%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP117^1 : 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 : n012.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 13.95s 3.57s
% Output : Refutation 14.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 265
% Syntax : Number of formulae : 578 ( 345 unt; 0 typ; 1 def)
% Number of atoms : 1248 ( 636 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 4827 ( 152 ~; 44 |; 115 &;4105 @)
% ( 0 <=>; 411 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 19 ( 18 usr)
% Number of type conns : 495 ( 495 >; 0 *; 0 +; 0 <<)
% Number of symbols : 89 ( 86 usr; 15 con; 0-2 aty)
% Number of variables : 1725 ( 220 ^;1411 !; 93 ?;1725 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sigma_1422848389real_n_type,type,
sigma_1422848389real_n: $tType ).
thf(set_Si1125517487real_n_type,type,
set_Si1125517487real_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_se944069346_int_n_type,type,
set_se944069346_int_n: $tType ).
thf(set_Fi1058188332real_n_type,type,
set_Fi1058188332real_n: $tType ).
thf(set_Fi160064172_int_n_type,type,
set_Fi160064172_int_n: $tType ).
thf(finite1489363574real_n_type,type,
finite1489363574real_n: $tType ).
thf(finite964658038_int_n_type,type,
finite964658038_int_n: $tType ).
thf(set_Ex113815278nnreal_type,type,
set_Ex113815278nnreal: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(extend1728876344nnreal_type,type,
extend1728876344nnreal: $tType ).
thf(sigma_measure_o_type,type,
sigma_measure_o: $tType ).
thf(set_set_o_type,type,
set_set_o: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(set_o_type,type,
set_o: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(comple1413366923nnreal_decl,type,
comple1413366923nnreal: set_Ex113815278nnreal > extend1728876344nnreal ).
thf(comple2042271945real_n_decl,type,
comple2042271945real_n: set_Fi1058188332real_n > finite1489363574real_n ).
thf(comple970917503_int_n_decl,type,
comple970917503_int_n: set_se944069346_int_n > set_Fi160064172_int_n ).
thf(comple825005695real_n_decl,type,
comple825005695real_n: set_se2111327970real_n > set_Fi1058188332real_n ).
thf(comple1682161881et_nat_decl,type,
comple1682161881et_nat: set_set_nat > set_nat ).
thf(comple488165692real_n_decl,type,
comple488165692real_n: set_Si1125517487real_n > sigma_1466784463real_n ).
thf(comple230862828real_n_decl,type,
comple230862828real_n: sigma_1466784463real_n > sigma_1466784463real_n ).
thf(counta1142393929_int_n_decl,type,
counta1142393929_int_n: set_Fi160064172_int_n > nat > finite964658038_int_n ).
thf(minus_1196255695_int_n_decl,type,
minus_1196255695_int_n: finite964658038_int_n > finite964658038_int_n > finite964658038_int_n ).
thf(minus_1037315151real_n_decl,type,
minus_1037315151real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
thf(minus_1686442501real_n_decl,type,
minus_1686442501real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(one_on705384445nnreal_decl,type,
one_on705384445nnreal: extend1728876344nnreal ).
thf(one_on1253059131real_n_decl,type,
one_on1253059131real_n: finite1489363574real_n ).
thf(plus_p1763960001nnreal_decl,type,
plus_p1763960001nnreal: extend1728876344nnreal > extend1728876344nnreal > extend1728876344nnreal ).
thf(plus_p1654784127_int_n_decl,type,
plus_p1654784127_int_n: finite964658038_int_n > finite964658038_int_n > finite964658038_int_n ).
thf(plus_p585657087real_n_decl,type,
plus_p585657087real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
thf(zero_z1963244097nnreal_decl,type,
zero_z1963244097nnreal: extend1728876344nnreal ).
thf(zero_z200130687real_n_decl,type,
zero_z200130687real_n: finite1489363574real_n ).
thf(inf_in1108485182_int_n_decl,type,
inf_in1108485182_int_n: set_Fi160064172_int_n > set_Fi160064172_int_n > set_Fi160064172_int_n ).
thf(inf_in1974387902real_n_decl,type,
inf_in1974387902real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(inf_inf_set_nat_decl,type,
inf_inf_set_nat: set_nat > set_nat > set_nat ).
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(measur1402256771real_n_decl,type,
measur1402256771real_n: sigma_1466784463real_n > set_se2111327970real_n ).
thf(minkow1134813771n_real_decl,type,
minkow1134813771n_real: finite964658038_int_n > finite1489363574real_n ).
thf(ord_le2133614988nnreal_decl,type,
ord_le2133614988nnreal: extend1728876344nnreal > extend1728876344nnreal > $o ).
thf(top_to287930409nt_n_o_decl,type,
top_to287930409nt_n_o: finite964658038_int_n > $o ).
thf(top_top_nat_o_decl,type,
top_top_nat_o: nat > $o ).
thf(top_to1845833192nnreal_decl,type,
top_to1845833192nnreal: extend1728876344nnreal ).
thf(top_to131672412_int_n_decl,type,
top_to131672412_int_n: set_Fi160064172_int_n ).
thf(top_to1292442332real_n_decl,type,
top_to1292442332real_n: set_Fi1058188332real_n ).
thf(top_top_set_nat_decl,type,
top_top_set_nat: set_nat ).
thf(top_to20708754real_n_decl,type,
top_to20708754real_n: set_se2111327970real_n ).
thf(sums_E1192373732nnreal_decl,type,
sums_E1192373732nnreal: ( nat > extend1728876344nnreal ) > extend1728876344nnreal > $o ).
thf(collec1941932235_int_n_decl,type,
collec1941932235_int_n: ( finite964658038_int_n > $o ) > set_Fi160064172_int_n ).
thf(collec321817931real_n_decl,type,
collec321817931real_n: ( finite1489363574real_n > $o ) > set_Fi1058188332real_n ).
thf(collect_nat_decl,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(collec452821761real_n_decl,type,
collec452821761real_n: ( set_Fi1058188332real_n > $o ) > set_se2111327970real_n ).
thf(image_1599934780real_n_decl,type,
image_1599934780real_n: ( $o > sigma_1466784463real_n ) > set_o > set_Si1125517487real_n ).
thf(image_2066995319nnreal_decl,type,
image_2066995319nnreal: ( extend1728876344nnreal > extend1728876344nnreal ) > set_Ex113815278nnreal > set_Ex113815278nnreal ).
thf(image_1278151539_int_n_decl,type,
image_1278151539_int_n: ( finite964658038_int_n > finite964658038_int_n ) > set_Fi160064172_int_n > set_Fi160064172_int_n ).
thf(image_2058828787real_n_decl,type,
image_2058828787real_n: ( finite964658038_int_n > finite1489363574real_n ) > set_Fi160064172_int_n > set_Fi1058188332real_n ).
thf(image_497739341_n_nat_decl,type,
image_497739341_n_nat: ( finite964658038_int_n > nat ) > set_Fi160064172_int_n > set_nat ).
thf(image_1819506345_int_n_decl,type,
image_1819506345_int_n: ( finite964658038_int_n > set_Fi160064172_int_n ) > set_Fi160064172_int_n > set_se944069346_int_n ).
thf(image_355963305real_n_decl,type,
image_355963305real_n: ( finite964658038_int_n > set_Fi1058188332real_n ) > set_Fi160064172_int_n > set_se2111327970real_n ).
thf(image_1085873667et_nat_decl,type,
image_1085873667et_nat: ( finite964658038_int_n > set_nat ) > set_Fi160064172_int_n > set_set_nat ).
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_1961920973_int_n_decl,type,
image_1961920973_int_n: ( nat > finite964658038_int_n ) > set_nat > set_Fi160064172_int_n ).
thf(image_183184717real_n_decl,type,
image_183184717real_n: ( nat > finite1489363574real_n ) > set_nat > set_Fi1058188332real_n ).
thf(image_nat_nat_decl,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(image_968789251_int_n_decl,type,
image_968789251_int_n: ( nat > set_Fi160064172_int_n ) > set_nat > set_se944069346_int_n ).
thf(image_1856576259real_n_decl,type,
image_1856576259real_n: ( nat > set_Fi1058188332real_n ) > set_nat > set_se2111327970real_n ).
thf(image_nat_set_nat_decl,type,
image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
thf(image_792439519real_n_decl,type,
image_792439519real_n: ( set_Fi160064172_int_n > set_Fi1058188332real_n ) > set_se944069346_int_n > set_se2111327970real_n ).
thf(image_1661509983real_n_decl,type,
image_1661509983real_n: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_se2111327970real_n ).
thf(image_987430492real_n_decl,type,
image_987430492real_n: ( set_Fi1058188332real_n > sigma_1466784463real_n ) > set_se2111327970real_n > set_Si1125517487real_n ).
thf(image_933134521real_n_decl,type,
image_933134521real_n: ( set_nat > set_Fi1058188332real_n ) > set_set_nat > set_se2111327970real_n ).
thf(image_1298280374real_n_decl,type,
image_1298280374real_n: ( sigma_1466784463real_n > set_Fi1058188332real_n ) > set_Si1125517487real_n > set_se2111327970real_n ).
thf(vimage1122713129_int_n_decl,type,
vimage1122713129_int_n: ( finite964658038_int_n > finite964658038_int_n ) > set_Fi160064172_int_n > set_Fi160064172_int_n ).
thf(vimage1276736425real_n_decl,type,
vimage1276736425real_n: ( finite964658038_int_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi160064172_int_n ).
thf(vimage1398021123_n_nat_decl,type,
vimage1398021123_n_nat: ( finite964658038_int_n > nat ) > set_nat > set_Fi160064172_int_n ).
thf(vimage464515423real_n_decl,type,
vimage464515423real_n: ( finite964658038_int_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_Fi160064172_int_n ).
thf(vimage1233683625real_n_decl,type,
vimage1233683625real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(vimage714719107_int_n_decl,type,
vimage714719107_int_n: ( nat > finite964658038_int_n ) > set_Fi160064172_int_n > set_nat ).
thf(vimage1860757507real_n_decl,type,
vimage1860757507real_n: ( nat > finite1489363574real_n ) > set_Fi1058188332real_n > set_nat ).
thf(vimage_nat_nat_decl,type,
vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(vimage3210681real_n_decl,type,
vimage3210681real_n: ( nat > set_Fi1058188332real_n ) > set_se2111327970real_n > set_nat ).
thf(sigma_1536574303real_n_decl,type,
sigma_1536574303real_n: sigma_1466784463real_n > set_Fi1058188332real_n > extend1728876344nnreal ).
thf(sigma_1235138647real_n_decl,type,
sigma_1235138647real_n: sigma_1466784463real_n > set_se2111327970real_n ).
thf(sigma_476185326real_n_decl,type,
sigma_476185326real_n: sigma_1466784463real_n > set_Fi1058188332real_n ).
thf(member_o_decl,type,
member_o: $o > set_o > $o ).
thf(member1217042383nnreal_decl,type,
member1217042383nnreal: extend1728876344nnreal > set_Ex113815278nnreal > $o ).
thf(member27055245_int_n_decl,type,
member27055245_int_n: finite964658038_int_n > set_Fi160064172_int_n > $o ).
thf(member1352538125real_n_decl,type,
member1352538125real_n: finite1489363574real_n > set_Fi1058188332real_n > $o ).
thf(member_nat_decl,type,
member_nat: nat > set_nat > $o ).
thf(member223413699real_n_decl,type,
member223413699real_n: set_Fi1058188332real_n > set_se2111327970real_n > $o ).
thf(member1000184real_n_decl,type,
member1000184real_n: sigma_1466784463real_n > set_Si1125517487real_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(f_decl,type,
f: nat > finite964658038_int_n ).
thf(sk47_decl,type,
sk47: set_Fi1058188332real_n > set_Si1125517487real_n > sigma_1466784463real_n ).
thf(sk71_decl,type,
sk71: nat ).
thf(sk72_decl,type,
sk72: nat ).
thf(sk47_def,definition,
( sk47
= ( ^ [A: set_Fi1058188332real_n,B: set_Si1125517487real_n] :
@+[C: sigma_1466784463real_n] :
~ ( ( member1000184real_n @ C @ B )
=> ( ( sigma_476185326real_n @ C )
= A ) ) ) ) ).
thf(98,axiom,
! [A: finite964658038_int_n] : ( member27055245_int_n @ A @ top_to131672412_int_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_UNIV__I) ).
thf(628,plain,
! [A: finite964658038_int_n] : ( member27055245_int_n @ A @ top_to131672412_int_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(629,plain,
! [A: finite964658038_int_n] : ( member27055245_int_n @ A @ top_to131672412_int_n ),
inference(cnf,[status(esa)],[628]) ).
thf(209,axiom,
! [A: set_Fi1058188332real_n] :
( ( vimage1233683625real_n
@ ^ [B: finite1489363574real_n] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_vimage__ident) ).
thf(1024,plain,
! [A: set_Fi1058188332real_n] :
( ( vimage1233683625real_n
@ ^ [B: finite1489363574real_n] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(57,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_252_Int__def) ).
thf(478,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)],[57]) ).
thf(479,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(lifteq,[status(thm)],[478]) ).
thf(168,axiom,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n] :
( ( image_1856576259real_n
@ ^ [C: nat] : ( A @ ( B @ C ) )
@ top_top_set_nat )
= ( image_1661509983real_n @ A @ ( image_1856576259real_n @ B @ top_top_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_range__composition) ).
thf(893,plain,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n] :
( ( image_1856576259real_n
@ ^ [C: nat] : ( A @ ( B @ C ) )
@ top_top_set_nat )
= ( image_1661509983real_n @ A @ ( image_1856576259real_n @ B @ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(233,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_128_Diff__Int__distrib) ).
thf(1110,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)],[233]) ).
thf(27,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n] :
( ( A
= ( B @ C ) )
=> ( member1352538125real_n @ A @ ( image_439535603real_n @ B @ top_to1292442332real_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_range__eqI) ).
thf(352,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,C: finite1489363574real_n] :
( ( A
= ( B @ C ) )
=> ( member1352538125real_n @ A @ ( image_439535603real_n @ B @ top_to1292442332real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(251,axiom,
( t2
= ( ^ [A: finite964658038_int_n] : ( inf_in1974387902real_n @ s @ ( r @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_T__def) ).
thf(1168,plain,
( t2
= ( ^ [A: finite964658038_int_n] : ( inf_in1974387902real_n @ s @ ( r @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(135,axiom,
! [A: $o,B: set_o,C: $o > sigma_1466784463real_n,D: set_Fi1058188332real_n,E: set_Fi1058188332real_n] :
( ( member_o @ A @ B )
=> ( ! [F: $o] :
( ( member_o @ F @ B )
=> ( ( sigma_476185326real_n @ ( C @ F ) )
= D ) )
=> ( ( member223413699real_n @ E @ ( sigma_1235138647real_n @ ( C @ A ) ) )
=> ( member223413699real_n @ E @ ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_1599934780real_n @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_in__sets__SUP) ).
thf(760,plain,
! [A: $o,B: set_o,C: $o > sigma_1466784463real_n,D: set_Fi1058188332real_n,E: set_Fi1058188332real_n] :
( ( member_o @ A @ B )
=> ( ! [F: $o] :
( ( member_o @ F @ B )
=> ( ( sigma_476185326real_n @ ( C @ F ) )
= D ) )
=> ( ( member223413699real_n @ E @ ( sigma_1235138647real_n @ ( C @ A ) ) )
=> ( member223413699real_n @ E @ ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_1599934780real_n @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(173,axiom,
( top_top_set_nat
= ( collect_nat @ top_top_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_top__set__def) ).
thf(908,plain,
( top_top_set_nat
= ( collect_nat @ top_top_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(909,plain,
( ( collect_nat @ top_top_nat_o )
= top_top_set_nat ),
inference(lifteq,[status(thm)],[908]) ).
thf(247,axiom,
( s
= ( comple825005695real_n @ ( image_355963305real_n @ t2 @ top_to131672412_int_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_S__decompose) ).
thf(1158,plain,
( s
= ( comple825005695real_n @ ( image_355963305real_n @ t2 @ top_to131672412_int_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(203,axiom,
! [A: nat > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( image_183184717real_n @ A @ ( vimage1860757507real_n @ A @ B ) )
= ( inf_in1974387902real_n @ B @ ( image_183184717real_n @ A @ top_top_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_image__vimage__eq) ).
thf(1005,plain,
! [A: nat > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( image_183184717real_n @ A @ ( vimage1860757507real_n @ A @ B ) )
= ( inf_in1974387902real_n @ B @ ( image_183184717real_n @ A @ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(113,axiom,
! [A: set_Fi160064172_int_n] :
( ( inf_in1108485182_int_n @ top_to131672412_int_n @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_Int__UNIV__left) ).
thf(683,plain,
! [A: set_Fi160064172_int_n] :
( ( inf_in1108485182_int_n @ top_to131672412_int_n @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(6,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_226_Compr__image__eq) ).
thf(276,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)],[6]) ).
thf(162,axiom,
! [A: set_nat,B: set_nat] :
( ( ( inf_inf_set_nat @ A @ B )
= top_top_set_nat )
= ( ( A = top_top_set_nat )
& ( B = top_top_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Int__UNIV) ).
thf(873,plain,
! [A: set_nat,B: set_nat] :
( ( ( inf_inf_set_nat @ A @ B )
= top_top_set_nat )
= ( ( A = top_top_set_nat )
& ( B = top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(66,axiom,
( ( comple825005695real_n @ top_to20708754real_n )
= top_to1292442332real_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Sup__UNIV) ).
thf(511,plain,
( ( comple825005695real_n @ top_to20708754real_n )
= top_to1292442332real_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(111,axiom,
! [A: set_nat] :
( ( inf_inf_set_nat @ A @ top_top_set_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_Int__UNIV__right) ).
thf(677,plain,
! [A: set_nat] :
( ( inf_inf_set_nat @ A @ top_top_set_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(241,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: finite964658038_int_n] : ( member223413699real_n @ ( A @ B ) @ ( image_355963305real_n @ A @ top_to131672412_int_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_rangeI) ).
thf(1142,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: finite964658038_int_n] : ( member223413699real_n @ ( A @ B ) @ ( image_355963305real_n @ A @ top_to131672412_int_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(33,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n] :
( ! [C: finite1489363574real_n] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_439535603real_n @ A @ top_to1292442332real_n )
= top_to1292442332real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_surjI) ).
thf(379,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n] :
( ! [C: finite1489363574real_n] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_439535603real_n @ A @ top_to1292442332real_n )
= top_to1292442332real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(225,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 ) ) )
@ ( measur1402256771real_n @ A ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D ) ) )
@ ( measur1402256771real_n @ A ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D )
& ( B @ D ) ) )
@ ( measur1402256771real_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_null__sets_Osets__Collect__conj) ).
thf(1078,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 ) ) )
@ ( measur1402256771real_n @ A ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D ) ) )
@ ( measur1402256771real_n @ A ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D )
& ( B @ D ) ) )
@ ( measur1402256771real_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(121,axiom,
! [A: finite1489363574real_n] :
( ( image_439535603real_n
@ ^ [B: finite1489363574real_n] : ( minus_1037315151real_n @ B @ A )
@ top_to1292442332real_n )
= top_to1292442332real_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_surj__diff__right) ).
thf(715,plain,
! [A: finite1489363574real_n] :
( ( image_439535603real_n
@ ^ [B: finite1489363574real_n] : ( minus_1037315151real_n @ B @ A )
@ top_to1292442332real_n )
= top_to1292442332real_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(145,axiom,
~ ( ord_le2133614988nnreal @ zero_z1963244097nnreal @ zero_z1963244097nnreal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_less__numeral__extra_I3_J) ).
thf(813,plain,
~ ( ord_le2133614988nnreal @ zero_z1963244097nnreal @ zero_z1963244097nnreal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(814,plain,
~ ( ord_le2133614988nnreal @ zero_z1963244097nnreal @ zero_z1963244097nnreal ),
inference(polarity_switch,[status(thm)],[813]) ).
thf(175,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi160064172_int_n,C: set_Fi160064172_int_n] :
( ( comple825005695real_n @ ( image_355963305real_n @ A @ ( comple970917503_int_n @ ( image_1819506345_int_n @ B @ C ) ) ) )
= ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( comple825005695real_n @ ( image_355963305real_n @ A @ ( B @ D ) ) )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_UN__UN__flatten) ).
thf(913,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi160064172_int_n,C: set_Fi160064172_int_n] :
( ( comple825005695real_n @ ( image_355963305real_n @ A @ ( comple970917503_int_n @ ( image_1819506345_int_n @ B @ C ) ) ) )
= ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( comple825005695real_n @ ( image_355963305real_n @ A @ ( B @ D ) ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(180,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_se944069346_int_n] :
( ( comple825005695real_n
@ ( image_792439519real_n
@ ^ [C: set_Fi160064172_int_n] : ( comple825005695real_n @ ( image_355963305real_n @ A @ C ) )
@ B ) )
= ( comple825005695real_n @ ( image_355963305real_n @ A @ ( comple970917503_int_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_UN__extend__simps_I8_J) ).
thf(930,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_se944069346_int_n] :
( ( comple825005695real_n
@ ( image_792439519real_n
@ ^ [C: set_Fi160064172_int_n] : ( comple825005695real_n @ ( image_355963305real_n @ A @ C ) )
@ B ) )
= ( comple825005695real_n @ ( image_355963305real_n @ A @ ( comple970917503_int_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(262,axiom,
( sums_E1192373732nnreal
@ ^ [A: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ A ) ) )
@ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_calculation) ).
thf(1196,plain,
( sums_E1192373732nnreal
@ ^ [A: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ A ) ) )
@ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(152,axiom,
! [A: set_Si1125517487real_n,B: set_Fi1058188332real_n,C: sigma_1466784463real_n,D: set_Fi1058188332real_n] :
( ! [E: sigma_1466784463real_n] :
( ( member1000184real_n @ E @ A )
=> ( ( sigma_476185326real_n @ E )
= B ) )
=> ( ( member1000184real_n @ C @ A )
=> ( ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
=> ( member223413699real_n @ D @ ( sigma_1235138647real_n @ ( comple488165692real_n @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_in__sets__Sup) ).
thf(836,plain,
! [A: set_Si1125517487real_n,B: set_Fi1058188332real_n,C: sigma_1466784463real_n,D: set_Fi1058188332real_n] :
( ! [E: sigma_1466784463real_n] :
( ( member1000184real_n @ E @ A )
=> ( ( sigma_476185326real_n @ E )
= B ) )
=> ( ( member1000184real_n @ C @ A )
=> ( ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
=> ( member223413699real_n @ D @ ( sigma_1235138647real_n @ ( comple488165692real_n @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(837,plain,
! [A: set_Si1125517487real_n] :
( ? [B: set_Fi1058188332real_n] :
! [C: sigma_1466784463real_n] :
( ( member1000184real_n @ C @ A )
=> ( ( sigma_476185326real_n @ C )
= B ) )
=> ! [B: sigma_1466784463real_n] :
( ( member1000184real_n @ B @ A )
=> ! [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ C @ ( sigma_1235138647real_n @ ( comple488165692real_n @ A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[836]) ).
thf(838,plain,
! [D: set_Fi1058188332real_n,C: sigma_1466784463real_n,B: set_Fi1058188332real_n,A: set_Si1125517487real_n] :
( ( ( member1000184real_n @ ( sk47 @ B @ A ) @ A )
| ~ ( member1000184real_n @ C @ A )
| ~ ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
| ( member223413699real_n @ D @ ( sigma_1235138647real_n @ ( comple488165692real_n @ A ) ) ) )
& ( ( ( sigma_476185326real_n @ ( sk47 @ B @ A ) )
!= B )
| ~ ( member1000184real_n @ C @ A )
| ~ ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
| ( member223413699real_n @ D @ ( sigma_1235138647real_n @ ( comple488165692real_n @ A ) ) ) ) ),
inference(cnf,[status(esa)],[837]) ).
thf(840,plain,
! [D: set_Fi1058188332real_n,C: sigma_1466784463real_n,B: set_Fi1058188332real_n,A: set_Si1125517487real_n] :
( ( ( sigma_476185326real_n @ ( sk47 @ B @ A ) )
!= B )
| ~ ( member1000184real_n @ C @ A )
| ~ ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
| ( member223413699real_n @ D @ ( sigma_1235138647real_n @ ( comple488165692real_n @ A ) ) ) ),
inference(cnfConj,[status(thm)],[838]) ).
thf(841,plain,
! [D: set_Fi1058188332real_n,C: sigma_1466784463real_n,B: set_Fi1058188332real_n,A: set_Si1125517487real_n] :
( ( ( sigma_476185326real_n @ ( sk47 @ B @ A ) )
!= B )
| ~ ( member1000184real_n @ C @ A )
| ~ ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
| ( member223413699real_n @ D @ ( sigma_1235138647real_n @ ( comple488165692real_n @ A ) ) ) ),
inference(lifteq,[status(thm)],[840]) ).
thf(166,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( ( image_355963305real_n @ A @ top_to131672412_int_n )
= top_to20708754real_n )
=> ? [C: finite964658038_int_n] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_surjD) ).
thf(885,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( ( image_355963305real_n @ A @ top_to131672412_int_n )
= top_to20708754real_n )
=> ? [C: finite964658038_int_n] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(14,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_50_Int__iff) ).
thf(301,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)],[14]) ).
thf(19,axiom,
! [A: finite1489363574real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: set_Fi160064172_int_n] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ ( image_355963305real_n @ B @ C ) ) )
=> ~ ! [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ C )
=> ~ ( member1352538125real_n @ A @ ( B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_UN__E) ).
thf(320,plain,
! [A: finite1489363574real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: set_Fi160064172_int_n] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ ( image_355963305real_n @ B @ C ) ) )
=> ~ ! [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ C )
=> ~ ( member1352538125real_n @ A @ ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(103,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: finite1489363574real_n > $o] :
( ( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_ball__UN) ).
thf(651,plain,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: finite1489363574real_n > $o] :
( ( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(35,axiom,
! [A: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ top_to1292442332real_n )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_Int__UNIV__right) ).
thf(389,plain,
! [A: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ top_to1292442332real_n )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(81,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_220_vimageD) ).
thf(570,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)],[81]) ).
thf(31,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: finite1489363574real_n > $o] :
( ( ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_355963305real_n @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
& ? [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_bex__UN) ).
thf(372,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: finite1489363574real_n > $o] :
( ( ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_355963305real_n @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
& ? [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(64,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_72_vimageI) ).
thf(504,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)],[64]) ).
thf(95,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_253_vimage__def) ).
thf(619,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)],[95]) ).
thf(132,axiom,
! [A: nat > set_Fi1058188332real_n] :
( ( ( image_1856576259real_n @ A @ top_top_set_nat )
= top_to20708754real_n )
= ( ! [B: set_Fi1058188332real_n] :
? [C: nat] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_surj__def) ).
thf(751,plain,
! [A: nat > set_Fi1058188332real_n] :
( ( ( image_1856576259real_n @ A @ top_top_set_nat )
= top_to20708754real_n )
= ( ! [B: set_Fi1058188332real_n] :
? [C: nat] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(264,axiom,
ord_le2133614988nnreal @ one_on705384445nnreal @ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_assms_I2_J) ).
thf(1198,plain,
ord_le2133614988nnreal @ one_on705384445nnreal @ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(197,axiom,
~ ( ord_le2133614988nnreal @ one_on705384445nnreal @ one_on705384445nnreal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_less__numeral__extra_I4_J) ).
thf(988,plain,
~ ( ord_le2133614988nnreal @ one_on705384445nnreal @ one_on705384445nnreal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(989,plain,
~ ( ord_le2133614988nnreal @ one_on705384445nnreal @ one_on705384445nnreal ),
inference(polarity_switch,[status(thm)],[988]) ).
thf(1447,plain,
( ~ $true
| ( ( ord_le2133614988nnreal @ one_on705384445nnreal @ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s ) )
!= ( ord_le2133614988nnreal @ one_on705384445nnreal @ one_on705384445nnreal ) ) ),
inference(paramod_ordered,[status(thm)],[1198,989]) ).
thf(1448,plain,
( ( ord_le2133614988nnreal @ one_on705384445nnreal @ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s ) )
!= ( ord_le2133614988nnreal @ one_on705384445nnreal @ one_on705384445nnreal ) ),
inference(simp,[status(thm)],[1447]) ).
thf(1452,plain,
( ( one_on705384445nnreal != one_on705384445nnreal )
| ( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s )
!= one_on705384445nnreal ) ),
inference(simp,[status(thm)],[1448]) ).
thf(1455,plain,
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s )
!= one_on705384445nnreal ),
inference(simp,[status(thm)],[1452]) ).
thf(28,axiom,
! [A: finite964658038_int_n,B: set_Fi160064172_int_n,C: finite1489363574real_n,D: finite964658038_int_n > set_Fi1058188332real_n] :
( ( member27055245_int_n @ A @ B )
=> ( ( member1352538125real_n @ C @ ( D @ A ) )
=> ( member1352538125real_n @ C @ ( comple825005695real_n @ ( image_355963305real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_UN__I) ).
thf(357,plain,
! [A: finite964658038_int_n,B: set_Fi160064172_int_n,C: finite1489363574real_n,D: finite964658038_int_n > set_Fi1058188332real_n] :
( ( member27055245_int_n @ A @ B )
=> ( ( member1352538125real_n @ C @ ( D @ A ) )
=> ( member1352538125real_n @ C @ ( comple825005695real_n @ ( image_355963305real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(238,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: nat > finite964658038_int_n] :
( ( image_1856576259real_n
@ ^ [C: nat] : ( A @ ( B @ C ) )
@ top_top_set_nat )
= ( image_355963305real_n @ A @ ( image_1961920973_int_n @ B @ top_top_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_range__composition) ).
thf(1132,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: nat > finite964658038_int_n] :
( ( image_1856576259real_n
@ ^ [C: nat] : ( A @ ( B @ C ) )
@ top_top_set_nat )
= ( image_355963305real_n @ A @ ( image_1961920973_int_n @ B @ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(171,axiom,
! [A: finite964658038_int_n > nat > set_Fi1058188332real_n,B: set_nat,C: set_Fi160064172_int_n] :
( ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( comple825005695real_n @ ( image_1856576259real_n @ ( A @ D ) @ B ) )
@ C ) )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] :
( comple825005695real_n
@ ( image_355963305real_n
@ ^ [E: finite964658038_int_n] : ( A @ E @ D )
@ C ) )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_SUP__commute) ).
thf(902,plain,
! [A: finite964658038_int_n > nat > set_Fi1058188332real_n,B: set_nat,C: set_Fi160064172_int_n] :
( ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( comple825005695real_n @ ( image_1856576259real_n @ ( A @ D ) @ B ) )
@ C ) )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] :
( comple825005695real_n
@ ( image_355963305real_n
@ ^ [E: finite964658038_int_n] : ( A @ E @ D )
@ C ) )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(101,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n,E: set_Fi1058188332real_n > finite1489363574real_n] :
( ( A = B )
=> ( ! [F: finite1489363574real_n] :
( ( member1352538125real_n @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_439535603real_n @ C @ A ) )
= ( E @ ( image_439535603real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_Sup_OSUP__cong) ).
thf(638,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n,E: set_Fi1058188332real_n > finite1489363574real_n] :
( ( A = B )
=> ( ! [F: finite1489363574real_n] :
( ( member1352538125real_n @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_439535603real_n @ C @ A ) )
= ( E @ ( image_439535603real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(243,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( measur1402256771real_n @ B ) )
=> ( member223413699real_n @ ( minus_1686442501real_n @ A @ C ) @ ( measur1402256771real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_null__sets_ODiff) ).
thf(1147,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( measur1402256771real_n @ B ) )
=> ( member223413699real_n @ ( minus_1686442501real_n @ A @ C ) @ ( measur1402256771real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(161,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_130_Diff__Int2) ).
thf(870,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)],[161]) ).
thf(191,axiom,
( top_to131672412_int_n
= ( collec1941932235_int_n @ top_to287930409nt_n_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_top__set__def) ).
thf(969,plain,
( top_to131672412_int_n
= ( collec1941932235_int_n @ top_to287930409nt_n_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(9,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: finite1489363574real_n > $o] :
( ( ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: nat] :
( ( member_nat @ D @ B )
& ? [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_bex__UN) ).
thf(284,plain,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: finite1489363574real_n > $o] :
( ( ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: nat] :
( ( member_nat @ D @ B )
& ? [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(49,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_161_ball__imageD) ).
thf(448,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)],[49]) ).
thf(178,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( measur1402256771real_n @ B ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ A @ C ) @ ( measur1402256771real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_null__sets_OInt) ).
thf(924,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( measur1402256771real_n @ B ) )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ A @ C ) @ ( measur1402256771real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(60,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(492,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)],[60]) ).
thf(47,axiom,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: set_Fi160064172_int_n] :
( ( image_1661509983real_n @ A @ ( image_355963305real_n @ B @ C ) )
= ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_image__image) ).
thf(443,plain,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: set_Fi160064172_int_n] :
( ( image_1661509983real_n @ A @ ( image_355963305real_n @ B @ C ) )
= ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(97,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_237_imageE) ).
thf(623,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)],[97]) ).
thf(190,axiom,
! [A: set_se2111327970real_n,B: finite1489363574real_n > $o] :
( ( ! [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ ( comple825005695real_n @ A ) )
=> ( B @ C ) ) )
= ( ! [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ A )
=> ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ C )
=> ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_UN__ball__bex__simps_I1_J) ).
thf(966,plain,
! [A: set_se2111327970real_n,B: finite1489363574real_n > $o] :
( ( ! [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ ( comple825005695real_n @ A ) )
=> ( B @ C ) ) )
= ( ! [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ A )
=> ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ C )
=> ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(217,axiom,
! [A: nat > finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: set_nat] :
( ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] : ( comple825005695real_n @ ( image_355963305real_n @ ( A @ D ) @ B ) )
@ C ) )
= ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] :
( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [E: nat] : ( A @ E @ D )
@ C ) )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_SUP__commute) ).
thf(1051,plain,
! [A: nat > finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: set_nat] :
( ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] : ( comple825005695real_n @ ( image_355963305real_n @ ( A @ D ) @ B ) )
@ C ) )
= ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] :
( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [E: nat] : ( A @ E @ D )
@ C ) )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(148,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_97_vimage__Int) ).
thf(821,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)],[148]) ).
thf(172,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: nat > set_Fi160064172_int_n,C: set_nat] :
( ( comple825005695real_n @ ( image_355963305real_n @ A @ ( comple970917503_int_n @ ( image_968789251_int_n @ B @ C ) ) ) )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] : ( comple825005695real_n @ ( image_355963305real_n @ A @ ( B @ D ) ) )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_UN__UN__flatten) ).
thf(905,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: nat > set_Fi160064172_int_n,C: set_nat] :
( ( comple825005695real_n @ ( image_355963305real_n @ A @ ( comple970917503_int_n @ ( image_968789251_int_n @ B @ C ) ) ) )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] : ( comple825005695real_n @ ( image_355963305real_n @ A @ ( B @ D ) ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(58,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n,E: set_Fi1058188332real_n > finite1489363574real_n] :
( ( A = B )
=> ( ! [F: finite1489363574real_n] :
( ( member1352538125real_n @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_439535603real_n @ C @ A ) )
= ( E @ ( image_439535603real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Inf_OINF__cong) ).
thf(480,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n > finite1489363574real_n,D: finite1489363574real_n > finite1489363574real_n,E: set_Fi1058188332real_n > finite1489363574real_n] :
( ( A = B )
=> ( ! [F: finite1489363574real_n] :
( ( member1352538125real_n @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_439535603real_n @ C @ A ) )
= ( E @ ( image_439535603real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1169,plain,
( ( ^ [A: finite964658038_int_n] : ( inf_in1974387902real_n @ s @ ( r @ A ) ) )
= t2 ),
inference(lifteq,[status(thm)],[1168]) ).
thf(187,axiom,
! [A: finite1489363574real_n,B: set_se2111327970real_n] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ B ) )
=> ~ ! [C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ C )
=> ~ ( member223413699real_n @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_UnionE) ).
thf(956,plain,
! [A: finite1489363574real_n,B: set_se2111327970real_n] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ B ) )
=> ~ ! [C: set_Fi1058188332real_n] :
( ( member1352538125real_n @ A @ C )
=> ~ ( member223413699real_n @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(223,axiom,
! [A: set_Fi160064172_int_n] :
( ( inf_in1108485182_int_n @ A @ top_to131672412_int_n )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_Int__UNIV__right) ).
thf(1072,plain,
! [A: set_Fi160064172_int_n] :
( ( inf_in1108485182_int_n @ A @ top_to131672412_int_n )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(37,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n] :
( ( image_439535603real_n
@ ^ [C: finite1489363574real_n] : ( A @ ( B @ C ) )
@ top_to1292442332real_n )
= ( image_439535603real_n @ A @ ( image_439535603real_n @ B @ top_to1292442332real_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_range__composition) ).
thf(396,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n] :
( ( image_439535603real_n
@ ^ [C: finite1489363574real_n] : ( A @ ( B @ C ) )
@ top_to1292442332real_n )
= ( image_439535603real_n @ A @ ( image_439535603real_n @ B @ top_to1292442332real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(90,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_74_vimage__Collect__eq) ).
thf(602,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)],[90]) ).
thf(195,axiom,
! [A: finite964658038_int_n > nat,B: nat] :
( ( ( image_497739341_n_nat @ A @ top_to131672412_int_n )
= top_top_set_nat )
=> ? [C: finite964658038_int_n] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_surjD) ).
thf(981,plain,
! [A: finite964658038_int_n > nat,B: nat] :
( ( ( image_497739341_n_nat @ A @ top_to131672412_int_n )
= top_top_set_nat )
=> ? [C: finite964658038_int_n] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(16,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_195_IntD2) ).
thf(307,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)],[16]) ).
thf(512,plain,
( ( comple825005695real_n @ top_to20708754real_n )
= top_to1292442332real_n ),
inference(lifteq,[status(thm)],[511]) ).
thf(3,axiom,
! [A: set_se2111327970real_n] :
( ( collec452821761real_n
@ ^ [B: set_Fi1058188332real_n] : ( member223413699real_n @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Collect__mem__eq) ).
thf(268,plain,
! [A: set_se2111327970real_n] :
( ( collec452821761real_n
@ ^ [B: set_Fi1058188332real_n] : ( member223413699real_n @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(269,plain,
! [A: set_se2111327970real_n] :
( ( collec452821761real_n
@ ^ [B: set_Fi1058188332real_n] : ( member223413699real_n @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[268]) ).
thf(270,plain,
! [A: set_se2111327970real_n] :
( ( collec452821761real_n
@ ^ [B: set_Fi1058188332real_n] : ( member223413699real_n @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[269]) ).
thf(73,axiom,
! [A: finite1489363574real_n > finite1489363574real_n] :
( ( vimage1233683625real_n @ A @ top_to1292442332real_n )
= top_to1292442332real_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_vimage__UNIV) ).
thf(544,plain,
! [A: finite1489363574real_n > finite1489363574real_n] :
( ( vimage1233683625real_n @ A @ top_to1292442332real_n )
= top_to1292442332real_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(545,plain,
! [A: finite1489363574real_n > finite1489363574real_n] :
( ( vimage1233683625real_n @ A @ top_to1292442332real_n )
= top_to1292442332real_n ),
inference(cnf,[status(esa)],[544]) ).
thf(546,plain,
! [A: finite1489363574real_n > finite1489363574real_n] :
( ( vimage1233683625real_n @ A @ top_to1292442332real_n )
= top_to1292442332real_n ),
inference(lifteq,[status(thm)],[545]) ).
thf(265,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
=> ( ( sigma_1536574303real_n @ B @ ( minus_1686442501real_n @ C @ A ) )
= ( sigma_1536574303real_n @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_emeasure__Diff__null__set) ).
thf(1199,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
=> ( ( sigma_1536574303real_n @ B @ ( minus_1686442501real_n @ C @ A ) )
= ( sigma_1536574303real_n @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(245,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_12_T_H__altdef) ).
thf(1153,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)],[245]) ).
thf(221,axiom,
! [A: set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: set_Fi160064172_int_n] :
( ( member223413699real_n @ A @ ( image_355963305real_n @ B @ C ) )
= ( ? [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_image__iff) ).
thf(1067,plain,
! [A: set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: set_Fi160064172_int_n] :
( ( member223413699real_n @ A @ ( image_355963305real_n @ B @ C ) )
= ( ? [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(141,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: nat > finite1489363574real_n] :
( ( image_183184717real_n
@ ^ [C: nat] : ( A @ ( B @ C ) )
@ top_top_set_nat )
= ( image_439535603real_n @ A @ ( image_183184717real_n @ B @ top_top_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_range__composition) ).
thf(798,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: nat > finite1489363574real_n] :
( ( image_183184717real_n
@ ^ [C: nat] : ( A @ ( B @ C ) )
@ top_top_set_nat )
= ( image_439535603real_n @ A @ ( image_183184717real_n @ B @ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(249,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_25__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(1163,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)],[249]) ).
thf(174,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_131_Int__Diff) ).
thf(910,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)],[174]) ).
thf(229,axiom,
! [A: finite1489363574real_n > set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n,C: set_nat] :
( ( comple825005695real_n @ ( image_545463721real_n @ A @ ( comple825005695real_n @ ( image_1856576259real_n @ B @ C ) ) ) )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] : ( comple825005695real_n @ ( image_545463721real_n @ A @ ( B @ D ) ) )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_UN__UN__flatten) ).
thf(1091,plain,
! [A: finite1489363574real_n > set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n,C: set_nat] :
( ( comple825005695real_n @ ( image_545463721real_n @ A @ ( comple825005695real_n @ ( image_1856576259real_n @ B @ C ) ) ) )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] : ( comple825005695real_n @ ( image_545463721real_n @ A @ ( B @ D ) ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(149,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_190_Int__commute) ).
thf(824,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)],[149]) ).
thf(825,plain,
( inf_in1974387902real_n
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B @ A ) ) ),
inference(lifteq,[status(thm)],[824]) ).
thf(208,axiom,
! [A: nat > nat] :
( ( vimage_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_vimage__UNIV) ).
thf(1021,plain,
! [A: nat > nat] :
( ( vimage_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(26,axiom,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( ( inf_in1974387902real_n @ A @ B )
= top_to1292442332real_n )
= ( ( A = top_to1292442332real_n )
& ( B = top_to1292442332real_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Int__UNIV) ).
thf(349,plain,
! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( ( inf_in1974387902real_n @ A @ B )
= top_to1292442332real_n )
= ( ( A = top_to1292442332real_n )
& ( B = top_to1292442332real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(254,axiom,
! [A: finite964658038_int_n] : ( member223413699real_n @ ( t @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062a_O_AT_H_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).
thf(1174,plain,
! [A: finite964658038_int_n] : ( member223413699real_n @ ( t @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(36,axiom,
! [A: nat > nat,B: nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ~ ! [C: nat] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_surjE) ).
thf(392,plain,
! [A: nat > nat,B: nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ~ ! [C: nat] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(5,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_247_Int__Collect) ).
thf(273,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)],[5]) ).
thf(274,plain,
! [C: set_Fi1058188332real_n > $o,B: set_se2111327970real_n,A: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ ( collec452821761real_n @ C ) ) )
= ( ( member223413699real_n @ A @ B )
& ( C @ A ) ) ),
inference(cnf,[status(esa)],[273]) ).
thf(275,plain,
! [C: set_Fi1058188332real_n > $o,B: set_se2111327970real_n,A: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( inf_in632889204real_n @ B @ ( collec452821761real_n @ C ) ) )
= ( ( member223413699real_n @ A @ B )
& ( C @ A ) ) ),
inference(lifteq,[status(thm)],[274]) ).
thf(146,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_127_Diff__Int__distrib2) ).
thf(815,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)],[146]) ).
thf(125,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( image_439535603real_n @ A @ ( vimage1233683625real_n @ A @ B ) )
= ( inf_in1974387902real_n @ B @ ( image_439535603real_n @ A @ top_to1292442332real_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_image__vimage__eq) ).
thf(729,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( image_439535603real_n @ A @ ( vimage1233683625real_n @ A @ B ) )
= ( inf_in1974387902real_n @ B @ ( image_439535603real_n @ A @ top_to1292442332real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(214,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite964658038_int_n > finite1489363574real_n] :
( ( image_2058828787real_n
@ ^ [C: finite964658038_int_n] : ( A @ ( B @ C ) )
@ top_to131672412_int_n )
= ( image_439535603real_n @ A @ ( image_2058828787real_n @ B @ top_to131672412_int_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_range__composition) ).
thf(1042,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite964658038_int_n > finite1489363574real_n] :
( ( image_2058828787real_n
@ ^ [C: finite964658038_int_n] : ( A @ ( B @ C ) )
@ top_to131672412_int_n )
= ( image_439535603real_n @ A @ ( image_2058828787real_n @ B @ top_to131672412_int_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(186,axiom,
! [A: set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( image_1856576259real_n @ B @ top_top_set_nat ) )
=> ~ ! [C: nat] :
( A
!= ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_rangeE) ).
thf(952,plain,
! [A: set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( image_1856576259real_n @ B @ top_top_set_nat ) )
=> ~ ! [C: nat] :
( A
!= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(115,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( ( inf_in1974387902real_n @ ( sigma_476185326real_n @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_null__sets_OInt__space__eq1) ).
thf(693,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( ( inf_in1974387902real_n @ ( sigma_476185326real_n @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(99,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: finite1489363574real_n > $o] :
( ( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_355963305real_n @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
=> ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_ball__UN) ).
thf(630,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: finite1489363574real_n > $o] :
( ( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_355963305real_n @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
=> ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(176,axiom,
! [A: nat,B: set_nat,C: set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n] :
( ( member_nat @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member223413699real_n @ C @ ( image_1856576259real_n @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_rev__image__eqI) ).
thf(916,plain,
! [A: nat,B: set_nat,C: set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n] :
( ( member_nat @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member223413699real_n @ C @ ( image_1856576259real_n @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(155,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_132_vimage__Diff) ).
thf(847,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)],[155]) ).
thf(164,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_188_Int__left__commute) ).
thf(879,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)],[164]) ).
thf(45,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_249_Int__Collect) ).
thf(435,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)],[45]) ).
thf(167,axiom,
! [A: nat > finite964658038_int_n,B: finite964658038_int_n] :
( ( ( image_1961920973_int_n @ A @ top_top_set_nat )
= top_to131672412_int_n )
=> ? [C: nat] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_surjD) ).
thf(889,plain,
! [A: nat > finite964658038_int_n,B: finite964658038_int_n] :
( ( ( image_1961920973_int_n @ A @ top_top_set_nat )
= top_to131672412_int_n )
=> ? [C: nat] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1159,plain,
( ( comple825005695real_n @ ( image_355963305real_n @ t2 @ top_to131672412_int_n ) )
= s ),
inference(lifteq,[status(thm)],[1158]) ).
thf(1,conjecture,
( ( ^ [A: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ A ) ) ) )
= ( ^ [A: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( ^ [A: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ A ) ) ) )
!= ( ^ [A: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(266,plain,
( ( ^ [A: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ A ) ) ) )
!= ( ^ [A: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(267,plain,
( ( ^ [A: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ A ) ) ) )
!= ( ^ [A: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[266]) ).
thf(1207,plain,
( ( ( ^ [A: nat] : ( comple230862828real_n @ lebesg260170249real_n ) )
!= ( ^ [A: nat] : ( comple230862828real_n @ lebesg260170249real_n ) ) )
| ( ( ^ [A: nat] : ( t2 @ ( f @ A ) ) )
!= ( ^ [A: nat] : ( t @ ( f @ A ) ) ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(1209,plain,
( ( ^ [A: nat] : ( t2 @ ( f @ A ) ) )
!= ( ^ [A: nat] : ( t @ ( f @ A ) ) ) ),
inference(simp,[status(thm)],[1207]) ).
thf(1210,plain,
( ( t2 @ ( f @ sk72 ) )
!= ( t @ ( f @ sk72 ) ) ),
inference(func_ext,[status(esa)],[1209]) ).
thf(210,axiom,
! [A: nat,B: set_nat,C: nat > set_Fi1058188332real_n] :
( ( member_nat @ A @ B )
=> ( member223413699real_n @ ( C @ A ) @ ( image_1856576259real_n @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_imageI) ).
thf(1027,plain,
! [A: nat,B: set_nat,C: nat > set_Fi1058188332real_n] :
( ( member_nat @ A @ B )
=> ( member223413699real_n @ ( C @ A ) @ ( image_1856576259real_n @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(134,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_189_Int__left__absorb) ).
thf(757,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)],[134]) ).
thf(75,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: set_Fi1058188332real_n > $o] :
( ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_355963305real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_355963305real_n @ A
@ ( collec1941932235_int_n
@ ^ [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_Compr__image__eq) ).
thf(551,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: set_Fi1058188332real_n > $o] :
( ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_355963305real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_355963305real_n @ A
@ ( collec1941932235_int_n
@ ^ [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(153,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_se2111327970real_n] :
( ( vimage1233683625real_n @ A @ ( comple825005695real_n @ B ) )
= ( comple825005695real_n @ ( image_1661509983real_n @ ( vimage1233683625real_n @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_vimage__Union) ).
thf(842,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_se2111327970real_n] :
( ( vimage1233683625real_n @ A @ ( comple825005695real_n @ B ) )
= ( comple825005695real_n @ ( image_1661509983real_n @ ( vimage1233683625real_n @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(232,axiom,
! [A: nat > finite964658038_int_n,B: finite964658038_int_n] :
( ( ( image_1961920973_int_n @ A @ top_top_set_nat )
= top_to131672412_int_n )
=> ~ ! [C: nat] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_surjE) ).
thf(1106,plain,
! [A: nat > finite964658038_int_n,B: finite964658038_int_n] :
( ( ( image_1961920973_int_n @ A @ top_top_set_nat )
= top_to131672412_int_n )
=> ~ ! [C: nat] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(20,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_199_IntE) ).
thf(324,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)],[20]) ).
thf(193,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( ( image_1856576259real_n @ A @ top_top_set_nat )
= top_to20708754real_n )
=> ~ ! [C: nat] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_surjE) ).
thf(974,plain,
! [A: nat > set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( ( image_1856576259real_n @ A @ top_top_set_nat )
= top_to20708754real_n )
=> ~ ! [C: nat] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(185,axiom,
! [A: set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( image_355963305real_n @ B @ top_to131672412_int_n ) )
=> ~ ! [C: finite964658038_int_n] :
( A
!= ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_rangeE) ).
thf(948,plain,
! [A: set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( image_355963305real_n @ B @ top_to131672412_int_n ) )
=> ~ ! [C: finite964658038_int_n] :
( A
!= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(94,axiom,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ ( image_1661509983real_n @ B @ C ) ) )
=> ~ ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ C )
=> ~ ( member1352538125real_n @ A @ ( B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_UN__E) ).
thf(615,plain,
! [A: finite1489363574real_n,B: set_Fi1058188332real_n > set_Fi1058188332real_n,C: set_se2111327970real_n] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ ( image_1661509983real_n @ B @ C ) ) )
=> ~ ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ C )
=> ~ ( member1352538125real_n @ A @ ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(220,axiom,
! [A: set_Fi1058188332real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( A
@ ( image_439535603real_n
@ ^ [C: finite1489363574real_n] : C
@ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_Sup_OSUP__identity__eq) ).
thf(1064,plain,
! [A: set_Fi1058188332real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( A
@ ( image_439535603real_n
@ ^ [C: finite1489363574real_n] : C
@ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(240,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( ( image_1856576259real_n @ A @ top_top_set_nat )
= top_to20708754real_n )
=> ? [C: nat] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_surjD) ).
thf(1138,plain,
! [A: nat > set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( ( image_1856576259real_n @ A @ top_top_set_nat )
= top_to20708754real_n )
=> ? [C: nat] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(87,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_196_IntD1) ).
thf(593,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)],[87]) ).
thf(138,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_192_Int__assoc) ).
thf(783,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)],[138]) ).
thf(129,axiom,
! [A: set_Si1125517487real_n] :
( ( sigma_476185326real_n @ ( comple488165692real_n @ A ) )
= ( comple825005695real_n @ ( image_1298280374real_n @ sigma_476185326real_n @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_space__Sup__eq__UN) ).
thf(742,plain,
! [A: set_Si1125517487real_n] :
( ( sigma_476185326real_n @ ( comple488165692real_n @ A ) )
= ( comple825005695real_n @ ( image_1298280374real_n @ sigma_476185326real_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(84,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: finite1489363574real_n > $o] :
( ( ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: nat] :
( ( member_nat @ D @ B )
& ? [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_UN__ball__bex__simps_I4_J) ).
thf(578,plain,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: finite1489363574real_n > $o] :
( ( ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: nat] :
( ( member_nat @ D @ B )
& ? [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(21,axiom,
! [A: set_nat,B: set_nat,C: nat > set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [E: nat] :
( ( member_nat @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_1856576259real_n @ C @ A )
= ( image_1856576259real_n @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_image__cong) ).
thf(328,plain,
! [A: set_nat,B: set_nat,C: nat > set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [E: nat] :
( ( member_nat @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_1856576259real_n @ C @ A )
= ( image_1856576259real_n @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(248,axiom,
! [A: finite964658038_int_n] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ A ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_emeasure__T_H) ).
thf(1160,plain,
! [A: finite964658038_int_n] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ A ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(23,axiom,
! [A: finite964658038_int_n > finite964658038_int_n,B: finite964658038_int_n] :
( ( ( image_1278151539_int_n @ A @ top_to131672412_int_n )
= top_to131672412_int_n )
=> ~ ! [C: finite964658038_int_n] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_surjE) ).
thf(339,plain,
! [A: finite964658038_int_n > finite964658038_int_n,B: finite964658038_int_n] :
( ( ( image_1278151539_int_n @ A @ top_to131672412_int_n )
= top_to131672412_int_n )
=> ~ ! [C: finite964658038_int_n] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(181,axiom,
! [A: finite1489363574real_n > set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: set_Fi160064172_int_n] :
( ( comple825005695real_n @ ( image_545463721real_n @ A @ ( comple825005695real_n @ ( image_355963305real_n @ B @ C ) ) ) )
= ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( comple825005695real_n @ ( image_545463721real_n @ A @ ( B @ D ) ) )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_UN__UN__flatten) ).
thf(933,plain,
! [A: finite1489363574real_n > set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: set_Fi160064172_int_n] :
( ( comple825005695real_n @ ( image_545463721real_n @ A @ ( comple825005695real_n @ ( image_355963305real_n @ B @ C ) ) ) )
= ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( comple825005695real_n @ ( image_545463721real_n @ A @ ( B @ D ) ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(76,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_175_imageI) ).
thf(554,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)],[76]) ).
thf(256,axiom,
! [A: finite964658038_int_n,B: finite964658038_int_n] :
( ( A != B )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( r @ A ) @ ( r @ B ) ) @ ( measur1402256771real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_R__Int) ).
thf(1182,plain,
! [A: finite964658038_int_n,B: finite964658038_int_n] :
( ( A != B )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( r @ A ) @ ( r @ B ) ) @ ( measur1402256771real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(109,axiom,
! [A: set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n,C: set_nat] :
( ( member223413699real_n @ A @ ( image_1856576259real_n @ B @ C ) )
=> ~ ! [D: nat] :
( ( A
= ( B @ D ) )
=> ~ ( member_nat @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_imageE) ).
thf(669,plain,
! [A: set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n,C: set_nat] :
( ( member223413699real_n @ A @ ( image_1856576259real_n @ B @ C ) )
=> ~ ! [D: nat] :
( ( A
= ( B @ D ) )
=> ~ ( member_nat @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(59,axiom,
! [A: nat > set_Fi1058188332real_n,B: nat > nat,C: set_nat] :
( ( image_1856576259real_n @ A @ ( image_nat_nat @ B @ C ) )
= ( image_1856576259real_n
@ ^ [D: nat] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_image__image) ).
thf(489,plain,
! [A: nat > set_Fi1058188332real_n,B: nat > nat,C: set_nat] :
( ( image_1856576259real_n @ A @ ( image_nat_nat @ B @ C ) )
= ( image_1856576259real_n
@ ^ [D: nat] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(206,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ! [C: finite964658038_int_n] : ( member223413699real_n @ ( A @ C ) @ ( measur1402256771real_n @ B ) )
=> ( member223413699real_n @ ( comple825005695real_n @ ( image_355963305real_n @ A @ top_to131672412_int_n ) ) @ ( measur1402256771real_n @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_null__sets__UN) ).
thf(1016,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ! [C: finite964658038_int_n] : ( member223413699real_n @ ( A @ C ) @ ( measur1402256771real_n @ B ) )
=> ( member223413699real_n @ ( comple825005695real_n @ ( image_355963305real_n @ A @ top_to131672412_int_n ) ) @ ( measur1402256771real_n @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(970,plain,
( ( collec1941932235_int_n @ top_to287930409nt_n_o )
= top_to131672412_int_n ),
inference(lifteq,[status(thm)],[969]) ).
thf(74,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_201_IntE) ).
thf(547,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)],[74]) ).
thf(114,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: set_Fi1058188332real_n > $o] :
( ? [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_1856576259real_n @ A @ B ) )
& ( C @ D ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_bex__imageD) ).
thf(686,plain,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: set_Fi1058188332real_n > $o] :
( ? [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_1856576259real_n @ A @ B ) )
& ( C @ D ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(224,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 ) ) )
@ ( measur1402256771real_n @ A ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D ) ) )
@ ( measur1402256771real_n @ A ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( ( C @ D )
| ( B @ D ) ) ) )
@ ( measur1402256771real_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_null__sets_Osets__Collect__disj) ).
thf(1075,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 ) ) )
@ ( measur1402256771real_n @ A ) )
=> ( ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( C @ D ) ) )
@ ( measur1402256771real_n @ A ) )
=> ( member223413699real_n
@ ( collec321817931real_n
@ ^ [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( sigma_476185326real_n @ A ) )
& ( ( C @ D )
| ( B @ D ) ) ) )
@ ( measur1402256771real_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(56,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_193_IntD2) ).
thf(476,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)],[56]) ).
thf(102,axiom,
! [A: nat > nat,B: nat > nat] :
( ! [C: nat] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_surjI) ).
thf(647,plain,
! [A: nat > nat,B: nat > nat] :
( ! [C: nat] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(196,axiom,
! [A: set_Fi1058188332real_n] :
( ( comple2042271945real_n
@ ( image_439535603real_n
@ ^ [B: finite1489363574real_n] : B
@ A ) )
= ( comple2042271945real_n @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_SUP__identity__eq) ).
thf(985,plain,
! [A: set_Fi1058188332real_n] :
( ( comple2042271945real_n
@ ( image_439535603real_n
@ ^ [B: finite1489363574real_n] : B
@ A ) )
= ( comple2042271945real_n @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(117,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_139_translation__diff) ).
thf(701,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)],[117]) ).
thf(244,axiom,
! [A: set_se2111327970real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( comple825005695real_n @ A ) @ B )
= ( comple825005695real_n
@ ( image_1661509983real_n
@ ^ [C: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ C @ B )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Int__Union2) ).
thf(1150,plain,
! [A: set_se2111327970real_n,B: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ ( comple825005695real_n @ A ) @ B )
= ( comple825005695real_n
@ ( image_1661509983real_n
@ ^ [C: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ C @ B )
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(104,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: finite1489363574real_n > $o] :
( ( ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_355963305real_n @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
& ? [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_UN__ball__bex__simps_I4_J) ).
thf(654,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: finite1489363574real_n > $o] :
( ( ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_355963305real_n @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
& ? [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(260,axiom,
( sums_E1192373732nnreal
@ ^ [A: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ A ) ) )
@ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [A: nat] : ( t2 @ ( f @ A ) )
@ top_top_set_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__092_060open_062_I_092_060lambda_062n_O_Aemeasure_Alebesgue_A_IT_A_If_An_J_J_J_Asums_Aemeasure_Alebesgue_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062) ).
thf(1192,plain,
( sums_E1192373732nnreal
@ ^ [A: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ A ) ) )
@ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [A: nat] : ( t2 @ ( f @ A ) )
@ top_top_set_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(123,axiom,
! [A: set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n,C: nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( member_nat @ C @ D )
=> ( member223413699real_n @ A @ ( image_1856576259real_n @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_image__eqI) ).
thf(721,plain,
! [A: set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n,C: nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( member_nat @ C @ D )
=> ( member223413699real_n @ A @ ( image_1856576259real_n @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(202,axiom,
! [A: finite964658038_int_n] :
( ( image_1278151539_int_n @ ( plus_p1654784127_int_n @ A ) @ top_to131672412_int_n )
= top_to131672412_int_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_surj__plus) ).
thf(1002,plain,
! [A: finite964658038_int_n] :
( ( image_1278151539_int_n @ ( plus_p1654784127_int_n @ A ) @ top_to131672412_int_n )
= top_to131672412_int_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(1236,plain,
! [H: set_Fi1058188332real_n,G: sigma_1466784463real_n,F: set_Fi1058188332real_n,E: set_Si1125517487real_n,D: set_Fi1058188332real_n,C: sigma_1466784463real_n,B: set_Fi1058188332real_n,A: set_Si1125517487real_n] :
( ( ( sigma_476185326real_n @ ( sk47 @ B @ A ) )
!= B )
| ~ ( member1000184real_n @ C @ A )
| ~ ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
| ( ( sigma_476185326real_n @ ( sk47 @ F @ E ) )
!= F )
| ~ ( member1000184real_n @ G @ E )
| ~ $true
| ( member223413699real_n @ H @ ( sigma_1235138647real_n @ ( comple488165692real_n @ E ) ) )
| ( ( member223413699real_n @ D @ ( sigma_1235138647real_n @ ( comple488165692real_n @ A ) ) )
!= ( member223413699real_n @ H @ ( sigma_1235138647real_n @ G ) ) ) ),
inference(paramod_ordered,[status(thm)],[841,841]) ).
thf(1237,plain,
! [H: set_Fi1058188332real_n,G: sigma_1466784463real_n,F: set_Fi1058188332real_n,E: set_Si1125517487real_n,D: set_Fi1058188332real_n,C: sigma_1466784463real_n,B: set_Fi1058188332real_n,A: set_Si1125517487real_n] :
( ( ( sigma_476185326real_n @ ( sk47 @ B @ A ) )
!= B )
| ~ ( member1000184real_n @ C @ A )
| ~ ( member223413699real_n @ D @ ( sigma_1235138647real_n @ C ) )
| ( ( sigma_476185326real_n @ ( sk47 @ F @ E ) )
!= F )
| ~ ( member1000184real_n @ G @ E )
| ( member223413699real_n @ H @ ( sigma_1235138647real_n @ ( comple488165692real_n @ E ) ) )
| ( ( member223413699real_n @ D @ ( sigma_1235138647real_n @ ( comple488165692real_n @ A ) ) )
!= ( member223413699real_n @ H @ ( sigma_1235138647real_n @ G ) ) ) ),
inference(simp,[status(thm)],[1236]) ).
thf(1238,plain,
! [F: set_Si1125517487real_n,E: set_Fi1058188332real_n,D: set_Si1125517487real_n,C: set_Fi1058188332real_n,B: sigma_1466784463real_n,A: set_Fi1058188332real_n] :
( ( ( sigma_476185326real_n @ ( sk47 @ A @ F ) )
!= A )
| ~ ( member1000184real_n @ B @ F )
| ~ ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
| ( ( sigma_476185326real_n @ ( sk47 @ E @ D ) )
!= E )
| ~ ( member1000184real_n @ ( comple488165692real_n @ F ) @ D )
| ( member223413699real_n @ C @ ( sigma_1235138647real_n @ ( comple488165692real_n @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[1237:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( comple488165692real_n @ I )),bind(H,$thf( D ))]]) ).
thf(1246,plain,
! [F: set_Si1125517487real_n,E: set_Fi1058188332real_n,D: set_Si1125517487real_n,C: set_Fi1058188332real_n,B: sigma_1466784463real_n,A: set_Fi1058188332real_n] :
( ( ( sigma_476185326real_n @ ( sk47 @ A @ F ) )
!= A )
| ~ ( member1000184real_n @ B @ F )
| ~ ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
| ( ( sigma_476185326real_n @ ( sk47 @ E @ D ) )
!= E )
| ~ ( member1000184real_n @ ( comple488165692real_n @ F ) @ D )
| ( member223413699real_n @ C @ ( sigma_1235138647real_n @ ( comple488165692real_n @ D ) ) ) ),
inference(simp,[status(thm)],[1238]) ).
thf(91,axiom,
! [A: set_se2111327970real_n] :
( ( comple825005695real_n
@ ( image_1661509983real_n
@ ^ [B: set_Fi1058188332real_n] : B
@ A ) )
= ( comple825005695real_n @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_SUP__identity__eq) ).
thf(605,plain,
! [A: set_se2111327970real_n] :
( ( comple825005695real_n
@ ( image_1661509983real_n
@ ^ [B: set_Fi1058188332real_n] : B
@ A ) )
= ( comple825005695real_n @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1445,plain,
( ~ $true
| ( ( ord_le2133614988nnreal @ one_on705384445nnreal @ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s ) )
!= ( ord_le2133614988nnreal @ zero_z1963244097nnreal @ zero_z1963244097nnreal ) ) ),
inference(paramod_ordered,[status(thm)],[1198,814]) ).
thf(1446,plain,
( ( ord_le2133614988nnreal @ one_on705384445nnreal @ ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s ) )
!= ( ord_le2133614988nnreal @ zero_z1963244097nnreal @ zero_z1963244097nnreal ) ),
inference(simp,[status(thm)],[1445]) ).
thf(1451,plain,
( ( zero_z1963244097nnreal != one_on705384445nnreal )
| ( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ s )
!= zero_z1963244097nnreal ) ),
inference(simp,[status(thm)],[1446]) ).
thf(128,axiom,
! [A: finite964658038_int_n > nat,B: nat > finite964658038_int_n] :
( ! [C: nat] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_497739341_n_nat @ A @ top_to131672412_int_n )
= top_top_set_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_surjI) ).
thf(738,plain,
! [A: finite964658038_int_n > nat,B: nat > finite964658038_int_n] :
( ! [C: nat] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_497739341_n_nat @ A @ top_to131672412_int_n )
= top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(219,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_Fi1058188332real_n > nat] :
( ! [C: set_Fi1058188332real_n] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_1856576259real_n @ A @ top_top_set_nat )
= top_to20708754real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_surjI) ).
thf(1060,plain,
! [A: nat > set_Fi1058188332real_n,B: set_Fi1058188332real_n > nat] :
( ! [C: set_Fi1058188332real_n] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_1856576259real_n @ A @ top_top_set_nat )
= top_to20708754real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(51,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_156_rev__image__eqI) ).
thf(457,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)],[51]) ).
thf(24,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_205_vimage__Collect) ).
thf(343,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)],[24]) ).
thf(177,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: finite964658038_int_n > finite964658038_int_n] :
( ( image_355963305real_n
@ ^ [C: finite964658038_int_n] : ( A @ ( B @ C ) )
@ top_to131672412_int_n )
= ( image_355963305real_n @ A @ ( image_1278151539_int_n @ B @ top_to131672412_int_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_range__composition) ).
thf(921,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: finite964658038_int_n > finite964658038_int_n] :
( ( image_355963305real_n
@ ^ [C: finite964658038_int_n] : ( A @ ( B @ C ) )
@ top_to131672412_int_n )
= ( image_355963305real_n @ A @ ( image_1278151539_int_n @ B @ top_to131672412_int_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(72,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_51_IntI) ).
thf(541,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)],[72]) ).
thf(105,axiom,
? [A: nat] : ( member_nat @ A @ top_top_set_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_UNIV__witness) ).
thf(657,plain,
? [A: nat] : ( member_nat @ A @ top_top_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(218,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: set_Fi1058188332real_n > $o] :
( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_355963305real_n @ A @ B ) )
=> ( C @ D ) )
=> ! [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_ball__imageD) ).
thf(1054,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: set_Fi1058188332real_n > $o] :
( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_355963305real_n @ A @ B ) )
=> ( C @ D ) )
=> ! [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(252,axiom,
! [A: finite964658038_int_n] : ( member223413699real_n @ ( t2 @ A ) @ ( 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_092_060close_062) ).
thf(1170,plain,
! [A: finite964658038_int_n] : ( member223413699real_n @ ( t2 @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(70,axiom,
! [A: set_nat,B: set_nat,C: nat > set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n,E: set_se2111327970real_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [F: nat] :
( ( member_nat @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_1856576259real_n @ C @ A ) )
= ( E @ ( image_1856576259real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_Inf_OINF__cong) ).
thf(530,plain,
! [A: set_nat,B: set_nat,C: nat > set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n,E: set_se2111327970real_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [F: nat] :
( ( member_nat @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_1856576259real_n @ C @ A ) )
= ( E @ ( image_1856576259real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(257,axiom,
! [A: finite964658038_int_n] : ( member223413699real_n @ ( r @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).
thf(1185,plain,
! [A: finite964658038_int_n] : ( member223413699real_n @ ( r @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(136,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: set_Fi1058188332real_n > $o] :
( ? [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_355963305real_n @ A @ B ) )
& ( C @ D ) )
=> ? [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_bex__imageD) ).
thf(773,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: set_Fi1058188332real_n > $o] :
( ? [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_355963305real_n @ A @ B ) )
& ( C @ D ) )
=> ? [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(122,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n] :
( ( ( image_355963305real_n @ A @ top_to131672412_int_n )
= top_to20708754real_n )
= ( ! [B: set_Fi1058188332real_n] :
? [C: finite964658038_int_n] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_surj__def) ).
thf(718,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n] :
( ( ( image_355963305real_n @ A @ top_to131672412_int_n )
= top_to20708754real_n )
= ( ! [B: set_Fi1058188332real_n] :
? [C: finite964658038_int_n] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(100,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_40_image__eqI) ).
thf(633,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)],[100]) ).
thf(29,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: finite1489363574real_n,D: set_Fi1058188332real_n > set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ B )
=> ( ( member1352538125real_n @ C @ ( D @ A ) )
=> ( member1352538125real_n @ C @ ( comple825005695real_n @ ( image_1661509983real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_UN__I) ).
thf(360,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: finite1489363574real_n,D: set_Fi1058188332real_n > set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ B )
=> ( ( member1352538125real_n @ C @ ( D @ A ) )
=> ( member1352538125real_n @ C @ ( comple825005695real_n @ ( image_1661509983real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(258,axiom,
( f
= ( counta1142393929_int_n @ top_to131672412_int_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_f__def) ).
thf(1187,plain,
( f
= ( counta1142393929_int_n @ top_to131672412_int_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(110,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_13_of__int__vec__eq__iff) ).
thf(674,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)],[110]) ).
thf(13,axiom,
! [A: finite1489363574real_n,B: nat > set_Fi1058188332real_n,C: set_nat] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ ( image_1856576259real_n @ B @ C ) ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( member1352538125real_n @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_UN__iff) ).
thf(298,plain,
! [A: finite1489363574real_n,B: nat > set_Fi1058188332real_n,C: set_nat] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ ( image_1856576259real_n @ B @ C ) ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( member1352538125real_n @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(239,axiom,
! [A: finite964658038_int_n,B: set_Fi160064172_int_n,C: finite964658038_int_n > set_Fi1058188332real_n] :
( ( member27055245_int_n @ A @ B )
=> ( member223413699real_n @ ( C @ A ) @ ( image_355963305real_n @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_imageI) ).
thf(1135,plain,
! [A: finite964658038_int_n,B: set_Fi160064172_int_n,C: finite964658038_int_n > set_Fi1058188332real_n] :
( ( member27055245_int_n @ A @ B )
=> ( member223413699real_n @ ( C @ A ) @ ( image_355963305real_n @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(231,axiom,
! [A: finite964658038_int_n > nat] :
( ( vimage1398021123_n_nat @ A @ top_top_set_nat )
= top_to131672412_int_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_vimage__UNIV) ).
thf(1103,plain,
! [A: finite964658038_int_n > nat] :
( ( vimage1398021123_n_nat @ A @ top_top_set_nat )
= top_to131672412_int_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(130,axiom,
! [A: nat > set_Fi1058188332real_n,B: nat > set_nat,C: set_nat] :
( ( comple825005695real_n @ ( image_1856576259real_n @ A @ ( comple1682161881et_nat @ ( image_nat_set_nat @ B @ C ) ) ) )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] : ( comple825005695real_n @ ( image_1856576259real_n @ A @ ( B @ D ) ) )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_UN__UN__flatten) ).
thf(745,plain,
! [A: nat > set_Fi1058188332real_n,B: nat > set_nat,C: set_nat] :
( ( comple825005695real_n @ ( image_1856576259real_n @ A @ ( comple1682161881et_nat @ ( image_nat_set_nat @ B @ C ) ) ) )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] : ( comple825005695real_n @ ( image_1856576259real_n @ A @ ( B @ D ) ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(7,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_81_mem__Collect__eq) ).
thf(279,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)],[7]) ).
thf(32,axiom,
! [A: finite964658038_int_n > finite964658038_int_n,B: finite964658038_int_n] :
( ( ( image_1278151539_int_n @ A @ top_to131672412_int_n )
= top_to131672412_int_n )
=> ? [C: finite964658038_int_n] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_surjD) ).
thf(375,plain,
! [A: finite964658038_int_n > finite964658038_int_n,B: finite964658038_int_n] :
( ( ( image_1278151539_int_n @ A @ top_to131672412_int_n )
= top_to131672412_int_n )
=> ? [C: finite964658038_int_n] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(67,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_198_IntD1) ).
thf(513,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)],[67]) ).
thf(43,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_215_vimageE) ).
thf(430,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)],[43]) ).
thf(86,axiom,
! [A: set_nat,B: set_nat,C: nat > set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n,E: set_se2111327970real_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [F: nat] :
( ( member_nat @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_1856576259real_n @ C @ A ) )
= ( E @ ( image_1856576259real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Sup_OSUP__cong) ).
thf(584,plain,
! [A: set_nat,B: set_nat,C: nat > set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n,E: set_se2111327970real_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [F: nat] :
( ( member_nat @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_1856576259real_n @ C @ A ) )
= ( E @ ( image_1856576259real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(126,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_se2111327970real_n] :
( ( image_1856576259real_n @ A @ ( vimage3210681real_n @ A @ B ) )
= ( inf_in632889204real_n @ B @ ( image_1856576259real_n @ A @ top_top_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_image__vimage__eq) ).
thf(732,plain,
! [A: nat > set_Fi1058188332real_n,B: set_se2111327970real_n] :
( ( image_1856576259real_n @ A @ ( vimage3210681real_n @ A @ B ) )
= ( inf_in632889204real_n @ B @ ( image_1856576259real_n @ A @ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(150,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_312_vimage__inter__cong) ).
thf(826,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)],[150]) ).
thf(1225,plain,
( ( ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ A )
& ( member1352538125real_n @ C @ B ) ) ) )
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B @ A ) ) )
| ( inf_in1974387902real_n != inf_in1974387902real_n ) ),
inference(paramod_ordered,[status(thm)],[479,825]) ).
thf(1226,plain,
( ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ A )
& ( member1352538125real_n @ C @ B ) ) ) )
= ( ^ [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[1225:[]]) ).
thf(182,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_179_is__num__normalize_I1_J) ).
thf(936,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)],[182]) ).
thf(82,axiom,
! [A: set_nat] :
( ! [B: nat] : ( member_nat @ B @ A )
=> ( top_top_set_nat = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_UNIV__eq__I) ).
thf(572,plain,
! [A: set_nat] :
( ! [B: nat] : ( member_nat @ B @ A )
=> ( top_top_set_nat = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(53,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n] :
( ( ( image_439535603real_n @ A @ top_to1292442332real_n )
= top_to1292442332real_n )
=> ? [C: finite1489363574real_n] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_surjD) ).
thf(466,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n] :
( ( ( image_439535603real_n @ A @ top_to1292442332real_n )
= top_to1292442332real_n )
=> ? [C: finite1489363574real_n] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(143,axiom,
! [A: nat > nat > set_Fi1058188332real_n,B: set_nat,C: set_nat] :
( ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] : ( comple825005695real_n @ ( image_1856576259real_n @ ( A @ D ) @ B ) )
@ C ) )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] :
( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [E: nat] : ( A @ E @ D )
@ C ) )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_SUP__commute) ).
thf(804,plain,
! [A: nat > nat > set_Fi1058188332real_n,B: set_nat,C: set_nat] :
( ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] : ( comple825005695real_n @ ( image_1856576259real_n @ ( A @ D ) @ B ) )
@ C ) )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] :
( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [E: nat] : ( A @ E @ D )
@ C ) )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(118,axiom,
! [A: set_Ex113815278nnreal] :
( ( image_2066995319nnreal @ ( plus_p1763960001nnreal @ zero_z1963244097nnreal ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_image__add__0) ).
thf(704,plain,
! [A: set_Ex113815278nnreal] :
( ( image_2066995319nnreal @ ( plus_p1763960001nnreal @ zero_z1963244097nnreal ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(120,axiom,
! [A: nat > set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ! [C: nat] : ( member223413699real_n @ ( A @ C ) @ ( measur1402256771real_n @ B ) )
=> ( member223413699real_n @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ top_top_set_nat ) ) @ ( measur1402256771real_n @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_null__sets__UN) ).
thf(713,plain,
! [A: nat > set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ! [C: nat] : ( member223413699real_n @ ( A @ C ) @ ( measur1402256771real_n @ B ) )
=> ( member223413699real_n @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ top_top_set_nat ) ) @ ( measur1402256771real_n @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(62,axiom,
! [A: set_se2111327970real_n] :
( ! [B: set_Fi1058188332real_n] : ( member223413699real_n @ B @ A )
=> ( top_to20708754real_n = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_UNIV__eq__I) ).
thf(498,plain,
! [A: set_se2111327970real_n] :
( ! [B: set_Fi1058188332real_n] : ( member223413699real_n @ B @ A )
=> ( top_to20708754real_n = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(39,axiom,
! [A: set_Fi160064172_int_n,B: set_Fi160064172_int_n,C: finite964658038_int_n > set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n,E: set_se2111327970real_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [F: finite964658038_int_n] :
( ( member27055245_int_n @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_355963305real_n @ C @ A ) )
= ( E @ ( image_355963305real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_Inf_OINF__cong) ).
thf(406,plain,
! [A: set_Fi160064172_int_n,B: set_Fi160064172_int_n,C: finite964658038_int_n > set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n,E: set_se2111327970real_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [F: finite964658038_int_n] :
( ( member27055245_int_n @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_355963305real_n @ C @ A ) )
= ( E @ ( image_355963305real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(205,axiom,
! [A: finite964658038_int_n,B: set_Fi160064172_int_n,C: set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n] :
( ( member27055245_int_n @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member223413699real_n @ C @ ( image_355963305real_n @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_rev__image__eqI) ).
thf(1011,plain,
! [A: finite964658038_int_n,B: set_Fi160064172_int_n,C: set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n] :
( ( member27055245_int_n @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member223413699real_n @ C @ ( image_355963305real_n @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(216,axiom,
! [A: nat > finite964658038_int_n] :
( ( ( image_1961920973_int_n @ A @ top_top_set_nat )
= top_to131672412_int_n )
= ( ! [B: finite964658038_int_n] :
? [C: nat] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_surj__def) ).
thf(1048,plain,
! [A: nat > finite964658038_int_n] :
( ( ( image_1961920973_int_n @ A @ top_top_set_nat )
= top_to131672412_int_n )
= ( ! [B: finite964658038_int_n] :
? [C: nat] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(80,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_172_imageI) ).
thf(567,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)],[80]) ).
thf(242,axiom,
! [A: set_Ex113815278nnreal] :
( ( ( comple1413366923nnreal @ A )
= top_to1845833192nnreal )
= ( ! [B: extend1728876344nnreal] :
( ( ord_le2133614988nnreal @ B @ top_to1845833192nnreal )
=> ? [C: extend1728876344nnreal] :
( ( member1217042383nnreal @ C @ A )
& ( ord_le2133614988nnreal @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Sup__eq__top__iff) ).
thf(1144,plain,
! [A: set_Ex113815278nnreal] :
( ( ( comple1413366923nnreal @ A )
= top_to1845833192nnreal )
= ( ! [B: extend1728876344nnreal] :
( ( ord_le2133614988nnreal @ B @ top_to1845833192nnreal )
=> ? [C: extend1728876344nnreal] :
( ( member1217042383nnreal @ C @ A )
& ( ord_le2133614988nnreal @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(18,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n] : ( member1352538125real_n @ ( A @ B ) @ ( image_439535603real_n @ A @ top_to1292442332real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_rangeI) ).
thf(318,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n] : ( member1352538125real_n @ ( A @ B ) @ ( image_439535603real_n @ A @ top_to1292442332real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(65,axiom,
! [A: nat] : ( member_nat @ A @ top_top_set_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_UNIV__I) ).
thf(509,plain,
! [A: nat] : ( member_nat @ A @ top_top_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(235,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi1058188332real_n > finite964658038_int_n] :
( ! [C: set_Fi1058188332real_n] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_355963305real_n @ A @ top_to131672412_int_n )
= top_to20708754real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_surjI) ).
thf(1122,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi1058188332real_n > finite964658038_int_n] :
( ! [C: set_Fi1058188332real_n] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_355963305real_n @ A @ top_to131672412_int_n )
= top_to20708754real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(4,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_250_Int__def) ).
thf(271,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)],[4]) ).
thf(89,axiom,
! [A: finite1489363574real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: set_Fi160064172_int_n] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ ( image_355963305real_n @ B @ C ) ) )
= ( ? [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ C )
& ( member1352538125real_n @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_UN__iff) ).
thf(599,plain,
! [A: finite1489363574real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: set_Fi160064172_int_n] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ ( image_355963305real_n @ B @ C ) ) )
= ( ? [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ C )
& ( member1352538125real_n @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(198,axiom,
! [A: set_Fi160064172_int_n,B: set_Fi160064172_int_n] :
( ( ( inf_in1108485182_int_n @ A @ B )
= top_to131672412_int_n )
= ( ( A = top_to131672412_int_n )
& ( B = top_to131672412_int_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Int__UNIV) ).
thf(990,plain,
! [A: set_Fi160064172_int_n,B: set_Fi160064172_int_n] :
( ( ( inf_in1108485182_int_n @ A @ B )
= top_to131672412_int_n )
= ( ( A = top_to131672412_int_n )
& ( B = top_to131672412_int_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(200,axiom,
! [A: finite1489363574real_n,B: set_se2111327970real_n] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ B ) )
= ( ? [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ B )
& ( member1352538125real_n @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Union__iff) ).
thf(996,plain,
! [A: finite1489363574real_n,B: set_se2111327970real_n] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ B ) )
= ( ? [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ B )
& ( member1352538125real_n @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(158,axiom,
! [A: set_se2111327970real_n,B: set_Fi1058188332real_n > sigma_1466784463real_n,C: set_Fi1058188332real_n > sigma_1466784463real_n] :
( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ A )
=> ( ( sigma_1235138647real_n @ ( B @ D ) )
= ( sigma_1235138647real_n @ ( C @ D ) ) ) )
=> ( ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_987430492real_n @ B @ A ) ) )
= ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_987430492real_n @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_sets__SUP__cong) ).
thf(858,plain,
! [A: set_se2111327970real_n,B: set_Fi1058188332real_n > sigma_1466784463real_n,C: set_Fi1058188332real_n > sigma_1466784463real_n] :
( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ A )
=> ( ( sigma_1235138647real_n @ ( B @ D ) )
= ( sigma_1235138647real_n @ ( C @ D ) ) ) )
=> ( ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_987430492real_n @ B @ A ) ) )
= ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_987430492real_n @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(124,axiom,
! [A: set_nat] :
( ( inf_inf_set_nat @ top_top_set_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_Int__UNIV__left) ).
thf(726,plain,
! [A: set_nat] :
( ( inf_inf_set_nat @ top_top_set_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(96,axiom,
( ( comple825005695real_n @ top_to20708754real_n )
= top_to1292442332real_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_Union__UNIV) ).
thf(621,plain,
( ( comple825005695real_n @ top_to20708754real_n )
= top_to1292442332real_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(108,axiom,
( ( minus_1037315151real_n @ one_on1253059131real_n @ one_on1253059131real_n )
= zero_z200130687real_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_diff__numeral__special_I9_J) ).
thf(667,plain,
( ( minus_1037315151real_n @ one_on1253059131real_n @ one_on1253059131real_n )
= zero_z200130687real_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(668,plain,
( ( minus_1037315151real_n @ one_on1253059131real_n @ one_on1253059131real_n )
= zero_z200130687real_n ),
inference(lifteq,[status(thm)],[667]) ).
thf(52,axiom,
! [A: nat > nat,B: nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ? [C: nat] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_surjD) ).
thf(462,plain,
! [A: nat > nat,B: nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
=> ? [C: nat] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(69,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_164_image__cong) ).
thf(521,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)],[69]) ).
thf(38,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_167_bex__imageD) ).
thf(399,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)],[38]) ).
thf(137,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ ( comple825005695real_n @ ( image_355963305real_n @ A @ B ) ) @ C )
= ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( minus_1686442501real_n @ ( A @ D ) @ C )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_UN__extend__simps_I6_J) ).
thf(780,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ ( comple825005695real_n @ ( image_355963305real_n @ A @ B ) ) @ C )
= ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( minus_1686442501real_n @ ( A @ D ) @ C )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(234,axiom,
! [A: set_se2111327970real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > set_Fi1058188332real_n,D: set_Fi1058188332real_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comple825005695real_n @ ( image_1661509983real_n @ C @ A ) )
= ( comple825005695real_n @ ( image_1661509983real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_SUP__cong) ).
thf(1113,plain,
! [A: set_se2111327970real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > set_Fi1058188332real_n,D: set_Fi1058188332real_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [E: set_Fi1058188332real_n] :
( ( member223413699real_n @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comple825005695real_n @ ( image_1661509983real_n @ C @ A ) )
= ( comple825005695real_n @ ( image_1661509983real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(46,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_37_image__eqI) ).
thf(438,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)],[46]) ).
thf(255,axiom,
! [A: nat > set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ! [C: nat] : ( member223413699real_n @ ( A @ C ) @ ( sigma_1235138647real_n @ B ) )
=> ( ! [C: nat,D: nat] :
( ( C != D )
=> ( ( sigma_1536574303real_n @ B @ ( inf_in1974387902real_n @ ( A @ C ) @ ( A @ D ) ) )
= zero_z1963244097nnreal ) )
=> ( sums_E1192373732nnreal
@ ^ [C: nat] : ( sigma_1536574303real_n @ B @ ( A @ C ) )
@ ( sigma_1536574303real_n @ B @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ top_top_set_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_sums__emeasure_H) ).
thf(1176,plain,
! [A: nat > set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ! [C: nat] : ( member223413699real_n @ ( A @ C ) @ ( sigma_1235138647real_n @ B ) )
=> ( ! [C: nat,D: nat] :
( ( C != D )
=> ( ( sigma_1536574303real_n @ B @ ( inf_in1974387902real_n @ ( A @ C ) @ ( A @ D ) ) )
= zero_z1963244097nnreal ) )
=> ( sums_E1192373732nnreal
@ ^ [C: nat] : ( sigma_1536574303real_n @ B @ ( A @ C ) )
@ ( sigma_1536574303real_n @ B @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ top_top_set_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(92,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n] :
( ( ( image_439535603real_n @ A @ top_to1292442332real_n )
= top_to1292442332real_n )
=> ~ ! [C: finite1489363574real_n] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_surjE) ).
thf(608,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n] :
( ( ( image_439535603real_n @ A @ top_to1292442332real_n )
= top_to1292442332real_n )
=> ~ ! [C: finite1489363574real_n] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(55,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_48_Int__iff) ).
thf(473,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)],[55]) ).
thf(1208,plain,
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ sk71 ) ) )
!= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ sk71 ) ) ) ),
inference(func_ext,[status(esa)],[267]) ).
thf(184,axiom,
! [A: nat > finite964658038_int_n,B: finite964658038_int_n > nat] :
( ! [C: finite964658038_int_n] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_1961920973_int_n @ A @ top_top_set_nat )
= top_to131672412_int_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_surjI) ).
thf(944,plain,
! [A: nat > finite964658038_int_n,B: finite964658038_int_n > nat] :
( ! [C: finite964658038_int_n] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_1961920973_int_n @ A @ top_top_set_nat )
= top_to131672412_int_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(179,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( ( inf_in1974387902real_n @ A @ ( sigma_476185326real_n @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_null__sets_OInt__space__eq2) ).
thf(927,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( ( inf_in1974387902real_n @ A @ ( sigma_476185326real_n @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(226,axiom,
! [A: finite964658038_int_n > finite964658038_int_n] :
( ( vimage1122713129_int_n @ A @ top_to131672412_int_n )
= top_to131672412_int_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_vimage__UNIV) ).
thf(1081,plain,
! [A: finite964658038_int_n > finite964658038_int_n] :
( ( vimage1122713129_int_n @ A @ top_to131672412_int_n )
= top_to131672412_int_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(68,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_153_rev__image__eqI) ).
thf(516,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)],[68]) ).
thf(183,axiom,
! [A: set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: finite964658038_int_n,D: set_Fi160064172_int_n] :
( ( A
= ( B @ C ) )
=> ( ( member27055245_int_n @ C @ D )
=> ( member223413699real_n @ A @ ( image_355963305real_n @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_image__eqI) ).
thf(939,plain,
! [A: set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: finite964658038_int_n,D: set_Fi160064172_int_n] :
( ( A
= ( B @ C ) )
=> ( ( member27055245_int_n @ C @ D )
=> ( member223413699real_n @ A @ ( image_355963305real_n @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(207,axiom,
! [A: nat > set_Fi1058188332real_n,B: finite964658038_int_n > set_nat,C: set_Fi160064172_int_n] :
( ( comple825005695real_n @ ( image_1856576259real_n @ A @ ( comple1682161881et_nat @ ( image_1085873667et_nat @ B @ C ) ) ) )
= ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( comple825005695real_n @ ( image_1856576259real_n @ A @ ( B @ D ) ) )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_UN__UN__flatten) ).
thf(1018,plain,
! [A: nat > set_Fi1058188332real_n,B: finite964658038_int_n > set_nat,C: set_Fi160064172_int_n] :
( ( comple825005695real_n @ ( image_1856576259real_n @ A @ ( comple1682161881et_nat @ ( image_1085873667et_nat @ B @ C ) ) ) )
= ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( comple825005695real_n @ ( image_1856576259real_n @ A @ ( B @ D ) ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(133,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: finite1489363574real_n] :
( ( member223413699real_n @ A @ B )
=> ( ( member1352538125real_n @ C @ A )
=> ( member1352538125real_n @ C @ ( comple825005695real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_UnionI) ).
thf(754,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: finite1489363574real_n] :
( ( member223413699real_n @ A @ B )
=> ( ( member1352538125real_n @ C @ A )
=> ( member1352538125real_n @ C @ ( comple825005695real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(140,axiom,
! [A: nat > finite964658038_int_n] :
( ( vimage714719107_int_n @ A @ top_to131672412_int_n )
= top_top_set_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_vimage__UNIV) ).
thf(795,plain,
! [A: nat > finite964658038_int_n] :
( ( vimage714719107_int_n @ A @ top_to131672412_int_n )
= top_top_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(112,axiom,
! [A: finite964658038_int_n > finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: set_Fi160064172_int_n] :
( ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( comple825005695real_n @ ( image_355963305real_n @ ( A @ D ) @ B ) )
@ C ) )
= ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] :
( comple825005695real_n
@ ( image_355963305real_n
@ ^ [E: finite964658038_int_n] : ( A @ E @ D )
@ C ) )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_SUP__commute) ).
thf(680,plain,
! [A: finite964658038_int_n > finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: set_Fi160064172_int_n] :
( ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( comple825005695real_n @ ( image_355963305real_n @ ( A @ D ) @ B ) )
@ C ) )
= ( comple825005695real_n
@ ( image_355963305real_n
@ ^ [D: finite964658038_int_n] :
( comple825005695real_n
@ ( image_355963305real_n
@ ^ [E: finite964658038_int_n] : ( A @ E @ D )
@ C ) )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(77,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_53_IntI) ).
thf(557,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)],[77]) ).
thf(157,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n] :
( ( inf_in1974387902real_n @ A @ ( comple825005695real_n @ B ) )
= ( comple825005695real_n @ ( image_1661509983real_n @ ( inf_in1974387902real_n @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Int__Union) ).
thf(855,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n] :
( ( inf_in1974387902real_n @ A @ ( comple825005695real_n @ B ) )
= ( comple825005695real_n @ ( image_1661509983real_n @ ( inf_in1974387902real_n @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(222,axiom,
! [A: nat > set_Fi1058188332real_n,B: nat] : ( member223413699real_n @ ( A @ B ) @ ( image_1856576259real_n @ A @ top_top_set_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_rangeI) ).
thf(1070,plain,
! [A: nat > set_Fi1058188332real_n,B: nat] : ( member223413699real_n @ ( A @ B ) @ ( image_1856576259real_n @ A @ top_top_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(119,axiom,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > sigma_1466784463real_n,D: set_Fi1058188332real_n,E: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ B )
=> ( ! [F: set_Fi1058188332real_n] :
( ( member223413699real_n @ F @ B )
=> ( ( sigma_476185326real_n @ ( C @ F ) )
= D ) )
=> ( ( member223413699real_n @ E @ ( sigma_1235138647real_n @ ( C @ A ) ) )
=> ( member223413699real_n @ E @ ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_987430492real_n @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_in__sets__SUP) ).
thf(707,plain,
! [A: set_Fi1058188332real_n,B: set_se2111327970real_n,C: set_Fi1058188332real_n > sigma_1466784463real_n,D: set_Fi1058188332real_n,E: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ B )
=> ( ! [F: set_Fi1058188332real_n] :
( ( member223413699real_n @ F @ B )
=> ( ( sigma_476185326real_n @ ( C @ F ) )
= D ) )
=> ( ( member223413699real_n @ E @ ( sigma_1235138647real_n @ ( C @ A ) ) )
=> ( member223413699real_n @ E @ ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_987430492real_n @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(192,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_se2111327970real_n] :
( ( image_355963305real_n @ A @ ( vimage464515423real_n @ A @ B ) )
= ( inf_in632889204real_n @ B @ ( image_355963305real_n @ A @ top_to131672412_int_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_image__vimage__eq) ).
thf(971,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_se2111327970real_n] :
( ( image_355963305real_n @ A @ ( vimage464515423real_n @ A @ B ) )
= ( inf_in632889204real_n @ B @ ( image_355963305real_n @ A @ top_to131672412_int_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(199,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ ( minus_1686442501real_n @ A @ C ) @ ( measur1402256771real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_null__set__Diff) ).
thf(993,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n,C: set_Fi1058188332real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( ( member223413699real_n @ C @ ( sigma_1235138647real_n @ B ) )
=> ( member223413699real_n @ ( minus_1686442501real_n @ A @ C ) @ ( measur1402256771real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(8,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_210_vimageI2) ).
thf(282,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)],[8]) ).
thf(246,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_10_T_H__def) ).
thf(1156,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)],[246]) ).
thf(1188,plain,
( ( counta1142393929_int_n @ top_to131672412_int_n )
= f ),
inference(lifteq,[status(thm)],[1187]) ).
thf(213,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( ( image_355963305real_n @ A @ top_to131672412_int_n )
= top_to20708754real_n )
=> ~ ! [C: finite964658038_int_n] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_surjE) ).
thf(1038,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
( ( ( image_355963305real_n @ A @ top_to131672412_int_n )
= top_to20708754real_n )
=> ~ ! [C: finite964658038_int_n] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(54,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_169_image__iff) ).
thf(470,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)],[54]) ).
thf(159,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: nat > finite964658038_int_n,C: set_nat] :
( ( image_355963305real_n @ A @ ( image_1961920973_int_n @ B @ C ) )
= ( image_1856576259real_n
@ ^ [D: nat] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_image__image) ).
thf(864,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: nat > finite964658038_int_n,C: set_nat] :
( ( image_355963305real_n @ A @ ( image_1961920973_int_n @ B @ C ) )
= ( image_1856576259real_n
@ ^ [D: nat] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(204,axiom,
! [A: finite964658038_int_n > nat] :
( ( ( image_497739341_n_nat @ A @ top_to131672412_int_n )
= top_top_set_nat )
= ( ! [B: nat] :
? [C: finite964658038_int_n] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_surj__def) ).
thf(1008,plain,
! [A: finite964658038_int_n > nat] :
( ( ( image_497739341_n_nat @ A @ top_to131672412_int_n )
= top_top_set_nat )
= ( ! [B: nat] :
? [C: finite964658038_int_n] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(48,axiom,
! [A: set_Fi1058188332real_n] : ( member223413699real_n @ A @ top_to20708754real_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_UNIV__I) ).
thf(446,plain,
! [A: set_Fi1058188332real_n] : ( member223413699real_n @ A @ top_to20708754real_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(93,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: set_Fi1058188332real_n > $o] :
( ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_1856576259real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_1856576259real_n @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_Compr__image__eq) ).
thf(612,plain,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: set_Fi1058188332real_n > $o] :
( ( collec452821761real_n
@ ^ [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_1856576259real_n @ A @ B ) )
& ( C @ D ) ) )
= ( image_1856576259real_n @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(163,axiom,
! [A: finite1489363574real_n] :
( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ top_to1292442332real_n )
= top_to1292442332real_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_surj__plus) ).
thf(876,plain,
! [A: finite1489363574real_n] :
( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ top_to1292442332real_n )
= top_to1292442332real_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(230,axiom,
! [A: set_Fi160064172_int_n,B: set_Fi160064172_int_n,C: finite964658038_int_n > set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [E: finite964658038_int_n] :
( ( member27055245_int_n @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comple825005695real_n @ ( image_355963305real_n @ C @ A ) )
= ( comple825005695real_n @ ( image_355963305real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_SUP__cong) ).
thf(1094,plain,
! [A: set_Fi160064172_int_n,B: set_Fi160064172_int_n,C: finite964658038_int_n > set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [E: finite964658038_int_n] :
( ( member27055245_int_n @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comple825005695real_n @ ( image_355963305real_n @ C @ A ) )
= ( comple825005695real_n @ ( image_355963305real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(194,axiom,
! [A: nat > set_Fi1058188332real_n,B: finite964658038_int_n > nat,C: set_Fi160064172_int_n] :
( ( image_1856576259real_n @ A @ ( image_497739341_n_nat @ B @ C ) )
= ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_image__image) ).
thf(978,plain,
! [A: nat > set_Fi1058188332real_n,B: finite964658038_int_n > nat,C: set_Fi160064172_int_n] :
( ( image_1856576259real_n @ A @ ( image_497739341_n_nat @ B @ C ) )
= ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(154,axiom,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_null__setsD2) ).
thf(845,plain,
! [A: set_Fi1058188332real_n,B: sigma_1466784463real_n] :
( ( member223413699real_n @ A @ ( measur1402256771real_n @ B ) )
=> ( member223413699real_n @ A @ ( sigma_1235138647real_n @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(227,axiom,
! [A: finite964658038_int_n > nat,B: nat] :
( ( ( image_497739341_n_nat @ A @ top_to131672412_int_n )
= top_top_set_nat )
=> ~ ! [C: finite964658038_int_n] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_surjE) ).
thf(1084,plain,
! [A: finite964658038_int_n > nat,B: nat] :
( ( ( image_497739341_n_nat @ A @ top_to131672412_int_n )
= top_top_set_nat )
=> ~ ! [C: finite964658038_int_n] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(30,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 ) ) )
=> ( ( comple2042271945real_n @ ( image_439535603real_n @ C @ A ) )
= ( comple2042271945real_n @ ( image_439535603real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_SUP__cong) ).
thf(363,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 ) ) )
=> ( ( comple2042271945real_n @ ( image_439535603real_n @ C @ A ) )
= ( comple2042271945real_n @ ( image_439535603real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(71,axiom,
? [A: set_Fi1058188332real_n] : ( member223413699real_n @ A @ top_to20708754real_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_UNIV__witness) ).
thf(539,plain,
? [A: set_Fi1058188332real_n] : ( member223413699real_n @ A @ top_to20708754real_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1157,plain,
( ( ^ [A: finite964658038_int_n] :
( image_439535603real_n
@ ^ [B: finite1489363574real_n] : ( minus_1037315151real_n @ B @ ( minkow1134813771n_real @ A ) )
@ ( t2 @ A ) ) )
= t ),
inference(lifteq,[status(thm)],[1156]) ).
thf(85,axiom,
! [A: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ top_to1292442332real_n @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_Int__UNIV__left) ).
thf(581,plain,
! [A: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ top_to1292442332real_n @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(61,axiom,
! [A: finite964658038_int_n > finite964658038_int_n] :
( ( ( image_1278151539_int_n @ A @ top_to131672412_int_n )
= top_to131672412_int_n )
= ( ! [B: finite964658038_int_n] :
? [C: finite964658038_int_n] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_surj__def) ).
thf(495,plain,
! [A: finite964658038_int_n > finite964658038_int_n] :
( ( ( image_1278151539_int_n @ A @ top_to131672412_int_n )
= top_to131672412_int_n )
= ( ! [B: finite964658038_int_n] :
? [C: finite964658038_int_n] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(1215,plain,
( ( ( comple230862828real_n @ lebesg260170249real_n )
!= ( comple230862828real_n @ lebesg260170249real_n ) )
| ( ( t2 @ ( f @ sk71 ) )
!= ( t @ ( f @ sk71 ) ) ) ),
inference(simp,[status(thm)],[1208]) ).
thf(1216,plain,
( ( t2 @ ( f @ sk71 ) )
!= ( t @ ( f @ sk71 ) ) ),
inference(simp,[status(thm)],[1215]) ).
thf(236,axiom,
! [A: nat > set_Fi1058188332real_n,B: finite964658038_int_n > nat] :
( ( image_355963305real_n
@ ^ [C: finite964658038_int_n] : ( A @ ( B @ C ) )
@ top_to131672412_int_n )
= ( image_1856576259real_n @ A @ ( image_497739341_n_nat @ B @ top_to131672412_int_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_range__composition) ).
thf(1126,plain,
! [A: nat > set_Fi1058188332real_n,B: finite964658038_int_n > nat] :
( ( image_355963305real_n
@ ^ [C: finite964658038_int_n] : ( A @ ( B @ C ) )
@ top_to131672412_int_n )
= ( image_1856576259real_n @ A @ ( image_497739341_n_nat @ B @ top_to131672412_int_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(259,axiom,
! [A: finite964658038_int_n,B: finite964658038_int_n] :
( ( A != B )
=> ( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( inf_in1974387902real_n @ ( t2 @ A ) @ ( t2 @ B ) ) )
= zero_z1963244097nnreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_emeasure__T__Int) ).
thf(1189,plain,
! [A: finite964658038_int_n,B: finite964658038_int_n] :
( ( A != B )
=> ( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( inf_in1974387902real_n @ ( t2 @ A ) @ ( t2 @ B ) ) )
= zero_z1963244097nnreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(189,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_234_image__image) ).
thf(963,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)],[189]) ).
thf(15,axiom,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n,C: set_nat] :
( ( image_1661509983real_n @ A @ ( image_1856576259real_n @ B @ C ) )
= ( image_1856576259real_n
@ ^ [D: nat] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_image__image) ).
thf(304,plain,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n,C: set_nat] :
( ( image_1661509983real_n @ A @ ( image_1856576259real_n @ B @ C ) )
= ( image_1856576259real_n
@ ^ [D: nat] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(169,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_129_Diff__Diff__Int) ).
thf(896,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)],[169]) ).
thf(131,axiom,
! [A: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_Int__absorb) ).
thf(748,plain,
! [A: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(41,axiom,
! [A: set_Fi160064172_int_n,B: set_Fi160064172_int_n,C: finite964658038_int_n > set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n,E: set_se2111327970real_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [F: finite964658038_int_n] :
( ( member27055245_int_n @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_355963305real_n @ C @ A ) )
= ( E @ ( image_355963305real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_Sup_OSUP__cong) ).
thf(418,plain,
! [A: set_Fi160064172_int_n,B: set_Fi160064172_int_n,C: finite964658038_int_n > set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n,E: set_se2111327970real_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [F: finite964658038_int_n] :
( ( member27055245_int_n @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_355963305real_n @ C @ A ) )
= ( E @ ( image_355963305real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(139,axiom,
! [A: set_nat,B: set_nat,C: nat > set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [E: nat] :
( ( member_nat @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comple825005695real_n @ ( image_1856576259real_n @ C @ A ) )
= ( comple825005695real_n @ ( image_1856576259real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_SUP__cong) ).
thf(786,plain,
! [A: set_nat,B: set_nat,C: nat > set_Fi1058188332real_n,D: nat > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [E: nat] :
( ( member_nat @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comple825005695real_n @ ( image_1856576259real_n @ C @ A ) )
= ( comple825005695real_n @ ( image_1856576259real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(211,axiom,
! [A: finite964658038_int_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( image_2058828787real_n @ A @ ( vimage1276736425real_n @ A @ B ) )
= ( inf_in1974387902real_n @ B @ ( image_2058828787real_n @ A @ top_to131672412_int_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_image__vimage__eq) ).
thf(1030,plain,
! [A: finite964658038_int_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( image_2058828787real_n @ A @ ( vimage1276736425real_n @ A @ B ) )
= ( inf_in1974387902real_n @ B @ ( image_2058828787real_n @ A @ top_to131672412_int_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(11,axiom,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n] :
( ( member1352538125real_n @ A @ ( image_439535603real_n @ B @ top_to1292442332real_n ) )
=> ~ ! [C: finite1489363574real_n] :
( A
!= ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_rangeE) ).
thf(290,plain,
! [A: finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n] :
( ( member1352538125real_n @ A @ ( image_439535603real_n @ B @ top_to1292442332real_n ) )
=> ~ ! [C: finite1489363574real_n] :
( A
!= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(510,plain,
! [A: nat] : ( member_nat @ A @ top_top_set_nat ),
inference(cnf,[status(esa)],[509]) ).
thf(261,axiom,
! [A: finite964658038_int_n,B: finite964658038_int_n] :
( ( A != B )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( t2 @ A ) @ ( t2 @ B ) ) @ ( measur1402256771real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_T__Int) ).
thf(1193,plain,
! [A: finite964658038_int_n,B: finite964658038_int_n] :
( ( A != B )
=> ( member223413699real_n @ ( inf_in1974387902real_n @ ( t2 @ A ) @ ( t2 @ B ) ) @ ( measur1402256771real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(272,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(lifteq,[status(thm)],[271]) ).
thf(34,axiom,
! [A: set_o,B: $o > sigma_1466784463real_n,C: $o > sigma_1466784463real_n] :
( ! [D: $o] :
( ( member_o @ D @ A )
=> ( ( sigma_1235138647real_n @ ( B @ D ) )
= ( sigma_1235138647real_n @ ( C @ D ) ) ) )
=> ( ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_1599934780real_n @ B @ A ) ) )
= ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_1599934780real_n @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_sets__SUP__cong) ).
thf(383,plain,
! [A: set_o,B: $o > sigma_1466784463real_n,C: $o > sigma_1466784463real_n] :
( ! [D: $o] :
( ( member_o @ D @ A )
=> ( ( sigma_1235138647real_n @ ( B @ D ) )
= ( sigma_1235138647real_n @ ( C @ D ) ) ) )
=> ( ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_1599934780real_n @ B @ A ) ) )
= ( sigma_1235138647real_n @ ( comple488165692real_n @ ( image_1599934780real_n @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(170,axiom,
! [A: extend1728876344nnreal,B: set_Ex113815278nnreal] :
( ( ord_le2133614988nnreal @ A @ ( comple1413366923nnreal @ B ) )
= ( ? [C: extend1728876344nnreal] :
( ( member1217042383nnreal @ C @ B )
& ( ord_le2133614988nnreal @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_less__Sup__iff) ).
thf(899,plain,
! [A: extend1728876344nnreal,B: set_Ex113815278nnreal] :
( ( ord_le2133614988nnreal @ A @ ( comple1413366923nnreal @ B ) )
= ( ? [C: extend1728876344nnreal] :
( ( member1217042383nnreal @ C @ B )
& ( ord_le2133614988nnreal @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(25,axiom,
! [A: nat > nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
= ( ! [B: nat] :
? [C: nat] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_surj__def) ).
thf(346,plain,
! [A: nat > nat] :
( ( ( image_nat_nat @ A @ top_top_set_nat )
= top_top_set_nat )
= ( ! [B: nat] :
? [C: nat] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(215,axiom,
! [A: nat > set_Fi1058188332real_n,B: nat > nat] :
( ( image_1856576259real_n
@ ^ [C: nat] : ( A @ ( B @ C ) )
@ top_top_set_nat )
= ( image_1856576259real_n @ A @ ( image_nat_nat @ B @ top_top_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_range__composition) ).
thf(1045,plain,
! [A: nat > set_Fi1058188332real_n,B: nat > nat] :
( ( image_1856576259real_n
@ ^ [C: nat] : ( A @ ( B @ C ) )
@ top_top_set_nat )
= ( image_1856576259real_n @ A @ ( image_nat_nat @ B @ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(10,axiom,
! [A: nat,B: set_nat,C: finite1489363574real_n,D: nat > set_Fi1058188332real_n] :
( ( member_nat @ A @ B )
=> ( ( member1352538125real_n @ C @ ( D @ A ) )
=> ( member1352538125real_n @ C @ ( comple825005695real_n @ ( image_1856576259real_n @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_UN__I) ).
thf(287,plain,
! [A: nat,B: set_nat,C: finite1489363574real_n,D: nat > set_Fi1058188332real_n] :
( ( member_nat @ A @ B )
=> ( ( member1352538125real_n @ C @ ( D @ A ) )
=> ( member1352538125real_n @ C @ ( comple825005695real_n @ ( image_1856576259real_n @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(447,plain,
! [A: set_Fi1058188332real_n] : ( member223413699real_n @ A @ top_to20708754real_n ),
inference(cnf,[status(esa)],[446]) ).
thf(44,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: finite964658038_int_n > finite964658038_int_n,C: set_Fi160064172_int_n] :
( ( image_355963305real_n @ A @ ( image_1278151539_int_n @ B @ C ) )
= ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_image__image) ).
thf(432,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: finite964658038_int_n > finite964658038_int_n,C: set_Fi160064172_int_n] :
( ( image_355963305real_n @ A @ ( image_1278151539_int_n @ B @ C ) )
= ( image_355963305real_n
@ ^ [D: finite964658038_int_n] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(151,axiom,
! [A: set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n,C: set_nat] :
( ( member223413699real_n @ A @ ( image_1856576259real_n @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_image__iff) ).
thf(833,plain,
! [A: set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n,C: set_nat] :
( ( member223413699real_n @ A @ ( image_1856576259real_n @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(147,axiom,
! [A: set_se2111327970real_n,B: finite1489363574real_n > $o] :
( ( ? [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ ( comple825005695real_n @ A ) )
& ( B @ C ) ) )
= ( ? [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ A )
& ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ C )
& ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_UN__ball__bex__simps_I3_J) ).
thf(818,plain,
! [A: set_se2111327970real_n,B: finite1489363574real_n > $o] :
( ( ? [C: finite1489363574real_n] :
( ( member1352538125real_n @ C @ ( comple825005695real_n @ A ) )
& ( B @ C ) ) )
= ( ? [C: set_Fi1058188332real_n] :
( ( member223413699real_n @ C @ A )
& ? [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ C )
& ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(127,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_313_translation__subtract__diff) ).
thf(735,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)],[127]) ).
thf(201,axiom,
! [A: set_Fi1058188332real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( A
@ ( image_439535603real_n
@ ^ [C: finite1489363574real_n] : C
@ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_Inf_OINF__identity__eq) ).
thf(999,plain,
! [A: set_Fi1058188332real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( ( A
@ ( image_439535603real_n
@ ^ [C: finite1489363574real_n] : C
@ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(620,plain,
( vimage1233683625real_n
= ( ^ [A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [C: finite1489363574real_n] : ( member1352538125real_n @ ( A @ C ) @ B ) ) ) ),
inference(lifteq,[status(thm)],[619]) ).
thf(160,axiom,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n] :
( ( image_355963305real_n
@ ^ [C: finite964658038_int_n] : ( A @ ( B @ C ) )
@ top_to131672412_int_n )
= ( image_1661509983real_n @ A @ ( image_355963305real_n @ B @ top_to131672412_int_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_range__composition) ).
thf(867,plain,
! [A: set_Fi1058188332real_n > set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n] :
( ( image_355963305real_n
@ ^ [C: finite964658038_int_n] : ( A @ ( B @ C ) )
@ top_to131672412_int_n )
= ( image_1661509983real_n @ A @ ( image_355963305real_n @ B @ top_to131672412_int_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(79,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: finite1489363574real_n > $o] :
( ( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_UN__ball__bex__simps_I2_J) ).
thf(564,plain,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: finite1489363574real_n > $o] :
( ( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(144,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: set_Fi1058188332real_n > $o] :
( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_1856576259real_n @ A @ B ) )
=> ( C @ D ) )
=> ! [D: nat] :
( ( member_nat @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_ball__imageD) ).
thf(807,plain,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: set_Fi1058188332real_n > $o] :
( ! [D: set_Fi1058188332real_n] :
( ( member223413699real_n @ D @ ( image_1856576259real_n @ A @ B ) )
=> ( C @ D ) )
=> ! [D: nat] :
( ( member_nat @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(253,axiom,
( ( comple825005695real_n @ ( image_355963305real_n @ t2 @ top_to131672412_int_n ) )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [A: nat] : ( t2 @ ( f @ A ) )
@ top_top_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28__092_060open_062_092_060Union_062_A_Irange_AT_J_A_061_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062) ).
thf(1172,plain,
( ( comple825005695real_n @ ( image_355963305real_n @ t2 @ top_to131672412_int_n ) )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [A: nat] : ( t2 @ ( f @ A ) )
@ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(107,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ B ) ) @ C )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] : ( minus_1686442501real_n @ ( A @ D ) @ C )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_UN__extend__simps_I6_J) ).
thf(664,plain,
! [A: nat > set_Fi1058188332real_n,B: set_nat,C: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ ( comple825005695real_n @ ( image_1856576259real_n @ A @ B ) ) @ C )
= ( comple825005695real_n
@ ( image_1856576259real_n
@ ^ [D: nat] : ( minus_1686442501real_n @ ( A @ D ) @ C )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(188,axiom,
! [A: set_Fi1058188332real_n] :
( ( image_439535603real_n @ ( plus_p585657087real_n @ zero_z200130687real_n ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_image__add__0) ).
thf(960,plain,
! [A: set_Fi1058188332real_n] :
( ( image_439535603real_n @ ( plus_p585657087real_n @ zero_z200130687real_n ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(116,axiom,
! [A: set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n,C: nat] :
( ( A
= ( B @ C ) )
=> ( member223413699real_n @ A @ ( image_1856576259real_n @ B @ top_top_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_range__eqI) ).
thf(696,plain,
! [A: set_Fi1058188332real_n,B: nat > set_Fi1058188332real_n,C: nat] :
( ( A
= ( B @ C ) )
=> ( member223413699real_n @ A @ ( image_1856576259real_n @ B @ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(250,axiom,
! [A: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
( ( ( sigma_1536574303real_n @ A @ B )
= zero_z1963244097nnreal )
=> ( ( member223413699real_n @ B @ ( sigma_1235138647real_n @ A ) )
=> ( member223413699real_n @ B @ ( measur1402256771real_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_null__setsI) ).
thf(1165,plain,
! [A: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
( ( ( sigma_1536574303real_n @ A @ B )
= zero_z1963244097nnreal )
=> ( ( member223413699real_n @ B @ ( sigma_1235138647real_n @ A ) )
=> ( member223413699real_n @ B @ ( measur1402256771real_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(40,axiom,
! [A: finite1489363574real_n > finite1489363574real_n] :
( ( ( image_439535603real_n @ A @ top_to1292442332real_n )
= top_to1292442332real_n )
= ( ! [B: finite1489363574real_n] :
? [C: finite1489363574real_n] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_surj__def) ).
thf(415,plain,
! [A: finite1489363574real_n > finite1489363574real_n] :
( ( ( image_439535603real_n @ A @ top_to1292442332real_n )
= top_to1292442332real_n )
= ( ! [B: finite1489363574real_n] :
? [C: finite1489363574real_n] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(12,axiom,
! [A: finite964658038_int_n > finite964658038_int_n,B: finite964658038_int_n > finite964658038_int_n] :
( ! [C: finite964658038_int_n] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_1278151539_int_n @ A @ top_to131672412_int_n )
= top_to131672412_int_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_surjI) ).
thf(294,plain,
! [A: finite964658038_int_n > finite964658038_int_n,B: finite964658038_int_n > finite964658038_int_n] :
( ! [C: finite964658038_int_n] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_1278151539_int_n @ A @ top_to131672412_int_n )
= top_to131672412_int_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(142,axiom,
! [A: set_Fi1058188332real_n] :
( ( image_439535603real_n
@ ^ [B: finite1489363574real_n] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_image__ident) ).
thf(801,plain,
! [A: set_Fi1058188332real_n] :
( ( image_439535603real_n
@ ^ [B: finite1489363574real_n] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(212,axiom,
! [A: set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: finite964658038_int_n] :
( ( A
= ( B @ C ) )
=> ( member223413699real_n @ A @ ( image_355963305real_n @ B @ top_to131672412_int_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_range__eqI) ).
thf(1033,plain,
! [A: set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: finite964658038_int_n] :
( ( A
= ( B @ C ) )
=> ( member223413699real_n @ A @ ( image_355963305real_n @ B @ top_to131672412_int_n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(263,axiom,
member223413699real_n @ s @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms_I1_J) ).
thf(1197,plain,
member223413699real_n @ s @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(237,axiom,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_se2111327970real_n] :
( ( image_439535603real_n @ A @ ( comple825005695real_n @ B ) )
= ( comple825005695real_n @ ( image_1661509983real_n @ ( image_439535603real_n @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_image__Union) ).
thf(1129,plain,
! [A: finite1489363574real_n > finite1489363574real_n,B: set_se2111327970real_n] :
( ( image_439535603real_n @ A @ ( comple825005695real_n @ B ) )
= ( comple825005695real_n @ ( image_1661509983real_n @ ( image_439535603real_n @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(83,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_246_Collect__conj__eq) ).
thf(575,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)],[83]) ).
thf(42,axiom,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: finite1489363574real_n > $o] :
( ( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_355963305real_n @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
=> ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_UN__ball__bex__simps_I2_J) ).
thf(427,plain,
! [A: finite964658038_int_n > set_Fi1058188332real_n,B: set_Fi160064172_int_n,C: finite1489363574real_n > $o] :
( ( ! [D: finite1489363574real_n] :
( ( member1352538125real_n @ D @ ( comple825005695real_n @ ( image_355963305real_n @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: finite964658038_int_n] :
( ( member27055245_int_n @ D @ B )
=> ! [E: finite1489363574real_n] :
( ( member1352538125real_n @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(88,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_67_vimage__eq) ).
thf(596,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)],[88]) ).
thf(156,axiom,
! [A: set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: set_Fi160064172_int_n] :
( ( member223413699real_n @ A @ ( image_355963305real_n @ B @ C ) )
=> ~ ! [D: finite964658038_int_n] :
( ( A
= ( B @ D ) )
=> ~ ( member27055245_int_n @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_imageE) ).
thf(850,plain,
! [A: set_Fi1058188332real_n,B: finite964658038_int_n > set_Fi1058188332real_n,C: set_Fi160064172_int_n] :
( ( member223413699real_n @ A @ ( image_355963305real_n @ B @ C ) )
=> ~ ! [D: finite964658038_int_n] :
( ( A
= ( B @ D ) )
=> ~ ( member27055245_int_n @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(63,axiom,
! [A: set_Fi160064172_int_n] :
( ! [B: finite964658038_int_n] : ( member27055245_int_n @ B @ A )
=> ( top_to131672412_int_n = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_UNIV__eq__I) ).
thf(501,plain,
! [A: set_Fi160064172_int_n] :
( ! [B: finite964658038_int_n] : ( member27055245_int_n @ B @ A )
=> ( top_to131672412_int_n = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(22,axiom,
? [A: finite964658038_int_n] : ( member27055245_int_n @ A @ top_to131672412_int_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_UNIV__witness) ).
thf(337,plain,
? [A: finite964658038_int_n] : ( member27055245_int_n @ A @ top_to131672412_int_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(78,axiom,
! [A: finite1489363574real_n,B: nat > set_Fi1058188332real_n,C: set_nat] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ ( image_1856576259real_n @ B @ C ) ) )
=> ~ ! [D: nat] :
( ( member_nat @ D @ C )
=> ~ ( member1352538125real_n @ A @ ( B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_UN__E) ).
thf(560,plain,
! [A: finite1489363574real_n,B: nat > set_Fi1058188332real_n,C: set_nat] :
( ( member1352538125real_n @ A @ ( comple825005695real_n @ ( image_1856576259real_n @ B @ C ) ) )
=> ~ ! [D: nat] :
( ( member_nat @ D @ C )
=> ~ ( member1352538125real_n @ A @ ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(228,axiom,
! [A: finite964658038_int_n] :
( ( image_1278151539_int_n
@ ^ [B: finite964658038_int_n] : ( minus_1196255695_int_n @ B @ A )
@ top_to131672412_int_n )
= top_to131672412_int_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_surj__diff__right) ).
thf(1088,plain,
! [A: finite964658038_int_n] :
( ( image_1278151539_int_n
@ ^ [B: finite964658038_int_n] : ( minus_1196255695_int_n @ B @ A )
@ top_to131672412_int_n )
= top_to131672412_int_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(50,axiom,
! [A: finite1489363574real_n > set_Fi1058188332real_n,B: set_se2111327970real_n] :
( ( comple825005695real_n
@ ( image_1661509983real_n
@ ^ [C: set_Fi1058188332real_n] : ( comple825005695real_n @ ( image_545463721real_n @ A @ C ) )
@ B ) )
= ( comple825005695real_n @ ( image_545463721real_n @ A @ ( comple825005695real_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_UN__extend__simps_I8_J) ).
thf(454,plain,
! [A: finite1489363574real_n > set_Fi1058188332real_n,B: set_se2111327970real_n] :
( ( comple825005695real_n
@ ( image_1661509983real_n
@ ^ [C: set_Fi1058188332real_n] : ( comple825005695real_n @ ( image_545463721real_n @ A @ C ) )
@ B ) )
= ( comple825005695real_n @ ( image_545463721real_n @ A @ ( comple825005695real_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(165,axiom,
! [A: nat > set_Fi1058188332real_n,B: set_set_nat] :
( ( comple825005695real_n
@ ( image_933134521real_n
@ ^ [C: set_nat] : ( comple825005695real_n @ ( image_1856576259real_n @ A @ C ) )
@ B ) )
= ( comple825005695real_n @ ( image_1856576259real_n @ A @ ( comple1682161881et_nat @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_UN__extend__simps_I8_J) ).
thf(882,plain,
! [A: nat > set_Fi1058188332real_n,B: set_set_nat] :
( ( comple825005695real_n
@ ( image_933134521real_n
@ ^ [C: set_nat] : ( comple825005695real_n @ ( image_1856576259real_n @ A @ C ) )
@ B ) )
= ( comple825005695real_n @ ( image_1856576259real_n @ A @ ( comple1682161881et_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(17,axiom,
! [A: set_Fi160064172_int_n,B: set_Fi160064172_int_n,C: finite964658038_int_n > set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [E: finite964658038_int_n] :
( ( member27055245_int_n @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_355963305real_n @ C @ A )
= ( image_355963305real_n @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_image__cong) ).
thf(309,plain,
! [A: set_Fi160064172_int_n,B: set_Fi160064172_int_n,C: finite964658038_int_n > set_Fi1058188332real_n,D: finite964658038_int_n > set_Fi1058188332real_n] :
( ( A = B )
=> ( ! [E: finite964658038_int_n] :
( ( member27055245_int_n @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_355963305real_n @ C @ A )
= ( image_355963305real_n @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(106,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_240_imageE) ).
thf(659,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)],[106]) ).
thf(1604,plain,
$false,
inference(e,[status(thm)],[629,1024,479,893,1110,352,1168,760,909,628,1158,1005,683,276,873,511,677,1142,379,1078,715,814,913,930,1196,841,885,301,320,651,389,570,372,504,619,751,1455,357,1132,902,638,1147,870,969,284,448,924,492,443,623,966,1051,821,905,480,1169,956,1072,396,988,602,981,307,512,270,546,1199,1153,1067,798,1163,910,1091,825,1021,349,1174,392,275,815,729,1042,952,693,630,916,847,879,435,889,1159,1210,1027,757,551,842,1106,324,974,948,615,1064,1138,593,783,989,742,578,328,1160,339,933,554,1182,669,489,1016,970,547,686,1075,476,647,985,701,1150,654,1192,721,1002,1246,605,1451,738,1060,457,343,266,921,541,657,1054,1170,530,1185,773,718,633,360,1187,674,298,1135,1103,824,745,279,375,513,430,584,732,826,1226,936,572,466,804,704,713,498,1209,406,1011,1048,567,1144,318,509,1122,271,599,990,996,858,726,621,668,462,521,1198,399,780,1113,267,438,1176,608,473,1208,944,927,1081,516,939,1018,754,836,795,680,557,855,1070,707,971,993,282,1156,1188,1038,470,544,864,1008,446,612,876,1094,978,845,1084,363,539,1157,581,495,1216,1126,1189,813,963,304,896,748,418,786,1030,290,510,667,1193,478,272,383,899,346,1045,287,447,432,833,818,735,999,620,867,273,564,268,807,1172,664,960,696,1165,415,294,801,1033,1197,1129,575,427,596,908,850,501,337,560,1088,454,882,309,659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP117^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % 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
% 0.07/0.12 % Computer : n012.cluster.edu
% 0.07/0.12 % Model : x86_64 x86_64
% 0.07/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.12 % Memory : 8046.5625MB
% 0.07/0.12 % OS : Linux 6.8.0-71-generic
% 0.07/0.12 % CPULimit : 300
% 0.07/0.12 % WCLimit : 300
% 0.07/0.12 % DateTime : Tue Sep 29 19:55:48 UTC 2026
% 0.07/0.12 % CPUTime :
% 0.07/0.12 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
% 0.43/0.41 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.64 % [INFO] Parsing done (222ms).
% 1.23/0.65 % [INFO] Running in sequential loop mode.
% 1.92/0.85 % [INFO] eprover registered as external prover.
% 1.92/0.85 % [INFO] Scanning for conjecture ...
% 2.15/0.93 % [INFO] Found a conjecture (or negated_conjecture) and 353 axioms. Running axiom selection ...
% 2.51/1.02 % [INFO] Axiom selection finished. Selected 263 axioms (removed 90 axioms).
% 2.86/1.15 % [INFO] Problem is higher-order (TPTP THF).
% 2.86/1.17 % [INFO] Type checking passed.
% 2.86/1.17 % [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 ...
% 13.95/3.56 % External prover 'e' found a proof!
% 13.95/3.56 % [INFO] Killing All external provers ...
% 13.95/3.56 % Time passed: 3369ms (effective reasoning time: 2915ms)
% 13.95/3.57 % 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)>
% 13.95/3.57 % Axioms used in derivation (263): fact_23_image__vimage__eq, fact_321_range__composition, fact_4_assms_I1_J, fact_179_is__num__normalize_I1_J, fact_127_Diff__Int__distrib2, fact_345_UN__E, fact_180_UNIV__witness, fact_256_range__eqI, fact_85_bex__UN, fact_114_null__sets_OInt__space__eq2, fact_1__092_060open_062_092_060And_062a_O_AT_H_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_35_surj__plus, fact_172_imageI, fact_226_Compr__image__eq, fact_160_ball__imageD, fact_0_emeasure__T_H, fact_22_image__vimage__eq, fact_19_null__setsI, fact_222_Inf_OINF__identity__eq, fact_281_surjE, fact_277_surjI, fact_164_image__cong, fact_234_image__image, fact_285_surjE, fact_195_IntD2, fact_163_image__cong, fact_312_vimage__inter__cong, fact_56_Union__iff, fact_73_image__ident, fact_313_translation__subtract__diff, fact_291_surjD, fact_39_image__eqI, fact_6_T__Int, fact_320_range__composition, fact_130_Diff__Int2, fact_89_UN__ball__bex__simps_I4_J, fact_235_image__image, fact_75_vimage__ident, fact_326_rangeE, fact_15_R__Int, fact_201_IntE, fact_314_range__composition, fact_96_null__sets_OInt, fact_34_surj__plus, fact_198_IntD1, fact_51_IntI, fact_126_top__set__def, fact_117_in__sets__SUP, fact_138_null__sets_Osets__Collect__conj, fact_131_Int__Diff, fact_286_surjE, fact_280_surjE, fact_261_surj__def, fact_324_rangeE, fact_18_null__sets__UN, fact_116_in__sets__SUP, fact_11_f__def, fact_257_range__eqI, fact_33_Sup__eq__top__iff, fact_31_Sup__UNIV, fact_316_range__composition, fact_50_Int__iff, fact_323_rangeE, fact_77_Int__UNIV, fact_191_Int__absorb, fact_140_null__set__Diff, fact_61_UN__ball__bex__simps_I3_J, fact_173_imageI, fact_86_bex__UN, fact_171_image__iff, fact_125_top__set__def, fact_351_UN__extend__simps_I8_J, fact_224_Compr__image__eq, fact_297_SUP__cong, fact_302_Int__UNIV__right, fact_199_IntE, fact_143_vimage__Union, fact_182_UNIV__witness, fact_305_Int__UNIV__left, fact_238_imageE, fact_60_UN__ball__bex__simps_I1_J, fact_67_vimage__eq, fact_350_UN__extend__simps_I8_J, fact_124_space__Sup__eq__UN, fact_72_vimageI, fact_167_bex__imageD, fact_237_imageE, fact_331_SUP__commute, fact_97_vimage__Int, fact_144_UN__extend__simps_I6_J, fact_225_Compr__image__eq, fact_98_SUP__identity__eq, fact_139_translation__diff, fact_99_SUP__identity__eq, fact_340_UN__UN__flatten, fact_46_UNIV__I, fact_307_Int__UNIV__left, fact_346_UN__E, fact_311_null__setsD2, fact_254_less__numeral__extra_I3_J, fact_338_UN__UN__flatten, fact_223_Compr__image__eq, fact_262_surj__def, fact_161_ball__imageD, fact_306_Int__UNIV__left, fact_53_IntI, fact_190_Int__commute, fact_149_Sup_OSUP__cong, fact_91_vimage__UNIV, fact_336_UN__UN__flatten, fact_141_Int__Union2, fact_94_vimage__UNIV, fact_284_surjE, fact_205_vimage__Collect, fact_148_Sup_OSUP__cong, fact_221_Sup_OSUP__identity__eq, fact_220_vimageD, fact_155_rev__image__eqI, fact_317_range__composition, fact_13_of__int__vec__eq__iff, fact_48_Int__iff, fact_271_rangeI, fact_339_UN__UN__flatten, fact_9__092_060open_062_I_092_060lambda_062n_O_Aemeasure_Alebesgue_A_IT_A_If_An_J_J_J_Asums_Aemeasure_Alebesgue_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062, fact_276_surjI, fact_132_vimage__Diff, fact_259_range__eqI, fact_74_vimage__Collect__eq, fact_322_range__composition, fact_268_rangeI, fact_266_surj__def, fact_5_emeasure__T__Int, fact_120_sets__SUP__cong, fact_62_null__sets_ODiff, fact_28__092_060open_062_092_060Union_062_A_Irange_AT_J_A_061_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062, fact_174_imageI, fact_335_UN__UN__flatten, fact_79_ball__UN, fact_8__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_294_less__Sup__iff, fact_231_image__image, fact_283_surjE, fact_189_Int__left__absorb, fact_168_bex__imageD, fact_150_Inf_OINF__cong, fact_337_UN__UN__flatten, fact_267_surj__def, fact_112_image__add__0, fact_119_sets__SUP__cong, fact_292_surjD, fact_36_diff__numeral__special_I9_J, fact_38_image__eqI, fact_107_UN__I, fact_239_imageE, fact_204_UnionE, fact_279_surjI, fact_184_UNIV__eq__I, fact_347_UN__E, fact_20_image__vimage__eq, fact_24_image__vimage__eq, fact_186_UNIV__eq__I, fact_10_T_H__def, fact_187_UNIV__eq__I, fact_109_UN__I, fact_264_surj__def, fact_273_surjI, fact_128_Diff__Int__distrib, fact_196_IntD1, fact_328_SUP__commute, fact_147_Sup_OSUP__cong, fact_78_Int__UNIV, fact_95_vimage__UNIV, fact_92_vimage__UNIV, fact_3_calculation, fact_296_SUP__cong, fact_111_S__decompose, fact_247_Int__Collect, fact_188_Int__left__commute, fact_253_vimage__def, fact_315_range__composition, fact_40_image__eqI, fact_47_UNIV__I, fact_102_UN__iff, fact_108_UN__I, fact_290_surjD, fact_334_image__Union, fact_282_surjE, fact_162_ball__imageD, fact_319_range__composition, fact_113_image__add__0, fact_80_ball__UN, fact_318_range__composition, fact_115_null__sets_OInt__space__eq1, fact_252_Int__def, fact_293_surjD, fact_275_surjI, fact_37_image__eqI, fact_25__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_59_UnionI, fact_152_Inf_OINF__cong, fact_329_SUP__commute, fact_295_SUP__cong, fact_26_surj__diff__right, fact_193_IntD2, fact_154_rev__image__eqI, fact_170_image__iff, fact_12_T_H__altdef, fact_166_bex__imageD, fact_215_vimageE, fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_349_UN__extend__simps_I8_J, fact_101_UN__iff, fact_255_less__numeral__extra_I4_J, fact_210_vimageI2, fact_298_SUP__cong, fact_88_UN__ball__bex__simps_I2_J, fact_250_Int__def, fact_151_Inf_OINF__cong, fact_17_null__sets__UN, fact_289_surjD, fact_129_Diff__Diff__Int, fact_169_image__iff, fact_310_Union__UNIV, fact_81_mem__Collect__eq, fact_83_Collect__mem__eq, fact_145_UN__extend__simps_I6_J, fact_135_null__sets_Osets__Collect__disj, fact_76_Int__UNIV, fact_230_image__image, fact_87_UN__ball__bex__simps_I2_J, fact_27_surj__diff__right, fact_233_image__image, fact_303_Int__UNIV__right, fact_44_UNIV__I, fact_269_rangeI, fact_153_rev__image__eqI, fact_263_surj__def, fact_330_SUP__commute, fact_14_T__def, fact_265_surj__def, fact_304_Int__UNIV__right, fact_287_surjD, fact_146_emeasure__Diff__null__set, fact_240_imageE, fact_249_Int__Collect, fact_236_image__image, fact_16_sums__emeasure_H, fact_232_image__image, fact_288_surjD, fact_175_imageI, fact_142_Int__Union, fact_7_assms_I2_J, fact_246_Collect__conj__eq, fact_21_image__vimage__eq, fact_183_UNIV__witness, fact_278_surjI, fact_274_surjI, fact_165_image__cong, fact_192_Int__assoc, fact_156_rev__image__eqI, fact_90_UN__ball__bex__simps_I4_J, fact_118_in__sets__Sup, fact_93_vimage__UNIV
% 13.95/3.57 % No. of inferences in proof: 577
% 13.95/3.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3369 ms resp. 2915 ms w/o parsing
% 14.07/3.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.07/3.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------