%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP116^1 : 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 : n015.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 21.17s 5.96s
% Output : Refutation 22.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 338
% Syntax : Number of formulae : 678 ( 309 unt; 0 typ; 0 def)
% Number of atoms : 1845 ( 554 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 7471 ( 72 ~; 7 |; 232 &;6526 @)
% ( 0 <=>; 634 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 21 ( 20 usr)
% Number of type conns : 784 ( 784 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 91 usr; 8 con; 0-4 aty)
% Number of variables : 2324 ( 431 ^;1887 !; 6 ?;2324 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Fi1066397675real_n_type,type,
set_Fi1066397675real_n: $tType ).
thf(set_se830533260real_n_type,type,
set_se830533260real_n: $tType ).
thf(set_Fi909698444real_n_type,type,
set_Fi909698444real_n: $tType ).
thf(set_Fi1260307670real_n_type,type,
set_Fi1260307670real_n: $tType ).
thf(set_Fi1491909078real_n_type,type,
set_Fi1491909078real_n: $tType ).
thf(set_se1738601133real_n_type,type,
set_se1738601133real_n: $tType ).
thf(sigma_107786596real_n_type,type,
sigma_107786596real_n: $tType ).
thf(set_se221767415real_n_type,type,
set_se221767415real_n: $tType ).
thf(set_se955370231real_n_type,type,
set_se955370231real_n: $tType ).
thf(set_Fi1645173239real_n_type,type,
set_Fi1645173239real_n: $tType ).
thf(set_Fi1326602817real_n_type,type,
set_Fi1326602817real_n: $tType ).
thf(sigma_1422848389real_n_type,type,
sigma_1422848389real_n: $tType ).
thf(set_se820660888real_n_type,type,
set_se820660888real_n: $tType ).
thf(sigma_1466784463real_n_type,type,
sigma_1466784463real_n: $tType ).
thf(set_se2111327970real_n_type,type,
set_se2111327970real_n: $tType ).
thf(set_Fi1058188332real_n_type,type,
set_Fi1058188332real_n: $tType ).
thf(finite1489363574real_n_type,type,
finite1489363574real_n: $tType ).
thf(finite964658038_int_n_type,type,
finite964658038_int_n: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(borel_1962407338real_n_decl,type,
borel_1962407338real_n: ( finite1489363574real_n > finite1489363574real_n ) > sigma_1466784463real_n > $o ).
thf(borel_676189912real_n_decl,type,
borel_676189912real_n: sigma_1466784463real_n ).
thf(comple230862828real_n_decl,type,
comple230862828real_n: sigma_1466784463real_n > sigma_1466784463real_n ).
thf(comple1390568924real_n_decl,type,
comple1390568924real_n: sigma_1466784463real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(minus_391085931al_n_o_decl,type,
minus_391085931al_n_o: ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > ( finite1489363574real_n > finite1489363574real_n ) > $o ).
thf(minus_455231168al_n_o_decl,type,
minus_455231168al_n_o: ( finite1489363574real_n > $o ) > ( finite1489363574real_n > $o ) > finite1489363574real_n > $o ).
thf(minus_1832115082al_n_o_decl,type,
minus_1832115082al_n_o: ( set_Fi1058188332real_n > $o ) > ( set_Fi1058188332real_n > $o ) > set_Fi1058188332real_n > $o ).
thf(minus_1037315151real_n_decl,type,
minus_1037315151real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
thf(minus_725016986real_n_decl,type,
minus_725016986real_n: set_Fi1326602817real_n > set_Fi1326602817real_n > set_Fi1326602817real_n ).
thf(minus_1686442501real_n_decl,type,
minus_1686442501real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(minus_1698615483real_n_decl,type,
minus_1698615483real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n ).
thf(plus_p585657087real_n_decl,type,
plus_p585657087real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
thf(plus_p1606848693real_n_decl,type,
plus_p1606848693real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(plus_p565022571real_n_decl,type,
plus_p565022571real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n ).
thf(zero_z200130687real_n_decl,type,
zero_z200130687real_n: finite1489363574real_n ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(if_Fin413489477real_n_decl,type,
if_Fin413489477real_n: $o > ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ).
thf(if_Fin127821360real_n_decl,type,
if_Fin127821360real_n: $o > finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
thf(if_set11487206real_n_decl,type,
if_set11487206real_n: $o > set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(inf_in32002162al_n_o_decl,type,
inf_in32002162al_n_o: ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > ( finite1489363574real_n > finite1489363574real_n ) > $o ).
thf(inf_in1620715847al_n_o_decl,type,
inf_in1620715847al_n_o: ( finite1489363574real_n > $o ) > ( finite1489363574real_n > $o ) > finite1489363574real_n > $o ).
thf(inf_in409346577al_n_o_decl,type,
inf_in409346577al_n_o: ( set_Fi1058188332real_n > $o ) > ( set_Fi1058188332real_n > $o ) > set_Fi1058188332real_n > $o ).
thf(inf_in146441683real_n_decl,type,
inf_in146441683real_n: set_Fi1326602817real_n > set_Fi1326602817real_n > set_Fi1326602817real_n ).
thf(inf_in1974387902real_n_decl,type,
inf_in1974387902real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(inf_in632889204real_n_decl,type,
inf_in632889204real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n ).
thf(lebesg260170249real_n_decl,type,
lebesg260170249real_n: sigma_1466784463real_n ).
thf(minkow1134813771n_real_decl,type,
minkow1134813771n_real: finite964658038_int_n > finite1489363574real_n ).
thf(ord_Least_nat_decl,type,
ord_Least_nat: ( nat > $o ) > nat ).
thf(collec1190264032real_n_decl,type,
collec1190264032real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > set_Fi1326602817real_n ).
thf(collec321817931real_n_decl,type,
collec321817931real_n: ( finite1489363574real_n > $o ) > set_Fi1058188332real_n ).
thf(collec452821761real_n_decl,type,
collec452821761real_n: ( set_Fi1058188332real_n > $o ) > set_se2111327970real_n ).
thf(image_1123376925real_n_decl,type,
image_1123376925real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > set_Fi1326602817real_n ).
thf(image_449906696real_n_decl,type,
image_449906696real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ) > set_Fi1326602817real_n > set_Fi1058188332real_n ).
thf(image_128879038real_n_decl,type,
image_128879038real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n ) > set_Fi1326602817real_n > set_se2111327970real_n ).
thf(image_437359496real_n_decl,type,
image_437359496real_n: ( finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1326602817real_n ).
thf(image_439535603real_n_decl,type,
image_439535603real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(image_545463721real_n_decl,type,
image_545463721real_n: ( finite1489363574real_n > set_Fi1058188332real_n ) > set_Fi1058188332real_n > set_se2111327970real_n ).
thf(image_352856126real_n_decl,type,
image_352856126real_n: ( set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n ) > set_se2111327970real_n > set_Fi1326602817real_n ).
thf(image_1311908777real_n_decl,type,
image_1311908777real_n: ( set_Fi1058188332real_n > finite1489363574real_n ) > set_se2111327970real_n > set_Fi1058188332real_n ).
thf(image_1661509983real_n_decl,type,
image_1661509983real_n: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_se2111327970real_n ).
thf(vimage180751827real_n_decl,type,
vimage180751827real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > set_Fi1326602817real_n ).
thf(vimage1072397758real_n_decl,type,
vimage1072397758real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1326602817real_n ).
thf(vimage2098059032_n_nat_decl,type,
vimage2098059032_n_nat: ( ( finite1489363574real_n > finite1489363574real_n ) > nat ) > set_nat > set_Fi1326602817real_n ).
thf(vimage1910974324real_n_decl,type,
vimage1910974324real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n ) > set_se2111327970real_n > set_Fi1326602817real_n ).
thf(vimage1059850558real_n_decl,type,
vimage1059850558real_n: ( finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > set_Fi1058188332real_n ).
thf(vimage1233683625real_n_decl,type,
vimage1233683625real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(vimage281029891_n_nat_decl,type,
vimage281029891_n_nat: ( finite1489363574real_n > nat ) > set_nat > set_Fi1058188332real_n ).
thf(vimage207290975real_n_decl,type,
vimage207290975real_n: ( finite1489363574real_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_Fi1058188332real_n ).
thf(vimage2134951412real_n_decl,type,
vimage2134951412real_n: ( set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > set_se2111327970real_n ).
thf(vimage973736031real_n_decl,type,
vimage973736031real_n: ( set_Fi1058188332real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_se2111327970real_n ).
thf(vimage501526201_n_nat_decl,type,
vimage501526201_n_nat: ( set_Fi1058188332real_n > nat ) > set_nat > set_se2111327970real_n ).
thf(vimage784510485real_n_decl,type,
vimage784510485real_n: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_se2111327970real_n ).
thf(sigma_1185134568real_n_decl,type,
sigma_1185134568real_n: sigma_107786596real_n > sigma_107786596real_n > set_Fi1066397675real_n ).
thf(sigma_2028985427real_n_decl,type,
sigma_2028985427real_n: sigma_107786596real_n > sigma_1466784463real_n > set_Fi1491909078real_n ).
thf(sigma_364818953real_n_decl,type,
sigma_364818953real_n: sigma_107786596real_n > sigma_1422848389real_n > set_Fi909698444real_n ).
thf(sigma_2016438227real_n_decl,type,
sigma_2016438227real_n: sigma_1466784463real_n > sigma_107786596real_n > set_Fi1260307670real_n ).
thf(sigma_439801790real_n_decl,type,
sigma_439801790real_n: sigma_1466784463real_n > sigma_1466784463real_n > set_Fi1326602817real_n ).
thf(sigma_566919540real_n_decl,type,
sigma_566919540real_n: sigma_1466784463real_n > sigma_1422848389real_n > set_Fi1645173239real_n ).
thf(sigma_588796041real_n_decl,type,
sigma_588796041real_n: sigma_1422848389real_n > sigma_107786596real_n > set_se830533260real_n ).
thf(sigma_1333364596real_n_decl,type,
sigma_1333364596real_n: sigma_1422848389real_n > sigma_1466784463real_n > set_se955370231real_n ).
thf(sigma_239294762real_n_decl,type,
sigma_239294762real_n: sigma_1422848389real_n > sigma_1422848389real_n > set_se1738601133real_n ).
thf(sigma_1052429895real_n_decl,type,
sigma_1052429895real_n: sigma_107786596real_n > set_Fi1326602817real_n > sigma_107786596real_n ).
thf(sigma_346513458real_n_decl,type,
sigma_346513458real_n: sigma_1466784463real_n > set_Fi1058188332real_n > sigma_1466784463real_n ).
thf(sigma_993999336real_n_decl,type,
sigma_993999336real_n: sigma_1422848389real_n > set_se2111327970real_n > sigma_1422848389real_n ).
thf(sigma_522684908real_n_decl,type,
sigma_522684908real_n: sigma_107786596real_n > set_se221767415real_n ).
thf(sigma_1235138647real_n_decl,type,
sigma_1235138647real_n: sigma_1466784463real_n > set_se2111327970real_n ).
thf(sigma_433815053real_n_decl,type,
sigma_433815053real_n: sigma_1422848389real_n > set_se820660888real_n ).
thf(sigma_1483971331real_n_decl,type,
sigma_1483971331real_n: sigma_107786596real_n > set_Fi1326602817real_n ).
thf(sigma_476185326real_n_decl,type,
sigma_476185326real_n: sigma_1466784463real_n > set_Fi1058188332real_n ).
thf(sigma_607186084real_n_decl,type,
sigma_607186084real_n: sigma_1422848389real_n > set_se2111327970real_n ).
thf(sigma_136294295real_n_decl,type,
sigma_136294295real_n: set_Fi1326602817real_n > ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ) > sigma_1466784463real_n > sigma_107786596real_n ).
thf(sigma_821351682real_n_decl,type,
sigma_821351682real_n: set_Fi1058188332real_n > ( finite1489363574real_n > finite1489363574real_n ) > sigma_1466784463real_n > sigma_1466784463real_n ).
thf(sigma_1384150200real_n_decl,type,
sigma_1384150200real_n: set_se2111327970real_n > ( set_Fi1058188332real_n > finite1489363574real_n ) > sigma_1466784463real_n > sigma_1422848389real_n ).
thf(member117715276real_n_decl,type,
member117715276real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ) > set_Fi1066397675real_n > $o ).
thf(member1695588023real_n_decl,type,
member1695588023real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ) > set_Fi1491909078real_n > $o ).
thf(member640587117real_n_decl,type,
member640587117real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n ) > set_Fi909698444real_n > $o ).
thf(member408431031real_n_decl,type,
member408431031real_n: ( finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ) > set_Fi1260307670real_n > $o ).
thf(member1746150050real_n_decl,type,
member1746150050real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > $o ).
thf(member966061400real_n_decl,type,
member966061400real_n: ( finite1489363574real_n > set_Fi1058188332real_n ) > set_Fi1645173239real_n > $o ).
thf(member1764433517real_n_decl,type,
member1764433517real_n: ( set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n ) > set_se830533260real_n > $o ).
thf(member1759501912real_n_decl,type,
member1759501912real_n: ( set_Fi1058188332real_n > finite1489363574real_n ) > set_se955370231real_n > $o ).
thf(member1734791438real_n_decl,type,
member1734791438real_n: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se1738601133real_n > $o ).
thf(member1352538125real_n_decl,type,
member1352538125real_n: finite1489363574real_n > set_Fi1058188332real_n > $o ).
thf(member2104752728real_n_decl,type,
member2104752728real_n: set_Fi1326602817real_n > set_se221767415real_n > $o ).
thf(member223413699real_n_decl,type,
member223413699real_n: set_Fi1058188332real_n > set_se2111327970real_n > $o ).
thf(member1475136633real_n_decl,type,
member1475136633real_n: set_se2111327970real_n > set_se820660888real_n > $o ).
thf(r_decl,type,
r: finite964658038_int_n > set_Fi1058188332real_n ).
thf(s_decl,type,
s: set_Fi1058188332real_n ).
thf(t_decl,type,
t: finite964658038_int_n > set_Fi1058188332real_n ).
thf(t2_decl,type,
t2: finite964658038_int_n > set_Fi1058188332real_n ).
thf(a_decl,type,
a: finite964658038_int_n ).
thf(175,axiom,
! [A: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B: sigma_1422848389real_n,C: sigma_107786596real_n,D: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member1764433517real_n @ A @ ( sigma_588796041real_n @ B @ C ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_522684908real_n @ C ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_433815053real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_measurable__sets__Collect) ).
thf(892,plain,
! [A: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B: sigma_1422848389real_n,C: sigma_107786596real_n,D: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member1764433517real_n @ A @ ( sigma_588796041real_n @ B @ C ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_522684908real_n @ C ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_433815053real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(310,axiom,
! [A: set_se2111327970real_n,B: set_se2111327970real_n] :
( ( inf_in409346577al_n_o
@ ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ A )
@ ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ B ) )
= ( ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ ( inf_in632889204real_n @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_inf__Int__eq) ).
thf(1337,plain,
! [A: set_se2111327970real_n,B: set_se2111327970real_n] :
( ( inf_in409346577al_n_o
@ ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ A )
@ ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ B ) )
= ( ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ ( inf_in632889204real_n @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(91,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n] :
( ( if_Fin413489477real_n @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T) ).
thf(628,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n] :
( ( if_Fin413489477real_n @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(56,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
=> ( member1352538125real_n @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_IntD2) ).
thf(518,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
=> ( member1352538125real_n @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(104,axiom,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > $o,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( ( C @ D )
| ( B @ D ) ) ) )
@ ( sigma_522684908real_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_sets_Osets__Collect__disj) ).
thf(666,plain,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > $o,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( ( C @ D )
| ( B @ D ) ) ) )
@ ( sigma_522684908real_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(259,axiom,
! [A: set_se2111327970real_n,B: sigma_1422848389real_n,C: finite1489363574real_n,D: sigma_1466784463real_n,E: set_Fi1058188332real_n > finite1489363574real_n] :
( ( member1475136633real_n @ ( inf_in632889204real_n @ A @ ( sigma_607186084real_n @ B ) ) @ ( sigma_433815053real_n @ B ) )
=> ( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ D ) )
=> ( ( member1759501912real_n @ E @ ( sigma_1333364596real_n @ ( sigma_993999336real_n @ B @ A ) @ D ) )
= ( member1759501912real_n
@ ^ [F: set_Fi1058188332real_n] : ( if_Fin127821360real_n @ ( member223413699real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_1333364596real_n @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_measurable__restrict__space__iff) ).
thf(1168,plain,
! [A: set_se2111327970real_n,B: sigma_1422848389real_n,C: finite1489363574real_n,D: sigma_1466784463real_n,E: set_Fi1058188332real_n > finite1489363574real_n] :
( ( member1475136633real_n @ ( inf_in632889204real_n @ A @ ( sigma_607186084real_n @ B ) ) @ ( sigma_433815053real_n @ B ) )
=> ( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ D ) )
=> ( ( member1759501912real_n @ E @ ( sigma_1333364596real_n @ ( sigma_993999336real_n @ B @ A ) @ D ) )
= ( member1759501912real_n
@ ^ [F: set_Fi1058188332real_n] : ( if_Fin127821360real_n @ ( member223413699real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_1333364596real_n @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(136,axiom,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > set_Fi1058188332real_n,C: sigma_1422848389real_n] :
( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
=> ( member223413699real_n @ ( B @ D ) @ ( sigma_607186084real_n @ C ) ) )
=> ( ! [D: set_se2111327970real_n] :
( ( member1475136633real_n @ D @ ( sigma_433815053real_n @ C ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage207290975real_n @ B @ D ) @ ( sigma_476185326real_n @ A ) ) @ ( sigma_1235138647real_n @ A ) ) )
=> ( member966061400real_n @ B @ ( sigma_566919540real_n @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_measurableI) ).
thf(760,plain,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > set_Fi1058188332real_n,C: sigma_1422848389real_n] :
( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
=> ( member223413699real_n @ ( B @ D ) @ ( sigma_607186084real_n @ C ) ) )
=> ( ! [D: set_se2111327970real_n] :
( ( member1475136633real_n @ D @ ( sigma_433815053real_n @ C ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage207290975real_n @ B @ D ) @ ( sigma_476185326real_n @ A ) ) @ ( sigma_1235138647real_n @ A ) ) )
=> ( member966061400real_n @ B @ ( sigma_566919540real_n @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(198,axiom,
! [A: set_Fi1058188332real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,C: set_Fi1326602817real_n] :
( ( member223413699real_n @ A @ ( image_128879038real_n @ B @ C ) )
=> ~ ! [D: finite1489363574real_n > finite1489363574real_n] :
( ( A
= ( B @ D ) )
=> ~ ( member1746150050real_n @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_imageE) ).
thf(962,plain,
! [A: set_Fi1058188332real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,C: set_Fi1326602817real_n] :
( ( member223413699real_n @ A @ ( image_128879038real_n @ B @ C ) )
=> ~ ! [D: finite1489363574real_n > finite1489363574real_n] :
( ( A
= ( B @ D ) )
=> ~ ( member1746150050real_n @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(43,axiom,
! [A: sigma_1466784463real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: sigma_1466784463real_n,E: finite1489363574real_n > finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n] :
( ( A = B )
=> ( ( C = D )
=> ( ! [G: finite1489363574real_n] :
( ( member1352538125real_n @ G @ ( sigma_476185326real_n @ A ) )
=> ( ( E @ G )
= ( F @ G ) ) )
=> ( ( member1746150050real_n @ E @ ( sigma_439801790real_n @ A @ C ) )
= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_measurable__cong__simp) ).
thf(468,plain,
! [A: sigma_1466784463real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: sigma_1466784463real_n,E: finite1489363574real_n > finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n] :
( ( A = B )
=> ( ( C = D )
=> ( ! [G: finite1489363574real_n] :
( ( member1352538125real_n @ G @ ( sigma_476185326real_n @ A ) )
=> ( ( E @ G )
= ( F @ G ) ) )
=> ( ( member1746150050real_n @ E @ ( sigma_439801790real_n @ A @ C ) )
= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(271,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( minus_1698615483real_n @ B @ C ) )
=> ~ ( ( member223413699real_n @ A @ B )
=> ( member223413699real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_DiffE) ).
thf(1211,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( minus_1698615483real_n @ B @ C ) )
=> ~ ( ( member223413699real_n @ A @ B )
=> ( member223413699real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(77,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > $o] :
( ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( image_439535603real_n @ A @ B ) )
& ( C @ D ) )
=> ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_bex__imageD) ).
thf(582,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > $o] :
( ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( image_439535603real_n @ A @ B ) )
& ( C @ D ) )
=> ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(211,axiom,
! [A: finite1489363574real_n > $o] :
( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [B: finite1489363574real_n] :
( ( member1352538125real_n @ B @ ( sigma_476185326real_n @ borel_676189912real_n ) )
& ( A @ B ) ) )
@ ( sigma_1235138647real_n @ borel_676189912real_n ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [B: finite1489363574real_n] :
( ( member1352538125real_n @ B @ ( sigma_476185326real_n @ lebesg260170249real_n ) )
& ( A @ B ) ) )
@ ( sigma_1235138647real_n @ lebesg260170249real_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_lborelD__Collect) ).
thf(1005,plain,
! [A: finite1489363574real_n > $o] :
( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [B: finite1489363574real_n] :
( ( member1352538125real_n @ B @ ( sigma_476185326real_n @ borel_676189912real_n ) )
& ( A @ B ) ) )
@ ( sigma_1235138647real_n @ borel_676189912real_n ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [B: finite1489363574real_n] :
( ( member1352538125real_n @ B @ ( sigma_476185326real_n @ lebesg260170249real_n ) )
& ( A @ B ) ) )
@ ( sigma_1235138647real_n @ lebesg260170249real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(331,axiom,
! [A: set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1058188332real_n] :
( ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( inf_in1974387902real_n @ ( vimage1233683625real_n @ B @ D ) @ A )
= ( inf_in1974387902real_n @ ( vimage1233683625real_n @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_vimage__inter__cong) ).
thf(1406,plain,
! [A: set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1058188332real_n] :
( ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( inf_in1974387902real_n @ ( vimage1233683625real_n @ B @ D ) @ A )
= ( inf_in1974387902real_n @ ( vimage1233683625real_n @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(329,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ ( A @ B ) @ C )
=> ( member1746150050real_n @ B @ ( vimage1910974324real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_vimageI2) ).
thf(1401,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ ( A @ B ) @ C )
=> ( member1746150050real_n @ B @ ( vimage1910974324real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(232,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_space__restrict__space2) ).
thf(1073,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(289,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ A @ B ) )
= ( B = zero_z200130687real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_eq__add__iff) ).
thf(1269,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ A @ B ) )
= ( B = zero_z200130687real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(33,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
=> ( member1352538125real_n @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_IntD1) ).
thf(440,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
=> ( member1352538125real_n @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(299,axiom,
! [A: sigma_1422848389real_n,B: $o] :
( member1475136633real_n
@ ( collec452821761real_n
@ ^ [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_607186084real_n @ A ) )
& B ) )
@ ( sigma_433815053real_n @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_sets_Osets__Collect_I5_J) ).
thf(1305,plain,
! [A: sigma_1422848389real_n,B: $o] :
( member1475136633real_n
@ ( collec452821761real_n
@ ^ [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_607186084real_n @ A ) )
& B ) )
@ ( sigma_433815053real_n @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(169,axiom,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > $o] :
( ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_1661509983real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_1661509983real_n @ A
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_Compr__image__eq) ).
thf(873,plain,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > $o] :
( ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_1661509983real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_1661509983real_n @ A
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(269,axiom,
! [A: sigma_1466784463real_n] :
( ( sigma_439801790real_n @ A @ lebesg260170249real_n )
= ( sigma_439801790real_n @ A @ borel_676189912real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_measurable__lborel1) ).
thf(1205,plain,
! [A: sigma_1466784463real_n] :
( ( sigma_439801790real_n @ A @ lebesg260170249real_n )
= ( sigma_439801790real_n @ A @ borel_676189912real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(17,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: finite1489363574real_n > finite1489363574real_n,D: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member1746150050real_n @ C @ ( image_1123376925real_n @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_rev__image__eqI) ).
thf(384,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: finite1489363574real_n > finite1489363574real_n,D: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member1746150050real_n @ C @ ( image_1123376925real_n @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(120,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > $o] :
( ( member1352538125real_n @ A @ ( inf_in1974387902real_n @ B @ ( collec321817931real_n @ C ) ) )
= ( ( member1352538125real_n @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Int__Collect) ).
thf(715,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > $o] :
( ( member1352538125real_n @ A @ ( inf_in1974387902real_n @ B @ ( collec321817931real_n @ C ) ) )
= ( ( member1352538125real_n @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(291,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ C @ A ) @ D ) @ ( sigma_1235138647real_n @ ( sigma_821351682real_n @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_in__vimage__algebra) ).
thf(1275,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ C @ A ) @ D ) @ ( sigma_1235138647real_n @ ( sigma_821351682real_n @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1,conjecture,
( member223413699real_n
@ ( vimage1233683625real_n
@ ^ [A: finite1489363574real_n] : ( plus_p585657087real_n @ A @ ( minkow1134813771n_real @ a ) )
@ ( t2 @ a ) )
@ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member223413699real_n
@ ( vimage1233683625real_n
@ ^ [A: finite1489363574real_n] : ( plus_p585657087real_n @ A @ ( minkow1134813771n_real @ a ) )
@ ( t2 @ a ) )
@ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(340,plain,
~ ( member223413699real_n
@ ( vimage1233683625real_n
@ ^ [A: finite1489363574real_n] : ( plus_p585657087real_n @ A @ ( minkow1134813771n_real @ a ) )
@ ( t2 @ a ) )
@ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(273,axiom,
! [A: set_se2111327970real_n] :
( ( collec452821761real_n
@ ^ [B: set_Fi1058188332real_n] : ( member223413699real_n @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Collect__mem__eq) ).
thf(1222,plain,
! [A: set_se2111327970real_n] :
( ( collec452821761real_n
@ ^ [B: set_Fi1058188332real_n] : ( member223413699real_n @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(301,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n,D: set_se2111327970real_n] :
( ( member223413699real_n @ A @ B )
=> ( ( member223413699real_n @ C @ D )
=> ( member223413699real_n @ ( plus_p1606848693real_n @ A @ C ) @ ( plus_p565022571real_n @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_set__plus__intro) ).
thf(1310,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n,D: set_se2111327970real_n] :
( ( member223413699real_n @ A @ B )
=> ( ( member223413699real_n @ C @ D )
=> ( member223413699real_n @ ( plus_p1606848693real_n @ A @ C ) @ ( plus_p565022571real_n @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(60,axiom,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ A ) )
& ( B @ C ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ A ) )
& ~ ( B @ C ) ) )
@ ( sigma_522684908real_n @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_sets_Osets__Collect__neg) ).
thf(533,plain,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ A ) )
& ( B @ C ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ A ) )
& ~ ( B @ C ) ) )
@ ( sigma_522684908real_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(62,axiom,
! [A: sigma_1466784463real_n] :
( member1746150050real_n
@ ^ [B: finite1489363574real_n] : B
@ ( sigma_439801790real_n @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_measurable__id) ).
thf(538,plain,
! [A: sigma_1466784463real_n] :
( member1746150050real_n
@ ^ [B: finite1489363574real_n] : B
@ ( sigma_439801790real_n @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(315,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: finite1489363574real_n > finite1489363574real_n,D: sigma_107786596real_n,E: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n] :
( ( member223413699real_n @ ( inf_in1974387902real_n @ A @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) )
=> ( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ D ) )
=> ( ( member408431031real_n @ E @ ( sigma_2016438227real_n @ ( sigma_346513458real_n @ B @ A ) @ D ) )
= ( member408431031real_n
@ ^ [F: finite1489363574real_n] : ( if_Fin413489477real_n @ ( member1352538125real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_2016438227real_n @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_measurable__restrict__space__iff) ).
thf(1354,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: finite1489363574real_n > finite1489363574real_n,D: sigma_107786596real_n,E: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n] :
( ( member223413699real_n @ ( inf_in1974387902real_n @ A @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) )
=> ( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ D ) )
=> ( ( member408431031real_n @ E @ ( sigma_2016438227real_n @ ( sigma_346513458real_n @ B @ A ) @ D ) )
= ( member408431031real_n
@ ^ [F: finite1489363574real_n] : ( if_Fin413489477real_n @ ( member1352538125real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_2016438227real_n @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(154,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B: sigma_107786596real_n,C: sigma_1422848389real_n,D: set_Fi1058188332real_n > $o] :
( ( member640587117real_n @ A @ ( sigma_364818953real_n @ B @ C ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_433815053real_n @ C ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_522684908real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_measurable__sets__Collect) ).
thf(829,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B: sigma_107786596real_n,C: sigma_1422848389real_n,D: set_Fi1058188332real_n > $o] :
( ( member640587117real_n @ A @ ( sigma_364818953real_n @ B @ C ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_433815053real_n @ C ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_522684908real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(177,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_add__diff__cancel__right_H) ).
thf(898,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(118,axiom,
! [A: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
( ( sigma_476185326real_n @ ( sigma_346513458real_n @ A @ B ) )
= ( inf_in1974387902real_n @ B @ ( sigma_476185326real_n @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_space__restrict__space) ).
thf(709,plain,
! [A: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
( ( sigma_476185326real_n @ ( sigma_346513458real_n @ A @ B ) )
= ( inf_in1974387902real_n @ B @ ( sigma_476185326real_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(25,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n] :
( ( if_Fin413489477real_n @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T) ).
thf(417,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n] :
( ( if_Fin413489477real_n @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(201,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ C ) )
=> ( member223413699real_n @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_IntD1) ).
thf(973,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ C ) )
=> ( member223413699real_n @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(275,axiom,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,C: sigma_1466784463real_n] :
( ! [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
=> ( member1352538125real_n @ ( B @ D ) @ ( sigma_476185326real_n @ C ) ) )
=> ( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
=> ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage1072397758real_n @ B @ D ) @ ( sigma_1483971331real_n @ A ) ) @ ( sigma_522684908real_n @ A ) ) )
=> ( member1695588023real_n @ B @ ( sigma_2028985427real_n @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_measurableI) ).
thf(1228,plain,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,C: sigma_1466784463real_n] :
( ! [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
=> ( member1352538125real_n @ ( B @ D ) @ ( sigma_476185326real_n @ C ) ) )
=> ( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
=> ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage1072397758real_n @ B @ D ) @ ( sigma_1483971331real_n @ A ) ) @ ( sigma_522684908real_n @ A ) ) )
=> ( member1695588023real_n @ B @ ( sigma_2028985427real_n @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(99,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ D @ A )
@ ( minus_1686442501real_n @ B @ C ) )
= ( minus_1686442501real_n
@ ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ D @ A )
@ B )
@ ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ D @ A )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_translation__subtract__diff) ).
thf(651,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ D @ A )
@ ( minus_1686442501real_n @ B @ C ) )
= ( minus_1686442501real_n
@ ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ D @ A )
@ B )
@ ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ D @ A )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(18,axiom,
! [A: sigma_107786596real_n,B: $o] :
( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ A ) )
& B ) )
@ ( sigma_522684908real_n @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_sets_Osets__Collect__const) ).
thf(389,plain,
! [A: sigma_107786596real_n,B: $o] :
( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ A ) )
& B ) )
@ ( sigma_522684908real_n @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(123,axiom,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_inf__commute) ).
thf(724,plain,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(73,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( if_Fin127821360real_n @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T) ).
thf(570,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( if_Fin127821360real_n @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(337,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) @ C )
= ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add_Oassoc) ).
thf(1430,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) @ C )
= ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(297,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( comple1390568924real_n @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_main__part) ).
thf(1298,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( comple1390568924real_n @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(14,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( minus_725016986real_n @ B @ C ) )
=> ( member1746150050real_n @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_DiffD1) ).
thf(372,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( minus_725016986real_n @ B @ C ) )
=> ( member1746150050real_n @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(287,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ B @ C ) )
=> ( member223413699real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_vimageD) ).
thf(1264,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ B @ C ) )
=> ( member223413699real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(4,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ ( A @ B ) @ C )
=> ( member1746150050real_n @ B @ ( vimage180751827real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_vimageI2) ).
thf(344,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ ( A @ B ) @ C )
=> ( member1746150050real_n @ B @ ( vimage180751827real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(302,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_p585657087real_n @ A @ C )
= ( plus_p585657087real_n @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_add__mono__thms__linordered__semiring_I4_J) ).
thf(1313,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_p585657087real_n @ A @ C )
= ( plus_p585657087real_n @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(190,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( minus_1698615483real_n @ B @ C ) )
= ( ( member223413699real_n @ A @ B )
& ~ ( member223413699real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_Diff__iff) ).
thf(934,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( minus_1698615483real_n @ B @ C ) )
= ( ( member223413699real_n @ A @ B )
& ~ ( member223413699real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(250,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ ( inf_in1974387902real_n @ A @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) )
=> ( ( member223413699real_n @ ( inf_in1974387902real_n @ C @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) )
=> ( ( sigma_346513458real_n @ ( sigma_346513458real_n @ B @ A ) @ C )
= ( sigma_346513458real_n @ B @ ( inf_in1974387902real_n @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_restrict__restrict__space) ).
thf(1132,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ ( inf_in1974387902real_n @ A @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) )
=> ( ( member223413699real_n @ ( inf_in1974387902real_n @ C @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) )
=> ( ( sigma_346513458real_n @ ( sigma_346513458real_n @ B @ A ) @ C )
= ( sigma_346513458real_n @ B @ ( inf_in1974387902real_n @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(194,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: set_Fi1058188332real_n,D: set_se2111327970real_n] :
( ( A
= ( B @ C ) )
=> ( ( member223413699real_n @ C @ D )
=> ( member223413699real_n @ A @ ( image_1661509983real_n @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_image__eqI) ).
thf(949,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: set_Fi1058188332real_n,D: set_se2111327970real_n] :
( ( A
= ( B @ C ) )
=> ( ( member223413699real_n @ C @ D )
=> ( member223413699real_n @ A @ ( image_1661509983real_n @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(305,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ ( A @ B ) @ C )
=> ( member1352538125real_n @ B @ ( vimage1233683625real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_vimageI2) ).
thf(1323,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ ( A @ B ) @ C )
=> ( member1352538125real_n @ B @ ( vimage1233683625real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(88,axiom,
! [A: finite1489363574real_n] :
( ( minus_1037315151real_n @ A @ A )
= zero_z200130687real_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(619,plain,
! [A: finite1489363574real_n] :
( ( minus_1037315151real_n @ A @ A )
= zero_z200130687real_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(184,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ A @ ( sigma_1235138647real_n @ ( comple230862828real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_sets__completionI__sets) ).
thf(917,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ A @ ( sigma_1235138647real_n @ ( comple230862828real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(132,axiom,
! [A: sigma_1422848389real_n,B: nat > set_Fi1058188332real_n > $o,C: set_nat] :
( ! [D: nat] :
( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ A ) )
& ( B @ D @ E ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( member1475136633real_n
@ ( inf_in632889204real_n
@ ( vimage501526201_n_nat
@ ^ [D: set_Fi1058188332real_n] :
( ord_Least_nat
@ ^ [E: nat] : ( B @ E @ D ) )
@ C )
@ ( sigma_607186084real_n @ A ) )
@ ( sigma_433815053real_n @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_sets__Least) ).
thf(751,plain,
! [A: sigma_1422848389real_n,B: nat > set_Fi1058188332real_n > $o,C: set_nat] :
( ! [D: nat] :
( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ A ) )
& ( B @ D @ E ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( member1475136633real_n
@ ( inf_in632889204real_n
@ ( vimage501526201_n_nat
@ ^ [D: set_Fi1058188332real_n] :
( ord_Least_nat
@ ^ [E: nat] : ( B @ E @ D ) )
@ C )
@ ( sigma_607186084real_n @ A ) )
@ ( sigma_433815053real_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(151,axiom,
! [A: sigma_1466784463real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n,D: finite1489363574real_n > finite1489363574real_n] :
( ( ( sigma_1235138647real_n @ A )
= ( sigma_1235138647real_n @ B ) )
=> ( ( sigma_1235138647real_n @ ( sigma_821351682real_n @ C @ D @ A ) )
= ( sigma_1235138647real_n @ ( sigma_821351682real_n @ C @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_sets__vimage__algebra__cong) ).
thf(817,plain,
! [A: sigma_1466784463real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n,D: finite1489363574real_n > finite1489363574real_n] :
( ( ( sigma_1235138647real_n @ A )
= ( sigma_1235138647real_n @ B ) )
=> ( ( sigma_1235138647real_n @ ( sigma_821351682real_n @ C @ D @ A ) )
= ( sigma_1235138647real_n @ ( sigma_821351682real_n @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(237,axiom,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > $o,C: finite1489363574real_n > finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n,E: sigma_1466784463real_n] :
( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [F: finite1489363574real_n] :
( ( member1352538125real_n @ F @ ( sigma_476185326real_n @ A ) )
& ( B @ F ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( ( member1746150050real_n
@ ^ [F: finite1489363574real_n] : ( if_Fin127821360real_n @ ( B @ F ) @ ( C @ F ) @ ( D @ F ) )
@ ( sigma_439801790real_n @ A @ E ) )
= ( ( member1746150050real_n @ C @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ A @ ( collec321817931real_n @ B ) ) @ E ) )
& ( member1746150050real_n @ D
@ ( sigma_439801790real_n
@ ( sigma_346513458real_n @ A
@ ( collec321817931real_n
@ ^ [F: finite1489363574real_n] :
~ ( B @ F ) ) )
@ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_measurable__If__restrict__space__iff) ).
thf(1087,plain,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > $o,C: finite1489363574real_n > finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n,E: sigma_1466784463real_n] :
( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [F: finite1489363574real_n] :
( ( member1352538125real_n @ F @ ( sigma_476185326real_n @ A ) )
& ( B @ F ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( ( member1746150050real_n
@ ^ [F: finite1489363574real_n] : ( if_Fin127821360real_n @ ( B @ F ) @ ( C @ F ) @ ( D @ F ) )
@ ( sigma_439801790real_n @ A @ E ) )
= ( ( member1746150050real_n @ C @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ A @ ( collec321817931real_n @ B ) ) @ E ) )
& ( member1746150050real_n @ D
@ ( sigma_439801790real_n
@ ( sigma_346513458real_n @ A
@ ( collec321817931real_n
@ ^ [F: finite1489363574real_n] :
~ ( B @ F ) ) )
@ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(254,axiom,
! [A: set_se2111327970real_n,B: sigma_1422848389real_n,C: set_Fi1058188332real_n > $o] :
( ( member1475136633real_n @ A @ ( sigma_433815053real_n @ B ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ ( sigma_993999336real_n @ B @ A ) ) )
& ( C @ D ) ) )
@ ( sigma_433815053real_n @ ( sigma_993999336real_n @ B @ A ) ) )
= ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ B ) )
& ( member223413699real_n @ D @ A )
& ( C @ D ) ) )
@ ( sigma_433815053real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_sets__Collect__restrict__space__iff) ).
thf(1147,plain,
! [A: set_se2111327970real_n,B: sigma_1422848389real_n,C: set_Fi1058188332real_n > $o] :
( ( member1475136633real_n @ A @ ( sigma_433815053real_n @ B ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ ( sigma_993999336real_n @ B @ A ) ) )
& ( C @ D ) ) )
@ ( sigma_433815053real_n @ ( sigma_993999336real_n @ B @ A ) ) )
= ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ B ) )
& ( member223413699real_n @ D @ A )
& ( C @ D ) ) )
@ ( sigma_433815053real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(168,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_add__diff__cancel__left_H) ).
thf(870,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(328,axiom,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > $o,C: finite1489363574real_n > $o] :
( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( ( C @ D )
| ( B @ D ) ) ) )
@ ( sigma_1235138647real_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_sets_Osets__Collect__disj) ).
thf(1398,plain,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > $o,C: finite1489363574real_n > $o] :
( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( ( C @ D )
| ( B @ D ) ) ) )
@ ( sigma_1235138647real_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(36,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( inf_in146441683real_n @ B @ C ) )
=> ( member1746150050real_n @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_IntD1) ).
thf(448,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( inf_in146441683real_n @ B @ C ) )
=> ( member1746150050real_n @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(239,axiom,
! [A: set_Fi1058188332real_n] :
( ( image_439535603real_n @ ( plus_p585657087real_n @ zero_z200130687real_n ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_image__add__0) ).
thf(1100,plain,
! [A: set_Fi1058188332real_n] :
( ( image_439535603real_n @ ( plus_p585657087real_n @ zero_z200130687real_n ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(187,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member223413699real_n @ A @ ( vimage2134951412real_n @ B @ C ) )
=> ( member1746150050real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_vimageE) ).
thf(924,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member223413699real_n @ A @ ( vimage2134951412real_n @ B @ C ) )
=> ( member1746150050real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(134,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member223413699real_n @ A @ ( vimage2134951412real_n @ B @ C ) )
=> ( member1746150050real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_vimageD) ).
thf(756,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member223413699real_n @ A @ ( vimage2134951412real_n @ B @ C ) )
=> ( member1746150050real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(34,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ A @ B ) )
= ( inf_in1974387902real_n @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_inf__sup__aci_I4_J) ).
thf(443,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ A @ B ) )
= ( inf_in1974387902real_n @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(333,axiom,
( t2
= ( ^ [A: finite964658038_int_n] : ( inf_in1974387902real_n @ s @ ( r @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_T__def) ).
thf(1418,plain,
( t2
= ( ^ [A: finite964658038_int_n] : ( inf_in1974387902real_n @ s @ ( r @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(251,axiom,
! [A: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_107786596real_n,D: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member408431031real_n @ A @ ( sigma_2016438227real_n @ B @ C ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_522684908real_n @ C ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_1235138647real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_measurable__sets__Collect) ).
thf(1136,plain,
! [A: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_107786596real_n,D: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member408431031real_n @ A @ ( sigma_2016438227real_n @ B @ C ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_522684908real_n @ C ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_1235138647real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(6,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( vimage180751827real_n @ B @ C ) )
=> ( member1746150050real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_vimageE) ).
thf(348,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( vimage180751827real_n @ B @ C ) )
=> ( member1746150050real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ A @ B )
=> ( member1746150050real_n @ ( C @ A ) @ ( image_1123376925real_n @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_imageI) ).
thf(353,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ A @ B )
=> ( member1746150050real_n @ ( C @ A ) @ ( image_1123376925real_n @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(293,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n,D: set_se2111327970real_n] :
( ( A
= ( B @ C ) )
=> ( ( member223413699real_n @ C @ D )
=> ( member1746150050real_n @ A @ ( image_352856126real_n @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_image__eqI) ).
thf(1283,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n,D: set_se2111327970real_n] :
( ( A
= ( B @ C ) )
=> ( ( member223413699real_n @ C @ D )
=> ( member1746150050real_n @ A @ ( image_352856126real_n @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(45,axiom,
! [A: set_Fi1326602817real_n,B: set_Fi1326602817real_n] :
( ( inf_in32002162al_n_o
@ ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ A )
@ ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ B ) )
= ( ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ ( inf_in146441683real_n @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_inf__Int__eq) ).
thf(480,plain,
! [A: set_Fi1326602817real_n,B: set_Fi1326602817real_n] :
( ( inf_in32002162al_n_o
@ ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ A )
@ ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ B ) )
= ( ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ ( inf_in146441683real_n @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(309,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( minus_1698615483real_n @ B @ C ) )
=> ( member223413699real_n @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_DiffD1) ).
thf(1334,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( minus_1698615483real_n @ B @ C ) )
=> ( member223413699real_n @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(97,axiom,
( borel_1962407338real_n
= ( ^ [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n] : ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_is__borel__def) ).
thf(646,plain,
( borel_1962407338real_n
= ( ^ [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n] : ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(255,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= C )
=> ( A
= ( minus_1037315151real_n @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_add__implies__diff) ).
thf(1151,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= C )
=> ( A
= ( minus_1037315151real_n @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(191,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: finite1489363574real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( member1746150050real_n
@ ^ [D: finite1489363574real_n] : ( plus_p585657087real_n @ C @ ( A @ D ) )
@ ( sigma_439801790real_n @ B @ borel_676189912real_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_borel__measurable__const__add) ).
thf(937,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: finite1489363574real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( member1746150050real_n
@ ^ [D: finite1489363574real_n] : ( plus_p585657087real_n @ C @ ( A @ D ) )
@ ( sigma_439801790real_n @ B @ borel_676189912real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(225,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( plus_p585657087real_n @ ( minus_1037315151real_n @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_diff__add__cancel) ).
thf(1051,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( plus_p585657087real_n @ ( minus_1037315151real_n @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(152,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ B @ C ) )
= ( member223413699real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_vimage__eq) ).
thf(821,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ B @ C ) )
= ( member223413699real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(137,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) @ C )
= ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(766,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) @ C )
= ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(111,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n,D: set_Fi1058188332real_n] :
( ( A
= ( inf_in1974387902real_n @ B @ C ) )
=> ( ( inf_in1974387902real_n @ D @ A )
= ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_boolean__algebra__cancel_Oinf2) ).
thf(687,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n,D: set_Fi1058188332real_n] :
( ( A
= ( inf_in1974387902real_n @ B @ C ) )
=> ( ( inf_in1974387902real_n @ D @ A )
= ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(272,axiom,
! [A: set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n > finite1489363574real_n,D: sigma_1466784463real_n] :
( ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( member1746150050real_n @ B @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ A ) @ D ) )
= ( member1746150050real_n @ C @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_measurable__lebesgue__cong) ).
thf(1215,plain,
! [A: set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n > finite1489363574real_n,D: sigma_1466784463real_n] :
( ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( member1746150050real_n @ B @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ A ) @ D ) )
= ( member1746150050real_n @ C @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(112,axiom,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ( inf_in1620715847al_n_o
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ A )
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_inf__set__def) ).
thf(692,plain,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ( inf_in1620715847al_n_o
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ A )
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(102,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ C )
= ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_inf__assoc) ).
thf(660,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ C )
= ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(209,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( vimage784510485real_n @ B @ C ) )
=> ( member223413699real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_vimageD) ).
thf(998,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( vimage784510485real_n @ B @ C ) )
=> ( member223413699real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(23,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( ( member1746150050real_n @ C @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( member1746150050real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ ( A @ D ) @ ( C @ D ) )
@ ( sigma_439801790real_n @ B @ borel_676189912real_n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_borel__measurable__diff) ).
thf(411,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( ( member1746150050real_n @ C @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( member1746150050real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ ( A @ D ) @ ( C @ D ) )
@ ( sigma_439801790real_n @ B @ borel_676189912real_n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(338,axiom,
! [A: set_Fi1058188332real_n] : ( member223413699real_n @ A @ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_sets__lebesgue__on__refl) ).
thf(1433,plain,
! [A: set_Fi1058188332real_n] : ( member223413699real_n @ A @ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(29,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( minus_1686442501real_n @ A @ B ) @ C )
= ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A @ C ) @ ( inf_in1974387902real_n @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_Diff__Int__distrib2) ).
thf(428,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( minus_1686442501real_n @ A @ B ) @ C )
= ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A @ C ) @ ( inf_in1974387902real_n @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(279,axiom,
! [A: finite964658038_int_n] :
( ( t @ A )
= ( vimage1233683625real_n
@ ^ [B: finite1489363574real_n] : ( plus_p585657087real_n @ B @ ( minkow1134813771n_real @ A ) )
@ ( t2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_T_H__altdef) ).
thf(1242,plain,
! [A: finite964658038_int_n] :
( ( t @ A )
= ( vimage1233683625real_n
@ ^ [B: finite1489363574real_n] : ( plus_p585657087real_n @ B @ ( minkow1134813771n_real @ A ) )
@ ( t2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(16,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( minus_725016986real_n @ B @ C ) )
=> ~ ( ( member1746150050real_n @ A @ B )
=> ( member1746150050real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_DiffE) ).
thf(380,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( minus_725016986real_n @ B @ C ) )
=> ~ ( ( member1746150050real_n @ A @ B )
=> ( member1746150050real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(108,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ D @ A )
@ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n
@ ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ D @ A )
@ B )
@ ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ D @ A )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_translation__subtract__Int) ).
thf(678,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ D @ A )
@ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n
@ ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ D @ A )
@ B )
@ ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( minus_1037315151real_n @ D @ A )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(65,axiom,
! [A: finite1489363574real_n] :
( ( minus_1037315151real_n @ A @ zero_z200130687real_n )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_diff__0__right) ).
thf(546,plain,
! [A: finite1489363574real_n] :
( ( minus_1037315151real_n @ A @ zero_z200130687real_n )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(149,axiom,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > $o,C: set_Fi1058188332real_n > $o] :
( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( ( C @ D )
=> ( B @ D ) ) ) )
@ ( sigma_433815053real_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_sets_Osets__Collect__imp) ).
thf(810,plain,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > $o,C: set_Fi1058188332real_n > $o] :
( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( ( C @ D )
=> ( B @ D ) ) ) )
@ ( sigma_433815053real_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(230,axiom,
! [A: finite964658038_int_n,B: finite964658038_int_n] :
( ( ( minkow1134813771n_real @ A )
= ( minkow1134813771n_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_of__int__vec__eq__iff) ).
thf(1067,plain,
! [A: finite964658038_int_n,B: finite964658038_int_n] :
( ( ( minkow1134813771n_real @ A )
= ( minkow1134813771n_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(227,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ B @ C ) )
=> ( ( minus_1037315151real_n @ A @ D )
= ( plus_p585657087real_n @ B @ ( minus_1037315151real_n @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_group__cancel_Osub1) ).
thf(1057,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ B @ C ) )
=> ( ( minus_1037315151real_n @ A @ D )
= ( plus_p585657087real_n @ B @ ( minus_1037315151real_n @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(325,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( vimage784510485real_n @ B @ C ) )
=> ( member223413699real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_vimageE) ).
thf(1387,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( vimage784510485real_n @ B @ C ) )
=> ( member223413699real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(196,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ borel_676189912real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ ( vimage1233683625real_n @ A @ C ) @ ( sigma_1235138647real_n @ borel_676189912real_n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_measurable__sets__borel) ).
thf(957,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ borel_676189912real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ ( vimage1233683625real_n @ A @ C ) @ ( sigma_1235138647real_n @ borel_676189912real_n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(238,axiom,
! [A: set_se2111327970real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > finite1489363574real_n,D: set_Fi1058188332real_n > finite1489363574real_n,E: sigma_1466784463real_n,F: sigma_1466784463real_n] :
( ( A = B )
=> ( ! [G: set_Fi1058188332real_n] :
( ( member223413699real_n @ G @ B )
=> ( ( C @ G )
= ( D @ G ) ) )
=> ( ( ( sigma_1235138647real_n @ E )
= ( sigma_1235138647real_n @ F ) )
=> ( ( sigma_1384150200real_n @ A @ C @ E )
= ( sigma_1384150200real_n @ B @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_vimage__algebra__cong) ).
thf(1091,plain,
! [A: set_se2111327970real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > finite1489363574real_n,D: set_Fi1058188332real_n > finite1489363574real_n,E: sigma_1466784463real_n,F: sigma_1466784463real_n] :
( ( A = B )
=> ( ! [G: set_Fi1058188332real_n] :
( ( member223413699real_n @ G @ B )
=> ( ( C @ G )
= ( D @ G ) ) )
=> ( ( ( sigma_1235138647real_n @ E )
= ( sigma_1235138647real_n @ F ) )
=> ( ( sigma_1384150200real_n @ A @ C @ E )
= ( sigma_1384150200real_n @ B @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(141,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > $o] :
( ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ ( collec452821761real_n @ C ) ) )
= ( ( member223413699real_n @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Int__Collect) ).
thf(778,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > $o] :
( ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ ( collec452821761real_n @ C ) ) )
= ( ( member223413699real_n @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(222,axiom,
! [A: finite1489363574real_n > set_Fi1058188332real_n,B: sigma_1466784463real_n,C: sigma_1422848389real_n,D: set_Fi1058188332real_n > $o] :
( ( member966061400real_n @ A @ ( sigma_566919540real_n @ B @ C ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_433815053real_n @ C ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_1235138647real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_measurable__sets__Collect) ).
thf(1042,plain,
! [A: finite1489363574real_n > set_Fi1058188332real_n,B: sigma_1466784463real_n,C: sigma_1422848389real_n,D: set_Fi1058188332real_n > $o] :
( ( member966061400real_n @ A @ ( sigma_566919540real_n @ B @ C ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_433815053real_n @ C ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_1235138647real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(90,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_inf__sup__aci_I3_J) ).
thf(625,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(171,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1058188332real_n,D: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member223413699real_n @ C @ ( image_128879038real_n @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_rev__image__eqI) ).
thf(879,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1058188332real_n,D: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member223413699real_n @ C @ ( image_128879038real_n @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(162,axiom,
! [A: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ ( A @ B ) @ C )
=> ( member223413699real_n @ B @ ( vimage2134951412real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_vimageI2) ).
thf(852,plain,
! [A: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ ( A @ B ) @ C )
=> ( member223413699real_n @ B @ ( vimage2134951412real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(58,axiom,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,C: sigma_107786596real_n] :
( ! [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
=> ( member1746150050real_n @ ( B @ D ) @ ( sigma_1483971331real_n @ C ) ) )
=> ( ! [D: set_Fi1326602817real_n] :
( ( member2104752728real_n @ D @ ( sigma_522684908real_n @ C ) )
=> ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage180751827real_n @ B @ D ) @ ( sigma_1483971331real_n @ A ) ) @ ( sigma_522684908real_n @ A ) ) )
=> ( member117715276real_n @ B @ ( sigma_1185134568real_n @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_measurableI) ).
thf(522,plain,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,C: sigma_107786596real_n] :
( ! [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
=> ( member1746150050real_n @ ( B @ D ) @ ( sigma_1483971331real_n @ C ) ) )
=> ( ! [D: set_Fi1326602817real_n] :
( ( member2104752728real_n @ D @ ( sigma_522684908real_n @ C ) )
=> ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage180751827real_n @ B @ D ) @ ( sigma_1483971331real_n @ A ) ) @ ( sigma_522684908real_n @ A ) ) )
=> ( member117715276real_n @ B @ ( sigma_1185134568real_n @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(257,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( plus_p565022571real_n @ B @ C ) )
=> ~ ! [D: set_Fi1058188332real_n,E: set_Fi1058188332real_n] :
( ( A
= ( plus_p1606848693real_n @ D @ E ) )
=> ( ( member223413699real_n @ D @ B )
=> ~ ( member223413699real_n @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_set__plus__elim) ).
thf(1159,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( plus_p565022571real_n @ B @ C ) )
=> ~ ! [D: set_Fi1058188332real_n,E: set_Fi1058188332real_n] :
( ( A
= ( plus_p1606848693real_n @ D @ E ) )
=> ( ( member223413699real_n @ D @ B )
=> ~ ( member223413699real_n @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(327,axiom,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,C: sigma_107786596real_n] :
( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
=> ( member1746150050real_n @ ( B @ D ) @ ( sigma_1483971331real_n @ C ) ) )
=> ( ! [D: set_Fi1326602817real_n] :
( ( member2104752728real_n @ D @ ( sigma_522684908real_n @ C ) )
=> ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage2134951412real_n @ B @ D ) @ ( sigma_607186084real_n @ A ) ) @ ( sigma_433815053real_n @ A ) ) )
=> ( member1764433517real_n @ B @ ( sigma_588796041real_n @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_measurableI) ).
thf(1392,plain,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,C: sigma_107786596real_n] :
( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
=> ( member1746150050real_n @ ( B @ D ) @ ( sigma_1483971331real_n @ C ) ) )
=> ( ! [D: set_Fi1326602817real_n] :
( ( member2104752728real_n @ D @ ( sigma_522684908real_n @ C ) )
=> ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage2134951412real_n @ B @ D ) @ ( sigma_607186084real_n @ A ) ) @ ( sigma_433815053real_n @ A ) ) )
=> ( member1764433517real_n @ B @ ( sigma_588796041real_n @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(295,axiom,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > $o,C: finite1489363574real_n > $o] :
( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( ( C @ D )
=> ( B @ D ) ) ) )
@ ( sigma_1235138647real_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_sets_Osets__Collect__imp) ).
thf(1291,plain,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > $o,C: finite1489363574real_n > $o] :
( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( ( C @ D )
=> ( B @ D ) ) ) )
@ ( sigma_1235138647real_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(39,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,B: sigma_107786596real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > finite1489363574real_n] :
( ( member1695588023real_n @ A @ ( sigma_2028985427real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ B ) )
=> ( member1352538125real_n @ ( A @ D ) @ ( sigma_476185326real_n @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_measurable__space) ).
thf(456,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,B: sigma_107786596real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > finite1489363574real_n] :
( ( member1695588023real_n @ A @ ( sigma_2028985427real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ B ) )
=> ( member1352538125real_n @ ( A @ D ) @ ( sigma_476185326real_n @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(214,axiom,
! [A: finite1489363574real_n > set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n > $o] :
( ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_545463721real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_545463721real_n @ A
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_Compr__image__eq) ).
thf(1012,plain,
! [A: finite1489363574real_n > set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n > $o] :
( ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_545463721real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_545463721real_n @ A
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(234,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( member1746150050real_n @ A @ ( sigma_439801790real_n @ ( comple230862828real_n @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_measurable__completion) ).
thf(1079,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( member1746150050real_n @ A @ ( sigma_439801790real_n @ ( comple230862828real_n @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(219,axiom,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: sigma_1422848389real_n] :
( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
=> ( member223413699real_n @ ( B @ D ) @ ( sigma_607186084real_n @ C ) ) )
=> ( ! [D: set_se2111327970real_n] :
( ( member1475136633real_n @ D @ ( sigma_433815053real_n @ C ) )
=> ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage784510485real_n @ B @ D ) @ ( sigma_607186084real_n @ A ) ) @ ( sigma_433815053real_n @ A ) ) )
=> ( member1734791438real_n @ B @ ( sigma_239294762real_n @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_measurableI) ).
thf(1027,plain,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: sigma_1422848389real_n] :
( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
=> ( member223413699real_n @ ( B @ D ) @ ( sigma_607186084real_n @ C ) ) )
=> ( ! [D: set_se2111327970real_n] :
( ( member1475136633real_n @ D @ ( sigma_433815053real_n @ C ) )
=> ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage784510485real_n @ B @ D ) @ ( sigma_607186084real_n @ A ) ) @ ( sigma_433815053real_n @ A ) ) )
=> ( member1734791438real_n @ B @ ( sigma_239294762real_n @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(67,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_inf__left__commute) ).
thf(551,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(248,axiom,
! [A: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
=> ( member223413699real_n @ A @ ( sigma_1235138647real_n @ lebesg260170249real_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_lborelD) ).
thf(1128,plain,
! [A: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
=> ( member223413699real_n @ A @ ( sigma_1235138647real_n @ lebesg260170249real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(307,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ C ) )
=> ~ ( ( member223413699real_n @ A @ B )
=> ~ ( member223413699real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_IntE) ).
thf(1328,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ C ) )
=> ~ ( ( member223413699real_n @ A @ B )
=> ~ ( member223413699real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(229,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C )
= ( minus_1037315151real_n @ A @ ( plus_p585657087real_n @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_diff__diff__add) ).
thf(1064,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C )
= ( minus_1037315151real_n @ A @ ( plus_p585657087real_n @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(242,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( ( member1746150050real_n @ C @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ B ) )
& ( ( A @ D )
= ( C @ D ) ) ) )
@ ( sigma_1235138647real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_measurable__equality__set) ).
thf(1111,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( ( member1746150050real_n @ C @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ B ) )
& ( ( A @ D )
= ( C @ D ) ) ) )
@ ( sigma_1235138647real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(335,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ B )
=> ( member223413699real_n @ ( C @ A ) @ ( image_128879038real_n @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_imageI) ).
thf(1425,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ B )
=> ( member223413699real_n @ ( C @ A ) @ ( image_128879038real_n @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(9,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( vimage180751827real_n @ B @ C ) )
= ( member1746150050real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_vimage__eq) ).
thf(356,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( vimage180751827real_n @ B @ C ) )
= ( member1746150050real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(85,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member1746150050real_n @ A @ ( collec1190264032real_n @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_mem__Collect__eq) ).
thf(610,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member1746150050real_n @ A @ ( collec1190264032real_n @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(50,axiom,
! [A: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Int__absorb) ).
thf(499,plain,
! [A: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(164,axiom,
( minus_1698615483real_n
= ( ^ [A: set_se2111327970real_n,B: set_se2111327970real_n] :
( collec452821761real_n
@ ( minus_1832115082al_n_o
@ ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ A )
@ ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_minus__set__def) ).
thf(857,plain,
( minus_1698615483real_n
= ( ^ [A: set_se2111327970real_n,B: set_se2111327970real_n] :
( collec452821761real_n
@ ( minus_1832115082al_n_o
@ ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ A )
@ ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(129,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > $o] :
( ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( image_439535603real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_439535603real_n @ A
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_Compr__image__eq) ).
thf(742,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > $o] :
( ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( image_439535603real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_439535603real_n @ A
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(76,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( inf_in146441683real_n @ B @ C ) )
=> ~ ( ( member1746150050real_n @ A @ B )
=> ~ ( member1746150050real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_IntE) ).
thf(578,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( inf_in146441683real_n @ B @ C ) )
=> ~ ( ( member1746150050real_n @ A @ B )
=> ~ ( member1746150050real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(114,axiom,
! [A: finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n] :
( ( member1352538125real_n @ A @ ( sigma_476185326real_n @ B ) )
=> ( member1746150050real_n
@ ^ [D: finite1489363574real_n] : A
@ ( sigma_439801790real_n @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_measurable__const) ).
thf(697,plain,
! [A: finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n] :
( ( member1352538125real_n @ A @ ( sigma_476185326real_n @ B ) )
=> ( member1746150050real_n
@ ^ [D: finite1489363574real_n] : A
@ ( sigma_439801790real_n @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(276,axiom,
( minus_1698615483real_n
= ( ^ [A: set_se2111327970real_n,B: set_se2111327970real_n] :
( collec452821761real_n
@ ^ [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ A )
& ~ ( member223413699real_n @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_set__diff__eq) ).
thf(1234,plain,
( minus_1698615483real_n
= ( ^ [A: set_se2111327970real_n,B: set_se2111327970real_n] :
( collec452821761real_n
@ ^ [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ A )
& ~ ( member223413699real_n @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(321,axiom,
! [A: finite1489363574real_n] :
( ( plus_p585657087real_n @ A @ zero_z200130687real_n )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_add_Oright__neutral) ).
thf(1375,plain,
! [A: finite1489363574real_n] :
( ( plus_p585657087real_n @ A @ zero_z200130687real_n )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(246,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,C: set_se2111327970real_n] :
( ( member1746150050real_n @ A @ ( image_352856126real_n @ B @ C ) )
=> ~ ! [D: set_Fi1058188332real_n] :
( ( A
= ( B @ D ) )
=> ~ ( member223413699real_n @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_imageE) ).
thf(1121,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,C: set_se2111327970real_n] :
( ( member1746150050real_n @ A @ ( image_352856126real_n @ B @ C ) )
=> ~ ! [D: set_Fi1058188332real_n] :
( ( A
= ( B @ D ) )
=> ~ ( member223413699real_n @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(26,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ C )
= ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Int__assoc) ).
thf(420,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ C )
= ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(245,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > $o] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_1235138647real_n @ C ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_1235138647real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_measurable__sets__Collect) ).
thf(1118,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > $o] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_1235138647real_n @ C ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_1235138647real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(172,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= ( plus_p585657087real_n @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_add_Oleft__cancel) ).
thf(884,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= ( plus_p585657087real_n @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(317,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) )
=> ( ( member223413699real_n @ B @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ ( A @ C ) @ B ) )
@ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_lebesgue__measurable__vimage__borel) ).
thf(1361,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) )
=> ( ( member223413699real_n @ B @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ ( A @ C ) @ B ) )
@ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(68,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= ( minus_1037315151real_n @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_diff__eq__diff__eq) ).
thf(554,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= ( minus_1037315151real_n @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(105,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( image_1123376925real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_1123376925real_n @ A
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_Compr__image__eq) ).
thf(669,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( image_1123376925real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_1123376925real_n @ A
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(178,axiom,
! [A: sigma_1466784463real_n] : ( member223413699real_n @ ( sigma_476185326real_n @ A ) @ ( sigma_1235138647real_n @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_sets_Otop) ).
thf(901,plain,
! [A: sigma_1466784463real_n] : ( member223413699real_n @ ( sigma_476185326real_n @ A ) @ ( sigma_1235138647real_n @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(48,axiom,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n > finite1489363574real_n,D: sigma_1466784463real_n] :
( ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ A ) )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( member1746150050real_n @ B @ ( sigma_439801790real_n @ A @ D ) )
= ( member1746150050real_n @ C @ ( sigma_439801790real_n @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_measurable__cong) ).
thf(489,plain,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n > finite1489363574real_n,D: sigma_1466784463real_n] :
( ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ A ) )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( member1746150050real_n @ B @ ( sigma_439801790real_n @ A @ D ) )
= ( member1746150050real_n @ C @ ( sigma_439801790real_n @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(256,axiom,
! [A: sigma_1466784463real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( ( sigma_1235138647real_n @ A )
= ( sigma_1235138647real_n @ B ) )
=> ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ A @ C ) )
= ( sigma_1235138647real_n @ ( sigma_346513458real_n @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_sets__restrict__space__cong) ).
thf(1155,plain,
! [A: sigma_1466784463real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( ( sigma_1235138647real_n @ A )
= ( sigma_1235138647real_n @ B ) )
=> ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ A @ C ) )
= ( sigma_1235138647real_n @ ( sigma_346513458real_n @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(117,axiom,
! [A: finite1489363574real_n] :
( ( minus_1037315151real_n @ A @ A )
= zero_z200130687real_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_diff__self) ).
thf(706,plain,
! [A: finite1489363574real_n] :
( ( minus_1037315151real_n @ A @ A )
= zero_z200130687real_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(221,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ B ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_translation__Int) ).
thf(1039,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ B ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(200,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( minus_1037315151real_n @ A @ ( minus_1037315151real_n @ B @ C ) )
= ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_diff__diff__eq2) ).
thf(970,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( minus_1037315151real_n @ A @ ( minus_1037315151real_n @ B @ C ) )
= ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(204,axiom,
( t
= ( ^ [A: finite964658038_int_n] :
( image_439535603real_n
@ ^ [B: finite1489363574real_n] : ( minus_1037315151real_n @ B @ ( minkow1134813771n_real @ A ) )
@ ( t2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_T_H__def) ).
thf(985,plain,
( t
= ( ^ [A: finite964658038_int_n] :
( image_439535603real_n
@ ^ [B: finite1489363574real_n] : ( minus_1037315151real_n @ B @ ( minkow1134813771n_real @ A ) )
@ ( t2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(128,axiom,
! [A: set_Fi1326602817real_n,B: sigma_107786596real_n,C: finite1489363574real_n > finite1489363574real_n,D: sigma_107786596real_n,E: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] :
( ( member2104752728real_n @ ( inf_in146441683real_n @ A @ ( sigma_1483971331real_n @ B ) ) @ ( sigma_522684908real_n @ B ) )
=> ( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ D ) )
=> ( ( member117715276real_n @ E @ ( sigma_1185134568real_n @ ( sigma_1052429895real_n @ B @ A ) @ D ) )
= ( member117715276real_n
@ ^ [F: finite1489363574real_n > finite1489363574real_n] : ( if_Fin413489477real_n @ ( member1746150050real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_1185134568real_n @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_measurable__restrict__space__iff) ).
thf(738,plain,
! [A: set_Fi1326602817real_n,B: sigma_107786596real_n,C: finite1489363574real_n > finite1489363574real_n,D: sigma_107786596real_n,E: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] :
( ( member2104752728real_n @ ( inf_in146441683real_n @ A @ ( sigma_1483971331real_n @ B ) ) @ ( sigma_522684908real_n @ B ) )
=> ( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ D ) )
=> ( ( member117715276real_n @ E @ ( sigma_1185134568real_n @ ( sigma_1052429895real_n @ B @ A ) @ D ) )
= ( member117715276real_n
@ ^ [F: finite1489363574real_n > finite1489363574real_n] : ( if_Fin413489477real_n @ ( member1746150050real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_1185134568real_n @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(288,axiom,
! [A: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ A @ B ) )
= ( image_1661509983real_n @ ( inf_in1974387902real_n @ B ) @ ( sigma_1235138647real_n @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_sets__restrict__space) ).
thf(1266,plain,
! [A: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ A @ B ) )
= ( image_1661509983real_n @ ( inf_in1974387902real_n @ B ) @ ( sigma_1235138647real_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(100,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: finite1489363574real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ B ) )
=> ( member1352538125real_n @ ( A @ D ) @ ( sigma_476185326real_n @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_measurable__space) ).
thf(654,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: finite1489363574real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ B ) )
=> ( member1352538125real_n @ ( A @ D ) @ ( sigma_476185326real_n @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(182,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] :
( ( member223413699real_n @ A @ B )
=> ( member1746150050real_n @ ( C @ A ) @ ( image_352856126real_n @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_imageI) ).
thf(911,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] :
( ( member223413699real_n @ A @ B )
=> ( member1746150050real_n @ ( C @ A ) @ ( image_352856126real_n @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(13,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T) ).
thf(371,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(89,axiom,
! [A: sigma_107786596real_n,B: nat > ( finite1489363574real_n > finite1489363574real_n ) > $o,C: set_nat] :
( ! [D: nat] :
( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ A ) )
& ( B @ D @ E ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( member2104752728real_n
@ ( inf_in146441683real_n
@ ( vimage2098059032_n_nat
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ord_Least_nat
@ ^ [E: nat] : ( B @ E @ D ) )
@ C )
@ ( sigma_1483971331real_n @ A ) )
@ ( sigma_522684908real_n @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_sets__Least) ).
thf(622,plain,
! [A: sigma_107786596real_n,B: nat > ( finite1489363574real_n > finite1489363574real_n ) > $o,C: set_nat] :
( ! [D: nat] :
( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ A ) )
& ( B @ D @ E ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( member2104752728real_n
@ ( inf_in146441683real_n
@ ( vimage2098059032_n_nat
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ord_Least_nat
@ ^ [E: nat] : ( B @ E @ D ) )
@ C )
@ ( sigma_1483971331real_n @ A ) )
@ ( sigma_522684908real_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(157,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ A @ C ) @ ( sigma_1235138647real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_sets_OInt) ).
thf(837,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ A @ C ) @ ( sigma_1235138647real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(20,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n] :
( ( A = B )
=> ( ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_439535603real_n @ C @ A )
= ( image_439535603real_n @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_image__cong) ).
thf(393,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n] :
( ( A = B )
=> ( ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_439535603real_n @ C @ A )
= ( image_439535603real_n @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(243,axiom,
! [A: sigma_1466784463real_n] :
( ( sigma_476185326real_n @ ( comple230862828real_n @ A ) )
= ( sigma_476185326real_n @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_space__completion) ).
thf(1114,plain,
! [A: sigma_1466784463real_n] :
( ( sigma_476185326real_n @ ( comple230862828real_n @ A ) )
= ( sigma_476185326real_n @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(93,axiom,
! [A: finite1489363574real_n > $o,B: finite1489363574real_n > $o] :
( ( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_in1974387902real_n @ ( collec321817931real_n @ A ) @ ( collec321817931real_n @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Collect__conj__eq) ).
thf(633,plain,
! [A: finite1489363574real_n > $o,B: finite1489363574real_n > $o] :
( ( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_in1974387902real_n @ ( collec321817931real_n @ A ) @ ( collec321817931real_n @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(53,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( image_439535603real_n @ B @ C ) )
=> ~ ! [D: finite1489363574real_n] :
( ( A
= ( B @ D ) )
=> ~ ( member1352538125real_n @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_imageE) ).
thf(508,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( image_439535603real_n @ B @ C ) )
=> ~ ! [D: finite1489363574real_n] :
( ( A
= ( B @ D ) )
=> ~ ( member1352538125real_n @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(101,axiom,
! [A: finite1489363574real_n] :
( ( minus_1037315151real_n @ A @ zero_z200130687real_n )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_diff__zero) ).
thf(657,plain,
! [A: finite1489363574real_n] :
( ( minus_1037315151real_n @ A @ zero_z200130687real_n )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(226,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ ( minus_1686442501real_n @ A @ C ) @ ( sigma_1235138647real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_sets_ODiff) ).
thf(1054,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ ( minus_1686442501real_n @ A @ C ) @ ( sigma_1235138647real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(121,axiom,
( vimage1059850558real_n
= ( ^ [A: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( member1746150050real_n @ ( A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_vimage__def) ).
thf(718,plain,
( vimage1059850558real_n
= ( ^ [A: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( member1746150050real_n @ ( A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(188,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= ( plus_p585657087real_n @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_add_Oright__cancel) ).
thf(926,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= ( plus_p585657087real_n @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(268,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( A
= ( minus_1037315151real_n @ B @ C ) )
= ( ( plus_p585657087real_n @ A @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_eq__diff__eq) ).
thf(1202,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( A
= ( minus_1037315151real_n @ B @ C ) )
= ( ( plus_p585657087real_n @ A @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(145,axiom,
! [A: set_Fi1326602817real_n,B: set_Fi1326602817real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,D: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,E: sigma_1466784463real_n,F: sigma_1466784463real_n] :
( ( A = B )
=> ( ! [G: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ G @ B )
=> ( ( C @ G )
= ( D @ G ) ) )
=> ( ( ( sigma_1235138647real_n @ E )
= ( sigma_1235138647real_n @ F ) )
=> ( ( sigma_136294295real_n @ A @ C @ E )
= ( sigma_136294295real_n @ B @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_vimage__algebra__cong) ).
thf(792,plain,
! [A: set_Fi1326602817real_n,B: set_Fi1326602817real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,D: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,E: sigma_1466784463real_n,F: sigma_1466784463real_n] :
( ( A = B )
=> ( ! [G: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ G @ B )
=> ( ( C @ G )
= ( D @ G ) ) )
=> ( ( ( sigma_1235138647real_n @ E )
= ( sigma_1235138647real_n @ F ) )
=> ( ( sigma_136294295real_n @ A @ C @ E )
= ( sigma_136294295real_n @ B @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(180,axiom,
( vimage207290975real_n
= ( ^ [A: finite1489363574real_n > set_Fi1058188332real_n,B: set_se2111327970real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( member223413699real_n @ ( A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_vimage__def) ).
thf(906,plain,
( vimage207290975real_n
= ( ^ [A: finite1489363574real_n > set_Fi1058188332real_n,B: set_se2111327970real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( member223413699real_n @ ( A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(292,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= ( plus_p585657087real_n @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_add__left__imp__eq) ).
thf(1278,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= ( plus_p585657087real_n @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(54,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ B )
= ( inf_in1974387902real_n @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_inf_Oright__idem) ).
thf(513,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ B )
= ( inf_in1974387902real_n @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(240,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] :
( ( member223413699real_n @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member1746150050real_n @ C @ ( image_352856126real_n @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_rev__image__eqI) ).
thf(1103,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] :
( ( member223413699real_n @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member1746150050real_n @ C @ ( image_352856126real_n @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(153,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: sigma_1466784463real_n,D: sigma_1466784463real_n] :
( ( A = B )
=> ( ( ( sigma_1235138647real_n @ C )
= ( sigma_1235138647real_n @ D ) )
=> ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ C @ A ) )
= ( sigma_1235138647real_n @ ( sigma_346513458real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_restrict__space__sets__cong) ).
thf(824,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: sigma_1466784463real_n,D: sigma_1466784463real_n] :
( ( A = B )
=> ( ( ( sigma_1235138647real_n @ C )
= ( sigma_1235138647real_n @ D ) )
=> ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ C @ A ) )
= ( sigma_1235138647real_n @ ( sigma_346513458real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(130,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n > $o] :
( ( member1352538125real_n @ A @ ( collec321817931real_n @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_mem__Collect__eq) ).
thf(745,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n > $o] :
( ( member1352538125real_n @ A @ ( collec321817931real_n @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(298,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n,D: sigma_1422848389real_n,E: finite1489363574real_n > set_Fi1058188332real_n] :
( ( member223413699real_n @ ( inf_in1974387902real_n @ A @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_607186084real_n @ D ) )
=> ( ( member966061400real_n @ E @ ( sigma_566919540real_n @ ( sigma_346513458real_n @ B @ A ) @ D ) )
= ( member966061400real_n
@ ^ [F: finite1489363574real_n] : ( if_set11487206real_n @ ( member1352538125real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_566919540real_n @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_measurable__restrict__space__iff) ).
thf(1301,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n,D: sigma_1422848389real_n,E: finite1489363574real_n > set_Fi1058188332real_n] :
( ( member223413699real_n @ ( inf_in1974387902real_n @ A @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_607186084real_n @ D ) )
=> ( ( member966061400real_n @ E @ ( sigma_566919540real_n @ ( sigma_346513458real_n @ B @ A ) @ D ) )
= ( member966061400real_n
@ ^ [F: finite1489363574real_n] : ( if_set11487206real_n @ ( member1352538125real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_566919540real_n @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(74,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > finite1489363574real_n,E: sigma_1466784463real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_439801790real_n @ E @ B ) )
=> ( member1746150050real_n
@ ^ [F: finite1489363574real_n] : ( A @ ( D @ F ) )
@ ( sigma_439801790real_n @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_measurable__compose__rev) ).
thf(573,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > finite1489363574real_n,E: sigma_1466784463real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_439801790real_n @ E @ B ) )
=> ( member1746150050real_n
@ ^ [F: finite1489363574real_n] : ( A @ ( D @ F ) )
@ ( sigma_439801790real_n @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(15,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1326602817real_n] :
( ( ( A @ B )
= C )
=> ( ( member1746150050real_n @ C @ D )
=> ( member1746150050real_n @ B @ ( vimage180751827real_n @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_vimageI) ).
thf(375,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1326602817real_n] :
( ( ( A @ B )
= C )
=> ( ( member1746150050real_n @ C @ D )
=> ( member1746150050real_n @ B @ ( vimage180751827real_n @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(82,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B: sigma_107786596real_n,C: sigma_107786596real_n,D: finite1489363574real_n > finite1489363574real_n] :
( ( member117715276real_n @ A @ ( sigma_1185134568real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ B ) )
=> ( member1746150050real_n @ ( A @ D ) @ ( sigma_1483971331real_n @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_measurable__space) ).
thf(601,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B: sigma_107786596real_n,C: sigma_107786596real_n,D: finite1489363574real_n > finite1489363574real_n] :
( ( member117715276real_n @ A @ ( sigma_1185134568real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ B ) )
=> ( member1746150050real_n @ ( A @ D ) @ ( sigma_1483971331real_n @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(71,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n] :
( ( member1352538125real_n @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member1352538125real_n @ C @ ( image_439535603real_n @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_rev__image__eqI) ).
thf(562,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n] :
( ( member1352538125real_n @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member1352538125real_n @ C @ ( image_439535603real_n @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(27,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ A @ B ) )
= ( inf_in1974387902real_n @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_inf__left__idem) ).
thf(423,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ A @ B ) )
= ( inf_in1974387902real_n @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(21,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > finite1489363574real_n] :
( ( member1352538125real_n @ A @ B )
=> ( member1352538125real_n @ ( C @ A ) @ ( image_439535603real_n @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_imageI) ).
thf(402,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > finite1489363574real_n] :
( ( member1352538125real_n @ A @ B )
=> ( member1352538125real_n @ ( C @ A ) @ ( image_439535603real_n @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(326,axiom,
! [A: set_Fi1058188332real_n] :
( ( sigma_476185326real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_space__lebesgue__on) ).
thf(1389,plain,
! [A: set_Fi1058188332real_n] :
( ( sigma_476185326real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(159,axiom,
( plus_p585657087real_n
= ( ^ [A: finite1489363574real_n,B: finite1489363574real_n] : ( plus_p585657087real_n @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add_Ocommute) ).
thf(843,plain,
( plus_p585657087real_n
= ( ^ [A: finite1489363574real_n,B: finite1489363574real_n] : ( plus_p585657087real_n @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(139,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( ( member1746150050real_n @ C @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( member1746150050real_n
@ ^ [D: finite1489363574real_n] : ( plus_p585657087real_n @ ( A @ D ) @ ( C @ D ) )
@ ( sigma_439801790real_n @ B @ borel_676189912real_n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_borel__measurable__add) ).
thf(772,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( ( member1746150050real_n @ C @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
=> ( member1746150050real_n
@ ^ [D: finite1489363574real_n] : ( plus_p585657087real_n @ ( A @ D ) @ ( C @ D ) )
@ ( sigma_439801790real_n @ B @ borel_676189912real_n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(330,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ C ) )
= ( ( member223413699real_n @ A @ B )
& ( member223413699real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Int__iff) ).
thf(1403,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ C ) )
= ( ( member223413699real_n @ A @ B )
& ( member223413699real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(284,axiom,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ ( A @ B ) @ C )
=> ( member223413699real_n @ B @ ( vimage784510485real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_vimageI2) ).
thf(1256,plain,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ ( A @ B ) @ C )
=> ( member223413699real_n @ B @ ( vimage784510485real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(212,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ B @ C ) )
=> ( member223413699real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_vimageE) ).
thf(1007,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ B @ C ) )
=> ( member223413699real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(113,axiom,
! [A: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_inf__idem) ).
thf(694,plain,
! [A: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(336,axiom,
! [A: sigma_1466784463real_n,B: $o] :
( member223413699real_n
@ ( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ A ) )
& B ) )
@ ( sigma_1235138647real_n @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_sets_Osets__Collect__const) ).
thf(1428,plain,
! [A: sigma_1466784463real_n,B: $o] :
( member223413699real_n
@ ( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ A ) )
& B ) )
@ ( sigma_1235138647real_n @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(144,axiom,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n,D: set_se2111327970real_n] :
( ( ( A @ B )
= C )
=> ( ( member223413699real_n @ C @ D )
=> ( member223413699real_n @ B @ ( vimage784510485real_n @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_vimageI) ).
thf(787,plain,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n,D: set_se2111327970real_n] :
( ( ( A @ B )
= C )
=> ( ( member223413699real_n @ C @ D )
=> ( member223413699real_n @ B @ ( vimage784510485real_n @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(278,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member223413699real_n @ A @ ( vimage2134951412real_n @ B @ C ) )
= ( member1746150050real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_vimage__eq) ).
thf(1239,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member223413699real_n @ A @ ( vimage2134951412real_n @ B @ C ) )
= ( member1746150050real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(308,axiom,
( ( sigma_476185326real_n @ lebesg260170249real_n )
= ( sigma_476185326real_n @ borel_676189912real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_space__lborel) ).
thf(1332,plain,
( ( sigma_476185326real_n @ lebesg260170249real_n )
= ( sigma_476185326real_n @ borel_676189912real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(285,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > finite1489363574real_n,E: finite1489363574real_n > $o] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [F: finite1489363574real_n] :
( ( member1352538125real_n @ F @ ( sigma_476185326real_n @ B ) )
& ( E @ F ) ) )
@ ( sigma_1235138647real_n @ B ) )
=> ( member1746150050real_n
@ ^ [F: finite1489363574real_n] : ( if_Fin127821360real_n @ ( E @ F ) @ ( A @ F ) @ ( D @ F ) )
@ ( sigma_439801790real_n @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_measurable__If) ).
thf(1258,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > finite1489363574real_n,E: finite1489363574real_n > $o] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [F: finite1489363574real_n] :
( ( member1352538125real_n @ F @ ( sigma_476185326real_n @ B ) )
& ( E @ F ) ) )
@ ( sigma_1235138647real_n @ B ) )
=> ( member1746150050real_n
@ ^ [F: finite1489363574real_n] : ( if_Fin127821360real_n @ ( E @ F ) @ ( A @ F ) @ ( D @ F ) )
@ ( sigma_439801790real_n @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(7,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( minus_725016986real_n @ B @ C ) )
= ( ( member1746150050real_n @ A @ B )
& ~ ( member1746150050real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_Diff__iff) ).
thf(350,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( minus_725016986real_n @ B @ C ) )
= ( ( member1746150050real_n @ A @ B )
& ~ ( member1746150050real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(63,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,B: set_Fi1326602817real_n,C: finite1489363574real_n > $o] :
( ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( image_449906696real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_449906696real_n @ A
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_Compr__image__eq) ).
thf(540,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,B: set_Fi1326602817real_n,C: finite1489363574real_n > $o] :
( ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( image_449906696real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_449906696real_n @ A
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(106,axiom,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > $o,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( C @ D )
& ( B @ D ) ) )
@ ( sigma_522684908real_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_sets_Osets__Collect__conj) ).
thf(672,plain,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > $o,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( C @ D )
& ( B @ D ) ) )
@ ( sigma_522684908real_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(19,axiom,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_inf_Ocommute) ).
thf(391,plain,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(252,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n,D: set_se2111327970real_n] :
( ( ( A @ B )
= C )
=> ( ( member223413699real_n @ C @ D )
=> ( member1746150050real_n @ B @ ( vimage1910974324real_n @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_vimageI) ).
thf(1139,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n,D: set_se2111327970real_n] :
( ( ( A @ B )
= C )
=> ( ( member223413699real_n @ C @ D )
=> ( member1746150050real_n @ B @ ( vimage1910974324real_n @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(185,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ A @ D ) @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_measurable__sets) ).
thf(919,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ A @ D ) @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(147,axiom,
! [A: sigma_1466784463real_n,B: sigma_1466784463real_n] :
( ( ( sigma_1235138647real_n @ A )
= ( sigma_1235138647real_n @ B ) )
=> ( member1746150050real_n
@ ^ [C: finite1489363574real_n] : C
@ ( sigma_439801790real_n @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_measurable__ident__sets) ).
thf(804,plain,
! [A: sigma_1466784463real_n,B: sigma_1466784463real_n] :
( ( ( sigma_1235138647real_n @ A )
= ( sigma_1235138647real_n @ B ) )
=> ( member1746150050real_n
@ ^ [C: finite1489363574real_n] : C
@ ( sigma_439801790real_n @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(266,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ ( plus_p585657087real_n @ A @ C ) )
= ( minus_1037315151real_n @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_add__diff__cancel__left) ).
thf(1194,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ ( plus_p585657087real_n @ A @ C ) )
= ( minus_1037315151real_n @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(109,axiom,
! [A: nat > $o] :
( ( A @ zero_zero_nat )
=> ( ( ord_Least_nat @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_Least__eq__0) ).
thf(681,plain,
! [A: nat > $o] :
( ( A @ zero_zero_nat )
=> ( ( ord_Least_nat @ A )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(313,axiom,
! [A: set_Fi1058188332real_n > finite1489363574real_n,B: sigma_1422848389real_n,C: sigma_1466784463real_n,D: set_Fi1058188332real_n] :
( ( member1759501912real_n @ A @ ( sigma_1333364596real_n @ B @ C ) )
=> ( ( member223413699real_n @ D @ ( sigma_607186084real_n @ B ) )
=> ( member1352538125real_n @ ( A @ D ) @ ( sigma_476185326real_n @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_measurable__space) ).
thf(1349,plain,
! [A: set_Fi1058188332real_n > finite1489363574real_n,B: sigma_1422848389real_n,C: sigma_1466784463real_n,D: set_Fi1058188332real_n] :
( ( member1759501912real_n @ A @ ( sigma_1333364596real_n @ B @ C ) )
=> ( ( member223413699real_n @ D @ ( sigma_607186084real_n @ B ) )
=> ( member1352538125real_n @ ( A @ D ) @ ( sigma_476185326real_n @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(208,axiom,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > $o] :
( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ A ) )
& ( B @ C ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ A ) )
& ~ ( B @ C ) ) )
@ ( sigma_1235138647real_n @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_sets_Osets__Collect__neg) ).
thf(996,plain,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > $o] :
( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ A ) )
& ( B @ C ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ A ) )
& ~ ( B @ C ) ) )
@ ( sigma_1235138647real_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(253,axiom,
! [A: sigma_1466784463real_n,B: sigma_1466784463real_n] :
( ( ( sigma_1235138647real_n @ A )
= ( sigma_1235138647real_n @ B ) )
=> ( ( sigma_476185326real_n @ A )
= ( sigma_476185326real_n @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_sets__eq__imp__space__eq) ).
thf(1144,plain,
! [A: sigma_1466784463real_n,B: sigma_1466784463real_n] :
( ( ( sigma_1235138647real_n @ A )
= ( sigma_1235138647real_n @ B ) )
=> ( ( sigma_476185326real_n @ A )
= ( sigma_476185326real_n @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(31,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( minus_1686442501real_n @ B @ C ) )
= ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A @ B ) @ ( inf_in1974387902real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_Diff__Int__distrib) ).
thf(434,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( minus_1686442501real_n @ B @ C ) )
= ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A @ B ) @ ( inf_in1974387902real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(87,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ A @ B ) )
= ( inf_in1974387902real_n @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_inf_Oleft__idem) ).
thf(616,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ A @ B ) )
= ( inf_in1974387902real_n @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(81,axiom,
! [A: finite1489363574real_n,B: sigma_1466784463real_n] :
( member1746150050real_n
@ ^ [C: finite1489363574real_n] : A
@ ( sigma_439801790real_n @ B @ borel_676189912real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_borel__measurable__const) ).
thf(599,plain,
! [A: finite1489363574real_n,B: sigma_1466784463real_n] :
( member1746150050real_n
@ ^ [C: finite1489363574real_n] : A
@ ( sigma_439801790real_n @ B @ borel_676189912real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(300,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= ( plus_p585657087real_n @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_add__left__cancel) ).
thf(1307,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= ( plus_p585657087real_n @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(203,axiom,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,C: sigma_107786596real_n] :
( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
=> ( member1746150050real_n @ ( B @ D ) @ ( sigma_1483971331real_n @ C ) ) )
=> ( ! [D: set_Fi1326602817real_n] :
( ( member2104752728real_n @ D @ ( sigma_522684908real_n @ C ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1059850558real_n @ B @ D ) @ ( sigma_476185326real_n @ A ) ) @ ( sigma_1235138647real_n @ A ) ) )
=> ( member408431031real_n @ B @ ( sigma_2016438227real_n @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_measurableI) ).
thf(979,plain,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,C: sigma_107786596real_n] :
( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
=> ( member1746150050real_n @ ( B @ D ) @ ( sigma_1483971331real_n @ C ) ) )
=> ( ! [D: set_Fi1326602817real_n] :
( ( member2104752728real_n @ D @ ( sigma_522684908real_n @ C ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1059850558real_n @ B @ D ) @ ( sigma_476185326real_n @ A ) ) @ ( sigma_1235138647real_n @ A ) ) )
=> ( member408431031real_n @ B @ ( sigma_2016438227real_n @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(83,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ B )
=> ( ( member1746150050real_n @ A @ C )
=> ( member1746150050real_n @ A @ ( inf_in146441683real_n @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_IntI) ).
thf(604,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ B )
=> ( ( member1746150050real_n @ A @ C )
=> ( member1746150050real_n @ A @ ( inf_in146441683real_n @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(143,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ B ) @ C ) )
= ( image_439535603real_n @ ( plus_p585657087real_n @ ( plus_p585657087real_n @ B @ A ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_translation__assoc) ).
thf(784,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ B ) @ C ) )
= ( image_439535603real_n @ ( plus_p585657087real_n @ ( plus_p585657087real_n @ B @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(244,axiom,
member223413699real_n @ s @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(1117,plain,
member223413699real_n @ s @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(224,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ B )
=> ( member223413699real_n @ ( C @ A ) @ ( image_1661509983real_n @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_imageI) ).
thf(1048,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ B )
=> ( member223413699real_n @ ( C @ A ) @ ( image_1661509983real_n @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(127,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( inf_in146441683real_n @ B @ C ) )
=> ( member1746150050real_n @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_IntD2) ).
thf(736,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( inf_in146441683real_n @ B @ C ) )
=> ( member1746150050real_n @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(37,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( inf_in146441683real_n @ B @ C ) )
= ( ( member1746150050real_n @ A @ B )
& ( member1746150050real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_Int__iff) ).
thf(451,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( inf_in146441683real_n @ B @ C ) )
= ( ( member1746150050real_n @ A @ B )
& ( member1746150050real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(72,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B: sigma_107786596real_n,C: sigma_107786596real_n,D: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member117715276real_n @ A @ ( sigma_1185134568real_n @ B @ C ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_522684908real_n @ C ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_522684908real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_measurable__sets__Collect) ).
thf(567,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B: sigma_107786596real_n,C: sigma_107786596real_n,D: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member117715276real_n @ A @ ( sigma_1185134568real_n @ B @ C ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_522684908real_n @ C ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_522684908real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(166,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n,D: set_Fi1058188332real_n > set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member223413699real_n @ C @ ( image_1661509983real_n @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_rev__image__eqI) ).
thf(863,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n,D: set_Fi1058188332real_n > set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member223413699real_n @ C @ ( image_1661509983real_n @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(261,axiom,
( inf_in632889204real_n
= ( ^ [A: set_se2111327970real_n,B: set_se2111327970real_n] :
( collec452821761real_n
@ ( inf_in409346577al_n_o
@ ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ A )
@ ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_inf__set__def) ).
thf(1175,plain,
( inf_in632889204real_n
= ( ^ [A: set_se2111327970real_n,B: set_se2111327970real_n] :
( collec452821761real_n
@ ( inf_in409346577al_n_o
@ ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ A )
@ ^ [C: set_Fi1058188332real_n] : ( member223413699real_n @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(174,axiom,
( vimage1233683625real_n
= ( ^ [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ ( A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_vimage__def) ).
thf(890,plain,
( vimage1233683625real_n
= ( ^ [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ ( A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(44,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ A @ B ) )
= ( inf_in1974387902real_n @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Int__left__absorb) ).
thf(477,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ A @ B ) )
= ( inf_in1974387902real_n @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(92,axiom,
( minus_1686442501real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ( minus_455231168al_n_o
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ A )
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_minus__set__def) ).
thf(631,plain,
( minus_1686442501real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ( minus_455231168al_n_o
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ A )
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(135,axiom,
( ( sigma_1235138647real_n @ lebesg260170249real_n )
= ( sigma_1235138647real_n @ borel_676189912real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_sets__lborel) ).
thf(758,plain,
( ( sigma_1235138647real_n @ lebesg260170249real_n )
= ( sigma_1235138647real_n @ borel_676189912real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(61,axiom,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > $o,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( ( C @ D )
=> ( B @ D ) ) ) )
@ ( sigma_522684908real_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_sets_Osets__Collect__imp) ).
thf(535,plain,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > $o,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_522684908real_n @ A ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
& ( ( C @ D )
=> ( B @ D ) ) ) )
@ ( sigma_522684908real_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(124,axiom,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Int__commute) ).
thf(726,plain,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(46,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( if_Fin127821360real_n @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T) ).
thf(483,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( if_Fin127821360real_n @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(306,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B: sigma_107786596real_n,C: sigma_1422848389real_n,D: finite1489363574real_n > finite1489363574real_n] :
( ( member640587117real_n @ A @ ( sigma_364818953real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ B ) )
=> ( member223413699real_n @ ( A @ D ) @ ( sigma_607186084real_n @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_measurable__space) ).
thf(1325,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B: sigma_107786596real_n,C: sigma_1422848389real_n,D: finite1489363574real_n > finite1489363574real_n] :
( ( member640587117real_n @ A @ ( sigma_364818953real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ B ) )
=> ( member223413699real_n @ ( A @ D ) @ ( sigma_607186084real_n @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(176,axiom,
! [A: set_Fi1058188332real_n > finite1489363574real_n,B: set_se2111327970real_n,C: finite1489363574real_n > $o] :
( ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( image_1311908777real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_1311908777real_n @ A
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_Compr__image__eq) ).
thf(895,plain,
! [A: set_Fi1058188332real_n > finite1489363574real_n,B: set_se2111327970real_n,C: finite1489363574real_n > $o] :
( ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( image_1311908777real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_1311908777real_n @ A
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(312,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ B @ C ) )
=> ( ( plus_p585657087real_n @ D @ A )
= ( plus_p585657087real_n @ B @ ( plus_p585657087real_n @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_group__cancel_Oadd2) ).
thf(1344,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ B @ C ) )
=> ( ( plus_p585657087real_n @ D @ A )
= ( plus_p585657087real_n @ B @ ( plus_p585657087real_n @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(138,axiom,
! [A: finite1489363574real_n > $o,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n > $o] :
( ! [D: finite1489363574real_n] :
( ( A @ ( B @ D ) )
= ( C @ D ) )
=> ( ( vimage1233683625real_n @ B @ ( collec321817931real_n @ A ) )
= ( collec321817931real_n @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_vimage__Collect) ).
thf(769,plain,
! [A: finite1489363574real_n > $o,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n > $o] :
( ! [D: finite1489363574real_n] :
( ( A @ ( B @ D ) )
= ( C @ D ) )
=> ( ( vimage1233683625real_n @ B @ ( collec321817931real_n @ A ) )
= ( collec321817931real_n @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(41,axiom,
! [A: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_inf_Oidem) ).
thf(462,plain,
! [A: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(161,axiom,
! [A: set_se2111327970real_n,B: sigma_1422848389real_n,C: set_Fi1058188332real_n,D: sigma_1422848389real_n,E: set_Fi1058188332real_n > set_Fi1058188332real_n] :
( ( member1475136633real_n @ ( inf_in632889204real_n @ A @ ( sigma_607186084real_n @ B ) ) @ ( sigma_433815053real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_607186084real_n @ D ) )
=> ( ( member1734791438real_n @ E @ ( sigma_239294762real_n @ ( sigma_993999336real_n @ B @ A ) @ D ) )
= ( member1734791438real_n
@ ^ [F: set_Fi1058188332real_n] : ( if_set11487206real_n @ ( member223413699real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_239294762real_n @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_measurable__restrict__space__iff) ).
thf(848,plain,
! [A: set_se2111327970real_n,B: sigma_1422848389real_n,C: set_Fi1058188332real_n,D: sigma_1422848389real_n,E: set_Fi1058188332real_n > set_Fi1058188332real_n] :
( ( member1475136633real_n @ ( inf_in632889204real_n @ A @ ( sigma_607186084real_n @ B ) ) @ ( sigma_433815053real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_607186084real_n @ D ) )
=> ( ( member1734791438real_n @ E @ ( sigma_239294762real_n @ ( sigma_993999336real_n @ B @ A ) @ D ) )
= ( member1734791438real_n
@ ^ [F: set_Fi1058188332real_n] : ( if_set11487206real_n @ ( member223413699real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_239294762real_n @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(115,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A @ B ) @ C )
= ( inf_in1974387902real_n @ A @ ( minus_1686442501real_n @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_Int__Diff) ).
thf(700,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A @ B ) @ C )
= ( inf_in1974387902real_n @ A @ ( minus_1686442501real_n @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(57,axiom,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_inf__sup__aci_I1_J) ).
thf(520,plain,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(193,axiom,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > finite1489363574real_n,C: sigma_1466784463real_n] :
( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
=> ( member1352538125real_n @ ( B @ D ) @ ( sigma_476185326real_n @ C ) ) )
=> ( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
=> ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage973736031real_n @ B @ D ) @ ( sigma_607186084real_n @ A ) ) @ ( sigma_433815053real_n @ A ) ) )
=> ( member1759501912real_n @ B @ ( sigma_1333364596real_n @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_measurableI) ).
thf(943,plain,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > finite1489363574real_n,C: sigma_1466784463real_n] :
( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
=> ( member1352538125real_n @ ( B @ D ) @ ( sigma_476185326real_n @ C ) ) )
=> ( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
=> ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage973736031real_n @ B @ D ) @ ( sigma_607186084real_n @ A ) ) @ ( sigma_433815053real_n @ A ) ) )
=> ( member1759501912real_n @ B @ ( sigma_1333364596real_n @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(217,axiom,
! [A: set_Fi1058188332real_n,B: finite1489363574real_n,C: set_Fi1058188332real_n] :
( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ A )
= ( member1352538125real_n @ ( plus_p585657087real_n @ B @ D ) @ C ) )
=> ( C
= ( image_439535603real_n @ ( plus_p585657087real_n @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_affine__parallel__expl__aux) ).
thf(1022,plain,
! [A: set_Fi1058188332real_n,B: finite1489363574real_n,C: set_Fi1058188332real_n] :
( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ A )
= ( member1352538125real_n @ ( plus_p585657087real_n @ B @ D ) @ C ) )
=> ( C
= ( image_439535603real_n @ ( plus_p585657087real_n @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(262,axiom,
! [A: set_Fi1058188332real_n] :
( ( vimage1233683625real_n
@ ^ [B: finite1489363574real_n] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_vimage__ident) ).
thf(1177,plain,
! [A: set_Fi1058188332real_n] :
( ( vimage1233683625real_n
@ ^ [B: finite1489363574real_n] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(323,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( vimage1233683625real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n @ ( vimage1233683625real_n @ A @ B ) @ ( vimage1233683625real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_vimage__Int) ).
thf(1381,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( vimage1233683625real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n @ ( vimage1233683625real_n @ A @ B ) @ ( vimage1233683625real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(167,axiom,
! [A: sigma_1422848389real_n,B: $o] :
( member1475136633real_n
@ ( collec452821761real_n
@ ^ [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_607186084real_n @ A ) )
& B ) )
@ ( sigma_433815053real_n @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_sets_Osets__Collect__const) ).
thf(868,plain,
! [A: sigma_1422848389real_n,B: $o] :
( member1475136633real_n
@ ( collec452821761real_n
@ ^ [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_607186084real_n @ A ) )
& B ) )
@ ( sigma_433815053real_n @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(215,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= ( plus_p585657087real_n @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_add__right__cancel) ).
thf(1015,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= ( plus_p585657087real_n @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(52,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ C )
= ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_inf__sup__aci_I2_J) ).
thf(505,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ C )
= ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(30,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ C )
= ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_inf_Oassoc) ).
thf(431,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ C )
= ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(186,axiom,
! [A: finite964658038_int_n] :
( member1746150050real_n
@ ^ [B: finite1489363574real_n] : ( plus_p585657087real_n @ B @ ( minkow1134813771n_real @ A ) )
@ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( comple230862828real_n @ lebesg260170249real_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(922,plain,
! [A: finite964658038_int_n] :
( member1746150050real_n
@ ^ [B: finite1489363574real_n] : ( plus_p585657087real_n @ B @ ( minkow1134813771n_real @ A ) )
@ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(94,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
=> ~ ( ( member1352538125real_n @ A @ B )
=> ~ ( member1352538125real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_IntE) ).
thf(636,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
=> ~ ( ( member1352538125real_n @ A @ B )
=> ~ ( member1352538125real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(280,axiom,
! [A: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B: sigma_1422848389real_n,C: sigma_107786596real_n,D: set_Fi1058188332real_n] :
( ( member1764433517real_n @ A @ ( sigma_588796041real_n @ B @ C ) )
=> ( ( member223413699real_n @ D @ ( sigma_607186084real_n @ B ) )
=> ( member1746150050real_n @ ( A @ D ) @ ( sigma_1483971331real_n @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_measurable__space) ).
thf(1245,plain,
! [A: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B: sigma_1422848389real_n,C: sigma_107786596real_n,D: set_Fi1058188332real_n] :
( ( member1764433517real_n @ A @ ( sigma_588796041real_n @ B @ C ) )
=> ( ( member223413699real_n @ D @ ( sigma_607186084real_n @ B ) )
=> ( member1746150050real_n @ ( A @ D ) @ ( sigma_1483971331real_n @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(210,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( image_1661509983real_n @ B @ C ) )
=> ~ ! [D: set_Fi1058188332real_n] :
( ( A
= ( B @ D ) )
=> ~ ( member223413699real_n @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_imageE) ).
thf(1000,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( image_1661509983real_n @ B @ C ) )
=> ~ ! [D: set_Fi1058188332real_n] :
( ( A
= ( B @ D ) )
=> ~ ( member223413699real_n @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(339,axiom,
! [A: sigma_1466784463real_n,B: $o] :
( member223413699real_n
@ ( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ A ) )
& B ) )
@ ( sigma_1235138647real_n @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_sets_Osets__Collect_I5_J) ).
thf(1435,plain,
! [A: sigma_1466784463real_n,B: $o] :
( member223413699real_n
@ ( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ A ) )
& B ) )
@ ( sigma_1235138647real_n @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(318,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= C )
= ( A
= ( plus_p585657087real_n @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_diff__eq__eq) ).
thf(1364,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( minus_1037315151real_n @ A @ B )
= C )
= ( A
= ( plus_p585657087real_n @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(282,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ B @ C ) )
= ( member1352538125real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_vimage__eq) ).
thf(1250,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ B @ C ) )
= ( member1352538125real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(107,axiom,
! [A: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_107786596real_n,D: finite1489363574real_n] :
( ( member408431031real_n @ A @ ( sigma_2016438227real_n @ B @ C ) )
=> ( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ B ) )
=> ( member1746150050real_n @ ( A @ D ) @ ( sigma_1483971331real_n @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_measurable__space) ).
thf(675,plain,
! [A: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_107786596real_n,D: finite1489363574real_n] :
( ( member408431031real_n @ A @ ( sigma_2016438227real_n @ B @ C ) )
=> ( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ B ) )
=> ( member1746150050real_n @ ( A @ D ) @ ( sigma_1483971331real_n @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(28,axiom,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ A )
& ( member1352538125real_n @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Int__def) ).
thf(426,plain,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ A )
& ( member1352538125real_n @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(103,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( if_set11487206real_n @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T) ).
thf(663,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( if_set11487206real_n @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(334,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ B @ C ) )
=> ( ( plus_p585657087real_n @ A @ D )
= ( plus_p585657087real_n @ B @ ( plus_p585657087real_n @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_group__cancel_Oadd1) ).
thf(1420,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ B @ C ) )
=> ( ( plus_p585657087real_n @ A @ D )
= ( plus_p585657087real_n @ B @ ( plus_p585657087real_n @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(98,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( image_439535603real_n @ A @ ( image_439535603real_n @ B @ C ) )
= ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_image__image) ).
thf(648,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( image_439535603real_n @ A @ ( image_439535603real_n @ B @ C ) )
= ( image_439535603real_n
@ ^ [D: finite1489363574real_n] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(235,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ A @ B ) )
= ( B = zero_z200130687real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_add__cancel__right__right) ).
thf(1081,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ A @ B ) )
= ( B = zero_z200130687real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(55,axiom,
( inf_in146441683real_n
= ( ^ [A: set_Fi1326602817real_n,B: set_Fi1326602817real_n] :
( collec1190264032real_n
@ ^ [C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ C @ A )
& ( member1746150050real_n @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Int__def) ).
thf(516,plain,
( inf_in146441683real_n
= ( ^ [A: set_Fi1326602817real_n,B: set_Fi1326602817real_n] :
( collec1190264032real_n
@ ^ [C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ C @ A )
& ( member1746150050real_n @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(311,axiom,
! [A: set_Fi1326602817real_n,B: sigma_107786596real_n,C: set_Fi1058188332real_n,D: sigma_1422848389real_n,E: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] :
( ( member2104752728real_n @ ( inf_in146441683real_n @ A @ ( sigma_1483971331real_n @ B ) ) @ ( sigma_522684908real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_607186084real_n @ D ) )
=> ( ( member640587117real_n @ E @ ( sigma_364818953real_n @ ( sigma_1052429895real_n @ B @ A ) @ D ) )
= ( member640587117real_n
@ ^ [F: finite1489363574real_n > finite1489363574real_n] : ( if_set11487206real_n @ ( member1746150050real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_364818953real_n @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_measurable__restrict__space__iff) ).
thf(1340,plain,
! [A: set_Fi1326602817real_n,B: sigma_107786596real_n,C: set_Fi1058188332real_n,D: sigma_1422848389real_n,E: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] :
( ( member2104752728real_n @ ( inf_in146441683real_n @ A @ ( sigma_1483971331real_n @ B ) ) @ ( sigma_522684908real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_607186084real_n @ D ) )
=> ( ( member640587117real_n @ E @ ( sigma_364818953real_n @ ( sigma_1052429895real_n @ B @ A ) @ D ) )
= ( member640587117real_n
@ ^ [F: finite1489363574real_n > finite1489363574real_n] : ( if_set11487206real_n @ ( member1746150050real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_364818953real_n @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(216,axiom,
! [A: set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
=> ( ( member1746150050real_n
@ ^ [C: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ C @ A ) @ ( B @ C ) @ zero_z200130687real_n )
@ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) )
= ( member1746150050real_n @ B @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ A ) @ borel_676189912real_n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_borel__measurable__if) ).
thf(1018,plain,
! [A: set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
=> ( ( member1746150050real_n
@ ^ [C: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ C @ A ) @ ( B @ C ) @ zero_z200130687real_n )
@ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) )
= ( member1746150050real_n @ B @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ A ) @ borel_676189912real_n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(133,axiom,
! [A: finite964658038_int_n] : ( member223413699real_n @ ( t2 @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_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(754,plain,
! [A: finite964658038_int_n] : ( member223413699real_n @ ( t2 @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(332,axiom,
! [A: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1326602817real_n] :
( ( ( A @ B )
= C )
=> ( ( member1746150050real_n @ C @ D )
=> ( member223413699real_n @ B @ ( vimage2134951412real_n @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_vimageI) ).
thf(1413,plain,
! [A: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1326602817real_n] :
( ( ( A @ B )
= C )
=> ( ( member1746150050real_n @ C @ D )
=> ( member223413699real_n @ B @ ( vimage2134951412real_n @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(233,axiom,
! [A: finite1489363574real_n] :
( ( plus_p585657087real_n @ zero_z200130687real_n @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_add_Oleft__neutral) ).
thf(1076,plain,
! [A: finite1489363574real_n] :
( ( plus_p585657087real_n @ zero_z200130687real_n @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(270,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ B )
=> ( ~ ( member223413699real_n @ A @ C )
=> ( member223413699real_n @ A @ ( minus_1698615483real_n @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_DiffI) ).
thf(1208,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ B )
=> ( ~ ( member223413699real_n @ A @ C )
=> ( member223413699real_n @ A @ ( minus_1698615483real_n @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(78,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ A @ ( minus_1686442501real_n @ A @ B ) )
= ( inf_in1974387902real_n @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_Diff__Diff__Int) ).
thf(589,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ A @ ( minus_1686442501real_n @ A @ B ) )
= ( inf_in1974387902real_n @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(95,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A @ B ) @ ( inf_in1974387902real_n @ C @ B ) )
= ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_Diff__Int2) ).
thf(640,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A @ B ) @ ( inf_in1974387902real_n @ C @ B ) )
= ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(218,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ B @ C ) )
=> ( member1352538125real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_vimageE) ).
thf(1025,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ B @ C ) )
=> ( member1352538125real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(231,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > finite1489363574real_n,E: set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member223413699real_n @ ( inf_in1974387902real_n @ E @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) )
=> ( member1746150050real_n
@ ^ [F: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ F @ E ) @ ( A @ F ) @ ( D @ F ) )
@ ( sigma_439801790real_n @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_measurable__If__set) ).
thf(1070,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > finite1489363574real_n,E: set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member223413699real_n @ ( inf_in1974387902real_n @ E @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) )
=> ( member1746150050real_n
@ ^ [F: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ F @ E ) @ ( A @ F ) @ ( D @ F ) )
@ ( sigma_439801790real_n @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(274,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( vimage784510485real_n @ B @ C ) )
= ( member223413699real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_vimage__eq) ).
thf(1225,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( vimage784510485real_n @ B @ C ) )
= ( member223413699real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(173,axiom,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > $o,C: set_Fi1058188332real_n > $o] :
( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( C @ D )
& ( B @ D ) ) )
@ ( sigma_433815053real_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_sets_Osets__Collect__conj) ).
thf(887,plain,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > $o,C: set_Fi1058188332real_n > $o] :
( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( C @ D )
& ( B @ D ) ) )
@ ( sigma_433815053real_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(24,axiom,
! [A: set_Fi1326602817real_n] :
( ( collec1190264032real_n
@ ^ [B: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Collect__mem__eq) ).
thf(414,plain,
! [A: set_Fi1326602817real_n] :
( ( collec1190264032real_n
@ ^ [B: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(195,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( vimage1233683625real_n @ A @ ( minus_1686442501real_n @ B @ C ) )
= ( minus_1686442501real_n @ ( vimage1233683625real_n @ A @ B ) @ ( vimage1233683625real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_vimage__Diff) ).
thf(954,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( vimage1233683625real_n @ A @ ( minus_1686442501real_n @ B @ C ) )
= ( minus_1686442501real_n @ ( vimage1233683625real_n @ A @ B ) @ ( vimage1233683625real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(207,axiom,
! [A: sigma_1466784463real_n,B: nat > finite1489363574real_n > $o,C: set_nat] :
( ! [D: nat] :
( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ A ) )
& ( B @ D @ E ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( member223413699real_n
@ ( inf_in1974387902real_n
@ ( vimage281029891_n_nat
@ ^ [D: finite1489363574real_n] :
( ord_Least_nat
@ ^ [E: nat] : ( B @ E @ D ) )
@ C )
@ ( sigma_476185326real_n @ A ) )
@ ( sigma_1235138647real_n @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_sets__Least) ).
thf(993,plain,
! [A: sigma_1466784463real_n,B: nat > finite1489363574real_n > $o,C: set_nat] :
( ! [D: nat] :
( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ A ) )
& ( B @ D @ E ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( member223413699real_n
@ ( inf_in1974387902real_n
@ ( vimage281029891_n_nat
@ ^ [D: finite1489363574real_n] :
( ord_Least_nat
@ ^ [E: nat] : ( B @ E @ D ) )
@ C )
@ ( sigma_476185326real_n @ A ) )
@ ( sigma_1235138647real_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(119,axiom,
! [A: finite1489363574real_n > $o,B: finite1489363574real_n > $o] :
( ! [C: finite1489363574real_n] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec321817931real_n @ A )
= ( collec321817931real_n @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Collect__cong) ).
thf(712,plain,
! [A: finite1489363574real_n > $o,B: finite1489363574real_n > $o] :
( ! [C: finite1489363574real_n] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec321817931real_n @ A )
= ( collec321817931real_n @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(69,axiom,
! [A: set_Fi1058188332real_n] :
( ( collec321817931real_n
@ ^ [B: finite1489363574real_n] : ( member1352538125real_n @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Collect__mem__eq) ).
thf(557,plain,
! [A: set_Fi1058188332real_n] :
( ( collec321817931real_n
@ ^ [B: finite1489363574real_n] : ( member1352538125real_n @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(51,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Int__left__commute) ).
thf(502,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(158,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( minus_1686442501real_n @ B @ C ) )
= ( minus_1686442501real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ B ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_translation__diff) ).
thf(840,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( minus_1686442501real_n @ B @ C ) )
= ( minus_1686442501real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ B ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(303,axiom,
! [A: set_Fi1058188332real_n > finite1489363574real_n,B: sigma_1422848389real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > $o] :
( ( member1759501912real_n @ A @ ( sigma_1333364596real_n @ B @ C ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_1235138647real_n @ C ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_433815053real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_measurable__sets__Collect) ).
thf(1317,plain,
! [A: set_Fi1058188332real_n > finite1489363574real_n,B: sigma_1422848389real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > $o] :
( ( member1759501912real_n @ A @ ( sigma_1333364596real_n @ B @ C ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_1235138647real_n @ C ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_433815053real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(75,axiom,
( minus_1686442501real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ A )
& ~ ( member1352538125real_n @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_set__diff__eq) ).
thf(576,plain,
( minus_1686442501real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ A )
& ~ ( member1352538125real_n @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(10,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( image_1123376925real_n @ B @ C ) )
=> ~ ! [D: finite1489363574real_n > finite1489363574real_n] :
( ( A
= ( B @ D ) )
=> ~ ( member1746150050real_n @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_imageE) ).
thf(359,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( image_1123376925real_n @ B @ C ) )
=> ~ ! [D: finite1489363574real_n > finite1489363574real_n] :
( ( A
= ( B @ D ) )
=> ~ ( member1746150050real_n @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(249,axiom,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > $o] :
( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_607186084real_n @ A ) )
& ( B @ C ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_607186084real_n @ A ) )
& ~ ( B @ C ) ) )
@ ( sigma_433815053real_n @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_sets_Osets__Collect__neg) ).
thf(1130,plain,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > $o] :
( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_607186084real_n @ A ) )
& ( B @ C ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_607186084real_n @ A ) )
& ~ ( B @ C ) ) )
@ ( sigma_433815053real_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(96,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( member1746150050real_n @ A @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_measurable__restrict__space1) ).
thf(643,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( member1746150050real_n @ A @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(265,axiom,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,C: sigma_1422848389real_n] :
( ! [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
=> ( member223413699real_n @ ( B @ D ) @ ( sigma_607186084real_n @ C ) ) )
=> ( ! [D: set_se2111327970real_n] :
( ( member1475136633real_n @ D @ ( sigma_433815053real_n @ C ) )
=> ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage1910974324real_n @ B @ D ) @ ( sigma_1483971331real_n @ A ) ) @ ( sigma_522684908real_n @ A ) ) )
=> ( member640587117real_n @ B @ ( sigma_364818953real_n @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_measurableI) ).
thf(1188,plain,
! [A: sigma_107786596real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,C: sigma_1422848389real_n] :
( ! [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ A ) )
=> ( member223413699real_n @ ( B @ D ) @ ( sigma_607186084real_n @ C ) ) )
=> ( ! [D: set_se2111327970real_n] :
( ( member1475136633real_n @ D @ ( sigma_433815053real_n @ C ) )
=> ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage1910974324real_n @ B @ D ) @ ( sigma_1483971331real_n @ A ) ) @ ( sigma_522684908real_n @ A ) ) )
=> ( member640587117real_n @ B @ ( sigma_364818953real_n @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(264,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ B @ C ) )
=> ( member1352538125real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_vimageD) ).
thf(1186,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ B @ C ) )
=> ( member1352538125real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(316,axiom,
! [A: sigma_1466784463real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( sigma_346513458real_n @ A @ B ) @ C ) )
= ( sigma_1235138647real_n @ ( sigma_346513458real_n @ A @ ( inf_in1974387902real_n @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_sets__restrict__restrict__space) ).
thf(1358,plain,
! [A: sigma_1466784463real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( sigma_346513458real_n @ A @ B ) @ C ) )
= ( sigma_1235138647real_n @ ( sigma_346513458real_n @ A @ ( inf_in1974387902real_n @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(116,axiom,
! [A: set_Fi1058188332real_n] :
( ( image_439535603real_n
@ ^ [B: finite1489363574real_n] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_image__ident) ).
thf(703,plain,
! [A: set_Fi1058188332real_n] :
( ( image_439535603real_n
@ ^ [B: finite1489363574real_n] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(86,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > finite1489363574real_n,E: sigma_1466784463real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_439801790real_n @ C @ E ) )
=> ( member1746150050real_n
@ ^ [F: finite1489363574real_n] : ( D @ ( A @ F ) )
@ ( sigma_439801790real_n @ B @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_measurable__compose) ).
thf(613,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > finite1489363574real_n,E: sigma_1466784463real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ C ) )
=> ( ( member1746150050real_n @ D @ ( sigma_439801790real_n @ C @ E ) )
=> ( member1746150050real_n
@ ^ [F: finite1489363574real_n] : ( D @ ( A @ F ) )
@ ( sigma_439801790real_n @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(35,axiom,
( minus_725016986real_n
= ( ^ [A: set_Fi1326602817real_n,B: set_Fi1326602817real_n] :
( collec1190264032real_n
@ ( minus_391085931al_n_o
@ ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ A )
@ ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_minus__set__def) ).
thf(446,plain,
( minus_725016986real_n
= ( ^ [A: set_Fi1326602817real_n,B: set_Fi1326602817real_n] :
( collec1190264032real_n
@ ( minus_391085931al_n_o
@ ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ A )
@ ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(290,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ B @ A ) )
= ( B = zero_z200130687real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_add__cancel__right__left) ).
thf(1272,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ B @ A ) )
= ( B = zero_z200130687real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(170,axiom,
! [A: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B: set_se2111327970real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( image_352856126real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_352856126real_n @ A
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_Compr__image__eq) ).
thf(876,plain,
! [A: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B: set_se2111327970real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( image_352856126real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_352856126real_n @ A
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(165,axiom,
! [A: set_se2111327970real_n,B: sigma_1422848389real_n,C: finite1489363574real_n > finite1489363574real_n,D: sigma_107786596real_n,E: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] :
( ( member1475136633real_n @ ( inf_in632889204real_n @ A @ ( sigma_607186084real_n @ B ) ) @ ( sigma_433815053real_n @ B ) )
=> ( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ D ) )
=> ( ( member1764433517real_n @ E @ ( sigma_588796041real_n @ ( sigma_993999336real_n @ B @ A ) @ D ) )
= ( member1764433517real_n
@ ^ [F: set_Fi1058188332real_n] : ( if_Fin413489477real_n @ ( member223413699real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_588796041real_n @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_measurable__restrict__space__iff) ).
thf(859,plain,
! [A: set_se2111327970real_n,B: sigma_1422848389real_n,C: finite1489363574real_n > finite1489363574real_n,D: sigma_107786596real_n,E: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] :
( ( member1475136633real_n @ ( inf_in632889204real_n @ A @ ( sigma_607186084real_n @ B ) ) @ ( sigma_433815053real_n @ B ) )
=> ( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ D ) )
=> ( ( member1764433517real_n @ E @ ( sigma_588796041real_n @ ( sigma_993999336real_n @ B @ A ) @ D ) )
= ( member1764433517real_n
@ ^ [F: set_Fi1058188332real_n] : ( if_Fin413489477real_n @ ( member223413699real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_588796041real_n @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(206,axiom,
( inf_in632889204real_n
= ( ^ [A: set_se2111327970real_n,B: set_se2111327970real_n] :
( collec452821761real_n
@ ^ [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ A )
& ( member223413699real_n @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Int__def) ).
thf(991,plain,
( inf_in632889204real_n
= ( ^ [A: set_se2111327970real_n,B: set_se2111327970real_n] :
( collec452821761real_n
@ ^ [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ A )
& ( member223413699real_n @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(320,axiom,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: sigma_1422848389real_n,C: sigma_1422848389real_n,D: set_Fi1058188332real_n > $o] :
( ( member1734791438real_n @ A @ ( sigma_239294762real_n @ B @ C ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_433815053real_n @ C ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_433815053real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_measurable__sets__Collect) ).
thf(1372,plain,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: sigma_1422848389real_n,C: sigma_1422848389real_n,D: set_Fi1058188332real_n > $o] :
( ( member1734791438real_n @ A @ ( sigma_239294762real_n @ B @ C ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_433815053real_n @ C ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ ( sigma_607186084real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_433815053real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(80,axiom,
! [A: set_Fi1326602817real_n,B: sigma_107786596real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member2104752728real_n @ A @ ( sigma_522684908real_n @ B ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ ( sigma_1052429895real_n @ B @ A ) ) )
& ( C @ D ) ) )
@ ( sigma_522684908real_n @ ( sigma_1052429895real_n @ B @ A ) ) )
= ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ B ) )
& ( member1746150050real_n @ D @ A )
& ( C @ D ) ) )
@ ( sigma_522684908real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_sets__Collect__restrict__space__iff) ).
thf(595,plain,
! [A: set_Fi1326602817real_n,B: sigma_107786596real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member2104752728real_n @ A @ ( sigma_522684908real_n @ B ) )
=> ( ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ ( sigma_1052429895real_n @ B @ A ) ) )
& ( C @ D ) ) )
@ ( sigma_522684908real_n @ ( sigma_1052429895real_n @ B @ A ) ) )
= ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( sigma_1483971331real_n @ B ) )
& ( member1746150050real_n @ D @ A )
& ( C @ D ) ) )
@ ( sigma_522684908real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(160,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( inf_in1974387902real_n @ ( sigma_476185326real_n @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_sets_OInt__space__eq1) ).
thf(845,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( inf_in1974387902real_n @ ( sigma_476185326real_n @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(42,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member1746150050real_n @ A @ ( inf_in146441683real_n @ B @ ( collec1190264032real_n @ C ) ) )
= ( ( member1746150050real_n @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Int__Collect) ).
thf(465,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( member1746150050real_n @ A @ ( inf_in146441683real_n @ B @ ( collec1190264032real_n @ C ) ) )
= ( ( member1746150050real_n @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(236,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( minus_1037315151real_n @ A @ ( plus_p585657087real_n @ B @ C ) )
= ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_diff__add__eq__diff__diff__swap) ).
thf(1084,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( minus_1037315151real_n @ A @ ( plus_p585657087real_n @ B @ C ) )
= ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(263,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( plus_p1606848693real_n @ B @ C ) )
=> ~ ! [D: finite1489363574real_n,E: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ D @ E ) )
=> ( ( member1352538125real_n @ D @ B )
=> ~ ( member1352538125real_n @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_set__plus__elim) ).
thf(1180,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( plus_p1606848693real_n @ B @ C ) )
=> ~ ! [D: finite1489363574real_n,E: finite1489363574real_n] :
( ( A
= ( plus_p585657087real_n @ D @ E ) )
=> ( ( member1352538125real_n @ D @ B )
=> ~ ( member1352538125real_n @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(247,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( minus_1698615483real_n @ B @ C ) )
=> ~ ( member223413699real_n @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_DiffD2) ).
thf(1126,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( minus_1698615483real_n @ B @ C ) )
=> ~ ( member223413699real_n @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(241,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ ( plus_p585657087real_n @ C @ B ) )
= ( minus_1037315151real_n @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_add__diff__cancel__right) ).
thf(1108,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ ( plus_p585657087real_n @ C @ B ) )
= ( minus_1037315151real_n @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(202,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C ) )
= ( plus_p585657087real_n @ B @ ( plus_p585657087real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_add_Oleft__commute) ).
thf(976,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C ) )
= ( plus_p585657087real_n @ B @ ( plus_p585657087real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(179,axiom,
! [A: set_Fi1058188332real_n,B: finite1489363574real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
=> ( member223413699real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ B ) @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_lebesgue__sets__translation) ).
thf(903,plain,
! [A: set_Fi1058188332real_n,B: finite1489363574real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
=> ( member223413699real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ B ) @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(283,axiom,
! [A: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ A @ B ) )
= ( sigma_1235138647real_n
@ ( sigma_821351682real_n @ ( inf_in1974387902real_n @ B @ ( sigma_476185326real_n @ A ) )
@ ^ [C: finite1489363574real_n] : C
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_restrict__space__eq__vimage__algebra_H) ).
thf(1253,plain,
! [A: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ A @ B ) )
= ( sigma_1235138647real_n
@ ( sigma_821351682real_n @ ( inf_in1974387902real_n @ B @ ( sigma_476185326real_n @ A ) )
@ ^ [C: finite1489363574real_n] : C
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(150,axiom,
! [A: sigma_1466784463real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: sigma_1466784463real_n] :
( ( ( sigma_1235138647real_n @ A )
= ( sigma_1235138647real_n @ B ) )
=> ( ( ( sigma_1235138647real_n @ C )
= ( sigma_1235138647real_n @ D ) )
=> ( ( sigma_439801790real_n @ A @ C )
= ( sigma_439801790real_n @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_measurable__cong__sets) ).
thf(813,plain,
! [A: sigma_1466784463real_n,B: sigma_1466784463real_n,C: sigma_1466784463real_n,D: sigma_1466784463real_n] :
( ( ( sigma_1235138647real_n @ A )
= ( sigma_1235138647real_n @ B ) )
=> ( ( ( sigma_1235138647real_n @ C )
= ( sigma_1235138647real_n @ D ) )
=> ( ( sigma_439801790real_n @ A @ C )
= ( sigma_439801790real_n @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(131,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
= ( ! [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ A @ C ) @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_in__borel__measurable__borel) ).
thf(748,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: sigma_1466784463real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ B @ borel_676189912real_n ) )
= ( ! [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ A @ C ) @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(228,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ ( comple230862828real_n @ B ) ) )
=> ( member223413699real_n @ ( comple1390568924real_n @ B @ A ) @ ( sigma_1235138647real_n @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_main__part__sets) ).
thf(1062,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ ( comple230862828real_n @ B ) ) )
=> ( member223413699real_n @ ( comple1390568924real_n @ B @ A ) @ ( sigma_1235138647real_n @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(126,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n,D: set_Fi1058188332real_n] :
( ( A
= ( B @ C ) )
=> ( ( member1352538125real_n @ C @ D )
=> ( member1352538125real_n @ A @ ( image_439535603real_n @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_image__eqI) ).
thf(731,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n,D: set_Fi1058188332real_n] :
( ( A
= ( B @ C ) )
=> ( ( member1352538125real_n @ C @ D )
=> ( member1352538125real_n @ A @ ( image_439535603real_n @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(142,axiom,
! [A: finite1489363574real_n > set_Fi1058188332real_n,B: sigma_1466784463real_n,C: sigma_1422848389real_n,D: finite1489363574real_n] :
( ( member966061400real_n @ A @ ( sigma_566919540real_n @ B @ C ) )
=> ( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ B ) )
=> ( member223413699real_n @ ( A @ D ) @ ( sigma_607186084real_n @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_measurable__space) ).
thf(781,plain,
! [A: finite1489363574real_n > set_Fi1058188332real_n,B: sigma_1466784463real_n,C: sigma_1422848389real_n,D: finite1489363574real_n] :
( ( member966061400real_n @ A @ ( sigma_566919540real_n @ B @ C ) )
=> ( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ B ) )
=> ( member223413699real_n @ ( A @ D ) @ ( sigma_607186084real_n @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(183,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n,D: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ B )
=> ( ( member1352538125real_n @ C @ D )
=> ( member1352538125real_n @ ( plus_p585657087real_n @ A @ C ) @ ( plus_p1606848693real_n @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_set__plus__intro) ).
thf(914,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n,D: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ B )
=> ( ( member1352538125real_n @ C @ D )
=> ( member1352538125real_n @ ( plus_p585657087real_n @ A @ C ) @ ( plus_p1606848693real_n @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(296,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: finite1489363574real_n,D: sigma_1466784463real_n,E: finite1489363574real_n > finite1489363574real_n] :
( ( member223413699real_n @ ( inf_in1974387902real_n @ A @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) )
=> ( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ D ) )
=> ( ( member1746150050real_n @ E @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ B @ A ) @ D ) )
= ( member1746150050real_n
@ ^ [F: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_439801790real_n @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_measurable__restrict__space__iff) ).
thf(1294,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: finite1489363574real_n,D: sigma_1466784463real_n,E: finite1489363574real_n > finite1489363574real_n] :
( ( member223413699real_n @ ( inf_in1974387902real_n @ A @ ( sigma_476185326real_n @ B ) ) @ ( sigma_1235138647real_n @ B ) )
=> ( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ D ) )
=> ( ( member1746150050real_n @ E @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ B @ A ) @ D ) )
= ( member1746150050real_n
@ ^ [F: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_439801790real_n @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(189,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: set_Fi1058188332real_n] :
( ( ( A @ B )
= C )
=> ( ( member1352538125real_n @ C @ D )
=> ( member1352538125real_n @ B @ ( vimage1233683625real_n @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_vimageI) ).
thf(929,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: set_Fi1058188332real_n] :
( ( ( A @ B )
= C )
=> ( ( member1352538125real_n @ C @ D )
=> ( member1352538125real_n @ B @ ( vimage1233683625real_n @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(5,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( vimage180751827real_n @ B @ C ) )
=> ( member1746150050real_n @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_vimageD) ).
thf(346,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( vimage180751827real_n @ B @ C ) )
=> ( member1746150050real_n @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(66,axiom,
( inf_in146441683real_n
= ( ^ [A: set_Fi1326602817real_n,B: set_Fi1326602817real_n] :
( collec1190264032real_n
@ ( inf_in32002162al_n_o
@ ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ A )
@ ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_inf__set__def) ).
thf(549,plain,
( inf_in146441683real_n
= ( ^ [A: set_Fi1326602817real_n,B: set_Fi1326602817real_n] :
( collec1190264032real_n
@ ( inf_in32002162al_n_o
@ ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ A )
@ ^ [C: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(223,axiom,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: sigma_1422848389real_n,C: sigma_1422848389real_n,D: set_Fi1058188332real_n] :
( ( member1734791438real_n @ A @ ( sigma_239294762real_n @ B @ C ) )
=> ( ( member223413699real_n @ D @ ( sigma_607186084real_n @ B ) )
=> ( member223413699real_n @ ( A @ D ) @ ( sigma_607186084real_n @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_measurable__space) ).
thf(1045,plain,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: sigma_1422848389real_n,C: sigma_1422848389real_n,D: set_Fi1058188332real_n] :
( ( member1734791438real_n @ A @ ( sigma_239294762real_n @ B @ C ) )
=> ( ( member223413699real_n @ D @ ( sigma_607186084real_n @ B ) )
=> ( member223413699real_n @ ( A @ D ) @ ( sigma_607186084real_n @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(155,axiom,
! [A: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) )
= ( ! [B: set_Fi1058188332real_n] :
( ( member223413699real_n @ B @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ ( A @ C ) @ B ) )
@ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_borel__measurable__lebesgue__preimage__borel) ).
thf(832,plain,
! [A: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) )
= ( ! [B: set_Fi1058188332real_n] :
( ( member223413699real_n @ B @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ ( A @ C ) @ B ) )
@ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(110,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C )
= ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_diff__right__commute) ).
thf(684,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C )
= ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(199,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ B )
= ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_translation__invert) ).
thf(967,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ B )
= ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(156,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ C ) )
=> ( member223413699real_n @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_IntD2) ).
thf(835,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ C ) )
=> ( member223413699real_n @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(22,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > $o] :
( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( image_439535603real_n @ A @ B ) )
=> ( C @ D ) )
=> ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_ball__imageD) ).
thf(405,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > $o] :
( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( image_439535603real_n @ A @ B ) )
=> ( C @ D ) )
=> ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(163,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B: set_Fi1326602817real_n,C: set_Fi1058188332real_n > $o] :
( ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_128879038real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_128879038real_n @ A
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_Compr__image__eq) ).
thf(854,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B: set_Fi1326602817real_n,C: set_Fi1058188332real_n > $o] :
( ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_128879038real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_128879038real_n @ A
@ ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(281,axiom,
! [A: finite964658038_int_n] : ( member223413699real_n @ ( r @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_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(1248,plain,
! [A: finite964658038_int_n] : ( member223413699real_n @ ( r @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(146,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( plus_p585657087real_n @ A @ ( minus_1037315151real_n @ B @ C ) )
= ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_add__diff__eq) ).
thf(801,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( plus_p585657087real_n @ A @ ( minus_1037315151real_n @ B @ C ) )
= ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(3,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ B )
=> ( ~ ( member1746150050real_n @ A @ C )
=> ( member1746150050real_n @ A @ ( minus_725016986real_n @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_DiffI) ).
thf(341,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ B )
=> ( ~ ( member1746150050real_n @ A @ C )
=> ( member1746150050real_n @ A @ ( minus_725016986real_n @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(148,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ B )
=> ( ( member223413699real_n @ A @ C )
=> ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_IntI) ).
thf(807,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_se2111327970real_n] :
( ( member223413699real_n @ A @ B )
=> ( ( member223413699real_n @ A @ C )
=> ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(32,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( if_set11487206real_n @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T) ).
thf(437,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( if_set11487206real_n @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(260,axiom,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,B: sigma_107786596real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > $o] :
( ( member1695588023real_n @ A @ ( sigma_2028985427real_n @ B @ C ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_1235138647real_n @ C ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_522684908real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_measurable__sets__Collect) ).
thf(1172,plain,
! [A: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,B: sigma_107786596real_n,C: sigma_1466784463real_n,D: finite1489363574real_n > $o] :
( ( member1695588023real_n @ A @ ( sigma_2028985427real_n @ B @ C ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( sigma_476185326real_n @ C ) )
& ( D @ E ) ) )
@ ( sigma_1235138647real_n @ C ) )
=> ( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [E: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ E @ ( sigma_1483971331real_n @ B ) )
& ( D @ ( A @ E ) ) ) )
@ ( sigma_522684908real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(197,axiom,
! [A: finite964658038_int_n] :
( ( member223413699real_n @ ( t2 @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
=> ( member223413699real_n
@ ( inf_in1974387902real_n
@ ( vimage1233683625real_n
@ ^ [B: finite1489363574real_n] : ( plus_p585657087real_n @ B @ ( minkow1134813771n_real @ A ) )
@ ( t2 @ A ) )
@ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
@ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_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(960,plain,
! [A: finite964658038_int_n] :
( ( member223413699real_n @ ( t2 @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
=> ( member223413699real_n
@ ( inf_in1974387902real_n
@ ( vimage1233683625real_n
@ ^ [B: finite1489363574real_n] : ( plus_p585657087real_n @ B @ ( minkow1134813771n_real @ A ) )
@ ( t2 @ A ) )
@ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
@ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(220,axiom,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > finite1489363574real_n,C: sigma_1466784463real_n] :
( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
=> ( member1352538125real_n @ ( B @ D ) @ ( sigma_476185326real_n @ C ) ) )
=> ( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ B @ D ) @ ( sigma_476185326real_n @ A ) ) @ ( sigma_1235138647real_n @ A ) ) )
=> ( member1746150050real_n @ B @ ( sigma_439801790real_n @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_measurableI) ).
thf(1033,plain,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > finite1489363574real_n,C: sigma_1466784463real_n] :
( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
=> ( member1352538125real_n @ ( B @ D ) @ ( sigma_476185326real_n @ C ) ) )
=> ( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ B @ D ) @ ( sigma_476185326real_n @ A ) ) @ ( sigma_1235138647real_n @ A ) ) )
=> ( member1746150050real_n @ B @ ( sigma_439801790real_n @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(294,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= B )
= ( A = zero_z200130687real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_add__cancel__left__left) ).
thf(1288,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= B )
= ( A = zero_z200130687real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(267,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= ( plus_p585657087real_n @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_add__right__imp__eq) ).
thf(1197,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= ( plus_p585657087real_n @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(122,axiom,
! [A: set_Fi1326602817real_n,B: sigma_107786596real_n,C: finite1489363574real_n,D: sigma_1466784463real_n,E: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n] :
( ( member2104752728real_n @ ( inf_in146441683real_n @ A @ ( sigma_1483971331real_n @ B ) ) @ ( sigma_522684908real_n @ B ) )
=> ( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ D ) )
=> ( ( member1695588023real_n @ E @ ( sigma_2028985427real_n @ ( sigma_1052429895real_n @ B @ A ) @ D ) )
= ( member1695588023real_n
@ ^ [F: finite1489363574real_n > finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1746150050real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_2028985427real_n @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_measurable__restrict__space__iff) ).
thf(720,plain,
! [A: set_Fi1326602817real_n,B: sigma_107786596real_n,C: finite1489363574real_n,D: sigma_1466784463real_n,E: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n] :
( ( member2104752728real_n @ ( inf_in146441683real_n @ A @ ( sigma_1483971331real_n @ B ) ) @ ( sigma_522684908real_n @ B ) )
=> ( ( member1352538125real_n @ C @ ( sigma_476185326real_n @ D ) )
=> ( ( member1695588023real_n @ E @ ( sigma_2028985427real_n @ ( sigma_1052429895real_n @ B @ A ) @ D ) )
= ( member1695588023real_n
@ ^ [F: finite1489363574real_n > finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1746150050real_n @ F @ A ) @ ( E @ F ) @ C )
@ ( sigma_2028985427real_n @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(258,axiom,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > $o,C: finite1489363574real_n > $o] :
( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D )
& ( B @ D ) ) )
@ ( sigma_1235138647real_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_sets_Osets__Collect__conj) ).
thf(1165,plain,
! [A: sigma_1466784463real_n,B: finite1489363574real_n > $o,C: finite1489363574real_n > $o] :
( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_1235138647real_n @ A ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D )
& ( B @ D ) ) )
@ ( sigma_1235138647real_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(125,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_inf_Oleft__commute) ).
thf(728,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
= ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(314,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ ( minus_1686442501real_n @ ( sigma_476185326real_n @ B ) @ A ) @ ( sigma_1235138647real_n @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_sets_Ocompl__sets) ).
thf(1352,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ ( minus_1686442501real_n @ ( sigma_476185326real_n @ B ) @ A ) @ ( sigma_1235138647real_n @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(286,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ B ) @ borel_676189912real_n ) )
= ( ! [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ B )
& ( member1352538125real_n @ ( A @ D ) @ C ) ) )
@ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_borel__measurable__vimage__borel) ).
thf(1261,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( member1746150050real_n @ A @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ B ) @ borel_676189912real_n ) )
= ( ! [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ B )
& ( member1352538125real_n @ ( A @ D ) @ C ) ) )
@ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(324,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= A )
= ( B = zero_z200130687real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_add__cancel__left__right) ).
thf(1384,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( ( plus_p585657087real_n @ A @ B )
= A )
= ( B = zero_z200130687real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(322,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > $o] :
( ( member223413699real_n @ A @ ( collec452821761real_n @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_mem__Collect__eq) ).
thf(1378,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n > $o] :
( ( member223413699real_n @ A @ ( collec452821761real_n @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(59,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n,D: set_Fi1058188332real_n] :
( ( A
= ( inf_in1974387902real_n @ B @ C ) )
=> ( ( inf_in1974387902real_n @ A @ D )
= ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_boolean__algebra__cancel_Oinf1) ).
thf(528,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n,D: set_Fi1058188332real_n] :
( ( A
= ( inf_in1974387902real_n @ B @ C ) )
=> ( ( inf_in1974387902real_n @ A @ D )
= ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(40,axiom,
! [A: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( image_437359496real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_437359496real_n @ A
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_Compr__image__eq) ).
thf(459,plain,
! [A: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,C: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
( ( collec1190264032real_n
@ ^ [D: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ D @ ( image_437359496real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_437359496real_n @ A
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(181,axiom,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > $o,C: set_Fi1058188332real_n > $o] :
( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( ( C @ D )
| ( B @ D ) ) ) )
@ ( sigma_433815053real_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_sets_Osets__Collect__disj) ).
thf(908,plain,
! [A: sigma_1422848389real_n,B: set_Fi1058188332real_n > $o,C: set_Fi1058188332real_n > $o] :
( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( B @ D ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( C @ D ) ) )
@ ( sigma_433815053real_n @ A ) )
=> ( member1475136633real_n
@ ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( sigma_607186084real_n @ A ) )
& ( ( C @ D )
| ( B @ D ) ) ) )
@ ( sigma_433815053real_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(277,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > $o] :
( ( vimage1233683625real_n @ A @ ( collec321817931real_n @ B ) )
= ( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( B @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_vimage__Collect__eq) ).
thf(1236,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > $o] :
( ( vimage1233683625real_n @ A @ ( collec321817931real_n @ B ) )
= ( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( B @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(205,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: finite1489363574real_n > $o] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ ( sigma_346513458real_n @ B @ A ) ) )
& ( C @ D ) ) )
@ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ B @ A ) ) )
= ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ B ) )
& ( member1352538125real_n @ D @ A )
& ( C @ D ) ) )
@ ( sigma_1235138647real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_sets__Collect__restrict__space__iff) ).
thf(987,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: finite1489363574real_n > $o] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ ( sigma_346513458real_n @ B @ A ) ) )
& ( C @ D ) ) )
@ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ B @ A ) ) )
= ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ B ) )
& ( member1352538125real_n @ D @ A )
& ( C @ D ) ) )
@ ( sigma_1235138647real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(12,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( minus_725016986real_n @ B @ C ) )
=> ~ ( member1746150050real_n @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_DiffD2) ).
thf(369,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1326602817real_n,C: set_Fi1326602817real_n] :
( ( member1746150050real_n @ A @ ( minus_725016986real_n @ B @ C ) )
=> ~ ( member1746150050real_n @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(84,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( image_439535603real_n @ B @ C ) )
= ( ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_image__iff) ).
thf(607,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( image_439535603real_n @ B @ C ) )
= ( ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(47,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ B )
=> ( ( member1352538125real_n @ A @ C )
=> ( member1352538125real_n @ A @ ( inf_in1974387902real_n @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_IntI) ).
thf(486,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ B )
=> ( ( member1352538125real_n @ A @ C )
=> ( member1352538125real_n @ A @ ( inf_in1974387902real_n @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(304,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( plus_p585657087real_n @ ( minus_1037315151real_n @ A @ B ) @ C )
= ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_diff__add__eq) ).
thf(1320,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
( ( plus_p585657087real_n @ ( minus_1037315151real_n @ A @ B ) @ C )
= ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(213,axiom,
! [A: sigma_1466784463real_n] :
( ( sigma_439801790real_n @ lebesg260170249real_n @ A )
= ( sigma_439801790real_n @ borel_676189912real_n @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_measurable__lborel2) ).
thf(1009,plain,
! [A: sigma_1466784463real_n] :
( ( sigma_439801790real_n @ lebesg260170249real_n @ A )
= ( sigma_439801790real_n @ borel_676189912real_n @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(64,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ B )
= ( inf_in1974387902real_n @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_inf__right__idem) ).
thf(543,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ B )
= ( inf_in1974387902real_n @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(79,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1620715847al_n_o
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ A )
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ B ) )
= ( ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ ( inf_in1974387902real_n @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_inf__Int__eq) ).
thf(592,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( inf_in1620715847al_n_o
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ A )
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ B ) )
= ( ^ [C: finite1489363574real_n] : ( member1352538125real_n @ C @ ( inf_in1974387902real_n @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(11,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1326602817real_n] :
( ( A
= ( B @ C ) )
=> ( ( member1746150050real_n @ C @ D )
=> ( member1746150050real_n @ A @ ( image_1123376925real_n @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_image__eqI) ).
thf(364,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1326602817real_n] :
( ( A
= ( B @ C ) )
=> ( ( member1746150050real_n @ C @ D )
=> ( member1746150050real_n @ A @ ( image_1123376925real_n @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(319,axiom,
! [A: set_Fi1058188332real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1326602817real_n] :
( ( A
= ( B @ C ) )
=> ( ( member1746150050real_n @ C @ D )
=> ( member223413699real_n @ A @ ( image_128879038real_n @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_image__eqI) ).
thf(1367,plain,
! [A: set_Fi1058188332real_n,B: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,C: finite1489363574real_n > finite1489363574real_n,D: set_Fi1326602817real_n] :
( ( A
= ( B @ C ) )
=> ( ( member1746150050real_n @ C @ D )
=> ( member223413699real_n @ A @ ( image_128879038real_n @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(192,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_add__diff__cancel) ).
thf(940,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n] :
( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(140,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( inf_in1974387902real_n @ A @ ( sigma_476185326real_n @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_sets_OInt__space__eq2) ).
thf(775,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) )
=> ( ( inf_in1974387902real_n @ A @ ( sigma_476185326real_n @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(70,axiom,
( minus_725016986real_n
= ( ^ [A: set_Fi1326602817real_n,B: set_Fi1326602817real_n] :
( collec1190264032real_n
@ ^ [C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ C @ A )
& ~ ( member1746150050real_n @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_set__diff__eq) ).
thf(560,plain,
( minus_725016986real_n
= ( ^ [A: set_Fi1326602817real_n,B: set_Fi1326602817real_n] :
( collec1190264032real_n
@ ^ [C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ C @ A )
& ~ ( member1746150050real_n @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(49,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
= ( ( member1352538125real_n @ A @ B )
& ( member1352538125real_n @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_Int__iff) ).
thf(496,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ ( inf_in1974387902real_n @ B @ C ) )
= ( ( member1352538125real_n @ A @ B )
& ( member1352538125real_n @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(38,axiom,
! [A: sigma_107786596real_n,B: $o] :
( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ A ) )
& B ) )
@ ( sigma_522684908real_n @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_sets_Osets__Collect_I5_J) ).
thf(454,plain,
! [A: sigma_107786596real_n,B: $o] :
( member2104752728real_n
@ ( collec1190264032real_n
@ ^ [C: finite1489363574real_n > finite1489363574real_n] :
( ( member1746150050real_n @ C @ ( sigma_1483971331real_n @ A ) )
& B ) )
@ ( sigma_522684908real_n @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1487,plain,
$false,
inference(e,[status(thm)],[892,1337,628,518,666,1168,760,962,468,1211,582,1005,1406,1401,1073,1269,440,1305,873,1205,384,715,1275,340,1222,1310,533,538,1354,829,898,709,417,973,1228,651,389,724,570,1430,1298,372,1264,344,1313,934,1132,949,1323,619,917,751,817,1087,1147,870,1398,448,1100,924,756,443,1418,1136,348,353,1283,480,1334,646,1151,937,1051,821,766,687,1215,692,660,998,411,1433,428,1242,380,678,546,810,1067,1057,1387,957,1091,778,1042,625,879,852,522,1159,1392,1291,456,1012,1079,1027,551,1128,1328,1064,1111,1425,356,610,499,857,742,578,697,1234,1375,1121,420,1118,884,1361,554,669,901,489,1155,706,1039,970,985,738,1266,654,911,371,622,837,393,1114,633,508,657,1054,718,926,1202,792,906,1278,513,1103,824,745,1301,573,375,601,562,423,402,1389,843,772,1403,1256,1007,694,1428,787,1239,1332,1258,350,540,672,391,1139,919,804,1194,681,1349,996,1144,434,616,599,1307,979,604,784,1117,1048,736,451,567,863,1175,890,477,631,758,535,726,483,1325,895,1344,769,462,848,700,520,943,1022,1177,1381,868,1015,505,431,922,636,1245,1000,1435,1364,1250,675,426,663,1420,648,1081,516,1340,1018,754,1413,1076,1208,589,640,1025,1070,1225,887,414,954,993,712,557,502,840,1317,576,359,1130,643,1188,1186,1358,703,613,446,1272,876,859,991,1372,595,845,465,1084,1180,1126,1108,976,903,1253,813,748,1062,731,781,914,1294,929,346,549,1045,832,684,967,835,405,854,1248,801,341,807,437,1172,960,1033,1288,1197,720,1165,728,1352,1261,1384,1378,528,459,908,1236,987,369,607,486,1320,1009,543,592,364,1367,940,775,560,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP116^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % 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
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:59:18 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.85/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.06/1.19 % [INFO] Parsing done (412ms).
% 2.36/1.20 % [INFO] Running in sequential loop mode.
% 3.06/1.58 % [INFO] eprover registered as external prover.
% 3.06/1.59 % [INFO] Scanning for conjecture ...
% 3.46/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 361 axioms. Running axiom selection ...
% 4.09/1.92 % [INFO] Axiom selection finished. Selected 337 axioms (removed 24 axioms).
% 5.23/2.20 % [INFO] Problem is higher-order (TPTP THF).
% 5.23/2.22 % [INFO] Type checking passed.
% 5.23/2.23 % [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 ...
% 21.17/5.95 % External prover 'e' found a proof!
% 21.17/5.95 % [INFO] Killing All external provers ...
% 21.17/5.95 % Time passed: 5604ms (effective reasoning time: 4744ms)
% 21.17/5.95 % 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)>
% 21.17/5.96 % Axioms used in derivation (337): fact_13_vimageI, fact_151_measurable__space, fact_287_Diff__Int__distrib2, fact_218_Compr__image__eq, fact_274_measurable__If__restrict__space__iff, fact_32_vimageE, fact_113_measurable__sets__Collect, fact_268_space__restrict__space, fact_95_sets_OInt__space__eq2, fact_276_sets__lebesgue__on__refl, fact_275_space__lebesgue__on, fact_266_borel__measurable__add, fact_85_Collect__cong, fact_308_minus__set__def, fact_35_vimageE, fact_190_measurable__restrict__space__iff, fact_102_measurableI, fact_225_imageE, fact_36_vimageE, fact_286_Diff__Int__distrib, fact_150_measurable__space, fact_270_sets__Collect__restrict__space__iff, fact_319_translation__Int, fact_339_diff__0__right, fact_59_Int__left__commute, fact_298_restrict__restrict__space, fact_29_vimageD, fact_69_add__right__imp__eq, fact_62_Int__Collect, fact_166_sets_Osets__Collect__neg, fact_179_inf__Int__eq, help_If_1_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T, fact_322_affine__parallel__expl__aux, fact_115_measurable__sets__Collect, fact_229_imageE, fact_216_Compr__image__eq, fact_143_measurable__id, fact_156_measurable__cong, fact_161_sets_Osets__Collect__imp, fact_21_set__plus__intro, fact_217_Compr__image__eq, fact_121_inf_Oright__idem, fact_263_vimage__algebra__cong, fact_178_inf__Int__eq, fact_14_vimageI, fact_10_vimageI, fact_49_IntD1, fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_16_vimage__eq, fact_8_vimage__ident, fact_227_imageE, fact_84_Collect__mem__eq, fact_271_sets__Collect__restrict__space__iff, fact_241_image__iff, fact_9_vimage__Collect__eq, fact_272_sets__Collect__restrict__space__iff, fact_12_vimageI, fact_296_borel__measurable__vimage__borel, fact_94_vimageI2, fact_235_rev__image__eqI, fact_320_translation__invert, fact_300_Diff__iff, fact_131_inf__commute, fact_299_is__borel__def, fact_232_diff__eq__diff__eq, fact_305_set__diff__eq, fact_127_inf__set__def, fact_313_DiffD1, fact_206_add__diff__cancel__left_H, fact_107_sets_Otop, fact_349_Least__eq__0, fact_173_sets_Osets__Collect__const, fact_138_inf__sup__aci_I2_J, fact_224_image__image, 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_237_rev__image__eqI, fact_132_inf_Ocommute, fact_56_Int__absorb, fact_332_add__cancel__right__left, fact_126_inf__set__def, fact_309_minus__set__def, fact_80_mem__Collect__eq, fact_311_DiffD2, fact_30_vimageD, fact_180_inf__Int__eq, fact_174_sets_Osets__Collect__const, fact_54_IntD2, fact_345_image__add__0, fact_273_measurable__equality__set, fact_330_add__cancel__left__right, fact_111_measurable__sets__Collect, fact_245_imageI, fact_41_Int__iff, fact_282_sets__lborel, fact_199_image__eqI, fact_65_Int__def, fact_259_eq__diff__eq, fact_5__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_289_sets__restrict__space, fact_192_sets__Least, fact_240_bex__imageD, fact_92_vimageI2, fact_17_vimage__eq, fact_348_eq__add__iff, fact_125_inf_Oidem, fact_128_inf__set__def, fact_323_borel__measurable__if, fact_47_IntE, fact_265_borel__measurable__const__add, fact_172_sets_Osets__Collect__disj, fact_38_IntI, fact_328_add__cancel__left__left, fact_307_minus__set__def, fact_251_add__implies__diff, fact_96_sets_OInt__space__eq1, fact_253_diff__diff__add, fact_316_translation__subtract__diff, fact_28_vimageD, fact_88_ab__semigroup__add__class_Oadd__ac_I1_J, fact_182_measurable__restrict__space__iff, fact_285_Diff__Diff__Int, fact_124_inf__idem, fact_222_Compr__image__eq, fact_116_measurable__sets__Collect, fact_324_add_Oleft__neutral, fact_144_measurable__cong__sets, fact_75_add_Oassoc, fact_19_vimage__eq, fact_269_measurable__sets__borel, fact_154_measurable__space, fact_164_sets_Osets__Collect__neg, fact_135_boolean__algebra__cancel_Oinf2, fact_86_group__cancel_Oadd1, fact_6_sets__completionI__sets, fact_106_measurableI, fact_185_measurable__restrict__space__iff, fact_79_mem__Collect__eq, fact_212_main__part, fact_223_Compr__image__eq, fact_169_sets_Osets__Collect__conj, fact_55_Int__assoc, fact_315_DiffE, fact_67_measurable__completion, fact_304_set__diff__eq, fact_11_vimageI, fact_246_imageI, fact_50_IntD1, fact_220_Compr__image__eq, fact_34_vimageE, fact_45_T__def, fact_97_measurable__sets, fact_302_DiffI, fact_219_Compr__image__eq, fact_63_Int__Collect, fact_165_sets_Osets__Collect__neg, fact_25_vimage__def, fact_341_diff__zero, fact_120_inf__right__idem, fact_39_IntI, help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T, fact_247_borel__measurable__const, fact_70_add__left__imp__eq, fact_264_vimage__algebra__cong, fact_176_measurable__const, fact_52_IntD2, fact_18_vimage__eq, fact_145_sets__eq__imp__space__eq, fact_221_Compr__image__eq, fact_105_measurableI, fact_193_sets__Least, fact_226_imageE, fact_233_rev__image__eqI, fact_43_space__completion, fact_108_sets_OInt, fact_280_sets_ODiff, fact_314_DiffE, fact_293_lebesgue__sets__translation, fact_163_sets_Osets__Collect__imp, fact_160_sets_Osets__Collect_I5_J, fact_89_vimage__Collect, fact_236_rev__image__eqI, fact_297_restrict__space__eq__vimage__algebra_H, fact_157_measurable__ident__sets, fact_20_set__plus__intro, fact_147_measurable__space, fact_77_set__plus__elim, fact_210_diff__add__cancel, fact_312_DiffD1, fact_61_Int__Collect, fact_58_Int__left__absorb, fact_118_measurable__sets__Collect, fact_78_group__cancel_Oadd2, fact_181_main__part__sets, fact_153_measurable__space, fact_294_lebesgue__measurable__vimage__borel, fact_40_Int__iff, fact_48_IntE, fact_257_diff__diff__eq2, help_If_3_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T, fact_338_diff__self, fact_211_add__diff__cancel, fact_90_vimageI2, fact_91_vimageI2, fact_140_inf__sup__aci_I4_J, help_If_2_1_If_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T, fact_4_T_H__altdef, fact_26_vimage__def, fact_183_measurable__restrict__space__iff, fact_60_Collect__conj__eq, fact_255_diff__add__eq__diff__diff__swap, fact_1_of__int__vec__eq__iff, fact_33_vimageE, fact_37_IntI, fact_326_add_Oright__neutral, fact_189_measurable__restrict__space__iff, fact_170_sets_Osets__Collect__disj, fact_74_add_Oleft__cancel, fact_291_measurable__lebesgue__cong, fact_292_lborelD__Collect, fact_277_space__lborel, fact_228_imageE, fact_188_measurable__restrict__space__iff, fact_82_Collect__mem__eq, fact_100_measurableI, fact_284_Diff__Int2, fact_290_lborelD, fact_98_measurableI, fact_306_set__diff__eq, fact_122_inf__left__idem, fact_215_Compr__image__eq, fact_197_image__eqI, fact_343_cancel__comm__monoid__add__class_Odiff__cancel, fact_117_measurable__sets__Collect, fact_109_measurable__If__set, fact_295_borel__measurable__lebesgue__preimage__borel, fact_103_measurableI, fact_66_Int__def, fact_155_measurable__space, fact_202_add__diff__cancel__right_H, fact_198_image__eqI, fact_141_measurable__compose__rev, fact_184_measurable__restrict__space__iff, fact_186_measurable__restrict__space__iff, fact_27_vimageD, help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T, fact_234_rev__image__eqI, fact_31_vimageD, fact_64_Int__def, fact_110_measurable__sets__Collect, help_If_2_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T, fact_187_measurable__restrict__space__iff, fact_87_add__mono__thms__linordered__semiring_I4_J, fact_73_add_Oright__cancel, 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_130_inf_Oleft__commute, fact_208_add__diff__cancel__left, fact_93_vimageI2, fact_238_ball__imageD, fact_250_measurable__restrict__space1, fact_46_IntE, fact_248_sets__restrict__space__cong, fact_239_image__cong, fact_321_translation__assoc, fact_249_restrict__space__sets__cong, fact_256_diff__add__eq, fact_129_inf__left__commute, fact_262_sets__vimage__algebra__cong, fact_136_boolean__algebra__cancel_Oinf1, fact_76_set__plus__elim, help_If_1_1_If_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T, fact_244_imageI, fact_123_inf_Oleft__idem, fact_194_in__vimage__algebra, fact_57_Int__commute, fact_72_add_Ocommute, fact_177_T_H__def, fact_261_group__cancel_Osub1, fact_159_sets_Osets__Collect_I5_J, fact_167_sets_Osets__Collect__conj, fact_15_vimage__eq, fact_168_sets_Osets__Collect__conj, fact_51_IntD1, fact_133_inf__assoc, fact_99_measurableI, fact_281_sets_Ocompl__sets, fact_112_measurable__sets__Collect, fact_81_mem__Collect__eq, fact_83_Collect__mem__eq, fact_22_add__left__cancel, fact_258_add__diff__eq, fact_267_sets__restrict__restrict__space, fact_214_borel__measurable__diff, fact_53_IntD2, fact_134_inf_Oassoc, fact_68_vimage__inter__cong, fact_318_translation__diff, fact_171_sets_Osets__Collect__disj, fact_44_vimage__Int, fact_71_add_Oleft__commute, fact_213_space__restrict__space2, fact_201_image__ident, fact_0_assms_I1_J, fact_195_in__borel__measurable__borel, fact_142_measurable__compose, fact_101_measurableI, fact_243_imageI, fact_288_vimage__Diff, fact_334_add__cancel__right__right, fact_146_measurable__cong__simp, fact_278_measurable__lborel1, fact_104_measurableI, fact_301_Diff__iff, fact_137_inf__sup__aci_I1_J, fact_317_translation__subtract__Int, fact_191_sets__Least, fact_200_image__eqI, fact_152_measurable__space, fact_42_Int__iff, fact_114_measurable__sets__Collect, fact_204_add__diff__cancel__right, fact_310_DiffD2, fact_242_imageI, fact_23_add__right__cancel, fact_139_inf__sup__aci_I3_J, fact_175_sets_Osets__Collect__const, fact_149_measurable__space, fact_158_sets_Osets__Collect_I5_J, fact_230_diff__right__commute, fact_303_DiffI, fact_283_Int__Diff, fact_260_diff__eq__eq, fact_196_image__eqI, fact_162_sets_Osets__Collect__imp, fact_24_vimage__def, fact_279_measurable__lborel2, fact_119_measurable__If, fact_148_measurable__space
% 21.17/5.96 % No. of inferences in proof: 678
% 21.17/5.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5604 ms resp. 4744 ms w/o parsing
% 22.88/6.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.88/6.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------