).
thf(1088,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ^ [C: TA] : ( member @ TA @ C @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(225,axiom,
lattice @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Olattice_67) ).
thf(882,plain,
lattice @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(260,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Int__commute) ).
thf(972,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(60,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_diff__right__commute) ).
thf(496,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(40,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ D @ A )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_boolean__algebra__cancel_Oinf2) ).
thf(454,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ D @ A )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1350,plain,
$false,
inference(e,[status(thm)],[645,629,1024,1168,479,846,909,893,962,555,1005,730,1068,741,1269,614,861,408,977,873,1205,449,878,655,511,533,500,472,814,1063,538,670,1164,797,1001,782,436,651,829,404,1243,1127,841,417,885,1046,1287,570,1298,719,785,504,1264,934,1132,949,1055,724,587,1323,619,838,702,751,817,853,1147,1247,969,416,1115,448,1100,1232,421,870,492,756,591,514,1151,1183,1051,480,1040,1109,1334,646,1136,834,1215,956,453,660,998,1104,507,602,766,411,988,428,1201,1074,452,439,529,925,761,1338,1047,1311,534,1274,1021,1123,1174,1217,424,788,815,1223,894,746,1091,825,1343,407,630,847,1032,625,1178,1159,493,682,551,1281,710,1012,1106,1296,665,583,522,1079,1027,1143,615,1328,1096,1138,420,499,1111,1227,980,403,1160,1082,488,1292,554,537,489,1207,686,476,679,970,837,997,1249,738,1192,1060,911,721,569,503,605,792,938,1241,805,921,541,1071,1187,530,953,773,794,586,662,888,1278,412,750,618,425,1219,856,573,689,733,601,1154,819,975,423,1007,402,843,579,413,1256,1226,641,445,1271,787,1239,466,947,672,1258,704,831,1117,567,616,599,900,406,880,1043,811,758,858,609,594,1162,621,483,520,1029,769,1293,462,1112,1149,964,626,915,983,1198,399,959,827,1066,883,1015,986,563,1102,431,653,658,912,521,1171,1176,608,1034,1304,589,944,548,1340,1145,754,458,473,1076,1134,648,487,525,580,707,414,1267,1098,712,557,1003,409,1230,673,1300,791,1317,544,1085,576,951,808,1336,643,744,703,1141,1284,1052,864,727,1094,446,612,876,991,450,1180,931,1157,903,891,1126,1189,1010,1289,771,1276,1326,517,748,632,401,731,781,1253,699,568,667,763,684,433,510,716,800,447,835,818,405,867,735,410,967,564,918,1314,1056,400,635,1172,897,474,928,415,624,1236,464,1129,1261,596,459,908,822,850,691,442,871,1120,1331,486,803,1320,469,923,560,676,1088,882,972,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP116^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n017.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:51:22 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.63/0.55 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.74/0.86 % [INFO] Parsing done (305ms).
% 1.74/0.86 % [INFO] Running in sequential loop mode.
% 3.17/1.17 % [INFO] eprover registered as external prover.
% 3.17/1.18 % [INFO] Scanning for conjecture ...
% 3.56/1.36 % [INFO] Found a conjecture (or negated_conjecture) and 397 axioms. Running axiom selection ...
% 4.25/1.55 % [INFO] Axiom selection finished. Selected 396 axioms (removed 1 axioms).
% 5.71/1.96 % [INFO] Problem is higher-order (TPTP THF).
% 5.71/2.01 % [INFO] Type checking passed.
% 5.71/2.01 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 42.64/21.82 % External prover 'e' found a proof!
% 42.64/21.82 % [INFO] Killing All external provers ...
% 42.64/21.82 % Time passed: 21508ms (effective reasoning time: 20956ms)
% 42.64/21.82 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 42.64/21.83 % Axioms used in derivation (396): fact_11_vimage__eq, fact_250_add__le__same__cancel1, tcon_Nat_Onat___Lattices_Olattice_25, tcon_fun___Groups_Ominus, fact_150_vimage__algebra__cong, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_53, fact_23_IntE, fact_126_image__image, fact_130_rev__image__eqI, fact_57_measurableI, fact_26_Int__assoc, fact_31_Collect__conj__eq, fact_220_diff__zero, tfree_0, fact_229_zero__reorient, fact_221_cancel__comm__monoid__add__class_Odiff__cancel, tcon_Real_Oreal___Groups_Ocancel__semigroup__add_60, fact_167_sets_ODiff, tcon_Int_Oint___Groups_Oplus, fact_101_inf__Int__eq, fact_88_sets__eq__imp__space__eq, fact_76_inf_Oassoc, tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_79, tcon_Real_Oreal___Groups_Omonoid__add_66, fact_39_add_Ocommute, tcon_fun___Finite__Set_Ofinite, fact_166_measurable__lborel2, fact_145_add__diff__eq, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, tcon_Real_Oreal___Groups_Olinordered__ab__group__add_54, fact_89_measurable__cong__simp, fact_159_borel__measurable__neq, fact_185_restrict__restrict__space, fact_69_inf_Oidem, tcon_Set_Oset___Lattices_Osemilattice__inf_29, fact_139_measurable__restrict__space1, tcon_Real_Oreal___Groups_Ozero_71, tcon_Sigma__Algebra_Omeasure___Lattices_Olattice_74, fact_148_group__cancel_Osub1, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_16, fact_202_measurable__product__coordinates, fact_96_sets_Osets__Collect__conj, tcon_Int_Oint___Groups_Ozero, tcon_HOL_Obool___Countable_Ocountable_44, fact_65_inf_Oright__idem, fact_125_Compr__image__eq, fact_30_Int__left__commute, fact_242_inf_Obounded__iff, fact_142_diff__add__eq__diff__diff__swap, fact_184_restrict__space__eq__vimage__algebra_H, fact_32_Int__Collect, fact_224_eq__add__iff, fact_35_vimage__inter__cong, tcon_HOL_Obool___Lattices_Osemilattice__inf_43, fact_176_sets__restrict__space, fact_10_vimageI, tcon_Finite__Cartesian__Product_Ovec___Limits_Otopological__monoid__add_84, tcon_Int_Oint___Nat_Oring__char__0, tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_96, fact_18_IntI, tcon_Finite__Cartesian__Product_Ovec___Groups_Ogroup__add_98, fact_99_measurable__const, fact_25_IntD2, tcon_Nat_Onat___Groups_Oab__semigroup__add_20, fact_83_inf__sup__aci_I4_J, fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_8_vimage__ident, tcon_Int_Oint___Groups_Oordered__ab__group__add, fact_192_DiffD2, fact_171_Diff__Int2, fact_155_space__restrict__space, fact_244_set__plus__mono2, fact_151_borel__measurable__const__add, fact_226_comm__monoid__add__class_Oadd__0, fact_152_borel__measurable__add, tcon_Real_Oreal___Topological__Spaces_Ot2__space_58, fact_51_ab__semigroup__add__class_Oadd__ac_I1_J, fact_181_lebesgue__measurable__vimage__borel, tcon_Int_Oint___Groups_Oab__group__add, fact_144_diff__diff__eq2, fact_9_vimage__Collect__eq, tcon_Set_Oset___Groups_Osemigroup__add_32, tcon_Real_Oreal___Groups_Oab__semigroup__add_62, fact_63_inf__apply, fact_215_add__eq__0__iff__both__eq__0, tcon_Int_Oint___Limits_Otopological__monoid__add, tcon_Real_Oreal___Nat_Oring__char__0_69, tcon_Finite__Cartesian__Product_Ovec___Lattices_Olattice_97, fact_52_vimage__Collect, tcon_fun___Topological__Spaces_Otopological__space, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_50, fact_86_measurable__id, fact_79_inf__fun__def, fact_141_diff__diff__add, fact_14_add__right__cancel, fact_233_borel__measurable__if__lebesgue__on, fact_61_measurable__sets__Collect, tcon_Real_Oreal___Groups_Ogroup__add_68, fact_210_double__zero__sym, fact_134_image__iff, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__monoid__add__imp__le_75, fact_19_Int__iff, fact_157_sets__Collect__restrict__space__iff, tcon_Finite__Cartesian__Product_Ovec___Lattices_Osemilattice__inf_89, fact_71_inf__left__commute, tcon_Set_Oset___Groups_Oab__semigroup__add_30, fact_85_measurable__compose, 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, fact_72_inf_Oleft__commute, fact_92_measurable__ident__sets, fact_131_ball__imageD, fact_80_inf__sup__aci_I1_J, tcon_HOL_Obool___Topological__Spaces_Olinorder__topology_41, fact_117_space__vimage__algebra, fact_201_measurable__coordinatewise__then__product, tcon_Nat_Onat___Elementary__Topology_Osecond__countable__topology_9, fact_189_DiffI, tcon_Real_Oreal___Groups_Ocomm__monoid__add_63, tcon_Int_Oint___Groups_Ominus_7, tcon_Finite__Cartesian__Product_Ovec___Nat_Oring__char__0_99, fact_161_measurable__If__restrict__space__iff, fact_158_borel__measurable__eq, tcon_Int_Oint___Groups_Ocancel__semigroup__add, fact_98_sets_Osets__Collect__const, tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__semigroup__add_88, tcon_Int_Oint___Groups_Omonoid__add, fact_234_subsetI, fact_100_T_H__def, fact_188_Diff__iff, fact_5__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, tcon_HOL_Obool___Topological__Spaces_Ot2__space_42, fact_191_minus__set__def, fact_77_boolean__algebra__cancel_Oinf2, fact_118_main__part, tcon_HOL_Obool___Finite__Set_Ofinite_45, tcon_Finite__Cartesian__Product_Ovec___Groups_Ozero_101, tcon_Int_Oint___Groups_Osemigroup__add, fact_12_set__plus__intro, fact_49_group__cancel_Oadd1, tcon_Set_Oset___Groups_Oplus_39, tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Ot2__space_86, fact_46_Collect__mem__eq, tcon_Sigma__Algebra_Omeasure___Lattices_Osemilattice__inf_73, tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_1, tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector, tcon_Int_Oint___Groups_Oab__semigroup__add, fact_120_inf1E, tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__ab__semigroup__add_83, fact_41_add_Oleft__cancel, tcon_Set_Oset___Groups_Ominus_37, fact_251_diff__ge__0__iff__ge, tcon_Real_Oreal___Limits_Otopological__monoid__add_56, fact_27_Int__absorb, tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__vector_82, fact_94_sets_Osets__Collect__imp, tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__semigroup__add_90, subcl_Finite__Set_Ofinite___Countable_Ocountable, fact_174_Diff__Int__distrib2, fact_135_imageI, fact_207_add_Oleft__neutral, fact_200_measurable__product__then__coordinatewise, help_If_1_1_T, fact_146_eq__diff__eq, fact_252_subset__translation__eq, fact_74_inf_Ocommute, tcon_fun___Countable_Ocountable, fact_113_add__diff__cancel__left_H, fact_253_diffs0__imp__equal, tcon_Finite__Cartesian__Product_Ovec___Groups_Ominus_100, fact_6_sets__completionI__sets, fact_196_translation__subtract__diff, fact_128_diff__right__commute, fact_216_zero__eq__add__iff__both__eq__0, fact_137_sets__restrict__space__cong, tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_57, fact_214_add__cancel__right__right, fact_68_inf__idem, fact_82_inf__sup__aci_I3_J, tcon_Nat_Onat___Topological__Spaces_Ot2__space_17, tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le, tcon_Int_Oint___Groups_Ocancel__comm__monoid__add, fact_140_add__implies__diff, fact_93_sets_Osets__Collect_I5_J, tcon_Real_Oreal___Topological__Spaces_Otopological__space_51, tcon_Real_Oreal___Euclidean__Space_Oeuclidean__space, fact_124_fun__diff__def, fact_204_translation__assoc, fact_110_image__ident, fact_55_sets_OInt__space__eq1, fact_208_add_Oright__neutral, fact_67_inf_Oleft__idem, tcon_Finite__Cartesian__Product_Ovec___Countable_Ocountable_94, fact_13_add__left__cancel, fact_132_image__cong, fact_119_space__restrict__space2, fact_235_subset__antisym, tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector, fact_194_DiffE, fact_105_in__vimage__algebra, fact_199_translation__Int, tcon_Real_Oreal___Groups_Oab__group__add_65, tcon_fun___Lattices_Osemilattice__inf, fact_16_vimageD, tcon_Finite__Cartesian__Product_Ovec___Groups_Ocomm__monoid__add_91, fact_28_Int__commute, fact_122_inf1D2, fact_219_zero__diff, fact_20_space__completion, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_10, tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__group__add_93, tcon_Finite__Cartesian__Product_Ovec___Groups_Oplus_102, fact_87_measurable__cong__sets, fact_45_mem__Collect__eq, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add_80, fact_123_borel__measurable__diff, tcon_Set_Oset___Groups_Ocomm__monoid__add_31, fact_37_add__left__imp__eq, fact_104_sets__Least, fact_205_affine__parallel__expl__aux, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add__imp__le_77, fact_97_sets_Osets__Collect__disj, tcon_Set_Oset___Groups_Omonoid__add_34, fact_165_measurable__lborel1, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add, fact_198_translation__diff, fact_53_vimageI2, fact_168_sets_Ocompl__sets, tcon_Int_Oint___Countable_Ocountable_5, fact_187_Diff__idemp, fact_248_le__add__same__cancel1, fact_36_add__right__imp__eq, fact_90_measurable__space, tcon_Real_Oreal___Groups_Ominus_70, fact_228_add_Ogroup__left__neutral, fact_24_IntD1, fact_239_add__le__cancel__right, tcon_Nat_Onat___Countable_Ocountable_23, fact_60_measurable__If__set, tcon_Nat_Onat___Groups_Osemigroup__add_22, fact_136_borel__measurable__const, fact_42_add_Oassoc, tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add, tcon_Real_Oreal___Topological__Spaces_Olinorder__topology_52, fact_164_space__lborel, fact_149_sets__vimage__algebra__cong, tcon_Int_Oint___Groups_Ocomm__monoid__add, tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__comm__monoid__add_85, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_13, fact_50_add__mono__thms__linordered__semiring_I4_J, fact_180_lebesgue__sets__translation, fact_38_add_Oleft__commute, fact_179_lborelD__Collect, fact_121_inf1D1, fact_84_measurable__compose__rev, tcon_Int_Oint___Groups_Ogroup__add, tcon_Real_Oreal___Lattices_Osemilattice__inf_61, fact_47_Collect__cong, fact_66_inf__left__idem, fact_209_double__zero, tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space, fact_169_sets__lborel, help_If_3_1_T, fact_4_T_H__altdef, fact_178_measurable__lebesgue__cong, help_If_2_1_T, fact_58_sets_Otop, fact_217_diff__self, tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_55, fact_81_inf__sup__aci_I2_J, fact_156_measurable__sets__borel, fact_243_Int__subset__iff, fact_1_of__int__vec__eq__iff, fact_95_sets_Osets__Collect__neg, fact_211_add__cancel__left__left, fact_154_sets__restrict__restrict__space, tcon_Real_Oreal___Groups_Oplus_72, fact_91_measurable__cong, tcon_Real_Oreal___Groups_Oordered__ab__group__add_59, tcon_Nat_Onat___Topological__Spaces_Otopological__space_11, fact_183_borel__measurable__vimage__borel, tcon_Int_Oint___Groups_Olinordered__ab__group__add, fact_230_borel__measurable__if__D, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, fact_206_borel__measurable__if, fact_160_measurable__equality__set, fact_114_add__diff__cancel__left, fact_106_in__borel__measurable__borel, tcon_Int_Oint___Topological__Spaces_Otopological__space_3, fact_163_sets__lebesgue__on__refl, tcon_Nat_Onat___Groups_Oplus_28, fact_43_set__plus__elim, fact_33_Int__def, tcon_HOL_Obool___Topological__Spaces_Otopological__space_40, fact_75_inf__assoc, fact_177_lborelD, fact_237_diff__self__eq__0, fact_231_borel__measurable__if__I, tcon_Finite__Cartesian__Product_Ovec___Groups_Osemigroup__add_92, tcon_Int_Oint___Topological__Spaces_Olinorder__topology, fact_246_double__add__le__zero__iff__single__add__le__zero, fact_109_inf1I, tcon_Finite__Cartesian__Product_Ovec___Groups_Omonoid__add_95, fact_62_measurable__If, fact_143_diff__add__eq, fact_195_sets__vimage__algebra__space, fact_190_set__diff__eq, tcon_Set_Oset___Lattices_Olattice_36, fact_44_group__cancel_Oadd2, tcon_Int_Oint___Lattices_Olattice_6, fact_172_Diff__Diff__Int, subcl_Finite__Set_Ofinite___HOL_Otype, fact_111_add__diff__cancel__right_H, fact_193_DiffD1, tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_78, fact_213_add__cancel__right__left, fact_182_borel__measurable__lebesgue__preimage__borel, 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, fact_40_add_Oright__cancel, fact_102_main__part__sets, fact_129_diff__eq__diff__eq, tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Ometric__space, tcon_HOL_Obool___Lattices_Olattice_46, fact_70_inf__set__def, fact_54_sets_OInt__space__eq2, fact_15_vimage__def, fact_222_image__add__0, fact_138_restrict__space__sets__cong, fact_133_bex__imageD, fact_115_diff__add__cancel, fact_56_measurable__sets, fact_241_le__inf__iff, fact_107_image__eqI, fact_127_imageE, fact_78_boolean__algebra__cancel_Oinf1, tcon_Set_Oset___Countable_Ocountable_33, fact_147_diff__eq__eq, tcon_Nat_Onat___Lattices_Osemilattice__inf_19, tcon_Nat_Onat___Groups_Omonoid__add_24, fact_21_vimage__Int, fact_153_borel__measurable__inf, tcon_fun___Elementary__Topology_Osecond__countable__topology, fact_223_diff__add__zero, fact_170_Int__Diff, fact_245_zero__le__double__add__iff__zero__le__single__add, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_48, fact_249_add__le__same__cancel2, tcon_Nat_Onat___Topological__Spaces_Olinorder__topology_12, fact_227_add_Ocomm__neutral, tcon_Nat_Onat___Groups_Ocomm__monoid__add_21, fact_240_add__le__cancel__left, fact_186_is__borel__def, fact_238_le__zero__eq, fact_64_inf__right__idem, fact_0_assms_I1_J, fact_247_le__add__same__cancel2, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_8, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_29_Int__left__absorb, tcon_Finite__Cartesian__Product_Ovec___Euclidean__Space_Oeuclidean__space_81, fact_232_Least__eq__0, fact_116_add__diff__cancel, fact_236_diff__0__eq__0, fact_34_measurable__completion, fact_212_add__cancel__left__right, tcon_Real_Oreal___Elementary__Topology_Osecond__countable__topology_49, tcon_Nat_Onat___Groups_Ocancel__semigroup__add_18, tcon_Finite__Cartesian__Product_Ovec___Elementary__Topology_Osecond__countable__topology_76, fact_162_space__lebesgue__on, tcon_Int_Oint___Lattices_Osemilattice__inf_4, fact_103_measurable__restrict__space__iff, fact_218_diff__0__right, fact_108_minus__apply, fact_197_translation__subtract__Int, tcon_Nat_Onat___Limits_Otopological__monoid__add_15, fact_173_Diff__Int__distrib, fact_112_add__diff__cancel__right, tcon_Real_Oreal___Lattices_Olattice_67, tcon_Int_Oint___Topological__Spaces_Ot2__space, fact_22_T__def, tcon_Set_Oset___Finite__Set_Ofinite_35, fact_73_inf__commute, fact_17_vimageE, tcon_Set_Oset___Groups_Ozero_38, fact_59_sets_OInt, tcon_Real_Oreal___Groups_Osemigroup__add_64, tcon_Nat_Onat___Groups_Ominus_26, fact_225_eq__iff__diff__eq__0, fact_254_minus__nat_Odiff__0, fact_203_translation__invert, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_14, tcon_HOL_Obool___Groups_Ominus_47, tcon_Nat_Onat___Groups_Ozero_27, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add_87, tcon_fun___Lattices_Olattice, fact_175_vimage__Diff, tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space_2
% 42.64/21.83 % No. of inferences in proof: 796
% 42.64/21.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21508 ms resp. 20956 ms w/o parsing
% 44.21/22.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 44.21/22.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------