0.11/0.18 % Problem : Vampire---4.8_28020 : TPTP v0.0.0. 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). 0.41/0.65 0.41/0.65 thf(sy_c_member_001_062_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_M_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type, 0.41/0.65 member1764433517real_n: ( set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n ) > set_se830533260real_n > $o ). 0.41/0.65 0.41/0.65 thf(sy_c_member_001_062_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type, 0.41/0.65 member1759501912real_n: ( set_Fi1058188332real_n > finite1489363574real_n ) > set_se955370231real_n > $o ). 0.41/0.65 0.41/0.65 thf(sy_c_member_001_062_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type, 0.41/0.65 member1734791438real_n: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se1738601133real_n > $o ). 0.41/0.65 0.41/0.65 thf(sy_c_member_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type, 0.41/0.65 member1352538125real_n: finite1489363574real_n > set_Fi1058188332real_n > $o ). 0.41/0.65 0.41/0.65 thf(sy_c_member_001t__Set__Oset_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type, 0.41/0.65 member2104752728real_n: set_Fi1326602817real_n > set_se221767415real_n > $o ). 0.41/0.65 0.41/0.65 thf(sy_c_member_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type, 0.41/0.65 member223413699real_n: set_Fi1058188332real_n > set_se2111327970real_n > $o ). 0.41/0.65 0.41/0.65 thf(sy_c_member_001t__Set__Oset_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type, 0.41/0.65 member1475136633real_n: set_se2111327970real_n > set_se820660888real_n > $o ). 0.41/0.65 0.41/0.65 thf(sy_v_R____,type, 0.41/0.65 r: finite964658038_int_n > set_Fi1058188332real_n ). 0.41/0.65 0.41/0.65 thf(sy_v_S,type, 0.41/0.65 s: set_Fi1058188332real_n ). 0.41/0.65 0.41/0.65 thf(sy_v_T_H____,type, 0.41/0.65 t: finite964658038_int_n > set_Fi1058188332real_n ). 0.41/0.65 0.41/0.65 thf(sy_v_T____,type, 0.41/0.65 t2: finite964658038_int_n > set_Fi1058188332real_n ). 0.41/0.65 0.41/0.65 thf(sy_v_a____,type, 0.41/0.65 a: finite964658038_int_n ). 0.41/0.65 0.41/0.65 thf(fact_304_set__diff__eq,axiom, 0.41/0.65 ( minus_1698615483real_n 0.41/0.65 = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] : 0.41/0.65 ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ~ ( member223413699real_n @ X @ B3 ) 0.41/0.65 & ( member223413699real_n @ X @ A4 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_110_measurable__sets__Collect,axiom, 0.41/0.65 ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,M: sigma_1422848389real_n,N: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] : 0.41/0.65 ( ( ( member1475136633real_n 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) 0.41/0.65 & ( P @ ( F @ X ) ) ) ) 0.41/0.65 @ ( sigma_433815053real_n @ M ) ) 0.41/0.65 <= ( member1475136633real_n 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ N ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 @ ( sigma_433815053real_n @ N ) ) ) 0.41/0.65 <= ( member1734791438real_n @ F @ ( sigma_239294762real_n @ M @ N ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_219_Compr__image__eq,axiom, 0.41/0.65 ! [F: finite1489363574real_n > set_Fi1058188332real_n,A2: set_Fi1058188332real_n,P: set_Fi1058188332real_n > $o] : 0.41/0.65 ( ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X @ ( image_545463721real_n @ F @ A2 ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 = ( image_545463721real_n @ F 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ A2 ) 0.41/0.65 & ( P @ ( F @ X ) ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_317_translation__subtract__Int,axiom, 0.41/0.65 ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T3: set_Fi1058188332real_n] : 0.41/0.65 ( ( image_439535603real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A ) 0.41/0.65 @ ( inf_in1974387902real_n @ S2 @ T3 ) ) 0.41/0.65 = ( inf_in1974387902real_n 0.41/0.65 @ ( image_439535603real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A ) 0.41/0.65 @ S2 ) 0.41/0.65 @ ( image_439535603real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A ) 0.41/0.65 @ T3 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_273_measurable__equality__set,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) 0.41/0.65 => ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( ( F @ X ) 0.41/0.65 = ( G @ X ) ) 0.41/0.65 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) ) 0.41/0.65 <= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_142_measurable__compose,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n,L2: sigma_1466784463real_n] : 0.41/0.65 ( ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ N @ L2 ) ) 0.41/0.65 => ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( G @ ( F @ X ) ) 0.41/0.65 @ ( sigma_439801790real_n @ M @ L2 ) ) ) 0.41/0.65 <= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_55_Int__assoc,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A2 @ B2 ) @ C ) 0.41/0.65 = ( inf_in1974387902real_n @ A2 @ ( inf_in1974387902real_n @ B2 @ C ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_314_DiffE,axiom, 0.41/0.65 ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) ) 0.41/0.65 => ~ ( ( member223413699real_n @ C2 @ B2 ) 0.41/0.65 <= ( member223413699real_n @ C2 @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_234_rev__image__eqI,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n] : 0.41/0.65 ( ( ( member223413699real_n @ B @ ( image_1661509983real_n @ F @ A2 ) ) 0.41/0.65 <= ( B 0.41/0.65 = ( F @ X2 ) ) ) 0.41/0.65 <= ( member223413699real_n @ X2 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_158_sets_Osets__Collect_I5_J,axiom, 0.41/0.65 ! [M: sigma_1422848389real_n,Pb: $o] : 0.41/0.65 ( member1475136633real_n 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) 0.41/0.65 & Pb ) ) 0.41/0.65 @ ( sigma_433815053real_n @ M ) ) ). 0.41/0.65 0.41/0.65 thf(fact_115_measurable__sets__Collect,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.65 ( ( member408431031real_n @ F @ ( sigma_2016438227real_n @ M @ N ) ) 0.41/0.65 => ( ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ N ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ N ) ) 0.41/0.65 => ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( P @ ( F @ X ) ) 0.41/0.65 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_144_measurable__cong__sets,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,M2: sigma_1466784463real_n,N: sigma_1466784463real_n,N2: sigma_1466784463real_n] : 0.41/0.65 ( ( ( ( sigma_439801790real_n @ M @ N ) 0.41/0.65 = ( sigma_439801790real_n @ M2 @ N2 ) ) 0.41/0.65 <= ( ( sigma_1235138647real_n @ N ) 0.41/0.65 = ( sigma_1235138647real_n @ N2 ) ) ) 0.41/0.65 <= ( ( sigma_1235138647real_n @ M ) 0.41/0.65 = ( sigma_1235138647real_n @ M2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_60_Collect__conj__eq,axiom, 0.41/0.65 ! [P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] : 0.41/0.65 ( ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( Q @ X ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 = ( inf_in1974387902real_n @ ( collec321817931real_n @ P ) @ ( collec321817931real_n @ Q ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_14_vimageI,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( ( F @ A ) 0.41/0.65 = B ) 0.41/0.65 => ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ B2 ) ) 0.41/0.65 <= ( member1352538125real_n @ B @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_153_measurable__space,axiom, 0.41/0.65 ! [F: finite1489363574real_n > set_Fi1058188332real_n,M: sigma_1466784463real_n,A2: sigma_1422848389real_n,X2: finite1489363574real_n] : 0.41/0.65 ( ( ( member1352538125real_n @ X2 @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 => ( member223413699real_n @ ( F @ X2 ) @ ( sigma_607186084real_n @ A2 ) ) ) 0.41/0.65 <= ( member966061400real_n @ F @ ( sigma_566919540real_n @ M @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_4_T_H__altdef,axiom, 0.41/0.65 ! [A: finite964658038_int_n] : 0.41/0.65 ( ( t @ A ) 0.41/0.65 = ( vimage1233683625real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ X @ ( minkow1134813771n_real @ A ) ) 0.41/0.65 @ ( t2 @ A ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_301_Diff__iff,axiom, 0.41/0.65 ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] : 0.41/0.65 ( ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) ) 0.41/0.65 = ( ( member1746150050real_n @ C2 @ A2 ) 0.41/0.65 & ~ ( member1746150050real_n @ C2 @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_191_sets__Least,axiom, 0.41/0.65 ! [M: sigma_1422848389real_n,P: nat > set_Fi1058188332real_n > $o,A2: set_nat] : 0.41/0.65 ( ( member1475136633real_n 0.41/0.65 @ ( inf_in632889204real_n 0.41/0.65 @ ( vimage501526201_n_nat 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ord_Least_nat 0.41/0.65 @ ^ [J2: nat] : ( P @ J2 @ X ) ) 0.41/0.65 @ A2 ) 0.41/0.65 @ ( sigma_607186084real_n @ M ) ) 0.41/0.65 @ ( sigma_433815053real_n @ M ) ) 0.41/0.65 <= ! [I2: nat] : 0.41/0.65 ( member1475136633real_n 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( P @ I2 @ X ) 0.41/0.65 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_433815053real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_289_sets__restrict__space,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] : 0.41/0.65 ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ Omega ) ) 0.41/0.65 = ( image_1661509983real_n @ ( inf_in1974387902real_n @ Omega ) @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_56_Int__absorb,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ A2 @ A2 ) 0.41/0.65 = A2 ) ). 0.41/0.65 0.41/0.65 thf(fact_322_affine__parallel__expl__aux,axiom, 0.41/0.65 ! [S: set_Fi1058188332real_n,A: finite1489363574real_n,T: set_Fi1058188332real_n] : 0.41/0.65 ( ( T 0.41/0.65 = ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S ) ) 0.41/0.65 <= ! [X3: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X3 @ S ) 0.41/0.65 = ( member1352538125real_n @ ( plus_p585657087real_n @ A @ X3 ) @ T ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_195_in__borel__measurable__borel,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n] : 0.41/0.65 ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) 0.41/0.65 = ( ! [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ X ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 <= ( member223413699real_n @ X @ ( sigma_1235138647real_n @ borel_676189912real_n ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_310_DiffD2,axiom, 0.41/0.65 ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ~ ( member223413699real_n @ C2 @ B2 ) 0.41/0.65 <= ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_328_add__cancel__left__left,axiom, 0.41/0.65 ! [B: finite1489363574real_n,A: finite1489363574real_n] : 0.41/0.65 ( ( ( plus_p585657087real_n @ B @ A ) 0.41/0.65 = A ) 0.41/0.65 = ( B = zero_z200130687real_n ) ) ). 0.41/0.65 0.41/0.65 thf(fact_312_DiffD1,axiom, 0.41/0.65 ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ C2 @ A2 ) 0.41/0.65 <= ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_5__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom, 0.41/0.65 ! [A: finite964658038_int_n] : ( member223413699real_n @ ( r @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_20_set__plus__intro,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,C: set_se2111327970real_n,B: set_Fi1058188332real_n,D: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ A @ C ) 0.41/0.65 => ( ( member223413699real_n @ ( plus_p1606848693real_n @ A @ B ) @ ( plus_p565022571real_n @ C @ D ) ) 0.41/0.65 <= ( member223413699real_n @ B @ D ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_276_sets__lebesgue__on__refl,axiom, 0.41/0.65 ! [S: set_Fi1058188332real_n] : ( member223413699real_n @ S @ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_120_inf__right__idem,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ X2 @ Y3 ) @ Y3 ) 0.41/0.65 = ( inf_in1974387902real_n @ X2 @ Y3 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_117_measurable__sets__Collect,axiom, 0.41/0.65 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,M: sigma_107786596real_n,N: sigma_1466784463real_n,P: finite1489363574real_n > $o] : 0.41/0.65 ( ( member1695588023real_n @ F @ ( sigma_2028985427real_n @ M @ N ) ) 0.41/0.65 => ( ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ N ) ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ N ) ) 0.41/0.65 => ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) 0.41/0.65 & ( P @ ( F @ X ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_109_measurable__If__set,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,M2: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] : 0.41/0.65 ( ( ( ( member223413699real_n @ ( inf_in1974387902real_n @ A2 @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ X @ A2 ) @ ( F @ X ) @ ( G @ X ) ) 0.41/0.65 @ ( sigma_439801790real_n @ M @ M2 ) ) ) 0.41/0.65 <= ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ M2 ) ) ) 0.41/0.65 <= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ M2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_207_add__diff__cancel__left_H,axiom, 0.41/0.65 ! [A: nat,B: nat] : 0.41/0.65 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A ) 0.41/0.65 = B ) ). 0.41/0.65 0.41/0.65 thf(fact_165_sets_Osets__Collect__neg,axiom, 0.41/0.65 ! [M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.65 ( ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) 0.41/0.65 => ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) 0.41/0.65 & ~ ( P @ X ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_6_sets__completionI__sets,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n,M: sigma_1466784463real_n] : 0.41/0.65 ( ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ ( comple230862828real_n @ M ) ) ) 0.41/0.65 <= ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_295_borel__measurable__lebesgue__preimage__borel,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) ) 0.41/0.65 = ( ! [T2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ T2 @ ( sigma_1235138647real_n @ borel_676189912real_n ) ) 0.41/0.65 => ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ ( F @ X ) @ T2 ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_41_Int__iff,axiom, 0.41/0.65 ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] : 0.41/0.65 ( ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) ) 0.41/0.65 = ( ( member1746150050real_n @ C2 @ B2 ) 0.41/0.65 & ( member1746150050real_n @ C2 @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_215_Compr__image__eq,axiom, 0.41/0.65 ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,A2: set_se2111327970real_n,P: set_Fi1058188332real_n > $o] : 0.41/0.65 ( ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X @ ( image_1661509983real_n @ F @ A2 ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 = ( image_1661509983real_n @ F 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( P @ ( F @ X ) ) 0.41/0.65 & ( member223413699real_n @ X @ A2 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_338_diff__self,axiom, 0.41/0.65 ! [A: finite1489363574real_n] : 0.41/0.65 ( ( minus_1037315151real_n @ A @ A ) 0.41/0.65 = zero_z200130687real_n ) ). 0.41/0.65 0.41/0.65 thf(fact_253_diff__diff__add,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C2 ) 0.41/0.65 = ( minus_1037315151real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_200_image__eqI,axiom, 0.41/0.65 ! [B: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] : 0.41/0.65 ( ( ( member1746150050real_n @ X2 @ A2 ) 0.41/0.65 => ( member1746150050real_n @ B @ ( image_1123376925real_n @ F @ A2 ) ) ) 0.41/0.65 <= ( B 0.41/0.65 = ( F @ X2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_99_measurableI,axiom, 0.41/0.65 ! [M: sigma_1422848389real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n] : 0.41/0.65 ( ! [X3: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X3 @ ( sigma_607186084real_n @ M ) ) 0.41/0.65 => ( member1746150050real_n @ ( F @ X3 ) @ ( sigma_1483971331real_n @ N ) ) ) 0.41/0.65 => ( ( member1764433517real_n @ F @ ( sigma_588796041real_n @ M @ N ) ) 0.41/0.65 <= ! [A6: set_Fi1326602817real_n] : 0.41/0.65 ( ( member2104752728real_n @ A6 @ ( sigma_522684908real_n @ N ) ) 0.41/0.65 => ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage2134951412real_n @ F @ A6 ) @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_130_inf_Oleft__commute,axiom, 0.41/0.65 ! [B: set_Fi1058188332real_n,A: set_Fi1058188332real_n,C2: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ A @ C2 ) ) 0.41/0.65 = ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_140_inf__sup__aci_I4_J,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ X2 @ Y3 ) ) 0.41/0.65 = ( inf_in1974387902real_n @ X2 @ Y3 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_267_sets__restrict__restrict__space,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( sigma_346513458real_n @ M @ A2 ) @ B2 ) ) 0.41/0.65 = ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ ( inf_in1974387902real_n @ A2 @ B2 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_0_assms_I1_J,axiom, 0.41/0.65 member223413699real_n @ s @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ). 0.41/0.65 0.41/0.65 thf(fact_114_measurable__sets__Collect,axiom, 0.41/0.65 ! [F: finite1489363574real_n > set_Fi1058188332real_n,M: sigma_1466784463real_n,N: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] : 0.41/0.65 ( ( member966061400real_n @ F @ ( sigma_566919540real_n @ M @ N ) ) 0.41/0.65 => ( ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 & ( P @ ( F @ X ) ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 <= ( member1475136633real_n 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ N ) ) ) ) 0.41/0.65 @ ( sigma_433815053real_n @ N ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_67_measurable__completion,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n] : 0.41/0.65 ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( comple230862828real_n @ M ) @ N ) ) 0.41/0.65 <= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_42_Int__iff,axiom, 0.41/0.65 ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) ) 0.41/0.65 = ( ( member1352538125real_n @ C2 @ B2 ) 0.41/0.65 & ( member1352538125real_n @ C2 @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_168_sets_Osets__Collect__conj,axiom, 0.41/0.65 ! [M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o,Q: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.65 ( ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) 0.41/0.65 => ( ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( Q @ X ) 0.41/0.65 & ( P @ X ) 0.41/0.65 & ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) 0.41/0.65 <= ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) 0.41/0.65 & ( Q @ X ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_151_measurable__space,axiom, 0.41/0.65 ! [F: set_Fi1058188332real_n > finite1489363574real_n,M: sigma_1422848389real_n,A2: sigma_1466784463real_n,X2: set_Fi1058188332real_n] : 0.41/0.65 ( ( ( member1352538125real_n @ ( F @ X2 ) @ ( sigma_476185326real_n @ A2 ) ) 0.41/0.65 <= ( member223413699real_n @ X2 @ ( sigma_607186084real_n @ M ) ) ) 0.41/0.65 <= ( member1759501912real_n @ F @ ( sigma_1333364596real_n @ M @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_19_vimage__eq,axiom, 0.41/0.65 ! [A: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ B2 ) ) 0.41/0.65 = ( member1352538125real_n @ ( F @ A ) @ B2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_82_Collect__mem__eq,axiom, 0.41/0.65 ! [A2: set_se2111327970real_n] : 0.41/0.65 ( ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ A2 ) ) 0.41/0.65 = A2 ) ). 0.41/0.65 0.41/0.65 thf(fact_263_vimage__algebra__cong,axiom, 0.41/0.65 ! [X4: set_se2111327970real_n,Y: set_se2111327970real_n,F: set_Fi1058188332real_n > finite1489363574real_n,G: set_Fi1058188332real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n] : 0.41/0.65 ( ( ! [X3: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X3 @ Y ) 0.41/0.65 => ( ( F @ X3 ) 0.41/0.65 = ( G @ X3 ) ) ) 0.41/0.65 => ( ( ( sigma_1235138647real_n @ M ) 0.41/0.65 = ( sigma_1235138647real_n @ N ) ) 0.41/0.65 => ( ( sigma_1384150200real_n @ X4 @ F @ M ) 0.41/0.65 = ( sigma_1384150200real_n @ Y @ G @ N ) ) ) ) 0.41/0.65 <= ( X4 = Y ) ) ). 0.41/0.65 0.41/0.65 thf(fact_30_vimageD,axiom, 0.41/0.65 ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] : 0.41/0.65 ( ( member1746150050real_n @ ( F @ A ) @ A2 ) 0.41/0.65 <= ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_290_lborelD,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ lebesg260170249real_n ) ) 0.41/0.65 <= ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ borel_676189912real_n ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_220_Compr__image__eq,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.65 ( ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1746150050real_n @ X @ ( image_437359496real_n @ F @ A2 ) ) ) ) 0.41/0.65 = ( image_437359496real_n @ F 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( P @ ( F @ X ) ) 0.41/0.65 & ( member1352538125real_n @ X @ A2 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_126_inf__set__def,axiom, 0.41/0.65 ( inf_in632889204real_n 0.41/0.65 = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] : 0.41/0.65 ( collec452821761real_n 0.41/0.65 @ ( inf_in409346577al_n_o 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ A4 ) 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ B3 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_205_add__diff__cancel__right,axiom, 0.41/0.65 ! [A: nat,C2: nat,B: nat] : 0.41/0.65 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) 0.41/0.65 = ( minus_minus_nat @ A @ B ) ) ). 0.41/0.65 0.41/0.65 thf(fact_85_Collect__cong,axiom, 0.41/0.65 ! [P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] : 0.41/0.65 ( ! [X3: finite1489363574real_n] : 0.41/0.65 ( ( P @ X3 ) 0.41/0.65 = ( Q @ X3 ) ) 0.41/0.65 => ( ( collec321817931real_n @ P ) 0.41/0.65 = ( collec321817931real_n @ Q ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_308_minus__set__def,axiom, 0.41/0.65 ( minus_725016986real_n 0.41/0.65 = ( ^ [A4: set_Fi1326602817real_n,B3: set_Fi1326602817real_n] : 0.41/0.65 ( collec1190264032real_n 0.41/0.65 @ ( minus_391085931al_n_o 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ A4 ) 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ B3 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_344_cancel__comm__monoid__add__class_Odiff__cancel,axiom, 0.41/0.65 ! [A: nat] : 0.41/0.65 ( ( minus_minus_nat @ A @ A ) 0.41/0.65 = zero_zero_nat ) ). 0.41/0.65 0.41/0.65 thf(fact_239_image__cong,axiom, 0.41/0.65 ! [M: set_Fi1058188332real_n,N: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( ! [X3: finite1489363574real_n] : 0.41/0.65 ( ( ( F @ X3 ) 0.41/0.65 = ( G @ X3 ) ) 0.41/0.65 <= ( member1352538125real_n @ X3 @ N ) ) 0.41/0.65 => ( ( image_439535603real_n @ F @ M ) 0.41/0.65 = ( image_439535603real_n @ G @ N ) ) ) 0.41/0.65 <= ( M = N ) ) ). 0.41/0.65 0.41/0.65 thf(fact_218_Compr__image__eq,axiom, 0.41/0.65 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.65 ( ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ ( image_1123376925real_n @ F @ A2 ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 = ( image_1123376925real_n @ F 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ A2 ) 0.41/0.65 & ( P @ ( F @ X ) ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_189_measurable__restrict__space__iff,axiom, 0.41/0.65 ! [Omega: set_Fi1058188332real_n,M: sigma_1466784463real_n,C2: finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n,F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member223413699real_n @ ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( ( ( member408431031real_n @ F @ ( sigma_2016438227real_n @ ( sigma_346513458real_n @ M @ Omega ) @ N ) ) 0.41/0.65 = ( member408431031real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( if_Fin413489477real_n @ ( member1352538125real_n @ X @ Omega ) @ ( F @ X ) @ C2 ) 0.41/0.65 @ ( sigma_2016438227real_n @ M @ N ) ) ) 0.41/0.65 <= ( member1746150050real_n @ C2 @ ( sigma_1483971331real_n @ N ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_271_sets__Collect__restrict__space__iff,axiom, 0.41/0.65 ! [S: set_Fi1326602817real_n,M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.65 ( ( member2104752728real_n @ S @ ( sigma_522684908real_n @ M ) ) 0.41/0.65 => ( ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ ( sigma_1052429895real_n @ M @ S ) ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ ( sigma_1052429895real_n @ M @ S ) ) ) 0.41/0.65 = ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) 0.41/0.65 & ( member1746150050real_n @ X @ S ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_101_measurableI,axiom, 0.41/0.65 ! [M: sigma_107786596real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n] : 0.41/0.65 ( ( ( member117715276real_n @ F @ ( sigma_1185134568real_n @ M @ N ) ) 0.41/0.65 <= ! [A6: set_Fi1326602817real_n] : 0.41/0.65 ( ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage180751827real_n @ F @ A6 ) @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) ) 0.41/0.65 <= ( member2104752728real_n @ A6 @ ( sigma_522684908real_n @ N ) ) ) ) 0.41/0.65 <= ! [X3: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X3 @ ( sigma_1483971331real_n @ M ) ) 0.41/0.65 => ( member1746150050real_n @ ( F @ X3 ) @ ( sigma_1483971331real_n @ N ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_179_inf__Int__eq,axiom, 0.41/0.65 ! [R: set_Fi1326602817real_n,S: set_Fi1326602817real_n] : 0.41/0.65 ( ( inf_in32002162al_n_o 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ R ) 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ S ) ) 0.41/0.65 = ( ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ ( inf_in146441683real_n @ R @ S ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_25_vimage__def,axiom, 0.41/0.65 ( vimage1059850558real_n 0.41/0.65 = ( ^ [F2: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,B3: set_Fi1326602817real_n] : 0.41/0.65 ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( member1746150050real_n @ ( F2 @ X ) @ B3 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_171_sets_Osets__Collect__disj,axiom, 0.41/0.65 ! [M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o,Q: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.65 ( ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) 0.41/0.65 => ( ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( ( P @ X ) 0.41/0.65 | ( Q @ X ) ) 0.41/0.65 & ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) 0.41/0.65 <= ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( Q @ X ) 0.41/0.65 & ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_138_inf__sup__aci_I2_J,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n,Z: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ X2 @ Y3 ) @ Z ) 0.41/0.65 = ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ Y3 @ Z ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_259_eq__diff__eq,axiom, 0.41/0.65 ! [A: finite1489363574real_n,C2: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.65 ( ( A 0.41/0.65 = ( minus_1037315151real_n @ C2 @ B ) ) 0.41/0.65 = ( ( plus_p585657087real_n @ A @ B ) 0.41/0.65 = C2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_57_Int__commute,axiom, 0.41/0.65 ( inf_in1974387902real_n 0.41/0.65 = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B3 @ A4 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_176_measurable__const,axiom, 0.41/0.65 ! [C2: finite1489363574real_n,M2: sigma_1466784463real_n,M: sigma_1466784463real_n] : 0.41/0.65 ( ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : C2 0.41/0.65 @ ( sigma_439801790real_n @ M @ M2 ) ) 0.41/0.65 <= ( member1352538125real_n @ C2 @ ( sigma_476185326real_n @ M2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_24_vimage__def,axiom, 0.41/0.65 ( vimage207290975real_n 0.41/0.65 = ( ^ [F2: finite1489363574real_n > set_Fi1058188332real_n,B3: set_se2111327970real_n] : 0.41/0.65 ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( member223413699real_n @ ( F2 @ X ) @ B3 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_61_Int__Collect,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,P: set_Fi1058188332real_n > $o] : 0.41/0.65 ( ( member223413699real_n @ X2 @ ( inf_in632889204real_n @ A2 @ ( collec452821761real_n @ P ) ) ) 0.41/0.65 = ( ( member223413699real_n @ X2 @ A2 ) 0.41/0.65 & ( P @ X2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_162_sets_Osets__Collect__imp,axiom, 0.41/0.65 ! [M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o,Q: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.65 ( ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) 0.41/0.65 => ( ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( Q @ X ) 0.41/0.65 & ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) 0.41/0.65 => ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) 0.41/0.65 & ( ( P @ X ) 0.41/0.65 <= ( Q @ X ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_336_add__eq__0__iff__both__eq__0,axiom, 0.41/0.65 ! [X2: nat,Y3: nat] : 0.41/0.65 ( ( ( plus_plus_nat @ X2 @ Y3 ) 0.41/0.65 = zero_zero_nat ) 0.41/0.65 = ( ( Y3 = zero_zero_nat ) 0.41/0.65 & ( X2 = zero_zero_nat ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_187_measurable__restrict__space__iff,axiom, 0.41/0.65 ! [Omega: set_Fi1326602817real_n,M: sigma_107786596real_n,C2: finite1489363574real_n,N: sigma_1466784463real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n] : 0.41/0.65 ( ( ( ( member1695588023real_n @ F @ ( sigma_2028985427real_n @ ( sigma_1052429895real_n @ M @ Omega ) @ N ) ) 0.41/0.65 = ( member1695588023real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1746150050real_n @ X @ Omega ) @ ( F @ X ) @ C2 ) 0.41/0.65 @ ( sigma_2028985427real_n @ M @ N ) ) ) 0.41/0.65 <= ( member1352538125real_n @ C2 @ ( sigma_476185326real_n @ N ) ) ) 0.41/0.65 <= ( member2104752728real_n @ ( inf_in146441683real_n @ Omega @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_329_add__cancel__left__left,axiom, 0.41/0.65 ! [B: nat,A: nat] : 0.41/0.65 ( ( ( plus_plus_nat @ B @ A ) 0.41/0.65 = A ) 0.41/0.65 = ( B = zero_zero_nat ) ) ). 0.41/0.65 0.41/0.65 thf(fact_204_add__diff__cancel__right,axiom, 0.41/0.65 ! [A: finite1489363574real_n,C2: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.65 ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C2 ) @ ( plus_p585657087real_n @ B @ C2 ) ) 0.41/0.65 = ( minus_1037315151real_n @ A @ B ) ) ). 0.41/0.65 0.41/0.65 thf(fact_178_inf__Int__eq,axiom, 0.41/0.65 ! [R: set_se2111327970real_n,S: set_se2111327970real_n] : 0.41/0.65 ( ( inf_in409346577al_n_o 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ R ) 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ S ) ) 0.41/0.65 = ( ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ ( inf_in632889204real_n @ R @ S ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_321_translation__assoc,axiom, 0.41/0.65 ! [B: finite1489363574real_n,A: finite1489363574real_n,S: set_Fi1058188332real_n] : 0.41/0.65 ( ( image_439535603real_n @ ( plus_p585657087real_n @ B ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S ) ) 0.41/0.65 = ( image_439535603real_n @ ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) ) @ S ) ) ). 0.41/0.65 0.41/0.65 thf(fact_272_sets__Collect__restrict__space__iff,axiom, 0.41/0.65 ! [S: set_Fi1058188332real_n,M: sigma_1466784463real_n,P: finite1489363574real_n > $o] : 0.41/0.65 ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ ( sigma_346513458real_n @ M @ S ) ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ S ) ) ) 0.41/0.65 = ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 & ( member1352538125real_n @ X @ S ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_210_diff__add__cancel,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.65 ( ( plus_p585657087real_n @ ( minus_1037315151real_n @ A @ B ) @ B ) 0.41/0.65 = A ) ). 0.41/0.65 0.41/0.65 thf(fact_251_add__implies__diff,axiom, 0.41/0.65 ! [C2: finite1489363574real_n,B: finite1489363574real_n,A: finite1489363574real_n] : 0.41/0.65 ( ( C2 0.41/0.65 = ( minus_1037315151real_n @ A @ B ) ) 0.41/0.65 <= ( ( plus_p585657087real_n @ C2 @ B ) 0.41/0.65 = A ) ) ). 0.41/0.65 0.41/0.65 thf(fact_297_restrict__space__eq__vimage__algebra_H,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] : 0.41/0.65 ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ Omega ) ) 0.41/0.65 = ( sigma_1235138647real_n 0.41/0.65 @ ( sigma_821351682real_n @ ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 @ ^ [X: finite1489363574real_n] : X 0.41/0.65 @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_131_inf__commute,axiom, 0.41/0.65 ( inf_in1974387902real_n 0.41/0.65 = ( ^ [X: set_Fi1058188332real_n,Y2: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ Y2 @ X ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_95_sets_OInt__space__eq2,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,M: sigma_1466784463real_n] : 0.41/0.65 ( ( member223413699real_n @ X2 @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( ( inf_in1974387902real_n @ X2 @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 = X2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_193_sets__Least,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,P: nat > finite1489363574real_n > $o,A2: set_nat] : 0.41/0.65 ( ( member223413699real_n 0.41/0.65 @ ( inf_in1974387902real_n 0.41/0.65 @ ( vimage281029891_n_nat 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ord_Least_nat 0.41/0.65 @ ^ [J2: nat] : ( P @ J2 @ X ) ) 0.41/0.65 @ A2 ) 0.41/0.65 @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 <= ! [I2: nat] : 0.41/0.65 ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( P @ I2 @ X ) 0.41/0.65 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_201_image__ident,axiom, 0.41/0.65 ! [Y: set_Fi1058188332real_n] : 0.41/0.65 ( ( image_439535603real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : X 0.41/0.65 @ Y ) 0.41/0.65 = Y ) ). 0.41/0.65 0.41/0.65 thf(fact_258_add__diff__eq,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( plus_p585657087real_n @ A @ ( minus_1037315151real_n @ B @ C2 ) ) 0.41/0.65 = ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ C2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_185_measurable__restrict__space__iff,axiom, 0.41/0.65 ! [Omega: set_Fi1326602817real_n,M: sigma_107786596real_n,C2: finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member2104752728real_n @ ( inf_in146441683real_n @ Omega @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) ) 0.41/0.65 => ( ( member1746150050real_n @ C2 @ ( sigma_1483971331real_n @ N ) ) 0.41/0.65 => ( ( member117715276real_n @ F @ ( sigma_1185134568real_n @ ( sigma_1052429895real_n @ M @ Omega ) @ N ) ) 0.41/0.65 = ( member117715276real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( if_Fin413489477real_n @ ( member1746150050real_n @ X @ Omega ) @ ( F @ X ) @ C2 ) 0.41/0.65 @ ( sigma_1185134568real_n @ M @ N ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_146_measurable__cong__simp,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,N: sigma_1466784463real_n,M2: sigma_1466784463real_n,N2: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( M = N ) 0.41/0.65 => ( ( ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ M2 ) ) 0.41/0.65 = ( member1746150050real_n @ G @ ( sigma_439801790real_n @ N @ N2 ) ) ) 0.41/0.65 <= ! [W: finite1489363574real_n] : 0.41/0.65 ( ( ( F @ W ) 0.41/0.65 = ( G @ W ) ) 0.41/0.65 <= ( member1352538125real_n @ W @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.65 <= ( M2 = N2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_155_measurable__space,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A2: sigma_1466784463real_n,X2: finite1489363574real_n] : 0.41/0.65 ( ( ( member1352538125real_n @ ( F @ X2 ) @ ( sigma_476185326real_n @ A2 ) ) 0.41/0.65 <= ( member1352538125real_n @ X2 @ ( sigma_476185326real_n @ M ) ) ) 0.41/0.65 <= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_46_IntE,axiom, 0.41/0.65 ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ~ ( ~ ( member223413699real_n @ C2 @ B2 ) 0.41/0.65 <= ( member223413699real_n @ C2 @ A2 ) ) 0.41/0.65 <= ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_284_Diff__Int2,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n,C: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A2 @ C ) @ ( inf_in1974387902real_n @ B2 @ C ) ) 0.41/0.65 = ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A2 @ C ) @ B2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_72_add_Ocommute,axiom, 0.41/0.65 ( plus_p585657087real_n 0.41/0.65 = ( ^ [A3: finite1489363574real_n,B4: finite1489363574real_n] : ( plus_p585657087real_n @ B4 @ A3 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom, 0.41/0.65 ! [A: finite964658038_int_n] : 0.41/0.65 ( ( member223413699real_n @ ( t2 @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) 0.41/0.65 => ( member223413699real_n 0.41/0.65 @ ( inf_in1974387902real_n 0.41/0.65 @ ( vimage1233683625real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ X @ ( minkow1134813771n_real @ A ) ) 0.41/0.65 @ ( t2 @ A ) ) 0.41/0.65 @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_133_inf__assoc,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n,Z: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ X2 @ Y3 ) @ Z ) 0.41/0.65 = ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ Y3 @ Z ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_264_vimage__algebra__cong,axiom, 0.41/0.65 ! [X4: set_Fi1326602817real_n,Y: set_Fi1326602817real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,G: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n] : 0.41/0.65 ( ( ! [X3: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X3 @ Y ) 0.41/0.65 => ( ( F @ X3 ) 0.41/0.65 = ( G @ X3 ) ) ) 0.41/0.65 => ( ( ( sigma_1235138647real_n @ M ) 0.41/0.65 = ( sigma_1235138647real_n @ N ) ) 0.41/0.65 => ( ( sigma_136294295real_n @ X4 @ F @ M ) 0.41/0.65 = ( sigma_136294295real_n @ Y @ G @ N ) ) ) ) 0.41/0.65 <= ( X4 = Y ) ) ). 0.41/0.65 0.41/0.65 thf(fact_150_measurable__space,axiom, 0.41/0.65 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,M: sigma_107786596real_n,A2: sigma_107786596real_n,X2: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member117715276real_n @ F @ ( sigma_1185134568real_n @ M @ A2 ) ) 0.41/0.65 => ( ( member1746150050real_n @ ( F @ X2 ) @ ( sigma_1483971331real_n @ A2 ) ) 0.41/0.65 <= ( member1746150050real_n @ X2 @ ( sigma_1483971331real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_225_imageE,axiom, 0.41/0.65 ! [B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ A2 ) ) 0.41/0.65 => ~ ! [X3: finite1489363574real_n] : 0.41/0.65 ( ~ ( member1352538125real_n @ X3 @ A2 ) 0.41/0.65 <= ( B 0.41/0.65 = ( F @ X3 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_224_image__image,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] : 0.41/0.65 ( ( image_439535603real_n @ F @ ( image_439535603real_n @ G @ A2 ) ) 0.41/0.65 = ( image_439535603real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( F @ ( G @ X ) ) 0.41/0.65 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_156_measurable__cong,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,M2: sigma_1466784463real_n] : 0.41/0.65 ( ! [W: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ W @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 => ( ( F @ W ) 0.41/0.65 = ( G @ W ) ) ) 0.41/0.65 => ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ M2 ) ) 0.41/0.65 = ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ M2 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_149_measurable__space,axiom, 0.41/0.65 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,M: sigma_107786596real_n,A2: sigma_1422848389real_n,X2: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member640587117real_n @ F @ ( sigma_364818953real_n @ M @ A2 ) ) 0.41/0.65 => ( ( member223413699real_n @ ( F @ X2 ) @ ( sigma_607186084real_n @ A2 ) ) 0.41/0.65 <= ( member1746150050real_n @ X2 @ ( sigma_1483971331real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_62_Int__Collect,axiom, 0.41/0.65 ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.65 ( ( member1746150050real_n @ X2 @ ( inf_in146441683real_n @ A2 @ ( collec1190264032real_n @ P ) ) ) 0.41/0.65 = ( ( member1746150050real_n @ X2 @ A2 ) 0.41/0.65 & ( P @ X2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_223_Compr__image__eq,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,P: finite1489363574real_n > $o] : 0.41/0.65 ( ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1352538125real_n @ X @ ( image_439535603real_n @ F @ A2 ) ) ) ) 0.41/0.65 = ( image_439535603real_n @ F 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ A2 ) 0.41/0.65 & ( P @ ( F @ X ) ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_286_Diff__Int__distrib,axiom, 0.41/0.65 ! [C: set_Fi1058188332real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ C @ ( minus_1686442501real_n @ A2 @ B2 ) ) 0.41/0.65 = ( minus_1686442501real_n @ ( inf_in1974387902real_n @ C @ A2 ) @ ( inf_in1974387902real_n @ C @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_279_measurable__lborel2,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n] : 0.41/0.65 ( ( sigma_439801790real_n @ lebesg260170249real_n @ M ) 0.41/0.65 = ( sigma_439801790real_n @ borel_676189912real_n @ M ) ) ). 0.41/0.65 0.41/0.65 thf(fact_170_sets_Osets__Collect__disj,axiom, 0.41/0.65 ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o,Q: set_Fi1058188332real_n > $o] : 0.41/0.65 ( ( member1475136633real_n 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_433815053real_n @ M ) ) 0.41/0.65 => ( ( member1475136633real_n 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) 0.41/0.65 & ( ( Q @ X ) 0.41/0.65 | ( P @ X ) ) ) ) 0.41/0.65 @ ( sigma_433815053real_n @ M ) ) 0.41/0.65 <= ( member1475136633real_n 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) 0.41/0.65 & ( Q @ X ) ) ) 0.41/0.65 @ ( sigma_433815053real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_236_rev__image__eqI,axiom, 0.41/0.65 ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B: set_Fi1058188332real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] : 0.41/0.65 ( ( member1746150050real_n @ X2 @ A2 ) 0.41/0.65 => ( ( B 0.41/0.65 = ( F @ X2 ) ) 0.41/0.65 => ( member223413699real_n @ B @ ( image_128879038real_n @ F @ A2 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_16_vimage__eq,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] : 0.41/0.65 ( ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ B2 ) ) 0.41/0.65 = ( member1746150050real_n @ ( F @ A ) @ B2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_291_measurable__lebesgue__cong,axiom, 0.41/0.65 ! [S: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n] : 0.41/0.65 ( ! [X3: finite1489363574real_n] : 0.41/0.65 ( ( ( F @ X3 ) 0.41/0.65 = ( G @ X3 ) ) 0.41/0.65 <= ( member1352538125real_n @ X3 @ S ) ) 0.41/0.65 => ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) @ M ) ) 0.41/0.65 = ( member1746150050real_n @ G @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_87_add__mono__thms__linordered__semiring_I4_J,axiom, 0.41/0.65 ! [I: finite1489363574real_n,J: finite1489363574real_n,K: finite1489363574real_n,L: finite1489363574real_n] : 0.41/0.65 ( ( ( plus_p585657087real_n @ I @ K ) 0.41/0.65 = ( plus_p585657087real_n @ J @ L ) ) 0.41/0.65 <= ( ( I = J ) 0.41/0.65 & ( K = L ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_119_measurable__If,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,M2: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n,P: finite1489363574real_n > $o] : 0.41/0.65 ( ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ M2 ) ) 0.41/0.65 => ( ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( P @ X ) @ ( F @ X ) @ ( G @ X ) ) 0.41/0.65 @ ( sigma_439801790real_n @ M @ M2 ) ) ) ) 0.41/0.65 <= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ M2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_147_measurable__space,axiom, 0.41/0.65 ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,M: sigma_1422848389real_n,A2: sigma_1422848389real_n,X2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1734791438real_n @ F @ ( sigma_239294762real_n @ M @ A2 ) ) 0.41/0.65 => ( ( member223413699real_n @ X2 @ ( sigma_607186084real_n @ M ) ) 0.41/0.65 => ( member223413699real_n @ ( F @ X2 ) @ ( sigma_607186084real_n @ A2 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T,axiom, 0.41/0.65 ! [X2: finite1489363574real_n,Y3: finite1489363574real_n] : 0.41/0.65 ( ( if_Fin127821360real_n @ $false @ X2 @ Y3 ) 0.41/0.65 = Y3 ) ). 0.41/0.65 0.41/0.65 thf(fact_217_Compr__image__eq,axiom, 0.41/0.65 ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A2: set_se2111327970real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.65 ( ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ ( image_352856126real_n @ F @ A2 ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 = ( image_352856126real_n @ F 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( P @ ( F @ X ) ) 0.41/0.65 & ( member223413699real_n @ X @ A2 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_90_vimageI2,axiom, 0.41/0.65 ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,A: set_Fi1058188332real_n,A2: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ A2 ) ) 0.41/0.65 <= ( member223413699real_n @ ( F @ A ) @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_124_inf__idem,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ X2 @ X2 ) 0.41/0.65 = X2 ) ). 0.41/0.65 0.41/0.65 thf(fact_157_measurable__ident__sets,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,M2: sigma_1466784463real_n] : 0.41/0.65 ( ( ( sigma_1235138647real_n @ M ) 0.41/0.65 = ( sigma_1235138647real_n @ M2 ) ) 0.41/0.65 => ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : X 0.41/0.65 @ ( sigma_439801790real_n @ M @ M2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_65_Int__def,axiom, 0.41/0.65 ( inf_in146441683real_n 0.41/0.65 = ( ^ [A4: set_Fi1326602817real_n,B3: set_Fi1326602817real_n] : 0.41/0.65 ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ A4 ) 0.41/0.65 & ( member1746150050real_n @ X @ B3 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_334_add__cancel__right__right,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.65 ( ( A 0.41/0.65 = ( plus_p585657087real_n @ A @ B ) ) 0.41/0.65 = ( B = zero_z200130687real_n ) ) ). 0.41/0.65 0.41/0.65 thf(fact_166_sets_Osets__Collect__neg,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o] : 0.41/0.65 ( ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 & ~ ( P @ X ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_327_add_Oright__neutral,axiom, 0.41/0.65 ! [A: nat] : 0.41/0.65 ( ( plus_plus_nat @ A @ zero_zero_nat ) 0.41/0.65 = A ) ). 0.41/0.65 0.41/0.65 thf(fact_7__092_060open_062_092_060And_062a_O_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_092_060in_062_Alebesgue_A_092_060rightarrow_062_092_060_094sub_062M_Alebesgue_092_060close_062,axiom, 0.41/0.65 ! [A: finite964658038_int_n] : 0.41/0.65 ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ X @ ( minkow1134813771n_real @ A ) ) 0.41/0.65 @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_127_inf__set__def,axiom, 0.41/0.65 ( inf_in146441683real_n 0.41/0.65 = ( ^ [A4: set_Fi1326602817real_n,B3: set_Fi1326602817real_n] : 0.41/0.65 ( collec1190264032real_n 0.41/0.65 @ ( inf_in32002162al_n_o 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ A4 ) 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ B3 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_318_translation__diff,axiom, 0.41/0.65 ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T3: set_Fi1058188332real_n] : 0.41/0.65 ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( minus_1686442501real_n @ S2 @ T3 ) ) 0.41/0.65 = ( minus_1686442501real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S2 ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ T3 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_63_Int__Collect,axiom, 0.41/0.65 ! [X2: finite1489363574real_n,A2: set_Fi1058188332real_n,P: finite1489363574real_n > $o] : 0.41/0.65 ( ( member1352538125real_n @ X2 @ ( inf_in1974387902real_n @ A2 @ ( collec321817931real_n @ P ) ) ) 0.41/0.65 = ( ( member1352538125real_n @ X2 @ A2 ) 0.41/0.65 & ( P @ X2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_32_vimageE,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ B2 ) ) 0.41/0.65 => ( member223413699real_n @ ( F @ A ) @ B2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_233_rev__image__eqI,axiom, 0.41/0.65 ! [X2: finite1489363574real_n,A2: set_Fi1058188332real_n,B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ A2 ) ) 0.41/0.65 <= ( B 0.41/0.65 = ( F @ X2 ) ) ) 0.41/0.65 <= ( member1352538125real_n @ X2 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_214_borel__measurable__diff,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) 0.41/0.65 => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) 0.41/0.65 => ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ ( F @ X ) @ ( G @ X ) ) 0.41/0.65 @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_18_vimage__eq,axiom, 0.41/0.65 ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] : 0.41/0.65 ( ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ B2 ) ) 0.41/0.65 = ( member1746150050real_n @ ( F @ A ) @ B2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_347_diff__add__zero,axiom, 0.41/0.65 ! [A: nat,B: nat] : 0.41/0.65 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) ) 0.41/0.65 = zero_zero_nat ) ). 0.41/0.65 0.41/0.65 thf(fact_255_diff__add__eq__diff__diff__swap,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( minus_1037315151real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) 0.41/0.65 = ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C2 ) @ B ) ) ). 0.41/0.65 0.41/0.65 thf(fact_340_zero__diff,axiom, 0.41/0.65 ! [A: nat] : 0.41/0.65 ( ( minus_minus_nat @ zero_zero_nat @ A ) 0.41/0.65 = zero_zero_nat ) ). 0.41/0.65 0.41/0.65 thf(fact_221_Compr__image__eq,axiom, 0.41/0.65 ! [F: set_Fi1058188332real_n > finite1489363574real_n,A2: set_se2111327970real_n,P: finite1489363574real_n > $o] : 0.41/0.65 ( ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1352538125real_n @ X @ ( image_1311908777real_n @ F @ A2 ) ) ) ) 0.41/0.65 = ( image_1311908777real_n @ F 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X @ A2 ) 0.41/0.65 & ( P @ ( F @ X ) ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_33_vimageE,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] : 0.41/0.65 ( ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ B2 ) ) 0.41/0.65 => ( member1746150050real_n @ ( F @ A ) @ B2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_188_measurable__restrict__space__iff,axiom, 0.41/0.65 ! [Omega: set_Fi1058188332real_n,M: sigma_1466784463real_n,C2: set_Fi1058188332real_n,N: sigma_1422848389real_n,F: finite1489363574real_n > set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( ( member223413699real_n @ C2 @ ( sigma_607186084real_n @ N ) ) 0.41/0.65 => ( ( member966061400real_n @ F @ ( sigma_566919540real_n @ ( sigma_346513458real_n @ M @ Omega ) @ N ) ) 0.41/0.65 = ( member966061400real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( if_set11487206real_n @ ( member1352538125real_n @ X @ Omega ) @ ( F @ X ) @ C2 ) 0.41/0.65 @ ( sigma_566919540real_n @ M @ N ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_257_diff__diff__eq2,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( minus_1037315151real_n @ A @ ( minus_1037315151real_n @ B @ C2 ) ) 0.41/0.65 = ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C2 ) @ B ) ) ). 0.41/0.65 0.41/0.65 thf(fact_240_bex__imageD,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,P: finite1489363574real_n > $o] : 0.41/0.65 ( ? [X5: finite1489363574real_n] : 0.41/0.65 ( ( P @ X5 ) 0.41/0.65 & ( member1352538125real_n @ X5 @ ( image_439535603real_n @ F @ A2 ) ) ) 0.41/0.65 => ? [X3: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X3 @ A2 ) 0.41/0.65 & ( P @ ( F @ X3 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_212_main__part,axiom, 0.41/0.65 ! [S: set_Fi1058188332real_n,M: sigma_1466784463real_n] : 0.41/0.65 ( ( ( comple1390568924real_n @ M @ S ) 0.41/0.65 = S ) 0.41/0.65 <= ( member223413699real_n @ S @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_298_restrict__restrict__space,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n,M: sigma_1466784463real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( ( ( sigma_346513458real_n @ ( sigma_346513458real_n @ M @ A2 ) @ B2 ) 0.41/0.65 = ( sigma_346513458real_n @ M @ ( inf_in1974387902real_n @ A2 @ B2 ) ) ) 0.41/0.65 <= ( member223413699real_n @ ( inf_in1974387902real_n @ B2 @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) ) 0.41/0.65 <= ( member223413699real_n @ ( inf_in1974387902real_n @ A2 @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_248_sets__restrict__space__cong,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,N: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] : 0.41/0.65 ( ( ( sigma_1235138647real_n @ M ) 0.41/0.65 = ( sigma_1235138647real_n @ N ) ) 0.41/0.65 => ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ Omega ) ) 0.41/0.65 = ( sigma_1235138647real_n @ ( sigma_346513458real_n @ N @ Omega ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_352_diffs0__imp__equal,axiom, 0.41/0.65 ! [M4: nat,N3: nat] : 0.41/0.65 ( ( ( M4 = N3 ) 0.41/0.65 <= ( ( minus_minus_nat @ N3 @ M4 ) 0.41/0.65 = zero_zero_nat ) ) 0.41/0.65 <= ( ( minus_minus_nat @ M4 @ N3 ) 0.41/0.65 = zero_zero_nat ) ) ). 0.41/0.65 0.41/0.65 thf(fact_154_measurable__space,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A2: sigma_107786596real_n,X2: finite1489363574real_n] : 0.41/0.65 ( ( ( member1746150050real_n @ ( F @ X2 ) @ ( sigma_1483971331real_n @ A2 ) ) 0.41/0.65 <= ( member1352538125real_n @ X2 @ ( sigma_476185326real_n @ M ) ) ) 0.41/0.65 <= ( member408431031real_n @ F @ ( sigma_2016438227real_n @ M @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_342_diff__zero,axiom, 0.41/0.65 ! [A: nat] : 0.41/0.65 ( ( minus_minus_nat @ A @ zero_zero_nat ) 0.41/0.65 = A ) ). 0.41/0.65 0.41/0.65 thf(fact_102_measurableI,axiom, 0.41/0.65 ! [M: sigma_1422848389real_n,F: set_Fi1058188332real_n > finite1489363574real_n,N: sigma_1466784463real_n] : 0.41/0.65 ( ! [X3: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1352538125real_n @ ( F @ X3 ) @ ( sigma_476185326real_n @ N ) ) 0.41/0.65 <= ( member223413699real_n @ X3 @ ( sigma_607186084real_n @ M ) ) ) 0.41/0.65 => ( ! [A6: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage973736031real_n @ F @ A6 ) @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) ) 0.41/0.65 <= ( member223413699real_n @ A6 @ ( sigma_1235138647real_n @ N ) ) ) 0.41/0.65 => ( member1759501912real_n @ F @ ( sigma_1333364596real_n @ M @ N ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_134_inf_Oassoc,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C2: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ C2 ) 0.41/0.65 = ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_174_sets_Osets__Collect__const,axiom, 0.41/0.65 ! [M: sigma_107786596real_n,P: $o] : 0.41/0.65 ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( P 0.41/0.65 & ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) ). 0.41/0.65 0.41/0.65 thf(fact_353_minus__nat_Odiff__0,axiom, 0.41/0.65 ! [M4: nat] : 0.41/0.65 ( ( minus_minus_nat @ M4 @ zero_zero_nat ) 0.41/0.65 = M4 ) ). 0.41/0.65 0.41/0.65 thf(fact_197_image__eqI,axiom, 0.41/0.65 ! [B: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,X2: set_Fi1058188332real_n,A2: set_se2111327970real_n] : 0.41/0.65 ( ( B 0.41/0.65 = ( F @ X2 ) ) 0.41/0.65 => ( ( member223413699real_n @ X2 @ A2 ) 0.41/0.65 => ( member223413699real_n @ B @ ( image_1661509983real_n @ F @ A2 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_346_image__add__0,axiom, 0.41/0.65 ! [S: set_nat] : 0.41/0.65 ( ( image_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ S ) 0.41/0.65 = S ) ). 0.41/0.65 0.41/0.65 thf(fact_68_vimage__inter__cong,axiom, 0.41/0.65 ! [S: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,Y3: set_Fi1058188332real_n] : 0.41/0.65 ( ! [W: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ W @ S ) 0.41/0.65 => ( ( F @ W ) 0.41/0.65 = ( G @ W ) ) ) 0.41/0.65 => ( ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ Y3 ) @ S ) 0.41/0.65 = ( inf_in1974387902real_n @ ( vimage1233683625real_n @ G @ Y3 ) @ S ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_351_diff__self__eq__0,axiom, 0.41/0.65 ! [M4: nat] : 0.41/0.65 ( ( minus_minus_nat @ M4 @ M4 ) 0.41/0.65 = zero_zero_nat ) ). 0.41/0.65 0.41/0.65 thf(fact_292_lborelD__Collect,axiom, 0.41/0.65 ! [P: finite1489363574real_n > $o] : 0.41/0.65 ( ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ lebesg260170249real_n ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ lebesg260170249real_n ) ) 0.41/0.65 <= ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ borel_676189912real_n ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ borel_676189912real_n ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_182_measurable__restrict__space__iff,axiom, 0.41/0.65 ! [Omega: set_se2111327970real_n,M: sigma_1422848389real_n,C2: set_Fi1058188332real_n,N: sigma_1422848389real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n] : 0.41/0.65 ( ( ( member223413699real_n @ C2 @ ( sigma_607186084real_n @ N ) ) 0.41/0.65 => ( ( member1734791438real_n @ F @ ( sigma_239294762real_n @ ( sigma_993999336real_n @ M @ Omega ) @ N ) ) 0.41/0.65 = ( member1734791438real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : ( if_set11487206real_n @ ( member223413699real_n @ X @ Omega ) @ ( F @ X ) @ C2 ) 0.41/0.65 @ ( sigma_239294762real_n @ M @ N ) ) ) ) 0.41/0.65 <= ( member1475136633real_n @ ( inf_in632889204real_n @ Omega @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom, 0.41/0.65 ! [A: finite964658038_int_n] : ( member223413699real_n @ ( t2 @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_345_image__add__0,axiom, 0.41/0.65 ! [S: set_Fi1058188332real_n] : 0.41/0.65 ( ( image_439535603real_n @ ( plus_p585657087real_n @ zero_z200130687real_n ) @ S ) 0.41/0.65 = S ) ). 0.41/0.65 0.41/0.65 thf(fact_226_imageE,axiom, 0.41/0.65 ! [B: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,A2: set_se2111327970real_n] : 0.41/0.65 ( ~ ! [X3: set_Fi1058188332real_n] : 0.41/0.65 ( ~ ( member223413699real_n @ X3 @ A2 ) 0.41/0.65 <= ( B 0.41/0.65 = ( F @ X3 ) ) ) 0.41/0.65 <= ( member223413699real_n @ B @ ( image_1661509983real_n @ F @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_222_Compr__image__eq,axiom, 0.41/0.65 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,A2: set_Fi1326602817real_n,P: finite1489363574real_n > $o] : 0.41/0.65 ( ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1352538125real_n @ X @ ( image_449906696real_n @ F @ A2 ) ) ) ) 0.41/0.65 = ( image_449906696real_n @ F 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ A2 ) 0.41/0.65 & ( P @ ( F @ X ) ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_300_Diff__iff,axiom, 0.41/0.65 ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) ) 0.41/0.65 = ( ( member223413699real_n @ C2 @ A2 ) 0.41/0.65 & ~ ( member223413699real_n @ C2 @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_241_image__iff,axiom, 0.41/0.65 ! [Z: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1352538125real_n @ Z @ ( image_439535603real_n @ F @ A2 ) ) 0.41/0.65 = ( ? [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ A2 ) 0.41/0.65 & ( Z 0.41/0.65 = ( F @ X ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_230_diff__right__commute,axiom, 0.41/0.65 ! [A: finite1489363574real_n,C2: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.65 ( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C2 ) @ B ) 0.41/0.65 = ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_324_add_Oleft__neutral,axiom, 0.41/0.65 ! [A: finite1489363574real_n] : 0.41/0.65 ( ( plus_p585657087real_n @ zero_z200130687real_n @ A ) 0.41/0.65 = A ) ). 0.41/0.65 0.41/0.65 thf(fact_64_Int__def,axiom, 0.41/0.65 ( inf_in632889204real_n 0.41/0.65 = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] : 0.41/0.65 ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X @ B3 ) 0.41/0.65 & ( member223413699real_n @ X @ A4 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_332_add__cancel__right__left,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.65 ( ( A 0.41/0.65 = ( plus_p585657087real_n @ B @ A ) ) 0.41/0.65 = ( B = zero_z200130687real_n ) ) ). 0.41/0.65 0.41/0.65 thf(fact_252_add__implies__diff,axiom, 0.41/0.65 ! [C2: nat,B: nat,A: nat] : 0.41/0.65 ( ( ( plus_plus_nat @ C2 @ B ) 0.41/0.65 = A ) 0.41/0.65 => ( C2 0.41/0.65 = ( minus_minus_nat @ A @ B ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_73_add_Oright__cancel,axiom, 0.41/0.65 ! [B: finite1489363574real_n,A: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( ( plus_p585657087real_n @ B @ A ) 0.41/0.65 = ( plus_p585657087real_n @ C2 @ A ) ) 0.41/0.65 = ( B = C2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_13_vimageI,axiom, 0.41/0.65 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] : 0.41/0.65 ( ( ( F @ A ) 0.41/0.65 = B ) 0.41/0.65 => ( ( member1746150050real_n @ B @ B2 ) 0.41/0.65 => ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ B2 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_229_imageE,axiom, 0.41/0.65 ! [B: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] : 0.41/0.65 ( ~ ! [X3: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ~ ( member1746150050real_n @ X3 @ A2 ) 0.41/0.65 <= ( B 0.41/0.65 = ( F @ X3 ) ) ) 0.41/0.65 <= ( member1746150050real_n @ B @ ( image_1123376925real_n @ F @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_313_DiffD1,axiom, 0.41/0.65 ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] : 0.41/0.65 ( ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) ) 0.41/0.65 => ( member1746150050real_n @ C2 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_98_measurableI,axiom, 0.41/0.65 ! [M: sigma_1422848389real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,N: sigma_1422848389real_n] : 0.41/0.65 ( ( ( member1734791438real_n @ F @ ( sigma_239294762real_n @ M @ N ) ) 0.41/0.65 <= ! [A6: set_se2111327970real_n] : 0.41/0.65 ( ( member1475136633real_n @ A6 @ ( sigma_433815053real_n @ N ) ) 0.41/0.65 => ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage784510485real_n @ F @ A6 ) @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) ) ) ) 0.41/0.65 <= ! [X3: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X3 @ ( sigma_607186084real_n @ M ) ) 0.41/0.65 => ( member223413699real_n @ ( F @ X3 ) @ ( sigma_607186084real_n @ N ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_143_measurable__id,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n] : 0.41/0.65 ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : X 0.41/0.65 @ ( sigma_439801790real_n @ M @ M ) ) ). 0.41/0.65 0.41/0.65 thf(fact_84_Collect__mem__eq,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n] : 0.41/0.65 ( ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ A2 ) ) 0.41/0.65 = A2 ) ). 0.41/0.65 0.41/0.65 thf(fact_192_sets__Least,axiom, 0.41/0.65 ! [M: sigma_107786596real_n,P: nat > ( finite1489363574real_n > finite1489363574real_n ) > $o,A2: set_nat] : 0.41/0.65 ( ( member2104752728real_n 0.41/0.65 @ ( inf_in146441683real_n 0.41/0.65 @ ( vimage2098059032_n_nat 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ord_Least_nat 0.41/0.65 @ ^ [J2: nat] : ( P @ J2 @ X ) ) 0.41/0.65 @ A2 ) 0.41/0.65 @ ( sigma_1483971331real_n @ M ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) 0.41/0.65 <= ! [I2: nat] : 0.41/0.65 ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( P @ I2 @ X ) 0.41/0.65 & ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_339_diff__0__right,axiom, 0.41/0.65 ! [A: finite1489363574real_n] : 0.41/0.65 ( ( minus_1037315151real_n @ A @ zero_z200130687real_n ) 0.41/0.65 = A ) ). 0.41/0.65 0.41/0.65 thf(fact_77_set__plus__elim,axiom, 0.41/0.65 ! [X2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1352538125real_n @ X2 @ ( plus_p1606848693real_n @ A2 @ B2 ) ) 0.41/0.65 => ~ ! [A5: finite1489363574real_n,B5: finite1489363574real_n] : 0.41/0.65 ( ( ~ ( member1352538125real_n @ B5 @ B2 ) 0.41/0.65 <= ( member1352538125real_n @ A5 @ A2 ) ) 0.41/0.65 <= ( X2 0.41/0.65 = ( plus_p585657087real_n @ A5 @ B5 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_275_space__lebesgue__on,axiom, 0.41/0.65 ! [S: set_Fi1058188332real_n] : 0.41/0.65 ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) ) 0.41/0.65 = S ) ). 0.41/0.65 0.41/0.65 thf(help_If_1_1_If_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] : 0.41/0.65 ( ( if_set11487206real_n @ $true @ X2 @ Y3 ) 0.41/0.65 = X2 ) ). 0.41/0.65 0.41/0.65 thf(fact_242_imageI,axiom, 0.41/0.65 ! [X2: finite1489363574real_n,A2: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ ( F @ X2 ) @ ( image_439535603real_n @ F @ A2 ) ) 0.41/0.65 <= ( member1352538125real_n @ X2 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_244_imageI,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ ( F @ X2 ) @ ( image_352856126real_n @ F @ A2 ) ) 0.41/0.65 <= ( member223413699real_n @ X2 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_105_measurableI,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n] : 0.41/0.65 ( ( ! [A6: set_Fi1326602817real_n] : 0.41/0.65 ( ( member2104752728real_n @ A6 @ ( sigma_522684908real_n @ N ) ) 0.41/0.65 => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1059850558real_n @ F @ A6 ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) ) 0.41/0.65 => ( member408431031real_n @ F @ ( sigma_2016438227real_n @ M @ N ) ) ) 0.41/0.65 <= ! [X3: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X3 @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 => ( member1746150050real_n @ ( F @ X3 ) @ ( sigma_1483971331real_n @ N ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_296_borel__measurable__vimage__borel,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,S: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) @ borel_676189912real_n ) ) 0.41/0.65 = ( ! [T2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ T2 @ ( sigma_1235138647real_n @ borel_676189912real_n ) ) 0.41/0.65 => ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ ( F @ X ) @ T2 ) 0.41/0.65 & ( member1352538125real_n @ X @ S ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_75_add_Oassoc,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) @ C2 ) 0.41/0.65 = ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_81_mem__Collect__eq,axiom, 0.41/0.65 ! [A: finite1489363574real_n,P: finite1489363574real_n > $o] : 0.41/0.65 ( ( member1352538125real_n @ A @ ( collec321817931real_n @ P ) ) 0.41/0.65 = ( P @ A ) ) ). 0.41/0.65 0.41/0.65 thf(fact_10_vimageI,axiom, 0.41/0.65 ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( ( member223413699real_n @ B @ B2 ) 0.41/0.65 => ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ B2 ) ) ) 0.41/0.65 <= ( ( F @ A ) 0.41/0.65 = B ) ) ). 0.41/0.65 0.41/0.65 thf(fact_260_diff__eq__eq,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( ( minus_1037315151real_n @ A @ B ) 0.41/0.65 = C2 ) 0.41/0.65 = ( A 0.41/0.65 = ( plus_p585657087real_n @ C2 @ B ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_58_Int__left__absorb,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ A2 @ ( inf_in1974387902real_n @ A2 @ B2 ) ) 0.41/0.65 = ( inf_in1974387902real_n @ A2 @ B2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_136_boolean__algebra__cancel_Oinf1,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n,K: set_Fi1058188332real_n,A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : 0.41/0.65 ( ( ( inf_in1974387902real_n @ A2 @ B ) 0.41/0.65 = ( inf_in1974387902real_n @ K @ ( inf_in1974387902real_n @ A @ B ) ) ) 0.41/0.65 <= ( A2 0.41/0.65 = ( inf_in1974387902real_n @ K @ A ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_216_Compr__image__eq,axiom, 0.41/0.65 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A2: set_Fi1326602817real_n,P: set_Fi1058188332real_n > $o] : 0.41/0.65 ( ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member223413699real_n @ X @ ( image_128879038real_n @ F @ A2 ) ) ) ) 0.41/0.65 = ( image_128879038real_n @ F 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( P @ ( F @ X ) ) 0.41/0.65 & ( member1746150050real_n @ X @ A2 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_280_sets_ODiff,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,M: sigma_1466784463real_n,B: set_Fi1058188332real_n] : 0.41/0.65 ( ( ( member223413699real_n @ ( minus_1686442501real_n @ A @ B ) @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 <= ( member223413699real_n @ B @ ( sigma_1235138647real_n @ M ) ) ) 0.41/0.65 <= ( member223413699real_n @ A @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_266_borel__measurable__add,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) 0.41/0.65 => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) 0.41/0.65 => ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ ( F @ X ) @ ( G @ X ) ) 0.41/0.65 @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_70_add__left__imp__eq,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( B = C2 ) 0.41/0.65 <= ( ( plus_p585657087real_n @ A @ B ) 0.41/0.65 = ( plus_p585657087real_n @ A @ C2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_235_rev__image__eqI,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B: finite1489363574real_n > finite1489363574real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( ( B 0.41/0.65 = ( F @ X2 ) ) 0.41/0.65 => ( member1746150050real_n @ B @ ( image_352856126real_n @ F @ A2 ) ) ) 0.41/0.65 <= ( member223413699real_n @ X2 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_44_vimage__Int,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( vimage1233683625real_n @ F @ ( inf_in1974387902real_n @ A2 @ B2 ) ) 0.41/0.65 = ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ A2 ) @ ( vimage1233683625real_n @ F @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_78_group__cancel_Oadd2,axiom, 0.41/0.65 ! [B2: finite1489363574real_n,K: finite1489363574real_n,B: finite1489363574real_n,A: finite1489363574real_n] : 0.41/0.65 ( ( B2 0.41/0.65 = ( plus_p585657087real_n @ K @ B ) ) 0.41/0.65 => ( ( plus_p585657087real_n @ A @ B2 ) 0.41/0.65 = ( plus_p585657087real_n @ K @ ( plus_p585657087real_n @ A @ B ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_15_vimage__eq,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ B2 ) ) 0.41/0.65 = ( member223413699real_n @ ( F @ A ) @ B2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_278_measurable__lborel1,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n] : 0.41/0.65 ( ( sigma_439801790real_n @ M @ lebesg260170249real_n ) 0.41/0.65 = ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ). 0.41/0.65 0.41/0.65 thf(fact_269_measurable__sets__borel,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ borel_676189912real_n @ M ) ) 0.41/0.65 => ( ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( member223413699real_n @ ( vimage1233683625real_n @ F @ A2 ) @ ( sigma_1235138647real_n @ borel_676189912real_n ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_325_add_Oleft__neutral,axiom, 0.41/0.65 ! [A: nat] : 0.41/0.65 ( ( plus_plus_nat @ zero_zero_nat @ A ) 0.41/0.65 = A ) ). 0.41/0.65 0.41/0.65 thf(fact_262_sets__vimage__algebra__cong,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,N: sigma_1466784463real_n,X4: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( ( sigma_1235138647real_n @ M ) 0.41/0.65 = ( sigma_1235138647real_n @ N ) ) 0.41/0.65 => ( ( sigma_1235138647real_n @ ( sigma_821351682real_n @ X4 @ F @ M ) ) 0.41/0.65 = ( sigma_1235138647real_n @ ( sigma_821351682real_n @ X4 @ F @ N ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_50_IntD1,axiom, 0.41/0.65 ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] : 0.41/0.65 ( ( member1746150050real_n @ C2 @ A2 ) 0.41/0.65 <= ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_91_vimageI2,axiom, 0.41/0.65 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A: finite1489363574real_n > finite1489363574real_n,A2: set_se2111327970real_n] : 0.41/0.65 ( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ A2 ) ) 0.41/0.65 <= ( member223413699real_n @ ( F @ A ) @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_79_mem__Collect__eq,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,P: set_Fi1058188332real_n > $o] : 0.41/0.65 ( ( member223413699real_n @ A @ ( collec452821761real_n @ P ) ) 0.41/0.65 = ( P @ A ) ) ). 0.41/0.65 0.41/0.65 thf(fact_69_add__right__imp__eq,axiom, 0.41/0.65 ! [B: finite1489363574real_n,A: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( B = C2 ) 0.41/0.65 <= ( ( plus_p585657087real_n @ B @ A ) 0.41/0.65 = ( plus_p585657087real_n @ C2 @ A ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_183_measurable__restrict__space__iff,axiom, 0.41/0.65 ! [Omega: set_Fi1326602817real_n,M: sigma_107786596real_n,C2: set_Fi1058188332real_n,N: sigma_1422848389real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] : 0.41/0.65 ( ( ( member223413699real_n @ C2 @ ( sigma_607186084real_n @ N ) ) 0.41/0.65 => ( ( member640587117real_n @ F @ ( sigma_364818953real_n @ ( sigma_1052429895real_n @ M @ Omega ) @ N ) ) 0.41/0.65 = ( member640587117real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( if_set11487206real_n @ ( member1746150050real_n @ X @ Omega ) @ ( F @ X ) @ C2 ) 0.41/0.65 @ ( sigma_364818953real_n @ M @ N ) ) ) ) 0.41/0.65 <= ( member2104752728real_n @ ( inf_in146441683real_n @ Omega @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_122_inf__left__idem,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ X2 @ Y3 ) ) 0.41/0.65 = ( inf_in1974387902real_n @ X2 @ Y3 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_311_DiffD2,axiom, 0.41/0.65 ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] : 0.41/0.65 ( ~ ( member1746150050real_n @ C2 @ B2 ) 0.41/0.65 <= ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_243_imageI,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ ( F @ X2 ) @ ( image_1661509983real_n @ F @ A2 ) ) 0.41/0.65 <= ( member223413699real_n @ X2 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_113_measurable__sets__Collect,axiom, 0.41/0.65 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,M: sigma_107786596real_n,N: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.65 ( ( member117715276real_n @ F @ ( sigma_1185134568real_n @ M @ N ) ) 0.41/0.65 => ( ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) 0.41/0.65 & ( P @ ( F @ X ) ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) 0.41/0.65 <= ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ N ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 @ ( sigma_522684908real_n @ N ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_261_group__cancel_Osub1,axiom, 0.41/0.65 ! [A2: finite1489363574real_n,K: finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.65 ( ( A2 0.41/0.65 = ( plus_p585657087real_n @ K @ A ) ) 0.41/0.65 => ( ( minus_1037315151real_n @ A2 @ B ) 0.41/0.65 = ( plus_p585657087real_n @ K @ ( minus_1037315151real_n @ A @ B ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_181_main__part__sets,axiom, 0.41/0.65 ! [S: set_Fi1058188332real_n,M: sigma_1466784463real_n] : 0.41/0.65 ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ ( comple230862828real_n @ M ) ) ) 0.41/0.65 => ( member223413699real_n @ ( comple1390568924real_n @ M @ S ) @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_245_imageI,axiom, 0.41/0.65 ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] : 0.41/0.65 ( ( member1746150050real_n @ X2 @ A2 ) 0.41/0.65 => ( member223413699real_n @ ( F @ X2 ) @ ( image_128879038real_n @ F @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_89_vimage__Collect,axiom, 0.41/0.65 ! [P: finite1489363574real_n > $o,F: finite1489363574real_n > finite1489363574real_n,Q: finite1489363574real_n > $o] : 0.41/0.65 ( ! [X3: finite1489363574real_n] : 0.41/0.65 ( ( P @ ( F @ X3 ) ) 0.41/0.65 = ( Q @ X3 ) ) 0.41/0.65 => ( ( vimage1233683625real_n @ F @ ( collec321817931real_n @ P ) ) 0.41/0.65 = ( collec321817931real_n @ Q ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_303_DiffI,axiom, 0.41/0.65 ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] : 0.41/0.65 ( ( ~ ( member1746150050real_n @ C2 @ B2 ) 0.41/0.65 => ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) ) ) 0.41/0.65 <= ( member1746150050real_n @ C2 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_28_vimageD,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] : 0.41/0.65 ( ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ A2 ) ) 0.41/0.65 => ( member1746150050real_n @ ( F @ A ) @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_274_measurable__If__restrict__space__iff,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,N: sigma_1466784463real_n] : 0.41/0.65 ( ( ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( P @ X ) @ ( F @ X ) @ ( G @ X ) ) 0.41/0.65 @ ( sigma_439801790real_n @ M @ N ) ) 0.41/0.65 = ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ M @ ( collec321817931real_n @ P ) ) @ N ) ) 0.41/0.65 & ( member1746150050real_n @ G 0.41/0.65 @ ( sigma_439801790real_n 0.41/0.65 @ ( sigma_346513458real_n @ M 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ~ ( P @ X ) ) ) 0.41/0.65 @ N ) ) ) ) 0.41/0.65 <= ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_1_of__int__vec__eq__iff,axiom, 0.41/0.65 ! [A: finite964658038_int_n,B: finite964658038_int_n] : 0.41/0.65 ( ( ( minkow1134813771n_real @ A ) 0.41/0.65 = ( minkow1134813771n_real @ B ) ) 0.41/0.65 = ( A = B ) ) ). 0.41/0.65 0.41/0.65 thf(fact_348_eq__add__iff,axiom, 0.41/0.65 ! [X2: finite1489363574real_n,Y3: finite1489363574real_n] : 0.41/0.65 ( ( X2 0.41/0.65 = ( plus_p585657087real_n @ X2 @ Y3 ) ) 0.41/0.65 = ( Y3 = zero_z200130687real_n ) ) ). 0.41/0.65 0.41/0.65 thf(fact_17_vimage__eq,axiom, 0.41/0.65 ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ B2 ) ) 0.41/0.65 = ( member223413699real_n @ ( F @ A ) @ B2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_128_inf__set__def,axiom, 0.41/0.65 ( inf_in1974387902real_n 0.41/0.65 = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] : 0.41/0.65 ( collec321817931real_n 0.41/0.65 @ ( inf_in1620715847al_n_o 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ A4 ) 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ B3 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_161_sets_Osets__Collect__imp,axiom, 0.41/0.65 ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o,Q: set_Fi1058188332real_n > $o] : 0.41/0.65 ( ( ( member1475136633real_n 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) 0.41/0.65 & ( Q @ X ) ) ) 0.41/0.65 @ ( sigma_433815053real_n @ M ) ) 0.41/0.65 => ( member1475136633real_n 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( ( P @ X ) 0.41/0.65 <= ( Q @ X ) ) 0.41/0.65 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_433815053real_n @ M ) ) ) 0.41/0.65 <= ( member1475136633real_n 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_433815053real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_337_zero__eq__add__iff__both__eq__0,axiom, 0.41/0.65 ! [X2: nat,Y3: nat] : 0.41/0.65 ( ( zero_zero_nat 0.41/0.65 = ( plus_plus_nat @ X2 @ Y3 ) ) 0.41/0.65 = ( ( Y3 = zero_zero_nat ) 0.41/0.65 & ( X2 = zero_zero_nat ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_282_sets__lborel,axiom, 0.41/0.65 ( ( sigma_1235138647real_n @ lebesg260170249real_n ) 0.41/0.65 = ( sigma_1235138647real_n @ borel_676189912real_n ) ) ). 0.41/0.65 0.41/0.65 thf(fact_172_sets_Osets__Collect__disj,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] : 0.41/0.65 ( ( ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( Q @ X ) 0.41/0.65 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( ( Q @ X ) 0.41/0.65 | ( P @ X ) ) 0.41/0.65 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) ) 0.41/0.65 <= ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 & ( P @ X ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_209_add__diff__cancel__left,axiom, 0.41/0.65 ! [C2: nat,A: nat,B: nat] : 0.41/0.65 ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) 0.41/0.65 = ( minus_minus_nat @ A @ B ) ) ). 0.41/0.65 0.41/0.65 thf(fact_145_sets__eq__imp__space__eq,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,M2: sigma_1466784463real_n] : 0.41/0.65 ( ( ( sigma_1235138647real_n @ M ) 0.41/0.65 = ( sigma_1235138647real_n @ M2 ) ) 0.41/0.65 => ( ( sigma_476185326real_n @ M ) 0.41/0.65 = ( sigma_476185326real_n @ M2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_254_diff__diff__add,axiom, 0.41/0.65 ! [A: nat,B: nat,C2: nat] : 0.41/0.65 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 ) 0.41/0.65 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_169_sets_Osets__Collect__conj,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] : 0.41/0.65 ( ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 & ( P @ X ) 0.41/0.65 & ( Q @ X ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 <= ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 & ( Q @ X ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_8_vimage__ident,axiom, 0.41/0.65 ! [Y: set_Fi1058188332real_n] : 0.41/0.65 ( ( vimage1233683625real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : X 0.41/0.65 @ Y ) 0.41/0.65 = Y ) ). 0.41/0.65 0.41/0.65 thf(fact_268_space__restrict__space,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] : 0.41/0.65 ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ M @ Omega ) ) 0.41/0.65 = ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_159_sets_Osets__Collect_I5_J,axiom, 0.41/0.65 ! [M: sigma_107786596real_n,Pb: $o] : 0.41/0.65 ( member2104752728real_n 0.41/0.65 @ ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) 0.41/0.65 & Pb ) ) 0.41/0.65 @ ( sigma_522684908real_n @ M ) ) ). 0.41/0.65 0.41/0.65 thf(fact_92_vimageI2,axiom, 0.41/0.65 ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A: set_Fi1058188332real_n,A2: set_Fi1326602817real_n] : 0.41/0.65 ( ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ A2 ) ) 0.41/0.65 <= ( member1746150050real_n @ ( F @ A ) @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_21_set__plus__intro,axiom, 0.41/0.65 ! [A: finite1489363574real_n,C: set_Fi1058188332real_n,B: finite1489363574real_n,D: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1352538125real_n @ A @ C ) 0.41/0.65 => ( ( member1352538125real_n @ ( plus_p585657087real_n @ A @ B ) @ ( plus_p1606848693real_n @ C @ D ) ) 0.41/0.65 <= ( member1352538125real_n @ B @ D ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_341_diff__zero,axiom, 0.41/0.65 ! [A: finite1489363574real_n] : 0.41/0.65 ( ( minus_1037315151real_n @ A @ zero_z200130687real_n ) 0.41/0.65 = A ) ). 0.41/0.65 0.41/0.65 thf(fact_232_diff__eq__diff__eq,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n,D2: finite1489363574real_n] : 0.41/0.65 ( ( ( minus_1037315151real_n @ A @ B ) 0.41/0.65 = ( minus_1037315151real_n @ C2 @ D2 ) ) 0.41/0.65 => ( ( A = B ) 0.41/0.65 = ( C2 = D2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_37_IntI,axiom, 0.41/0.65 ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) ) 0.41/0.65 <= ( member223413699real_n @ C2 @ B2 ) ) 0.41/0.65 <= ( member223413699real_n @ C2 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(help_If_2_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom, 0.41/0.65 ! [X2: finite1489363574real_n > finite1489363574real_n,Y3: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( if_Fin413489477real_n @ $false @ X2 @ Y3 ) 0.41/0.65 = Y3 ) ). 0.41/0.65 0.41/0.65 thf(fact_59_Int__left__commute,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ A2 @ ( inf_in1974387902real_n @ B2 @ C ) ) 0.41/0.65 = ( inf_in1974387902real_n @ B2 @ ( inf_in1974387902real_n @ A2 @ C ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_129_inf__left__commute,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n,Z: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ Y3 @ Z ) ) 0.41/0.65 = ( inf_in1974387902real_n @ Y3 @ ( inf_in1974387902real_n @ X2 @ Z ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_135_boolean__algebra__cancel_Oinf2,axiom, 0.41/0.65 ! [B2: set_Fi1058188332real_n,K: set_Fi1058188332real_n,B: set_Fi1058188332real_n,A: set_Fi1058188332real_n] : 0.41/0.65 ( ( B2 0.41/0.65 = ( inf_in1974387902real_n @ K @ B ) ) 0.41/0.65 => ( ( inf_in1974387902real_n @ A @ B2 ) 0.41/0.65 = ( inf_in1974387902real_n @ K @ ( inf_in1974387902real_n @ A @ B ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(help_If_2_1_If_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] : 0.41/0.65 ( ( if_set11487206real_n @ $false @ X2 @ Y3 ) 0.41/0.65 = Y3 ) ). 0.41/0.65 0.41/0.65 thf(fact_52_IntD2,axiom, 0.41/0.65 ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ C2 @ B2 ) 0.41/0.65 <= ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_11_vimageI,axiom, 0.41/0.65 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ B2 ) ) 0.41/0.65 <= ( member223413699real_n @ B @ B2 ) ) 0.41/0.65 <= ( ( F @ A ) 0.41/0.65 = B ) ) ). 0.41/0.65 0.41/0.65 thf(fact_306_set__diff__eq,axiom, 0.41/0.65 ( minus_1686442501real_n 0.41/0.65 = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] : 0.41/0.65 ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ~ ( member1352538125real_n @ X @ B3 ) 0.41/0.65 & ( member1352538125real_n @ X @ A4 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_116_measurable__sets__Collect,axiom, 0.41/0.65 ! [F: set_Fi1058188332real_n > finite1489363574real_n,M: sigma_1422848389real_n,N: sigma_1466784463real_n,P: finite1489363574real_n > $o] : 0.41/0.65 ( ( ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( P @ X ) 0.41/0.65 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ N ) ) ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ N ) ) 0.41/0.65 => ( member1475136633real_n 0.41/0.65 @ ( collec452821761real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.65 ( ( P @ ( F @ X ) ) 0.41/0.65 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) ) ) 0.41/0.65 @ ( sigma_433815053real_n @ M ) ) ) 0.41/0.65 <= ( member1759501912real_n @ F @ ( sigma_1333364596real_n @ M @ N ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_51_IntD1,axiom, 0.41/0.65 ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) ) 0.41/0.65 => ( member1352538125real_n @ C2 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_238_ball__imageD,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,P: finite1489363574real_n > $o] : 0.41/0.65 ( ! [X5: finite1489363574real_n] : 0.41/0.65 ( ( P @ ( F @ X5 ) ) 0.41/0.65 <= ( member1352538125real_n @ X5 @ A2 ) ) 0.41/0.65 <= ! [X3: finite1489363574real_n] : 0.41/0.65 ( ( P @ X3 ) 0.41/0.65 <= ( member1352538125real_n @ X3 @ ( image_439535603real_n @ F @ A2 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_287_Diff__Int__distrib2,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ ( minus_1686442501real_n @ A2 @ B2 ) @ C ) 0.41/0.65 = ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A2 @ C ) @ ( inf_in1974387902real_n @ B2 @ C ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_23_add__right__cancel,axiom, 0.41/0.65 ! [B: finite1489363574real_n,A: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( ( plus_p585657087real_n @ B @ A ) 0.41/0.65 = ( plus_p585657087real_n @ C2 @ A ) ) 0.41/0.65 = ( B = C2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_299_is__borel__def,axiom, 0.41/0.65 ( borel_1962407338real_n 0.41/0.65 = ( ^ [F2: finite1489363574real_n > finite1489363574real_n,M3: sigma_1466784463real_n] : ( member1746150050real_n @ F2 @ ( sigma_439801790real_n @ M3 @ borel_676189912real_n ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_71_add_Oleft__commute,axiom, 0.41/0.65 ! [B: finite1489363574real_n,A: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( plus_p585657087real_n @ B @ ( plus_p585657087real_n @ A @ C2 ) ) 0.41/0.65 = ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_53_IntD2,axiom, 0.41/0.65 ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] : 0.41/0.65 ( ( member1746150050real_n @ C2 @ B2 ) 0.41/0.65 <= ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_49_IntD1,axiom, 0.41/0.65 ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ C2 @ A2 ) 0.41/0.65 <= ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_203_add__diff__cancel__right_H,axiom, 0.41/0.65 ! [A: nat,B: nat] : 0.41/0.65 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B ) 0.41/0.65 = A ) ). 0.41/0.65 0.41/0.65 thf(fact_132_inf_Ocommute,axiom, 0.41/0.65 ( inf_in1974387902real_n 0.41/0.65 = ( ^ [A3: set_Fi1058188332real_n,B4: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B4 @ A3 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_96_sets_OInt__space__eq1,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,M: sigma_1466784463real_n] : 0.41/0.65 ( ( ( inf_in1974387902real_n @ ( sigma_476185326real_n @ M ) @ X2 ) 0.41/0.65 = X2 ) 0.41/0.65 <= ( member223413699real_n @ X2 @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_211_add__diff__cancel,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.65 ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ B ) 0.41/0.65 = A ) ). 0.41/0.65 0.41/0.65 thf(fact_104_measurableI,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,F: finite1489363574real_n > set_Fi1058188332real_n,N: sigma_1422848389real_n] : 0.41/0.65 ( ( ( member966061400real_n @ F @ ( sigma_566919540real_n @ M @ N ) ) 0.41/0.65 <= ! [A6: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage207290975real_n @ F @ A6 ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 <= ( member1475136633real_n @ A6 @ ( sigma_433815053real_n @ N ) ) ) ) 0.41/0.65 <= ! [X3: finite1489363574real_n] : 0.41/0.65 ( ( member223413699real_n @ ( F @ X3 ) @ ( sigma_607186084real_n @ N ) ) 0.41/0.65 <= ( member1352538125real_n @ X3 @ ( sigma_476185326real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_326_add_Oright__neutral,axiom, 0.41/0.65 ! [A: finite1489363574real_n] : 0.41/0.65 ( ( plus_p585657087real_n @ A @ zero_z200130687real_n ) 0.41/0.65 = A ) ). 0.41/0.65 0.41/0.65 thf(fact_76_set__plus__elim,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ X2 @ ( plus_p565022571real_n @ A2 @ B2 ) ) 0.41/0.65 => ~ ! [A5: set_Fi1058188332real_n,B5: set_Fi1058188332real_n] : 0.41/0.65 ( ( ( member223413699real_n @ A5 @ A2 ) 0.41/0.65 => ~ ( member223413699real_n @ B5 @ B2 ) ) 0.41/0.65 <= ( X2 0.41/0.65 = ( plus_p1606848693real_n @ A5 @ B5 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_194_in__vimage__algebra,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n,M: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n,X4: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ A2 ) @ X4 ) @ ( sigma_1235138647real_n @ ( sigma_821351682real_n @ X4 @ F @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_237_rev__image__eqI,axiom, 0.41/0.65 ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X2 @ A2 ) 0.41/0.65 => ( ( member1746150050real_n @ B @ ( image_1123376925real_n @ F @ A2 ) ) 0.41/0.65 <= ( B 0.41/0.65 = ( F @ X2 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_103_measurableI,axiom, 0.41/0.65 ! [M: sigma_107786596real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,N: sigma_1466784463real_n] : 0.41/0.65 ( ( ! [A6: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ A6 @ ( sigma_1235138647real_n @ N ) ) 0.41/0.65 => ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage1072397758real_n @ F @ A6 ) @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) ) ) 0.41/0.65 => ( member1695588023real_n @ F @ ( sigma_2028985427real_n @ M @ N ) ) ) 0.41/0.65 <= ! [X3: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ ( F @ X3 ) @ ( sigma_476185326real_n @ N ) ) 0.41/0.65 <= ( member1746150050real_n @ X3 @ ( sigma_1483971331real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_86_group__cancel_Oadd1,axiom, 0.41/0.65 ! [A2: finite1489363574real_n,K: finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.65 ( ( ( plus_p585657087real_n @ A2 @ B ) 0.41/0.65 = ( plus_p585657087real_n @ K @ ( plus_p585657087real_n @ A @ B ) ) ) 0.41/0.65 <= ( A2 0.41/0.65 = ( plus_p585657087real_n @ K @ A ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_331_add__cancel__left__right,axiom, 0.41/0.65 ! [A: nat,B: nat] : 0.41/0.65 ( ( ( plus_plus_nat @ A @ B ) 0.41/0.65 = A ) 0.41/0.65 = ( B = zero_zero_nat ) ) ). 0.41/0.65 0.41/0.65 thf(fact_281_sets_Ocompl__sets,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,M: sigma_1466784463real_n] : 0.41/0.65 ( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( member223413699real_n @ ( minus_1686442501real_n @ ( sigma_476185326real_n @ M ) @ A ) @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_106_measurableI,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n,N: sigma_1466784463real_n] : 0.41/0.65 ( ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) ) 0.41/0.65 <= ! [A6: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ A6 ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 <= ( member223413699real_n @ A6 @ ( sigma_1235138647real_n @ N ) ) ) ) 0.41/0.65 <= ! [X3: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X3 @ ( sigma_476185326real_n @ M ) ) 0.41/0.65 => ( member1352538125real_n @ ( F @ X3 ) @ ( sigma_476185326real_n @ N ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(conj_0,conjecture, 0.41/0.65 ( member223413699real_n 0.41/0.65 @ ( vimage1233683625real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ X @ ( minkow1134813771n_real @ a ) ) 0.41/0.65 @ ( t2 @ a ) ) 0.41/0.65 @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_302_DiffI,axiom, 0.41/0.65 ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ C2 @ A2 ) 0.41/0.65 => ( ~ ( member223413699real_n @ C2 @ B2 ) 0.41/0.65 => ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_249_restrict__space__sets__cong,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n] : 0.41/0.65 ( ( A2 = B2 ) 0.41/0.65 => ( ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ A2 ) ) 0.41/0.65 = ( sigma_1235138647real_n @ ( sigma_346513458real_n @ N @ B2 ) ) ) 0.41/0.65 <= ( ( sigma_1235138647real_n @ M ) 0.41/0.65 = ( sigma_1235138647real_n @ N ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_27_vimageD,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,A2: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ A2 ) ) 0.41/0.65 => ( member223413699real_n @ ( F @ A ) @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_265_borel__measurable__const__add,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A: finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ A @ ( F @ X ) ) 0.41/0.65 @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) 0.41/0.65 <= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_247_borel__measurable__const,axiom, 0.41/0.65 ! [C2: finite1489363574real_n,M: sigma_1466784463real_n] : 0.41/0.65 ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : C2 0.41/0.65 @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ). 0.41/0.65 0.41/0.65 thf(fact_283_Int__Diff,axiom, 0.41/0.65 ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C: set_Fi1058188332real_n] : 0.41/0.65 ( ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A2 @ B2 ) @ C ) 0.41/0.65 = ( inf_in1974387902real_n @ A2 @ ( minus_1686442501real_n @ B2 @ C ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_319_translation__Int,axiom, 0.41/0.65 ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T3: set_Fi1058188332real_n] : 0.41/0.65 ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( inf_in1974387902real_n @ S2 @ T3 ) ) 0.41/0.65 = ( inf_in1974387902real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S2 ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ T3 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_139_inf__sup__aci_I3_J,axiom, 0.41/0.65 ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n,Z: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ Y3 @ Z ) ) 0.41/0.65 = ( inf_in1974387902real_n @ Y3 @ ( inf_in1974387902real_n @ X2 @ Z ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_94_vimageI2,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n,A2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ A2 ) ) 0.41/0.65 <= ( member1352538125real_n @ ( F @ A ) @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_121_inf_Oright__idem,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ B ) 0.41/0.65 = ( inf_in1974387902real_n @ A @ B ) ) ). 0.41/0.65 0.41/0.65 thf(fact_88_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) @ C2 ) 0.41/0.65 = ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_141_measurable__compose__rev,axiom, 0.41/0.65 ! [F: finite1489363574real_n > finite1489363574real_n,L2: sigma_1466784463real_n,N: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n] : 0.41/0.65 ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ L2 @ N ) ) 0.41/0.65 => ( ( member1746150050real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( F @ ( G @ X ) ) 0.41/0.65 @ ( sigma_439801790real_n @ M @ N ) ) 0.41/0.65 <= ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ L2 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_213_space__restrict__space2,axiom, 0.41/0.65 ! [Omega: set_Fi1058188332real_n,M: sigma_1466784463real_n] : 0.41/0.65 ( ( member223413699real_n @ Omega @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ M @ Omega ) ) 0.41/0.65 = Omega ) ) ). 0.41/0.65 0.41/0.65 thf(fact_123_inf_Oleft__idem,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ A @ B ) ) 0.41/0.65 = ( inf_in1974387902real_n @ A @ B ) ) ). 0.41/0.65 0.41/0.65 thf(fact_66_Int__def,axiom, 0.41/0.65 ( inf_in1974387902real_n 0.41/0.65 = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] : 0.41/0.65 ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( ( member1352538125real_n @ X @ B3 ) 0.41/0.65 & ( member1352538125real_n @ X @ A4 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_29_vimageD,axiom, 0.41/0.65 ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A2: set_se2111327970real_n] : 0.41/0.65 ( ( member223413699real_n @ ( F @ A ) @ A2 ) 0.41/0.65 <= ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_36_vimageE,axiom, 0.41/0.65 ! [A: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1352538125real_n @ ( F @ A ) @ B2 ) 0.41/0.65 <= ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_54_IntD2,axiom, 0.41/0.65 ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) ) 0.41/0.65 => ( member1352538125real_n @ C2 @ B2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_246_imageI,axiom, 0.41/0.65 ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ ( F @ X2 ) @ ( image_1123376925real_n @ F @ A2 ) ) 0.41/0.65 <= ( member1746150050real_n @ X2 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(fact_148_measurable__space,axiom, 0.41/0.65 ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,M: sigma_1422848389real_n,A2: sigma_107786596real_n,X2: set_Fi1058188332real_n] : 0.41/0.65 ( ( ( member1746150050real_n @ ( F @ X2 ) @ ( sigma_1483971331real_n @ A2 ) ) 0.41/0.65 <= ( member223413699real_n @ X2 @ ( sigma_607186084real_n @ M ) ) ) 0.41/0.65 <= ( member1764433517real_n @ F @ ( sigma_588796041real_n @ M @ A2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_35_vimageE,axiom, 0.41/0.65 ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] : 0.41/0.65 ( ( member1746150050real_n @ ( F @ A ) @ B2 ) 0.41/0.65 <= ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_100_measurableI,axiom, 0.41/0.65 ! [M: sigma_107786596real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,N: sigma_1422848389real_n] : 0.41/0.65 ( ( ( member640587117real_n @ F @ ( sigma_364818953real_n @ M @ N ) ) 0.41/0.65 <= ! [A6: set_se2111327970real_n] : 0.41/0.65 ( ( member1475136633real_n @ A6 @ ( sigma_433815053real_n @ N ) ) 0.41/0.65 => ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage1910974324real_n @ F @ A6 ) @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) ) ) ) 0.41/0.65 <= ! [X3: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1746150050real_n @ X3 @ ( sigma_1483971331real_n @ M ) ) 0.41/0.65 => ( member223413699real_n @ ( F @ X3 ) @ ( sigma_607186084real_n @ N ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_125_inf_Oidem,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n] : 0.41/0.65 ( ( inf_in1974387902real_n @ A @ A ) 0.41/0.65 = A ) ). 0.41/0.65 0.41/0.65 thf(fact_48_IntE,axiom, 0.41/0.65 ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ~ ( ( member1352538125real_n @ C2 @ A2 ) 0.41/0.65 => ~ ( member1352538125real_n @ C2 @ B2 ) ) 0.41/0.65 <= ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_45_T__def,axiom, 0.41/0.65 ( t2 0.41/0.65 = ( ^ [A3: finite964658038_int_n] : ( inf_in1974387902real_n @ s @ ( r @ A3 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_206_add__diff__cancel__left_H,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.65 ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ A ) 0.41/0.65 = B ) ). 0.41/0.65 0.41/0.65 thf(fact_186_measurable__restrict__space__iff,axiom, 0.41/0.65 ! [Omega: set_se2111327970real_n,M: sigma_1422848389real_n,C2: finite1489363574real_n,N: sigma_1466784463real_n,F: set_Fi1058188332real_n > finite1489363574real_n] : 0.41/0.65 ( ( member1475136633real_n @ ( inf_in632889204real_n @ Omega @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) ) 0.41/0.65 => ( ( member1352538125real_n @ C2 @ ( sigma_476185326real_n @ N ) ) 0.41/0.65 => ( ( member1759501912real_n @ F @ ( sigma_1333364596real_n @ ( sigma_993999336real_n @ M @ Omega ) @ N ) ) 0.41/0.65 = ( member1759501912real_n 0.41/0.65 @ ^ [X: set_Fi1058188332real_n] : ( if_Fin127821360real_n @ ( member223413699real_n @ X @ Omega ) @ ( F @ X ) @ C2 ) 0.41/0.65 @ ( sigma_1333364596real_n @ M @ N ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_177_T_H__def,axiom, 0.41/0.65 ( t 0.41/0.65 = ( ^ [A3: finite964658038_int_n] : 0.41/0.65 ( image_439535603real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ ( minkow1134813771n_real @ A3 ) ) 0.41/0.65 @ ( t2 @ A3 ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_330_add__cancel__left__right,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.65 ( ( ( plus_p585657087real_n @ A @ B ) 0.41/0.65 = A ) 0.41/0.65 = ( B = zero_z200130687real_n ) ) ). 0.41/0.65 0.41/0.65 thf(fact_305_set__diff__eq,axiom, 0.41/0.65 ( minus_725016986real_n 0.41/0.65 = ( ^ [A4: set_Fi1326602817real_n,B3: set_Fi1326602817real_n] : 0.41/0.65 ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.65 ( ~ ( member1746150050real_n @ X @ B3 ) 0.41/0.65 & ( member1746150050real_n @ X @ A4 ) ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_39_IntI,axiom, 0.41/0.65 ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.65 ( ( ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) ) 0.41/0.65 <= ( member1352538125real_n @ C2 @ B2 ) ) 0.41/0.65 <= ( member1352538125real_n @ C2 @ A2 ) ) ). 0.41/0.65 0.41/0.65 thf(help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T,axiom, 0.41/0.65 ! [X2: finite1489363574real_n,Y3: finite1489363574real_n] : 0.41/0.65 ( ( if_Fin127821360real_n @ $true @ X2 @ Y3 ) 0.41/0.65 = X2 ) ). 0.41/0.65 0.41/0.65 thf(fact_256_diff__add__eq,axiom, 0.41/0.65 ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.65 ( ( plus_p585657087real_n @ ( minus_1037315151real_n @ A @ B ) @ C2 ) 0.41/0.65 = ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C2 ) @ B ) ) ). 0.41/0.65 0.41/0.65 thf(fact_83_Collect__mem__eq,axiom, 0.41/0.65 ! [A2: set_Fi1326602817real_n] : 0.41/0.65 ( ( collec1190264032real_n 0.41/0.65 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ A2 ) ) 0.41/0.65 = A2 ) ). 0.41/0.65 0.41/0.65 thf(fact_108_sets_OInt,axiom, 0.41/0.65 ! [A: set_Fi1058188332real_n,M: sigma_1466784463real_n,B: set_Fi1058188332real_n] : 0.41/0.65 ( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 => ( ( member223413699real_n @ ( inf_in1974387902real_n @ A @ B ) @ ( sigma_1235138647real_n @ M ) ) 0.41/0.65 <= ( member223413699real_n @ B @ ( sigma_1235138647real_n @ M ) ) ) ) ). 0.41/0.65 0.41/0.65 thf(fact_160_sets_Osets__Collect_I5_J,axiom, 0.41/0.65 ! [M: sigma_1466784463real_n,Pb: $o] : 0.41/0.65 ( member223413699real_n 0.41/0.65 @ ( collec321817931real_n 0.41/0.65 @ ^ [X: finite1489363574real_n] : 0.41/0.65 ( Pb 0.41/0.65 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.66 @ ( sigma_1235138647real_n @ M ) ) ). 0.41/0.66 0.41/0.66 thf(fact_180_inf__Int__eq,axiom, 0.41/0.66 ! [R: set_Fi1058188332real_n,S: set_Fi1058188332real_n] : 0.41/0.66 ( ( inf_in1620715847al_n_o 0.41/0.66 @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ R ) 0.41/0.66 @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ S ) ) 0.41/0.66 = ( ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ ( inf_in1974387902real_n @ R @ S ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_163_sets_Osets__Collect__imp,axiom, 0.41/0.66 ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] : 0.41/0.66 ( ( ( member223413699real_n 0.41/0.66 @ ( collec321817931real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : 0.41/0.66 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) 0.41/0.66 & ( ( P @ X ) 0.41/0.66 <= ( Q @ X ) ) ) ) 0.41/0.66 @ ( sigma_1235138647real_n @ M ) ) 0.41/0.66 <= ( member223413699real_n 0.41/0.66 @ ( collec321817931real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : 0.41/0.66 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) 0.41/0.66 & ( Q @ X ) ) ) 0.41/0.66 @ ( sigma_1235138647real_n @ M ) ) ) 0.41/0.66 <= ( member223413699real_n 0.41/0.66 @ ( collec321817931real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : 0.41/0.66 ( ( P @ X ) 0.41/0.66 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.66 @ ( sigma_1235138647real_n @ M ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_228_imageE,axiom, 0.41/0.66 ! [B: finite1489363574real_n > finite1489363574real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A2: set_se2111327970real_n] : 0.41/0.66 ( ~ ! [X3: set_Fi1058188332real_n] : 0.41/0.66 ( ~ ( member223413699real_n @ X3 @ A2 ) 0.41/0.66 <= ( B 0.41/0.66 = ( F @ X3 ) ) ) 0.41/0.66 <= ( member1746150050real_n @ B @ ( image_352856126real_n @ F @ A2 ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_175_sets_Osets__Collect__const,axiom, 0.41/0.66 ! [M: sigma_1466784463real_n,P: $o] : 0.41/0.66 ( member223413699real_n 0.41/0.66 @ ( collec321817931real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : 0.41/0.66 ( P 0.41/0.66 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.66 @ ( sigma_1235138647real_n @ M ) ) ). 0.41/0.66 0.41/0.66 thf(fact_12_vimageI,axiom, 0.41/0.66 ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A: set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] : 0.41/0.66 ( ( ( member1746150050real_n @ B @ B2 ) 0.41/0.66 => ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ B2 ) ) ) 0.41/0.66 <= ( ( F @ A ) 0.41/0.66 = B ) ) ). 0.41/0.66 0.41/0.66 thf(fact_198_image__eqI,axiom, 0.41/0.66 ! [B: finite1489363574real_n > finite1489363574real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,X2: set_Fi1058188332real_n,A2: set_se2111327970real_n] : 0.41/0.66 ( ( B 0.41/0.66 = ( F @ X2 ) ) 0.41/0.66 => ( ( member1746150050real_n @ B @ ( image_352856126real_n @ F @ A2 ) ) 0.41/0.66 <= ( member223413699real_n @ X2 @ A2 ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_315_DiffE,axiom, 0.41/0.66 ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] : 0.41/0.66 ( ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) ) 0.41/0.66 => ~ ( ( member1746150050real_n @ C2 @ A2 ) 0.41/0.66 => ( member1746150050real_n @ C2 @ B2 ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_167_sets_Osets__Collect__conj,axiom, 0.41/0.66 ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o,Q: set_Fi1058188332real_n > $o] : 0.41/0.66 ( ( member1475136633real_n 0.41/0.66 @ ( collec452821761real_n 0.41/0.66 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.66 ( ( P @ X ) 0.41/0.66 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) ) ) 0.41/0.66 @ ( sigma_433815053real_n @ M ) ) 0.41/0.66 => ( ( member1475136633real_n 0.41/0.66 @ ( collec452821761real_n 0.41/0.66 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.66 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) 0.41/0.66 & ( Q @ X ) 0.41/0.66 & ( P @ X ) ) ) 0.41/0.66 @ ( sigma_433815053real_n @ M ) ) 0.41/0.66 <= ( member1475136633real_n 0.41/0.66 @ ( collec452821761real_n 0.41/0.66 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.66 ( ( Q @ X ) 0.41/0.66 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) ) ) 0.41/0.66 @ ( sigma_433815053real_n @ M ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_184_measurable__restrict__space__iff,axiom, 0.41/0.66 ! [Omega: set_se2111327970real_n,M: sigma_1422848389real_n,C2: finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] : 0.41/0.66 ( ( member1475136633real_n @ ( inf_in632889204real_n @ Omega @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) ) 0.41/0.66 => ( ( member1746150050real_n @ C2 @ ( sigma_1483971331real_n @ N ) ) 0.41/0.66 => ( ( member1764433517real_n @ F @ ( sigma_588796041real_n @ ( sigma_993999336real_n @ M @ Omega ) @ N ) ) 0.41/0.66 = ( member1764433517real_n 0.41/0.66 @ ^ [X: set_Fi1058188332real_n] : ( if_Fin413489477real_n @ ( member223413699real_n @ X @ Omega ) @ ( F @ X ) @ C2 ) 0.41/0.66 @ ( sigma_588796041real_n @ M @ N ) ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_343_cancel__comm__monoid__add__class_Odiff__cancel,axiom, 0.41/0.66 ! [A: finite1489363574real_n] : 0.41/0.66 ( ( minus_1037315151real_n @ A @ A ) 0.41/0.66 = zero_z200130687real_n ) ). 0.41/0.66 0.41/0.66 thf(fact_190_measurable__restrict__space__iff,axiom, 0.41/0.66 ! [Omega: set_Fi1058188332real_n,M: sigma_1466784463real_n,C2: finite1489363574real_n,N: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n] : 0.41/0.66 ( ( member223413699real_n @ ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) 0.41/0.66 => ( ( member1352538125real_n @ C2 @ ( sigma_476185326real_n @ N ) ) 0.41/0.66 => ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ M @ Omega ) @ N ) ) 0.41/0.66 = ( member1746150050real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ X @ Omega ) @ ( F @ X ) @ C2 ) 0.41/0.66 @ ( sigma_439801790real_n @ M @ N ) ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_74_add_Oleft__cancel,axiom, 0.41/0.66 ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.66 ( ( ( plus_p585657087real_n @ A @ B ) 0.41/0.66 = ( plus_p585657087real_n @ A @ C2 ) ) 0.41/0.66 = ( B = C2 ) ) ). 0.41/0.66 0.41/0.66 thf(fact_227_imageE,axiom, 0.41/0.66 ! [B: set_Fi1058188332real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A2: set_Fi1326602817real_n] : 0.41/0.66 ( ~ ! [X3: finite1489363574real_n > finite1489363574real_n] : 0.41/0.66 ( ( B 0.41/0.66 = ( F @ X3 ) ) 0.41/0.66 => ~ ( member1746150050real_n @ X3 @ A2 ) ) 0.41/0.66 <= ( member223413699real_n @ B @ ( image_128879038real_n @ F @ A2 ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_47_IntE,axiom, 0.41/0.66 ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] : 0.41/0.66 ( ~ ( ~ ( member1746150050real_n @ C2 @ B2 ) 0.41/0.66 <= ( member1746150050real_n @ C2 @ A2 ) ) 0.41/0.66 <= ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_285_Diff__Diff__Int,axiom, 0.41/0.66 ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.66 ( ( minus_1686442501real_n @ A2 @ ( minus_1686442501real_n @ A2 @ B2 ) ) 0.41/0.66 = ( inf_in1974387902real_n @ A2 @ B2 ) ) ). 0.41/0.66 0.41/0.66 thf(fact_199_image__eqI,axiom, 0.41/0.66 ! [B: set_Fi1058188332real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] : 0.41/0.66 ( ( ( member1746150050real_n @ X2 @ A2 ) 0.41/0.66 => ( member223413699real_n @ B @ ( image_128879038real_n @ F @ A2 ) ) ) 0.41/0.66 <= ( B 0.41/0.66 = ( F @ X2 ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_333_add__cancel__right__left,axiom, 0.41/0.66 ! [A: nat,B: nat] : 0.41/0.66 ( ( A 0.41/0.66 = ( plus_plus_nat @ B @ A ) ) 0.41/0.66 = ( B = zero_zero_nat ) ) ). 0.41/0.66 0.41/0.66 thf(fact_196_image__eqI,axiom, 0.41/0.66 ! [B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,X2: finite1489363574real_n,A2: set_Fi1058188332real_n] : 0.41/0.66 ( ( B 0.41/0.66 = ( F @ X2 ) ) 0.41/0.66 => ( ( member1352538125real_n @ X2 @ A2 ) 0.41/0.66 => ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ A2 ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(help_If_3_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom, 0.41/0.66 ! [P: $o] : 0.41/0.66 ( ( P = $true ) 0.41/0.66 | ( P = $false ) ) ). 0.41/0.66 0.41/0.66 thf(fact_40_Int__iff,axiom, 0.41/0.66 ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] : 0.41/0.66 ( ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) ) 0.41/0.66 = ( ( member223413699real_n @ C2 @ A2 ) 0.41/0.66 & ( member223413699real_n @ C2 @ B2 ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_294_lebesgue__measurable__vimage__borel,axiom, 0.41/0.66 ! [F: finite1489363574real_n > finite1489363574real_n,T: set_Fi1058188332real_n] : 0.41/0.66 ( ( ( member223413699real_n 0.41/0.66 @ ( collec321817931real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ ( F @ X ) @ T ) ) 0.41/0.66 @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) 0.41/0.66 <= ( member223413699real_n @ T @ ( sigma_1235138647real_n @ borel_676189912real_n ) ) ) 0.41/0.66 <= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_323_borel__measurable__if,axiom, 0.41/0.66 ! [S: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n] : 0.41/0.66 ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) 0.41/0.66 => ( ( member1746150050real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ X @ S ) @ ( F @ X ) @ zero_z200130687real_n ) 0.41/0.66 @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) ) 0.41/0.66 = ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) @ borel_676189912real_n ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_309_minus__set__def,axiom, 0.41/0.66 ( minus_1686442501real_n 0.41/0.66 = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] : 0.41/0.66 ( collec321817931real_n 0.41/0.66 @ ( minus_455231168al_n_o 0.41/0.66 @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ A4 ) 0.41/0.66 @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ B3 ) ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_107_sets_Otop,axiom, 0.41/0.66 ! [M: sigma_1466784463real_n] : ( member223413699real_n @ ( sigma_476185326real_n @ M ) @ ( sigma_1235138647real_n @ M ) ) ). 0.41/0.66 0.41/0.66 thf(fact_118_measurable__sets__Collect,axiom, 0.41/0.66 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n,P: finite1489363574real_n > $o] : 0.41/0.66 ( ( ( member223413699real_n 0.41/0.66 @ ( collec321817931real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : 0.41/0.66 ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ N ) ) 0.41/0.66 & ( P @ X ) ) ) 0.41/0.66 @ ( sigma_1235138647real_n @ N ) ) 0.41/0.66 => ( member223413699real_n 0.41/0.66 @ ( collec321817931real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : 0.41/0.66 ( ( P @ ( F @ X ) ) 0.41/0.66 & ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) ) ) ) 0.41/0.66 @ ( sigma_1235138647real_n @ M ) ) ) 0.41/0.66 <= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_208_add__diff__cancel__left,axiom, 0.41/0.66 ! [C2: finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.66 ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ C2 @ A ) @ ( plus_p585657087real_n @ C2 @ B ) ) 0.41/0.66 = ( minus_1037315151real_n @ A @ B ) ) ). 0.41/0.66 0.41/0.66 thf(fact_34_vimageE,axiom, 0.41/0.66 ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B2: set_se2111327970real_n] : 0.41/0.66 ( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ B2 ) ) 0.41/0.66 => ( member223413699real_n @ ( F @ A ) @ B2 ) ) ). 0.41/0.66 0.41/0.66 thf(fact_22_add__left__cancel,axiom, 0.41/0.66 ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] : 0.41/0.66 ( ( ( plus_p585657087real_n @ A @ B ) 0.41/0.66 = ( plus_p585657087real_n @ A @ C2 ) ) 0.41/0.66 = ( B = C2 ) ) ). 0.41/0.66 0.41/0.66 thf(fact_164_sets_Osets__Collect__neg,axiom, 0.41/0.66 ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] : 0.41/0.66 ( ( member1475136633real_n 0.41/0.66 @ ( collec452821761real_n 0.41/0.66 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.66 ( ( P @ X ) 0.41/0.66 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) ) ) 0.41/0.66 @ ( sigma_433815053real_n @ M ) ) 0.41/0.66 => ( member1475136633real_n 0.41/0.66 @ ( collec452821761real_n 0.41/0.66 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.66 ( ~ ( P @ X ) 0.41/0.66 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) ) ) 0.41/0.66 @ ( sigma_433815053real_n @ M ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_137_inf__sup__aci_I1_J,axiom, 0.41/0.66 ( inf_in1974387902real_n 0.41/0.66 = ( ^ [X: set_Fi1058188332real_n,Y2: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ Y2 @ X ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_31_vimageD,axiom, 0.41/0.66 ! [A: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] : 0.41/0.66 ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ A2 ) ) 0.41/0.66 => ( member1352538125real_n @ ( F @ A ) @ A2 ) ) ). 0.41/0.66 0.41/0.66 thf(fact_173_sets_Osets__Collect__const,axiom, 0.41/0.66 ! [M: sigma_1422848389real_n,P: $o] : 0.41/0.66 ( member1475136633real_n 0.41/0.66 @ ( collec452821761real_n 0.41/0.66 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.66 ( P 0.41/0.66 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) ) ) 0.41/0.66 @ ( sigma_433815053real_n @ M ) ) ). 0.41/0.66 0.41/0.66 thf(fact_288_vimage__Diff,axiom, 0.41/0.66 ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.66 ( ( vimage1233683625real_n @ F @ ( minus_1686442501real_n @ A2 @ B2 ) ) 0.41/0.66 = ( minus_1686442501real_n @ ( vimage1233683625real_n @ F @ A2 ) @ ( vimage1233683625real_n @ F @ B2 ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_277_space__lborel,axiom, 0.41/0.66 ( ( sigma_476185326real_n @ lebesg260170249real_n ) 0.41/0.66 = ( sigma_476185326real_n @ borel_676189912real_n ) ) ). 0.41/0.66 0.41/0.66 thf(fact_231_diff__right__commute,axiom, 0.41/0.66 ! [A: nat,C2: nat,B: nat] : 0.41/0.66 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C2 ) @ B ) 0.41/0.66 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 ) ) ). 0.41/0.66 0.41/0.66 thf(fact_152_measurable__space,axiom, 0.41/0.66 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,M: sigma_107786596real_n,A2: sigma_1466784463real_n,X2: finite1489363574real_n > finite1489363574real_n] : 0.41/0.66 ( ( member1695588023real_n @ F @ ( sigma_2028985427real_n @ M @ A2 ) ) 0.41/0.66 => ( ( member1352538125real_n @ ( F @ X2 ) @ ( sigma_476185326real_n @ A2 ) ) 0.41/0.66 <= ( member1746150050real_n @ X2 @ ( sigma_1483971331real_n @ M ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_97_measurable__sets,axiom, 0.41/0.66 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A2: sigma_1466784463real_n,S: set_Fi1058188332real_n] : 0.41/0.66 ( ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ A2 ) ) 0.41/0.66 => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ S ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) ) 0.41/0.66 <= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ A2 ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_80_mem__Collect__eq,axiom, 0.41/0.66 ! [A: finite1489363574real_n > finite1489363574real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.66 ( ( member1746150050real_n @ A @ ( collec1190264032real_n @ P ) ) 0.41/0.66 = ( P @ A ) ) ). 0.41/0.66 0.41/0.66 thf(fact_350_diff__0__eq__0,axiom, 0.41/0.66 ! [N3: nat] : 0.41/0.66 ( ( minus_minus_nat @ zero_zero_nat @ N3 ) 0.41/0.66 = zero_zero_nat ) ). 0.41/0.66 0.41/0.66 thf(fact_93_vimageI2,axiom, 0.41/0.66 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] : 0.41/0.66 ( ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ A2 ) ) 0.41/0.66 <= ( member1746150050real_n @ ( F @ A ) @ A2 ) ) ). 0.41/0.66 0.41/0.66 thf(fact_320_translation__invert,axiom, 0.41/0.66 ! [A: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] : 0.41/0.66 ( ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ A2 ) 0.41/0.66 = ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ B2 ) ) 0.41/0.66 => ( A2 = B2 ) ) ). 0.41/0.66 0.41/0.66 thf(fact_270_sets__Collect__restrict__space__iff,axiom, 0.41/0.66 ! [S: set_se2111327970real_n,M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] : 0.41/0.66 ( ( ( member1475136633real_n 0.41/0.66 @ ( collec452821761real_n 0.41/0.66 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.66 ( ( P @ X ) 0.41/0.66 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ ( sigma_993999336real_n @ M @ S ) ) ) ) ) 0.41/0.66 @ ( sigma_433815053real_n @ ( sigma_993999336real_n @ M @ S ) ) ) 0.41/0.66 = ( member1475136633real_n 0.41/0.66 @ ( collec452821761real_n 0.41/0.66 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.66 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) 0.41/0.66 & ( P @ X ) 0.41/0.66 & ( member223413699real_n @ X @ S ) ) ) 0.41/0.66 @ ( sigma_433815053real_n @ M ) ) ) 0.41/0.66 <= ( member1475136633real_n @ S @ ( sigma_433815053real_n @ M ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_112_measurable__sets__Collect,axiom, 0.41/0.66 ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,M: sigma_1422848389real_n,N: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] : 0.41/0.66 ( ( member1764433517real_n @ F @ ( sigma_588796041real_n @ M @ N ) ) 0.41/0.66 => ( ( member1475136633real_n 0.41/0.66 @ ( collec452821761real_n 0.41/0.66 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.66 ( ( P @ ( F @ X ) ) 0.41/0.66 & ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) ) ) ) 0.41/0.66 @ ( sigma_433815053real_n @ M ) ) 0.41/0.66 <= ( member2104752728real_n 0.41/0.66 @ ( collec1190264032real_n 0.41/0.66 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.66 ( ( P @ X ) 0.41/0.66 & ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ N ) ) ) ) 0.41/0.66 @ ( sigma_522684908real_n @ N ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_202_add__diff__cancel__right_H,axiom, 0.41/0.66 ! [A: finite1489363574real_n,B: finite1489363574real_n] : 0.41/0.66 ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ B ) 0.41/0.66 = A ) ). 0.41/0.66 0.41/0.66 thf(help_If_1_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom, 0.41/0.66 ! [X2: finite1489363574real_n > finite1489363574real_n,Y3: finite1489363574real_n > finite1489363574real_n] : 0.41/0.66 ( ( if_Fin413489477real_n @ $true @ X2 @ Y3 ) 0.41/0.66 = X2 ) ). 0.41/0.66 0.41/0.66 thf(fact_316_translation__subtract__diff,axiom, 0.41/0.66 ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T3: set_Fi1058188332real_n] : 0.41/0.66 ( ( image_439535603real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A ) 0.41/0.66 @ ( minus_1686442501real_n @ S2 @ T3 ) ) 0.41/0.66 = ( minus_1686442501real_n 0.41/0.66 @ ( image_439535603real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A ) 0.41/0.66 @ S2 ) 0.41/0.66 @ ( image_439535603real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A ) 0.41/0.66 @ T3 ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_349_Least__eq__0,axiom, 0.41/0.66 ! [P: nat > $o] : 0.41/0.66 ( ( P @ zero_zero_nat ) 0.41/0.66 => ( ( ord_Least_nat @ P ) 0.41/0.66 = zero_zero_nat ) ) ). 0.41/0.66 0.41/0.66 thf(fact_250_measurable__restrict__space1,axiom, 0.41/0.66 ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] : 0.41/0.66 ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ M @ Omega ) @ N ) ) 0.41/0.66 <= ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_335_add__cancel__right__right,axiom, 0.41/0.66 ! [A: nat,B: nat] : 0.41/0.66 ( ( A 0.41/0.66 = ( plus_plus_nat @ A @ B ) ) 0.41/0.66 = ( B = zero_zero_nat ) ) ). 0.41/0.66 0.41/0.66 thf(fact_38_IntI,axiom, 0.41/0.66 ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] : 0.41/0.66 ( ( member1746150050real_n @ C2 @ A2 ) 0.41/0.66 => ( ( member1746150050real_n @ C2 @ B2 ) 0.41/0.66 => ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_293_lebesgue__sets__translation,axiom, 0.41/0.66 ! [S: set_Fi1058188332real_n,A: finite1489363574real_n] : 0.41/0.66 ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) 0.41/0.66 => ( member223413699real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_9_vimage__Collect__eq,axiom, 0.41/0.66 ! [F: finite1489363574real_n > finite1489363574real_n,P: finite1489363574real_n > $o] : 0.41/0.66 ( ( vimage1233683625real_n @ F @ ( collec321817931real_n @ P ) ) 0.41/0.66 = ( collec321817931real_n 0.41/0.66 @ ^ [Y2: finite1489363574real_n] : ( P @ ( F @ Y2 ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_26_vimage__def,axiom, 0.41/0.66 ( vimage1233683625real_n 0.41/0.66 = ( ^ [F2: finite1489363574real_n > finite1489363574real_n,B3: set_Fi1058188332real_n] : 0.41/0.66 ( collec321817931real_n 0.41/0.66 @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ ( F2 @ X ) @ B3 ) ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_111_measurable__sets__Collect,axiom, 0.41/0.66 ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,M: sigma_107786596real_n,N: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] : 0.41/0.66 ( ( ( member1475136633real_n 0.41/0.66 @ ( collec452821761real_n 0.41/0.66 @ ^ [X: set_Fi1058188332real_n] : 0.41/0.66 ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ N ) ) 0.41/0.66 & ( P @ X ) ) ) 0.41/0.66 @ ( sigma_433815053real_n @ N ) ) 0.41/0.66 => ( member2104752728real_n 0.41/0.66 @ ( collec1190264032real_n 0.41/0.66 @ ^ [X: finite1489363574real_n > finite1489363574real_n] : 0.41/0.66 ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) ) 0.41/0.66 & ( P @ ( F @ X ) ) ) ) 0.41/0.66 @ ( sigma_522684908real_n @ M ) ) ) 0.41/0.66 <= ( member640587117real_n @ F @ ( sigma_364818953real_n @ M @ N ) ) ) ). 0.41/0.66 0.41/0.66 thf(fact_307_minus__set__def,axiom, 0.41/0.66 ( minus_1698615483real_n 0.41/0.66 = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] : 0.41/0.66 ( collec452821761real_n 0.48/0.75 @ ( minus_1832115082al_n_o 0.48/0.75 @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ A4 ) 0.48/0.75 @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ B3 ) ) ) ) ) ). 0.48/0.75 0.48/0.75 thf(fact_43_space__completion,axiom, 0.48/0.75 ! [M: sigma_1466784463real_n] : 0.48/0.75 ( ( sigma_476185326real_n @ ( comple230862828real_n @ M ) ) 0.48/0.75 = ( sigma_476185326real_n @ M ) ) ). 0.48/0.75 0.48/0.75 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.C6SZAHLRfK/cvc5---1.0.5_28121.p... 0.48/0.75 (declare-sort $$unsorted 0) 0.48/0.75 (declare-sort tptp.set_Fi1066397675real_n 0) 0.48/0.75 (declare-sort tptp.set_se830533260real_n 0) 0.48/0.75 (declare-sort tptp.set_Fi909698444real_n 0) 0.48/0.75 (declare-sort tptp.set_Fi1260307670real_n 0) 0.48/0.75 (declare-sort tptp.set_Fi1491909078real_n 0) 0.48/0.75 (declare-sort tptp.set_se1738601133real_n 0) 0.48/0.75 (declare-sort tptp.sigma_107786596real_n 0) 0.48/0.75 (declare-sort tptp.set_se221767415real_n 0) 0.48/0.75 (declare-sort tptp.set_se955370231real_n 0) 0.48/0.75 (declare-sort tptp.set_Fi1645173239real_n 0) 0.48/0.75 (declare-sort tptp.set_Fi1326602817real_n 0) 0.48/0.75 (declare-sort tptp.sigma_1422848389real_n 0) 0.48/0.75 (declare-sort tptp.set_se820660888real_n 0) 0.48/0.75 (declare-sort tptp.sigma_1466784463real_n 0) 0.48/0.75 (declare-sort tptp.set_se2111327970real_n 0) 0.48/0.75 (declare-sort tptp.set_Fi1058188332real_n 0) 0.48/0.75 (declare-sort tptp.finite1489363574real_n 0) 0.48/0.75 (declare-sort tptp.finite964658038_int_n 0) 0.48/0.75 (declare-sort tptp.set_nat 0) 0.48/0.75 (declare-sort tptp.nat 0) 0.48/0.75 (declare-fun tptp.borel_1962407338real_n ((-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.sigma_1466784463real_n) Bool) 0.48/0.75 (declare-fun tptp.borel_676189912real_n () tptp.sigma_1466784463real_n) 0.48/0.75 (declare-fun tptp.comple230862828real_n (tptp.sigma_1466784463real_n) tptp.sigma_1466784463real_n) 0.48/0.75 (declare-fun tptp.comple1390568924real_n (tptp.sigma_1466784463real_n tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.minus_391085931al_n_o ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool) (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool) (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) Bool) 0.48/0.75 (declare-fun tptp.minus_455231168al_n_o ((-> tptp.finite1489363574real_n Bool) (-> tptp.finite1489363574real_n Bool) tptp.finite1489363574real_n) Bool) 0.48/0.75 (declare-fun tptp.minus_1832115082al_n_o ((-> tptp.set_Fi1058188332real_n Bool) (-> tptp.set_Fi1058188332real_n Bool) tptp.set_Fi1058188332real_n) Bool) 0.48/0.75 (declare-fun tptp.minus_1037315151real_n (tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n) 0.48/0.75 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat) 0.48/0.75 (declare-fun tptp.minus_725016986real_n (tptp.set_Fi1326602817real_n tptp.set_Fi1326602817real_n) tptp.set_Fi1326602817real_n) 0.48/0.75 (declare-fun tptp.minus_1686442501real_n (tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.minus_1698615483real_n (tptp.set_se2111327970real_n tptp.set_se2111327970real_n) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.plus_p585657087real_n (tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n) 0.48/0.75 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat) 0.48/0.75 (declare-fun tptp.plus_p1606848693real_n (tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.plus_p565022571real_n (tptp.set_se2111327970real_n tptp.set_se2111327970real_n) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.zero_z200130687real_n () tptp.finite1489363574real_n) 0.48/0.75 (declare-fun tptp.zero_zero_nat () tptp.nat) 0.48/0.75 (declare-fun tptp.if_Fin413489477real_n (Bool (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n) tptp.finite1489363574real_n) 0.48/0.75 (declare-fun tptp.if_Fin127821360real_n (Bool tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n) 0.48/0.75 (declare-fun tptp.if_set11487206real_n (Bool tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.inf_in32002162al_n_o ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool) (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool) (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) Bool) 0.48/0.75 (declare-fun tptp.inf_in1620715847al_n_o ((-> tptp.finite1489363574real_n Bool) (-> tptp.finite1489363574real_n Bool) tptp.finite1489363574real_n) Bool) 0.48/0.75 (declare-fun tptp.inf_in409346577al_n_o ((-> tptp.set_Fi1058188332real_n Bool) (-> tptp.set_Fi1058188332real_n Bool) tptp.set_Fi1058188332real_n) Bool) 0.48/0.75 (declare-fun tptp.inf_in146441683real_n (tptp.set_Fi1326602817real_n tptp.set_Fi1326602817real_n) tptp.set_Fi1326602817real_n) 0.48/0.75 (declare-fun tptp.inf_in1974387902real_n (tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.inf_in632889204real_n (tptp.set_se2111327970real_n tptp.set_se2111327970real_n) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.lebesg260170249real_n () tptp.sigma_1466784463real_n) 0.48/0.75 (declare-fun tptp.minkow1134813771n_real (tptp.finite964658038_int_n) tptp.finite1489363574real_n) 0.48/0.75 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat) 0.48/0.75 (declare-fun tptp.collec1190264032real_n ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool)) tptp.set_Fi1326602817real_n) 0.48/0.75 (declare-fun tptp.collec321817931real_n ((-> tptp.finite1489363574real_n Bool)) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.collec452821761real_n ((-> tptp.set_Fi1058188332real_n Bool)) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.image_1123376925real_n ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1326602817real_n) tptp.set_Fi1326602817real_n) 0.48/0.75 (declare-fun tptp.image_449906696real_n ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n) tptp.set_Fi1326602817real_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.image_128879038real_n ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n) tptp.set_Fi1326602817real_n) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.image_437359496real_n ((-> tptp.finite1489363574real_n tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n) tptp.set_Fi1326602817real_n) 0.48/0.75 (declare-fun tptp.image_439535603real_n ((-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.image_545463721real_n ((-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat) 0.48/0.75 (declare-fun tptp.image_352856126real_n ((-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_se2111327970real_n) tptp.set_Fi1326602817real_n) 0.48/0.75 (declare-fun tptp.image_1311908777real_n ((-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n) tptp.set_se2111327970real_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.image_1661509983real_n ((-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n) tptp.set_se2111327970real_n) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.vimage180751827real_n ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1326602817real_n) tptp.set_Fi1326602817real_n) 0.48/0.75 (declare-fun tptp.vimage1072397758real_n ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n) tptp.set_Fi1326602817real_n) 0.48/0.75 (declare-fun tptp.vimage2098059032_n_nat ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.nat) tptp.set_nat) tptp.set_Fi1326602817real_n) 0.48/0.75 (declare-fun tptp.vimage1910974324real_n ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n) tptp.set_se2111327970real_n) tptp.set_Fi1326602817real_n) 0.48/0.75 (declare-fun tptp.vimage1059850558real_n ((-> tptp.finite1489363574real_n tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1326602817real_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.vimage1233683625real_n ((-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.vimage281029891_n_nat ((-> tptp.finite1489363574real_n tptp.nat) tptp.set_nat) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.vimage207290975real_n ((-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n) tptp.set_se2111327970real_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.vimage2134951412real_n ((-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1326602817real_n) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.vimage973736031real_n ((-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.vimage501526201_n_nat ((-> tptp.set_Fi1058188332real_n tptp.nat) tptp.set_nat) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.vimage784510485real_n ((-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n) tptp.set_se2111327970real_n) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.sigma_1185134568real_n (tptp.sigma_107786596real_n tptp.sigma_107786596real_n) tptp.set_Fi1066397675real_n) 0.48/0.75 (declare-fun tptp.sigma_2028985427real_n (tptp.sigma_107786596real_n tptp.sigma_1466784463real_n) tptp.set_Fi1491909078real_n) 0.48/0.75 (declare-fun tptp.sigma_364818953real_n (tptp.sigma_107786596real_n tptp.sigma_1422848389real_n) tptp.set_Fi909698444real_n) 0.48/0.75 (declare-fun tptp.sigma_2016438227real_n (tptp.sigma_1466784463real_n tptp.sigma_107786596real_n) tptp.set_Fi1260307670real_n) 0.48/0.75 (declare-fun tptp.sigma_439801790real_n (tptp.sigma_1466784463real_n tptp.sigma_1466784463real_n) tptp.set_Fi1326602817real_n) 0.48/0.75 (declare-fun tptp.sigma_566919540real_n (tptp.sigma_1466784463real_n tptp.sigma_1422848389real_n) tptp.set_Fi1645173239real_n) 0.48/0.75 (declare-fun tptp.sigma_588796041real_n (tptp.sigma_1422848389real_n tptp.sigma_107786596real_n) tptp.set_se830533260real_n) 0.48/0.75 (declare-fun tptp.sigma_1333364596real_n (tptp.sigma_1422848389real_n tptp.sigma_1466784463real_n) tptp.set_se955370231real_n) 0.48/0.75 (declare-fun tptp.sigma_239294762real_n (tptp.sigma_1422848389real_n tptp.sigma_1422848389real_n) tptp.set_se1738601133real_n) 0.48/0.75 (declare-fun tptp.sigma_1052429895real_n (tptp.sigma_107786596real_n tptp.set_Fi1326602817real_n) tptp.sigma_107786596real_n) 0.48/0.75 (declare-fun tptp.sigma_346513458real_n (tptp.sigma_1466784463real_n tptp.set_Fi1058188332real_n) tptp.sigma_1466784463real_n) 0.48/0.75 (declare-fun tptp.sigma_993999336real_n (tptp.sigma_1422848389real_n tptp.set_se2111327970real_n) tptp.sigma_1422848389real_n) 0.48/0.75 (declare-fun tptp.sigma_522684908real_n (tptp.sigma_107786596real_n) tptp.set_se221767415real_n) 0.48/0.75 (declare-fun tptp.sigma_1235138647real_n (tptp.sigma_1466784463real_n) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.sigma_433815053real_n (tptp.sigma_1422848389real_n) tptp.set_se820660888real_n) 0.48/0.75 (declare-fun tptp.sigma_1483971331real_n (tptp.sigma_107786596real_n) tptp.set_Fi1326602817real_n) 0.48/0.75 (declare-fun tptp.sigma_476185326real_n (tptp.sigma_1466784463real_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.sigma_607186084real_n (tptp.sigma_1422848389real_n) tptp.set_se2111327970real_n) 0.48/0.75 (declare-fun tptp.sigma_136294295real_n (tptp.set_Fi1326602817real_n (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n) tptp.sigma_1466784463real_n) tptp.sigma_107786596real_n) 0.48/0.75 (declare-fun tptp.sigma_821351682real_n (tptp.set_Fi1058188332real_n (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.sigma_1466784463real_n) tptp.sigma_1466784463real_n) 0.48/0.75 (declare-fun tptp.sigma_1384150200real_n (tptp.set_se2111327970real_n (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n) tptp.sigma_1466784463real_n) tptp.sigma_1422848389real_n) 0.48/0.75 (declare-fun tptp.member117715276real_n ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1066397675real_n) Bool) 0.48/0.75 (declare-fun tptp.member1695588023real_n ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n) tptp.set_Fi1491909078real_n) Bool) 0.48/0.75 (declare-fun tptp.member640587117real_n ((-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n) tptp.set_Fi909698444real_n) Bool) 0.48/0.75 (declare-fun tptp.member408431031real_n ((-> tptp.finite1489363574real_n tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1260307670real_n) Bool) 0.48/0.75 (declare-fun tptp.member1746150050real_n ((-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1326602817real_n) Bool) 0.48/0.75 (declare-fun tptp.member966061400real_n ((-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n) tptp.set_Fi1645173239real_n) Bool) 0.48/0.75 (declare-fun tptp.member1764433517real_n ((-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_se830533260real_n) Bool) 0.48/0.75 (declare-fun tptp.member1759501912real_n ((-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n) tptp.set_se955370231real_n) Bool) 0.48/0.75 (declare-fun tptp.member1734791438real_n ((-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n) tptp.set_se1738601133real_n) Bool) 0.48/0.75 (declare-fun tptp.member1352538125real_n (tptp.finite1489363574real_n tptp.set_Fi1058188332real_n) Bool) 0.48/0.75 (declare-fun tptp.member2104752728real_n (tptp.set_Fi1326602817real_n tptp.set_se221767415real_n) Bool) 0.48/0.75 (declare-fun tptp.member223413699real_n (tptp.set_Fi1058188332real_n tptp.set_se2111327970real_n) Bool) 0.48/0.75 (declare-fun tptp.member1475136633real_n (tptp.set_se2111327970real_n tptp.set_se820660888real_n) Bool) 0.48/0.75 (declare-fun tptp.r (tptp.finite964658038_int_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.s () tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.t (tptp.finite964658038_int_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.t2 (tptp.finite964658038_int_n) tptp.set_Fi1058188332real_n) 0.48/0.75 (declare-fun tptp.a () tptp.finite964658038_int_n) 0.48/0.75 (assert (= tptp.minus_1698615483real_n (lambda ((A4 tptp.set_se2111327970real_n) (B3 tptp.set_se2111327970real_n)) (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member223413699real_n X))) (and (not (@ _let_1 B3)) (@ _let_1 A4)))))))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (M tptp.sigma_1422848389real_n) (N tptp.sigma_1422848389real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (=> (@ (@ tptp.member1734791438real_n F) (@ (@ tptp.sigma_239294762real_n M) N)) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n N)) (@ P X))))) (@ tptp.sigma_433815053real_n N)) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)) (@ P (@ F X)))))) (@ tptp.sigma_433815053real_n M)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n)) (A2 tptp.set_Fi1058188332real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (= (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ (@ tptp.image_545463721real_n F) A2)) (@ P X)))) (@ (@ tptp.image_545463721real_n F) (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) A2) (@ P (@ F X))))))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (S2 tptp.set_Fi1058188332real_n) (T3 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n X) A))) (@ (@ tptp.inf_in1974387902real_n S2) T3)) (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n X) A))) S2)) (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n X) A))) T3))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (let ((_let_1 (@ (@ tptp.sigma_439801790real_n M) tptp.borel_676189912real_n))) (=> (@ (@ tptp.member1746150050real_n F) _let_1) (=> (@ (@ tptp.member1746150050real_n G) _let_1) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (= (@ F X) (@ G X)) (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)))))) (@ tptp.sigma_1235138647real_n M))))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (N tptp.sigma_1466784463real_n) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (L2 tptp.sigma_1466784463real_n)) (let ((_let_1 (@ tptp.sigma_439801790real_n M))) (=> (@ (@ tptp.member1746150050real_n F) (@ _let_1 N)) (=> (@ (@ tptp.member1746150050real_n G) (@ (@ tptp.sigma_439801790real_n N) L2)) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) (@ G (@ F X)))) (@ _let_1 L2))))))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n) (C tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A2))) (= (@ (@ tptp.inf_in1974387902real_n (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.inf_in1974387902real_n B2) C)))))) 0.48/0.75 (assert (forall ((C2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C2))) (=> (@ _let_1 (@ (@ tptp.minus_1698615483real_n A2) B2)) (not (=> (@ _let_1 A2) (@ _let_1 B2))))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member223413699real_n X2) A2) (=> (= B (@ F X2)) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1661509983real_n F) A2)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1422848389real_n) (Pb Bool)) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)) Pb)))) (@ tptp.sigma_433815053real_n M)))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (N tptp.sigma_107786596real_n) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (=> (@ (@ tptp.member408431031real_n F) (@ (@ tptp.sigma_2016438227real_n M) N)) (=> (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n N)) (@ P X))))) (@ tptp.sigma_522684908real_n N)) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P (@ F X)) (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)))))) (@ tptp.sigma_1235138647real_n M)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (M2 tptp.sigma_1466784463real_n) (N tptp.sigma_1466784463real_n) (N2 tptp.sigma_1466784463real_n)) (=> (= (@ tptp.sigma_1235138647real_n M) (@ tptp.sigma_1235138647real_n M2)) (=> (= (@ tptp.sigma_1235138647real_n N) (@ tptp.sigma_1235138647real_n N2)) (= (@ (@ tptp.sigma_439801790real_n M) N) (@ (@ tptp.sigma_439801790real_n M2) N2)))))) 0.48/0.75 (assert (forall ((P (-> tptp.finite1489363574real_n Bool)) (Q (-> tptp.finite1489363574real_n Bool))) (= (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ Q X) (@ P X)))) (@ (@ tptp.inf_in1974387902real_n (@ tptp.collec321817931real_n P)) (@ tptp.collec321817931real_n Q))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (B2 tptp.set_Fi1058188332real_n)) (=> (= (@ F A) B) (=> (@ (@ tptp.member1352538125real_n B) B2) (@ (@ tptp.member1352538125real_n A) (@ (@ tptp.vimage1233683625real_n F) B2)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n)) (M tptp.sigma_1466784463real_n) (A2 tptp.sigma_1422848389real_n) (X2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member966061400real_n F) (@ (@ tptp.sigma_566919540real_n M) A2)) (=> (@ (@ tptp.member1352538125real_n X2) (@ tptp.sigma_476185326real_n M)) (@ (@ tptp.member223413699real_n (@ F X2)) (@ tptp.sigma_607186084real_n A2)))))) 0.48/0.75 (assert (forall ((A tptp.finite964658038_int_n)) (= (@ tptp.t A) (@ (@ tptp.vimage1233683625real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.plus_p585657087real_n X) (@ tptp.minkow1134813771n_real A)))) (@ tptp.t2 A))))) 0.48/0.75 (assert (forall ((C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (B2 tptp.set_Fi1326602817real_n)) (let ((_let_1 (@ tptp.member1746150050real_n C2))) (= (@ _let_1 (@ (@ tptp.minus_725016986real_n A2) B2)) (and (@ _let_1 A2) (not (@ _let_1 B2))))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1422848389real_n) (P (-> tptp.nat tptp.set_Fi1058188332real_n Bool)) (A2 tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ P I2) X) (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)))))) (@ tptp.sigma_433815053real_n M))) (@ (@ tptp.member1475136633real_n (@ (@ tptp.inf_in632889204real_n (@ (@ tptp.vimage501526201_n_nat (lambda ((X tptp.set_Fi1058188332real_n)) (@ tptp.ord_Least_nat (lambda ((J2 tptp.nat)) (@ (@ P J2) X))))) A2)) (@ tptp.sigma_607186084real_n M))) (@ tptp.sigma_433815053real_n M))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (Omega tptp.set_Fi1058188332real_n)) (= (@ tptp.sigma_1235138647real_n (@ (@ tptp.sigma_346513458real_n M) Omega)) (@ (@ tptp.image_1661509983real_n (@ tptp.inf_in1974387902real_n Omega)) (@ tptp.sigma_1235138647real_n M))))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.inf_in1974387902real_n A2) A2) A2))) 0.48/0.75 (assert (forall ((S tptp.set_Fi1058188332real_n) (A tptp.finite1489363574real_n) (T tptp.set_Fi1058188332real_n)) (=> (forall ((X3 tptp.finite1489363574real_n)) (= (@ (@ tptp.member1352538125real_n X3) S) (@ (@ tptp.member1352538125real_n (@ (@ tptp.plus_p585657087real_n A) X3)) T))) (= T (@ (@ tptp.image_439535603real_n (@ tptp.plus_p585657087real_n A)) S))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n)) (= (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n M) tptp.borel_676189912real_n)) (forall ((X tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_1235138647real_n tptp.borel_676189912real_n)) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage1233683625real_n F) X)) (@ tptp.sigma_476185326real_n M))) (@ tptp.sigma_1235138647real_n M))))))) 0.48/0.75 (assert (forall ((C2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C2))) (=> (@ _let_1 (@ (@ tptp.minus_1698615483real_n A2) B2)) (not (@ _let_1 B2)))))) 0.48/0.75 (assert (forall ((B tptp.finite1489363574real_n) (A tptp.finite1489363574real_n)) (= (= (@ (@ tptp.plus_p585657087real_n B) A) A) (= B tptp.zero_z200130687real_n)))) 0.48/0.75 (assert (forall ((C2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C2))) (=> (@ _let_1 (@ (@ tptp.minus_1698615483real_n A2) B2)) (@ _let_1 A2))))) 0.48/0.75 (assert (forall ((A tptp.finite964658038_int_n)) (@ (@ tptp.member223413699real_n (@ tptp.r A)) (@ tptp.sigma_1235138647real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n))))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (C tptp.set_se2111327970real_n) (B tptp.set_Fi1058188332real_n) (D tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n A) C) (=> (@ (@ tptp.member223413699real_n B) D) (@ (@ tptp.member223413699real_n (@ (@ tptp.plus_p1606848693real_n A) B)) (@ (@ tptp.plus_p565022571real_n C) D)))))) 0.48/0.75 (assert (forall ((S tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n S) (@ tptp.sigma_1235138647real_n (@ (@ tptp.sigma_346513458real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) S))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (Y3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ (@ tptp.inf_in1974387902real_n X2) Y3))) (= (@ (@ tptp.inf_in1974387902real_n _let_1) Y3) _let_1)))) 0.48/0.75 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n)) (M tptp.sigma_107786596real_n) (N tptp.sigma_1466784463real_n) (P (-> tptp.finite1489363574real_n Bool))) (=> (@ (@ tptp.member1695588023real_n F) (@ (@ tptp.sigma_2028985427real_n M) N)) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P X) (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n N)))))) (@ tptp.sigma_1235138647real_n N)) (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)) (@ P (@ F X)))))) (@ tptp.sigma_522684908real_n M)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (M2 tptp.sigma_1466784463real_n) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ (@ tptp.sigma_439801790real_n M) M2))) (=> (@ (@ tptp.member1746150050real_n F) _let_1) (=> (@ (@ tptp.member1746150050real_n G) _let_1) (=> (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n A2) (@ tptp.sigma_476185326real_n M))) (@ tptp.sigma_1235138647real_n M)) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ (@ tptp.if_Fin127821360real_n (@ (@ tptp.member1352538125real_n X) A2)) (@ F X)) (@ G X)))) _let_1))))))) 0.48/0.75 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B))) 0.48/0.75 (assert (forall ((M tptp.sigma_107786596real_n) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (let ((_let_1 (@ tptp.sigma_522684908real_n M))) (=> (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ P X) (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)))))) _let_1) (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)) (not (@ P X)))))) _let_1))))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n)) (let ((_let_1 (@ tptp.member223413699real_n A2))) (=> (@ _let_1 (@ tptp.sigma_1235138647real_n M)) (@ _let_1 (@ tptp.sigma_1235138647real_n (@ tptp.comple230862828real_n M))))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (= (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) tptp.borel_676189912real_n)) (forall ((T2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n T2) (@ tptp.sigma_1235138647real_n tptp.borel_676189912real_n)) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n (@ F X)) T2)))) (@ tptp.sigma_1235138647real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)))))))) 0.48/0.75 (assert (forall ((C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (B2 tptp.set_Fi1326602817real_n)) (let ((_let_1 (@ tptp.member1746150050real_n C2))) (= (@ _let_1 (@ (@ tptp.inf_in146441683real_n A2) B2)) (and (@ _let_1 B2) (@ _let_1 A2)))))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (A2 tptp.set_se2111327970real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (= (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ (@ tptp.image_1661509983real_n F) A2)) (@ P X)))) (@ (@ tptp.image_1661509983real_n F) (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ P (@ F X)) (@ (@ tptp.member223413699real_n X) A2)))))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n)) (= (@ (@ tptp.minus_1037315151real_n A) A) tptp.zero_z200130687real_n))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.minus_1037315151real_n A))) (= (@ (@ tptp.minus_1037315151real_n (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_p585657087real_n B) C2)))))) 0.48/0.75 (assert (forall ((B (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n)) (X2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n)) (=> (= B (@ F X2)) (=> (@ (@ tptp.member1746150050real_n X2) A2) (@ (@ tptp.member1746150050real_n B) (@ (@ tptp.image_1123376925real_n F) A2)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1422848389real_n) (F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (N tptp.sigma_107786596real_n)) (=> (forall ((X3 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X3) (@ tptp.sigma_607186084real_n M)) (@ (@ tptp.member1746150050real_n (@ F X3)) (@ tptp.sigma_1483971331real_n N)))) (=> (forall ((A6 tptp.set_Fi1326602817real_n)) (=> (@ (@ tptp.member2104752728real_n A6) (@ tptp.sigma_522684908real_n N)) (@ (@ tptp.member1475136633real_n (@ (@ tptp.inf_in632889204real_n (@ (@ tptp.vimage2134951412real_n F) A6)) (@ tptp.sigma_607186084real_n M))) (@ tptp.sigma_433815053real_n M)))) (@ (@ tptp.member1764433517real_n F) (@ (@ tptp.sigma_588796041real_n M) N)))))) 0.48/0.75 (assert (forall ((B tptp.set_Fi1058188332real_n) (A tptp.set_Fi1058188332real_n) (C2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n B))) (let ((_let_2 (@ tptp.inf_in1974387902real_n A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2))))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (Y3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n X2))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.sigma_346513458real_n M))) (= (@ tptp.sigma_1235138647real_n (@ (@ tptp.sigma_346513458real_n (@ _let_1 A2)) B2)) (@ tptp.sigma_1235138647real_n (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A2) B2))))))) 0.48/0.75 (assert (@ (@ tptp.member223413699real_n tptp.s) (@ tptp.sigma_1235138647real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n)) (M tptp.sigma_1466784463real_n) (N tptp.sigma_1422848389real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (=> (@ (@ tptp.member966061400real_n F) (@ (@ tptp.sigma_566919540real_n M) N)) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ P X) (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n N)))))) (@ tptp.sigma_433815053real_n N)) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (@ P (@ F X)))))) (@ tptp.sigma_1235138647real_n M)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (N tptp.sigma_1466784463real_n)) (let ((_let_1 (@ tptp.member1746150050real_n F))) (=> (@ _let_1 (@ (@ tptp.sigma_439801790real_n M) N)) (@ _let_1 (@ (@ tptp.sigma_439801790real_n (@ tptp.comple230862828real_n M)) N)))))) 0.48/0.75 (assert (forall ((C2 tptp.finite1489363574real_n) (A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member1352538125real_n C2))) (= (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A2) B2)) (and (@ _let_1 B2) (@ _let_1 A2)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_107786596real_n) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool)) (Q (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (let ((_let_1 (@ tptp.sigma_522684908real_n M))) (=> (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ P X) (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)))))) _let_1) (=> (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)) (@ Q X))))) _let_1) (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ Q X) (@ P X) (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)))))) _let_1)))))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n)) (M tptp.sigma_1422848389real_n) (A2 tptp.sigma_1466784463real_n) (X2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1759501912real_n F) (@ (@ tptp.sigma_1333364596real_n M) A2)) (=> (@ (@ tptp.member223413699real_n X2) (@ tptp.sigma_607186084real_n M)) (@ (@ tptp.member1352538125real_n (@ F X2)) (@ tptp.sigma_476185326real_n A2)))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B2 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.member1352538125real_n A) (@ (@ tptp.vimage1233683625real_n F) B2)) (@ (@ tptp.member1352538125real_n (@ F A)) B2)))) 0.48/0.75 (assert (forall ((A2 tptp.set_se2111327970real_n)) (= (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n X) A2))) A2))) 0.48/0.75 (assert (forall ((X4 tptp.set_se2111327970real_n) (Y tptp.set_se2111327970real_n) (F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n)) (G (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (N tptp.sigma_1466784463real_n)) (=> (= X4 Y) (=> (forall ((X3 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X3) Y) (= (@ F X3) (@ G X3)))) (=> (= (@ tptp.sigma_1235138647real_n M) (@ tptp.sigma_1235138647real_n N)) (= (@ (@ (@ tptp.sigma_1384150200real_n X4) F) M) (@ (@ (@ tptp.sigma_1384150200real_n Y) G) N))))))) 0.48/0.75 (assert (forall ((A (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n)) (=> (@ (@ tptp.member1746150050real_n A) (@ (@ tptp.vimage180751827real_n F) A2)) (@ (@ tptp.member1746150050real_n (@ F A)) A2)))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member223413699real_n A2))) (=> (@ _let_1 (@ tptp.sigma_1235138647real_n tptp.borel_676189912real_n)) (@ _let_1 (@ tptp.sigma_1235138647real_n tptp.lebesg260170249real_n)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1058188332real_n) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (= (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ P X) (@ (@ tptp.member1746150050real_n X) (@ (@ tptp.image_437359496real_n F) A2))))) (@ (@ tptp.image_437359496real_n F) (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P (@ F X)) (@ (@ tptp.member1352538125real_n X) A2)))))))) 0.48/0.75 (assert (= tptp.inf_in632889204real_n (lambda ((A4 tptp.set_se2111327970real_n) (B3 tptp.set_se2111327970real_n)) (@ tptp.collec452821761real_n (@ (@ tptp.inf_in409346577al_n_o (lambda ((X tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n X) A4))) (lambda ((X tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n X) B3))))))) 0.48/0.75 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.minus_minus_nat A) B)))) 0.48/0.75 (assert (forall ((P (-> tptp.finite1489363574real_n Bool)) (Q (-> tptp.finite1489363574real_n Bool))) (=> (forall ((X3 tptp.finite1489363574real_n)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec321817931real_n P) (@ tptp.collec321817931real_n Q))))) 0.48/0.75 (assert (= tptp.minus_725016986real_n (lambda ((A4 tptp.set_Fi1326602817real_n) (B3 tptp.set_Fi1326602817real_n)) (@ tptp.collec1190264032real_n (@ (@ tptp.minus_391085931al_n_o (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (@ (@ tptp.member1746150050real_n X) A4))) (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (@ (@ tptp.member1746150050real_n X) B3))))))) 0.48/0.75 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat))) 0.48/0.75 (assert (forall ((M tptp.set_Fi1058188332real_n) (N tptp.set_Fi1058188332real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (= M N) (=> (forall ((X3 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X3) N) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.image_439535603real_n F) M) (@ (@ tptp.image_439535603real_n G) N)))))) 0.48/0.75 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (= (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) (@ (@ tptp.image_1123376925real_n F) A2)) (@ P X)))) (@ (@ tptp.image_1123376925real_n F) (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) A2) (@ P (@ F X))))))))) 0.48/0.75 (assert (forall ((Omega tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (N tptp.sigma_107786596real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n Omega) (@ tptp.sigma_476185326real_n M))) (@ tptp.sigma_1235138647real_n M)) (=> (@ (@ tptp.member1746150050real_n C2) (@ tptp.sigma_1483971331real_n N)) (= (@ (@ tptp.member408431031real_n F) (@ (@ tptp.sigma_2016438227real_n (@ (@ tptp.sigma_346513458real_n M) Omega)) N)) (@ (@ tptp.member408431031real_n (lambda ((X tptp.finite1489363574real_n) (__flatten_var_0 tptp.finite1489363574real_n)) (@ (@ (@ (@ tptp.if_Fin413489477real_n (@ (@ tptp.member1352538125real_n X) Omega)) (@ F X)) C2) __flatten_var_0))) (@ (@ tptp.sigma_2016438227real_n M) N))))))) 0.48/0.75 (assert (forall ((S tptp.set_Fi1326602817real_n) (M tptp.sigma_107786596real_n) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (let ((_let_1 (@ tptp.sigma_522684908real_n M))) (=> (@ (@ tptp.member2104752728real_n S) _let_1) (= (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ P X) (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n (@ (@ tptp.sigma_1052429895real_n M) S))))))) (@ tptp.sigma_522684908real_n (@ (@ tptp.sigma_1052429895real_n M) S))) (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (let ((_let_1 (@ tptp.member1746150050real_n X))) (and (@ _let_1 (@ tptp.sigma_1483971331real_n M)) (@ _let_1 S) (@ P X)))))) _let_1)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_107786596real_n) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n)) (N tptp.sigma_107786596real_n)) (=> (forall ((X3 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1746150050real_n X3) (@ tptp.sigma_1483971331real_n M)) (@ (@ tptp.member1746150050real_n (@ F X3)) (@ tptp.sigma_1483971331real_n N)))) (=> (forall ((A6 tptp.set_Fi1326602817real_n)) (=> (@ (@ tptp.member2104752728real_n A6) (@ tptp.sigma_522684908real_n N)) (@ (@ tptp.member2104752728real_n (@ (@ tptp.inf_in146441683real_n (@ (@ tptp.vimage180751827real_n F) A6)) (@ tptp.sigma_1483971331real_n M))) (@ tptp.sigma_522684908real_n M)))) (@ (@ tptp.member117715276real_n F) (@ (@ tptp.sigma_1185134568real_n M) N)))))) 0.48/0.75 (assert (forall ((R tptp.set_Fi1326602817real_n) (S tptp.set_Fi1326602817real_n)) (= (@ (@ tptp.inf_in32002162al_n_o (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (@ (@ tptp.member1746150050real_n X) R))) (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (@ (@ tptp.member1746150050real_n X) S))) (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (@ (@ tptp.member1746150050real_n X) (@ (@ tptp.inf_in146441683real_n R) S)))))) 0.48/0.75 (assert (= tptp.vimage1059850558real_n (lambda ((F2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B3 tptp.set_Fi1326602817real_n)) (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1746150050real_n (@ F2 X)) B3)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_107786596real_n) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool)) (Q (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (let ((_let_1 (@ tptp.sigma_522684908real_n M))) (=> (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)) (@ P X))))) _let_1) (=> (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ Q X) (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)))))) _let_1) (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (or (@ P X) (@ Q X)) (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)))))) _let_1)))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (Y3 tptp.set_Fi1058188332real_n) (Z tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n X2))) (= (@ (@ tptp.inf_in1974387902real_n (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.inf_in1974387902real_n Y3) Z)))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (= (= A (@ (@ tptp.minus_1037315151real_n C2) B)) (= (@ (@ tptp.plus_p585657087real_n A) B) C2)))) 0.48/0.75 (assert (= tptp.inf_in1974387902real_n (lambda ((A4 tptp.set_Fi1058188332real_n) (B3 tptp.set_Fi1058188332real_n)) (@ (@ tptp.inf_in1974387902real_n B3) A4)))) 0.48/0.75 (assert (forall ((C2 tptp.finite1489363574real_n) (M2 tptp.sigma_1466784463real_n) (M tptp.sigma_1466784463real_n)) (=> (@ (@ tptp.member1352538125real_n C2) (@ tptp.sigma_476185326real_n M2)) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) C2)) (@ (@ tptp.sigma_439801790real_n M) M2))))) 0.48/0.75 (assert (= tptp.vimage207290975real_n (lambda ((F2 (-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n)) (B3 tptp.set_se2111327970real_n)) (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member223413699real_n (@ F2 X)) B3)))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (let ((_let_1 (@ tptp.member223413699real_n X2))) (= (@ _let_1 (@ (@ tptp.inf_in632889204real_n A2) (@ tptp.collec452821761real_n P))) (and (@ _let_1 A2) (@ P X2)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_107786596real_n) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool)) (Q (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (let ((_let_1 (@ tptp.sigma_522684908real_n M))) (=> (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ P X) (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)))))) _let_1) (=> (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ Q X) (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)))))) _let_1) (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)) (=> (@ Q X) (@ P X)))))) _let_1)))))) 0.48/0.75 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X2) Y3) tptp.zero_zero_nat) (and (= Y3 tptp.zero_zero_nat) (= X2 tptp.zero_zero_nat))))) 0.48/0.75 (assert (forall ((Omega tptp.set_Fi1326602817real_n) (M tptp.sigma_107786596real_n) (C2 tptp.finite1489363574real_n) (N tptp.sigma_1466784463real_n) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n))) (=> (@ (@ tptp.member2104752728real_n (@ (@ tptp.inf_in146441683real_n Omega) (@ tptp.sigma_1483971331real_n M))) (@ tptp.sigma_522684908real_n M)) (=> (@ (@ tptp.member1352538125real_n C2) (@ tptp.sigma_476185326real_n N)) (= (@ (@ tptp.member1695588023real_n F) (@ (@ tptp.sigma_2028985427real_n (@ (@ tptp.sigma_1052429895real_n M) Omega)) N)) (@ (@ tptp.member1695588023real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (@ (@ (@ tptp.if_Fin127821360real_n (@ (@ tptp.member1746150050real_n X) Omega)) (@ F X)) C2))) (@ (@ tptp.sigma_2028985427real_n M) N))))))) 0.48/0.75 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat)))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (= (@ (@ tptp.minus_1037315151real_n (@ (@ tptp.plus_p585657087real_n A) C2)) (@ (@ tptp.plus_p585657087real_n B) C2)) (@ (@ tptp.minus_1037315151real_n A) B)))) 0.48/0.75 (assert (forall ((R tptp.set_se2111327970real_n) (S tptp.set_se2111327970real_n)) (= (@ (@ tptp.inf_in409346577al_n_o (lambda ((X tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n X) R))) (lambda ((X tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n X) S))) (lambda ((X tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n X) (@ (@ tptp.inf_in632889204real_n R) S)))))) 0.48/0.75 (assert (forall ((B tptp.finite1489363574real_n) (A tptp.finite1489363574real_n) (S tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n A))) (= (@ (@ tptp.image_439535603real_n (@ tptp.plus_p585657087real_n B)) (@ (@ tptp.image_439535603real_n _let_1) S)) (@ (@ tptp.image_439535603real_n (@ tptp.plus_p585657087real_n (@ _let_1 B))) S))))) 0.48/0.75 (assert (forall ((S tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (P (-> tptp.finite1489363574real_n Bool))) (let ((_let_1 (@ tptp.sigma_1235138647real_n M))) (=> (@ (@ tptp.member223413699real_n S) _let_1) (= (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n (@ (@ tptp.sigma_346513458real_n M) S))) (@ P X))))) (@ tptp.sigma_1235138647real_n (@ (@ tptp.sigma_346513458real_n M) S))) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.member1352538125real_n X))) (and (@ _let_1 (@ tptp.sigma_476185326real_n M)) (@ _let_1 S) (@ P X)))))) _let_1)))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (= (@ (@ tptp.plus_p585657087real_n (@ (@ tptp.minus_1037315151real_n A) B)) B) A))) 0.48/0.75 (assert (forall ((C2 tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (A tptp.finite1489363574real_n)) (=> (= (@ (@ tptp.plus_p585657087real_n C2) B) A) (= C2 (@ (@ tptp.minus_1037315151real_n A) B))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (Omega tptp.set_Fi1058188332real_n)) (= (@ tptp.sigma_1235138647real_n (@ (@ tptp.sigma_346513458real_n M) Omega)) (@ tptp.sigma_1235138647real_n (@ (@ (@ tptp.sigma_821351682real_n (@ (@ tptp.inf_in1974387902real_n Omega) (@ tptp.sigma_476185326real_n M))) (lambda ((X tptp.finite1489363574real_n)) X)) M))))) 0.48/0.75 (assert (= tptp.inf_in1974387902real_n (lambda ((X tptp.set_Fi1058188332real_n) (Y2 tptp.set_Fi1058188332real_n)) (@ (@ tptp.inf_in1974387902real_n Y2) X)))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n)) (=> (@ (@ tptp.member223413699real_n X2) (@ tptp.sigma_1235138647real_n M)) (= (@ (@ tptp.inf_in1974387902real_n X2) (@ tptp.sigma_476185326real_n M)) X2)))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (P (-> tptp.nat tptp.finite1489363574real_n Bool)) (A2 tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ P I2) X) (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)))))) (@ tptp.sigma_1235138647real_n M))) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage281029891_n_nat (lambda ((X tptp.finite1489363574real_n)) (@ tptp.ord_Least_nat (lambda ((J2 tptp.nat)) (@ (@ P J2) X))))) A2)) (@ tptp.sigma_476185326real_n M))) (@ tptp.sigma_1235138647real_n M))))) 0.48/0.75 (assert (forall ((Y tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) X)) Y) Y))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n A))) (= (@ _let_1 (@ (@ tptp.minus_1037315151real_n B) C2)) (@ (@ tptp.minus_1037315151real_n (@ _let_1 B)) C2))))) 0.48/0.75 (assert (forall ((Omega tptp.set_Fi1326602817real_n) (M tptp.sigma_107786596real_n) (C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (N tptp.sigma_107786596real_n) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member2104752728real_n (@ (@ tptp.inf_in146441683real_n Omega) (@ tptp.sigma_1483971331real_n M))) (@ tptp.sigma_522684908real_n M)) (=> (@ (@ tptp.member1746150050real_n C2) (@ tptp.sigma_1483971331real_n N)) (= (@ (@ tptp.member117715276real_n F) (@ (@ tptp.sigma_1185134568real_n (@ (@ tptp.sigma_1052429895real_n M) Omega)) N)) (@ (@ tptp.member117715276real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (__flatten_var_0 tptp.finite1489363574real_n)) (@ (@ (@ (@ tptp.if_Fin413489477real_n (@ (@ tptp.member1746150050real_n X) Omega)) (@ F X)) C2) __flatten_var_0))) (@ (@ tptp.sigma_1185134568real_n M) N))))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (N tptp.sigma_1466784463real_n) (M2 tptp.sigma_1466784463real_n) (N2 tptp.sigma_1466784463real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (= M N) (=> (= M2 N2) (=> (forall ((W tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n W) (@ tptp.sigma_476185326real_n M)) (= (@ F W) (@ G W)))) (= (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n M) M2)) (@ (@ tptp.member1746150050real_n G) (@ (@ tptp.sigma_439801790real_n N) N2)))))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (A2 tptp.sigma_1466784463real_n) (X2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n M) A2)) (=> (@ (@ tptp.member1352538125real_n X2) (@ tptp.sigma_476185326real_n M)) (@ (@ tptp.member1352538125real_n (@ F X2)) (@ tptp.sigma_476185326real_n A2)))))) 0.48/0.75 (assert (forall ((C2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C2))) (=> (@ _let_1 (@ (@ tptp.inf_in632889204real_n A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2)))))))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n) (C tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.minus_1686442501real_n (@ (@ tptp.inf_in1974387902real_n A2) C)))) (= (@ _let_1 (@ (@ tptp.inf_in1974387902real_n B2) C)) (@ _let_1 B2))))) 0.48/0.75 (assert (= tptp.plus_p585657087real_n (lambda ((A3 tptp.finite1489363574real_n) (B4 tptp.finite1489363574real_n)) (@ (@ tptp.plus_p585657087real_n B4) A3)))) 0.48/0.75 (assert (forall ((A tptp.finite964658038_int_n)) (let ((_let_1 (@ tptp.comple230862828real_n tptp.lebesg260170249real_n))) (let ((_let_2 (@ tptp.sigma_1235138647real_n _let_1))) (let ((_let_3 (@ tptp.t2 A))) (=> (@ (@ tptp.member223413699real_n _let_3) _let_2) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage1233683625real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.plus_p585657087real_n X) (@ tptp.minkow1134813771n_real A)))) _let_3)) (@ tptp.sigma_476185326real_n _let_1))) _let_2))))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (Y3 tptp.set_Fi1058188332real_n) (Z tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n X2))) (= (@ (@ tptp.inf_in1974387902real_n (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.inf_in1974387902real_n Y3) Z)))))) 0.48/0.75 (assert (forall ((X4 tptp.set_Fi1326602817real_n) (Y tptp.set_Fi1326602817real_n) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n)) (G (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (N tptp.sigma_1466784463real_n)) (=> (= X4 Y) (=> (forall ((X3 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1746150050real_n X3) Y) (= (@ F X3) (@ G X3)))) (=> (= (@ tptp.sigma_1235138647real_n M) (@ tptp.sigma_1235138647real_n N)) (= (@ (@ (@ tptp.sigma_136294295real_n X4) F) M) (@ (@ (@ tptp.sigma_136294295real_n Y) G) N))))))) 0.48/0.75 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_107786596real_n) (A2 tptp.sigma_107786596real_n) (X2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member117715276real_n F) (@ (@ tptp.sigma_1185134568real_n M) A2)) (=> (@ (@ tptp.member1746150050real_n X2) (@ tptp.sigma_1483971331real_n M)) (@ (@ tptp.member1746150050real_n (@ F X2)) (@ tptp.sigma_1483971331real_n A2)))))) 0.48/0.75 (assert (forall ((B tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1352538125real_n B) (@ (@ tptp.image_439535603real_n F) A2)) (not (forall ((X3 tptp.finite1489363574real_n)) (=> (= B (@ F X3)) (not (@ (@ tptp.member1352538125real_n X3) A2)))))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.image_439535603real_n F) (@ (@ tptp.image_439535603real_n G) A2)) (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ F (@ G X)))) A2)))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M2 tptp.sigma_1466784463real_n)) (let ((_let_1 (@ (@ tptp.sigma_439801790real_n M) M2))) (=> (forall ((W tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n W) (@ tptp.sigma_476185326real_n M)) (= (@ F W) (@ G W)))) (= (@ (@ tptp.member1746150050real_n F) _let_1) (@ (@ tptp.member1746150050real_n G) _let_1)))))) 0.48/0.75 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n)) (M tptp.sigma_107786596real_n) (A2 tptp.sigma_1422848389real_n) (X2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member640587117real_n F) (@ (@ tptp.sigma_364818953real_n M) A2)) (=> (@ (@ tptp.member1746150050real_n X2) (@ tptp.sigma_1483971331real_n M)) (@ (@ tptp.member223413699real_n (@ F X2)) (@ tptp.sigma_607186084real_n A2)))))) 0.48/0.75 (assert (forall ((X2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (let ((_let_1 (@ tptp.member1746150050real_n X2))) (= (@ _let_1 (@ (@ tptp.inf_in146441683real_n A2) (@ tptp.collec1190264032real_n P))) (and (@ _let_1 A2) (@ P X2)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1058188332real_n) (P (-> tptp.finite1489363574real_n Bool))) (= (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P X) (@ (@ tptp.member1352538125real_n X) (@ (@ tptp.image_439535603real_n F) A2))))) (@ (@ tptp.image_439535603real_n F) (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) A2) (@ P (@ F X))))))))) 0.48/0.75 (assert (forall ((C tptp.set_Fi1058188332real_n) (A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n C))) (= (@ _let_1 (@ (@ tptp.minus_1686442501real_n A2) B2)) (@ (@ tptp.minus_1686442501real_n (@ _let_1 A2)) (@ _let_1 B2)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n)) (= (@ (@ tptp.sigma_439801790real_n tptp.lebesg260170249real_n) M) (@ (@ tptp.sigma_439801790real_n tptp.borel_676189912real_n) M)))) 0.48/0.75 (assert (forall ((M tptp.sigma_1422848389real_n) (P (-> tptp.set_Fi1058188332real_n Bool)) (Q (-> tptp.set_Fi1058188332real_n Bool))) (let ((_let_1 (@ tptp.sigma_433815053real_n M))) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ P X) (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)))))) _let_1) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)) (@ Q X))))) _let_1) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)) (or (@ Q X) (@ P X)))))) _let_1)))))) 0.48/0.75 (assert (forall ((X2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (B tptp.set_Fi1058188332real_n) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member1746150050real_n X2) A2) (=> (= B (@ F X2)) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_128879038real_n F) A2)))))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B2 tptp.set_Fi1326602817real_n)) (= (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage2134951412real_n F) B2)) (@ (@ tptp.member1746150050real_n (@ F A)) B2)))) 0.48/0.75 (assert (forall ((S tptp.set_Fi1058188332real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n)) (let ((_let_1 (@ (@ tptp.sigma_439801790real_n (@ (@ tptp.sigma_346513458real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) S)) M))) (=> (forall ((X3 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X3) S) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.member1746150050real_n F) _let_1) (@ (@ tptp.member1746150050real_n G) _let_1)))))) 0.48/0.75 (assert (forall ((I tptp.finite1489363574real_n) (J tptp.finite1489363574real_n) (K tptp.finite1489363574real_n) (L tptp.finite1489363574real_n)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_p585657087real_n I) K) (@ (@ tptp.plus_p585657087real_n J) L))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (M2 tptp.sigma_1466784463real_n) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (P (-> tptp.finite1489363574real_n Bool))) (let ((_let_1 (@ (@ tptp.sigma_439801790real_n M) M2))) (=> (@ (@ tptp.member1746150050real_n F) _let_1) (=> (@ (@ tptp.member1746150050real_n G) _let_1) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P X) (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)))))) (@ tptp.sigma_1235138647real_n M)) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ (@ tptp.if_Fin127821360real_n (@ P X)) (@ F X)) (@ G X)))) _let_1))))))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (M tptp.sigma_1422848389real_n) (A2 tptp.sigma_1422848389real_n) (X2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1734791438real_n F) (@ (@ tptp.sigma_239294762real_n M) A2)) (=> (@ (@ tptp.member223413699real_n X2) (@ tptp.sigma_607186084real_n M)) (@ (@ tptp.member223413699real_n (@ F X2)) (@ tptp.sigma_607186084real_n A2)))))) 0.48/0.75 (assert (forall ((X2 tptp.finite1489363574real_n) (Y3 tptp.finite1489363574real_n)) (= (@ (@ (@ tptp.if_Fin127821360real_n false) X2) Y3) Y3))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_se2111327970real_n) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (= (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) (@ (@ tptp.image_352856126real_n F) A2)) (@ P X)))) (@ (@ tptp.image_352856126real_n F) (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ P (@ F X)) (@ (@ tptp.member223413699real_n X) A2)))))))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (A tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n (@ F A)) A2) (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage784510485real_n F) A2))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.inf_in1974387902real_n X2) X2) X2))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (M2 tptp.sigma_1466784463real_n)) (=> (= (@ tptp.sigma_1235138647real_n M) (@ tptp.sigma_1235138647real_n M2)) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) X)) (@ (@ tptp.sigma_439801790real_n M) M2))))) 0.48/0.75 (assert (= tptp.inf_in146441683real_n (lambda ((A4 tptp.set_Fi1326602817real_n) (B3 tptp.set_Fi1326602817real_n)) (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (let ((_let_1 (@ tptp.member1746150050real_n X))) (and (@ _let_1 A4) (@ _let_1 B3)))))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (= (= A (@ (@ tptp.plus_p585657087real_n A) B)) (= B tptp.zero_z200130687real_n)))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (P (-> tptp.finite1489363574real_n Bool))) (let ((_let_1 (@ tptp.sigma_1235138647real_n M))) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P X) (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)))))) _let_1) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (not (@ P X)))))) _let_1))))) 0.48/0.75 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A))) 0.48/0.75 (assert (forall ((A tptp.finite964658038_int_n)) (let ((_let_1 (@ tptp.comple230862828real_n tptp.lebesg260170249real_n))) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.plus_p585657087real_n X) (@ tptp.minkow1134813771n_real A)))) (@ (@ tptp.sigma_439801790real_n _let_1) _let_1))))) 0.48/0.75 (assert (= tptp.inf_in146441683real_n (lambda ((A4 tptp.set_Fi1326602817real_n) (B3 tptp.set_Fi1326602817real_n)) (@ tptp.collec1190264032real_n (@ (@ tptp.inf_in32002162al_n_o (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (@ (@ tptp.member1746150050real_n X) A4))) (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (@ (@ tptp.member1746150050real_n X) B3))))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (S2 tptp.set_Fi1058188332real_n) (T3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.image_439535603real_n (@ tptp.plus_p585657087real_n A)))) (= (@ _let_1 (@ (@ tptp.minus_1686442501real_n S2) T3)) (@ (@ tptp.minus_1686442501real_n (@ _let_1 S2)) (@ _let_1 T3)))))) 0.48/0.75 (assert (forall ((X2 tptp.finite1489363574real_n) (A2 tptp.set_Fi1058188332real_n) (P (-> tptp.finite1489363574real_n Bool))) (let ((_let_1 (@ tptp.member1352538125real_n X2))) (= (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A2) (@ tptp.collec321817931real_n P))) (and (@ _let_1 A2) (@ P X2)))))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (B2 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage784510485real_n F) B2)) (@ (@ tptp.member223413699real_n (@ F A)) B2)))) 0.48/0.75 (assert (forall ((X2 tptp.finite1489363574real_n) (A2 tptp.set_Fi1058188332real_n) (B tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1352538125real_n X2) A2) (=> (= B (@ F X2)) (@ (@ tptp.member1352538125real_n B) (@ (@ tptp.image_439535603real_n F) A2)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (let ((_let_1 (@ (@ tptp.sigma_439801790real_n M) tptp.borel_676189912real_n))) (=> (@ (@ tptp.member1746150050real_n F) _let_1) (=> (@ (@ tptp.member1746150050real_n G) _let_1) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n (@ F X)) (@ G X)))) _let_1)))))) 0.48/0.75 (assert (forall ((A (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B2 tptp.set_Fi1326602817real_n)) (= (@ (@ tptp.member1746150050real_n A) (@ (@ tptp.vimage180751827real_n F) B2)) (@ (@ tptp.member1746150050real_n (@ F A)) B2)))) 0.48/0.75 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.minus_1037315151real_n A))) (= (@ _let_1 (@ (@ tptp.plus_p585657087real_n B) C2)) (@ (@ tptp.minus_1037315151real_n (@ _let_1 C2)) B))))) 0.48/0.75 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n)) (A2 tptp.set_se2111327970real_n) (P (-> tptp.finite1489363574real_n Bool))) (= (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P X) (@ (@ tptp.member1352538125real_n X) (@ (@ tptp.image_1311908777real_n F) A2))))) (@ (@ tptp.image_1311908777real_n F) (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) A2) (@ P (@ F X))))))))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B2 tptp.set_Fi1326602817real_n)) (=> (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage2134951412real_n F) B2)) (@ (@ tptp.member1746150050real_n (@ F A)) B2)))) 0.48/0.75 (assert (forall ((Omega tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (C2 tptp.set_Fi1058188332real_n) (N tptp.sigma_1422848389real_n) (F (-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n Omega) (@ tptp.sigma_476185326real_n M))) (@ tptp.sigma_1235138647real_n M)) (=> (@ (@ tptp.member223413699real_n C2) (@ tptp.sigma_607186084real_n N)) (= (@ (@ tptp.member966061400real_n F) (@ (@ tptp.sigma_566919540real_n (@ (@ tptp.sigma_346513458real_n M) Omega)) N)) (@ (@ tptp.member966061400real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ (@ tptp.if_set11487206real_n (@ (@ tptp.member1352538125real_n X) Omega)) (@ F X)) C2))) (@ (@ tptp.sigma_566919540real_n M) N))))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (= (@ (@ tptp.minus_1037315151real_n A) (@ (@ tptp.minus_1037315151real_n B) C2)) (@ (@ tptp.minus_1037315151real_n (@ (@ tptp.plus_p585657087real_n A) C2)) B)))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1058188332real_n) (P (-> tptp.finite1489363574real_n Bool))) (=> (exists ((X5 tptp.finite1489363574real_n)) (and (@ P X5) (@ (@ tptp.member1352538125real_n X5) (@ (@ tptp.image_439535603real_n F) A2)))) (exists ((X3 tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X3) A2) (@ P (@ F X3))))))) 0.48/0.75 (assert (forall ((S tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n)) (=> (@ (@ tptp.member223413699real_n S) (@ tptp.sigma_1235138647real_n M)) (= (@ (@ tptp.comple1390568924real_n M) S) S)))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A2))) (let ((_let_2 (@ tptp.sigma_346513458real_n M))) (let ((_let_3 (@ tptp.sigma_1235138647real_n M))) (let ((_let_4 (@ tptp.sigma_476185326real_n M))) (=> (@ (@ tptp.member223413699real_n (@ _let_1 _let_4)) _let_3) (=> (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n B2) _let_4)) _let_3) (= (@ (@ tptp.sigma_346513458real_n (@ _let_2 A2)) B2) (@ _let_2 (@ _let_1 B2))))))))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (N tptp.sigma_1466784463real_n) (Omega tptp.set_Fi1058188332real_n)) (=> (= (@ tptp.sigma_1235138647real_n M) (@ tptp.sigma_1235138647real_n N)) (= (@ tptp.sigma_1235138647real_n (@ (@ tptp.sigma_346513458real_n M) Omega)) (@ tptp.sigma_1235138647real_n (@ (@ tptp.sigma_346513458real_n N) Omega)))))) 0.48/0.75 (assert (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M4) N3) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N3) M4) tptp.zero_zero_nat) (= M4 N3))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (A2 tptp.sigma_107786596real_n) (X2 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member408431031real_n F) (@ (@ tptp.sigma_2016438227real_n M) A2)) (=> (@ (@ tptp.member1352538125real_n X2) (@ tptp.sigma_476185326real_n M)) (@ (@ tptp.member1746150050real_n (@ F X2)) (@ tptp.sigma_1483971331real_n A2)))))) 0.48/0.75 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A))) 0.48/0.75 (assert (forall ((M tptp.sigma_1422848389real_n) (F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n)) (N tptp.sigma_1466784463real_n)) (=> (forall ((X3 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X3) (@ tptp.sigma_607186084real_n M)) (@ (@ tptp.member1352538125real_n (@ F X3)) (@ tptp.sigma_476185326real_n N)))) (=> (forall ((A6 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n A6) (@ tptp.sigma_1235138647real_n N)) (@ (@ tptp.member1475136633real_n (@ (@ tptp.inf_in632889204real_n (@ (@ tptp.vimage973736031real_n F) A6)) (@ tptp.sigma_607186084real_n M))) (@ tptp.sigma_433815053real_n M)))) (@ (@ tptp.member1759501912real_n F) (@ (@ tptp.sigma_1333364596real_n M) N)))))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (B tptp.set_Fi1058188332real_n) (C2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A))) (= (@ (@ tptp.inf_in1974387902real_n (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_in1974387902real_n B) C2)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_107786596real_n) (P Bool)) (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and P (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)))))) (@ tptp.sigma_522684908real_n M)))) 0.48/0.75 (assert (forall ((M4 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M4) tptp.zero_zero_nat) M4))) 0.48/0.75 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (X2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n)) (=> (= B (@ F X2)) (=> (@ (@ tptp.member223413699real_n X2) A2) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1661509983real_n F) A2)))))) 0.48/0.75 (assert (forall ((S tptp.set_nat)) (= (@ (@ tptp.image_nat_nat (@ tptp.plus_plus_nat tptp.zero_zero_nat)) S) S))) 0.48/0.75 (assert (forall ((S tptp.set_Fi1058188332real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (Y3 tptp.set_Fi1058188332real_n)) (=> (forall ((W tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n W) S) (= (@ F W) (@ G W)))) (= (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage1233683625real_n F) Y3)) S) (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage1233683625real_n G) Y3)) S))))) 0.48/0.75 (assert (forall ((M4 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M4) M4) tptp.zero_zero_nat))) 0.48/0.75 (assert (forall ((P (-> tptp.finite1489363574real_n Bool))) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n tptp.borel_676189912real_n)) (@ P X))))) (@ tptp.sigma_1235138647real_n tptp.borel_676189912real_n)) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n tptp.lebesg260170249real_n)) (@ P X))))) (@ tptp.sigma_1235138647real_n tptp.lebesg260170249real_n))))) 0.48/0.75 (assert (forall ((Omega tptp.set_se2111327970real_n) (M tptp.sigma_1422848389real_n) (C2 tptp.set_Fi1058188332real_n) (N tptp.sigma_1422848389real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member1475136633real_n (@ (@ tptp.inf_in632889204real_n Omega) (@ tptp.sigma_607186084real_n M))) (@ tptp.sigma_433815053real_n M)) (=> (@ (@ tptp.member223413699real_n C2) (@ tptp.sigma_607186084real_n N)) (= (@ (@ tptp.member1734791438real_n F) (@ (@ tptp.sigma_239294762real_n (@ (@ tptp.sigma_993999336real_n M) Omega)) N)) (@ (@ tptp.member1734791438real_n (lambda ((X tptp.set_Fi1058188332real_n)) (@ (@ (@ tptp.if_set11487206real_n (@ (@ tptp.member223413699real_n X) Omega)) (@ F X)) C2))) (@ (@ tptp.sigma_239294762real_n M) N))))))) 0.48/0.75 (assert (forall ((A tptp.finite964658038_int_n)) (@ (@ tptp.member223413699real_n (@ tptp.t2 A)) (@ tptp.sigma_1235138647real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n))))) 0.48/0.75 (assert (forall ((S tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.image_439535603real_n (@ tptp.plus_p585657087real_n tptp.zero_z200130687real_n)) S) S))) 0.48/0.75 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (A2 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_1661509983real_n F) A2)) (not (forall ((X3 tptp.set_Fi1058188332real_n)) (=> (= B (@ F X3)) (not (@ (@ tptp.member223413699real_n X3) A2)))))))) 0.48/0.75 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (P (-> tptp.finite1489363574real_n Bool))) (= (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P X) (@ (@ tptp.member1352538125real_n X) (@ (@ tptp.image_449906696real_n F) A2))))) (@ (@ tptp.image_449906696real_n F) (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) A2) (@ P (@ F X))))))))) 0.48/0.75 (assert (forall ((C2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C2))) (= (@ _let_1 (@ (@ tptp.minus_1698615483real_n A2) B2)) (and (@ _let_1 A2) (not (@ _let_1 B2))))))) 0.48/0.75 (assert (forall ((Z tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.member1352538125real_n Z) (@ (@ tptp.image_439535603real_n F) A2)) (exists ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) A2) (= Z (@ F X))))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.minus_1037315151real_n A))) (= (@ (@ tptp.minus_1037315151real_n (@ _let_1 C2)) B) (@ (@ tptp.minus_1037315151real_n (@ _let_1 B)) C2))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n)) (= (@ (@ tptp.plus_p585657087real_n tptp.zero_z200130687real_n) A) A))) 0.48/0.75 (assert (= tptp.inf_in632889204real_n (lambda ((A4 tptp.set_se2111327970real_n) (B3 tptp.set_se2111327970real_n)) (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member223413699real_n X))) (and (@ _let_1 B3) (@ _let_1 A4)))))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (= (= A (@ (@ tptp.plus_p585657087real_n B) A)) (= B tptp.zero_z200130687real_n)))) 0.48/0.75 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C2) B) A) (= C2 (@ (@ tptp.minus_minus_nat A) B))))) 0.48/0.75 (assert (forall ((B tptp.finite1489363574real_n) (A tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (= (= (@ (@ tptp.plus_p585657087real_n B) A) (@ (@ tptp.plus_p585657087real_n C2) A)) (= B C2)))) 0.48/0.75 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B2 tptp.set_Fi1326602817real_n)) (=> (= (@ F A) B) (=> (@ (@ tptp.member1746150050real_n B) B2) (@ (@ tptp.member1746150050real_n A) (@ (@ tptp.vimage180751827real_n F) B2)))))) 0.48/0.75 (assert (forall ((B (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n)) (=> (@ (@ tptp.member1746150050real_n B) (@ (@ tptp.image_1123376925real_n F) A2)) (not (forall ((X3 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (= B (@ F X3)) (not (@ (@ tptp.member1746150050real_n X3) A2)))))))) 0.48/0.75 (assert (forall ((C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (B2 tptp.set_Fi1326602817real_n)) (let ((_let_1 (@ tptp.member1746150050real_n C2))) (=> (@ _let_1 (@ (@ tptp.minus_725016986real_n A2) B2)) (@ _let_1 A2))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1422848389real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (N tptp.sigma_1422848389real_n)) (=> (forall ((X3 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n X3) (@ tptp.sigma_607186084real_n M)) (@ (@ tptp.member223413699real_n (@ F X3)) (@ tptp.sigma_607186084real_n N)))) (=> (forall ((A6 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member1475136633real_n A6) (@ tptp.sigma_433815053real_n N)) (@ (@ tptp.member1475136633real_n (@ (@ tptp.inf_in632889204real_n (@ (@ tptp.vimage784510485real_n F) A6)) (@ tptp.sigma_607186084real_n M))) (@ tptp.sigma_433815053real_n M)))) (@ (@ tptp.member1734791438real_n F) (@ (@ tptp.sigma_239294762real_n M) N)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n)) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) X)) (@ (@ tptp.sigma_439801790real_n M) M)))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n)) (= (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n X) A2))) A2))) 0.48/0.75 (assert (forall ((M tptp.sigma_107786596real_n) (P (-> tptp.nat (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool)) (A2 tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ P I2) X) (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)))))) (@ tptp.sigma_522684908real_n M))) (@ (@ tptp.member2104752728real_n (@ (@ tptp.inf_in146441683real_n (@ (@ tptp.vimage2098059032_n_nat (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (@ tptp.ord_Least_nat (lambda ((J2 tptp.nat)) (@ (@ P J2) X))))) A2)) (@ tptp.sigma_1483971331real_n M))) (@ tptp.sigma_522684908real_n M))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n)) (= (@ (@ tptp.minus_1037315151real_n A) tptp.zero_z200130687real_n) A))) 0.48/0.75 (assert (forall ((X2 tptp.finite1489363574real_n) (A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1352538125real_n X2) (@ (@ tptp.plus_p1606848693real_n A2) B2)) (not (forall ((A5 tptp.finite1489363574real_n) (B5 tptp.finite1489363574real_n)) (=> (= X2 (@ (@ tptp.plus_p585657087real_n A5) B5)) (=> (@ (@ tptp.member1352538125real_n A5) A2) (not (@ (@ tptp.member1352538125real_n B5) B2))))))))) 0.48/0.75 (assert (forall ((S tptp.set_Fi1058188332real_n)) (= (@ tptp.sigma_476185326real_n (@ (@ tptp.sigma_346513458real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) S)) S))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (Y3 tptp.set_Fi1058188332real_n)) (= (@ (@ (@ tptp.if_set11487206real_n true) X2) Y3) X2))) 0.48/0.75 (assert (forall ((X2 tptp.finite1489363574real_n) (A2 tptp.set_Fi1058188332real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1352538125real_n X2) A2) (@ (@ tptp.member1352538125real_n (@ F X2)) (@ (@ tptp.image_439535603real_n F) A2))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member223413699real_n X2) A2) (@ (@ tptp.member1746150050real_n (@ F X2)) (@ (@ tptp.image_352856126real_n F) A2))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (N tptp.sigma_107786596real_n)) (=> (forall ((X3 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X3) (@ tptp.sigma_476185326real_n M)) (@ (@ tptp.member1746150050real_n (@ F X3)) (@ tptp.sigma_1483971331real_n N)))) (=> (forall ((A6 tptp.set_Fi1326602817real_n)) (=> (@ (@ tptp.member2104752728real_n A6) (@ tptp.sigma_522684908real_n N)) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage1059850558real_n F) A6)) (@ tptp.sigma_476185326real_n M))) (@ tptp.sigma_1235138647real_n M)))) (@ (@ tptp.member408431031real_n F) (@ (@ tptp.sigma_2016438227real_n M) N)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (S tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n (@ (@ tptp.sigma_346513458real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) S)) tptp.borel_676189912real_n)) (forall ((T2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n T2) (@ tptp.sigma_1235138647real_n tptp.borel_676189912real_n)) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n (@ F X)) T2) (@ (@ tptp.member1352538125real_n X) S))))) (@ tptp.sigma_1235138647real_n (@ (@ tptp.sigma_346513458real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)) S)))))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n A))) (= (@ (@ tptp.plus_p585657087real_n (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_p585657087real_n B) C2)))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (P (-> tptp.finite1489363574real_n Bool))) (= (@ (@ tptp.member1352538125real_n A) (@ tptp.collec321817931real_n P)) (@ P A)))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (A tptp.set_Fi1058188332real_n) (B tptp.set_Fi1058188332real_n) (B2 tptp.set_se2111327970real_n)) (=> (= (@ F A) B) (=> (@ (@ tptp.member223413699real_n B) B2) (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage784510485real_n F) B2)))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (= (= (@ (@ tptp.minus_1037315151real_n A) B) C2) (= A (@ (@ tptp.plus_p585657087real_n C2) B))))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2))))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n) (K tptp.set_Fi1058188332real_n) (A tptp.set_Fi1058188332real_n) (B tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.inf_in1974387902real_n A2) B) (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A) B))))))) 0.48/0.75 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n)) (A2 tptp.set_Fi1326602817real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (= (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ P X) (@ (@ tptp.member223413699real_n X) (@ (@ tptp.image_128879038real_n F) A2))))) (@ (@ tptp.image_128879038real_n F) (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ P (@ F X)) (@ (@ tptp.member1746150050real_n X) A2)))))))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (B tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.sigma_1235138647real_n M))) (=> (@ (@ tptp.member223413699real_n A) _let_1) (=> (@ (@ tptp.member223413699real_n B) _let_1) (@ (@ tptp.member223413699real_n (@ (@ tptp.minus_1686442501real_n A) B)) _let_1)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (let ((_let_1 (@ (@ tptp.sigma_439801790real_n M) tptp.borel_676189912real_n))) (=> (@ (@ tptp.member1746150050real_n F) _let_1) (=> (@ (@ tptp.member1746150050real_n G) _let_1) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.plus_p585657087real_n (@ F X)) (@ G X)))) _let_1)))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member223413699real_n X2) A2) (=> (= B (@ F X2)) (@ (@ tptp.member1746150050real_n B) (@ (@ tptp.image_352856126real_n F) A2)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.vimage1233683625real_n F))) (= (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A2) B2)) (@ (@ tptp.inf_in1974387902real_n (@ _let_1 A2)) (@ _let_1 B2)))))) 0.48/0.75 (assert (forall ((B2 tptp.finite1489363574real_n) (K tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (A tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n A))) (let ((_let_2 (@ tptp.plus_p585657087real_n K))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B)))))))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (B2 tptp.set_se2111327970real_n)) (= (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage784510485real_n F) B2)) (@ (@ tptp.member223413699real_n (@ F A)) B2)))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n)) (let ((_let_1 (@ tptp.sigma_439801790real_n M))) (= (@ _let_1 tptp.lebesg260170249real_n) (@ _let_1 tptp.borel_676189912real_n))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (A2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n tptp.borel_676189912real_n) M)) (=> (@ (@ tptp.member223413699real_n A2) (@ tptp.sigma_1235138647real_n M)) (@ (@ tptp.member223413699real_n (@ (@ tptp.vimage1233683625real_n F) A2)) (@ tptp.sigma_1235138647real_n tptp.borel_676189912real_n)))))) 0.48/0.75 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (N tptp.sigma_1466784463real_n) (X4 tptp.set_Fi1058188332real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (let ((_let_1 (@ (@ tptp.sigma_821351682real_n X4) F))) (=> (= (@ tptp.sigma_1235138647real_n M) (@ tptp.sigma_1235138647real_n N)) (= (@ tptp.sigma_1235138647real_n (@ _let_1 M)) (@ tptp.sigma_1235138647real_n (@ _let_1 N))))))) 0.48/0.75 (assert (forall ((C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (B2 tptp.set_Fi1326602817real_n)) (let ((_let_1 (@ tptp.member1746150050real_n C2))) (=> (@ _let_1 (@ (@ tptp.inf_in146441683real_n A2) B2)) (@ _let_1 A2))))) 0.48/0.75 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n)) (A (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n (@ F A)) A2) (@ (@ tptp.member1746150050real_n A) (@ (@ tptp.vimage1910974324real_n F) A2))))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (= (@ (@ tptp.member223413699real_n A) (@ tptp.collec452821761real_n P)) (@ P A)))) 0.48/0.75 (assert (forall ((B tptp.finite1489363574real_n) (A tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (=> (= (@ (@ tptp.plus_p585657087real_n B) A) (@ (@ tptp.plus_p585657087real_n C2) A)) (= B C2)))) 0.48/0.75 (assert (forall ((Omega tptp.set_Fi1326602817real_n) (M tptp.sigma_107786596real_n) (C2 tptp.set_Fi1058188332real_n) (N tptp.sigma_1422848389real_n) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member2104752728real_n (@ (@ tptp.inf_in146441683real_n Omega) (@ tptp.sigma_1483971331real_n M))) (@ tptp.sigma_522684908real_n M)) (=> (@ (@ tptp.member223413699real_n C2) (@ tptp.sigma_607186084real_n N)) (= (@ (@ tptp.member640587117real_n F) (@ (@ tptp.sigma_364818953real_n (@ (@ tptp.sigma_1052429895real_n M) Omega)) N)) (@ (@ tptp.member640587117real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (@ (@ (@ tptp.if_set11487206real_n (@ (@ tptp.member1746150050real_n X) Omega)) (@ F X)) C2))) (@ (@ tptp.sigma_364818953real_n M) N))))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (Y3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n X2))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2))))) 0.48/0.75 (assert (forall ((C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (B2 tptp.set_Fi1326602817real_n)) (let ((_let_1 (@ tptp.member1746150050real_n C2))) (=> (@ _let_1 (@ (@ tptp.minus_725016986real_n A2) B2)) (not (@ _let_1 B2)))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member223413699real_n X2) A2) (@ (@ tptp.member223413699real_n (@ F X2)) (@ (@ tptp.image_1661509983real_n F) A2))))) 0.48/0.75 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_107786596real_n) (N tptp.sigma_107786596real_n) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (=> (@ (@ tptp.member117715276real_n F) (@ (@ tptp.sigma_1185134568real_n M) N)) (=> (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n N)) (@ P X))))) (@ tptp.sigma_522684908real_n N)) (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)) (@ P (@ F X)))))) (@ tptp.sigma_522684908real_n M)))))) 0.48/0.75 (assert (forall ((A2 tptp.finite1489363574real_n) (K tptp.finite1489363574real_n) (A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_1037315151real_n A2) B) (@ _let_1 (@ (@ tptp.minus_1037315151real_n A) B))))))) 0.48/0.75 (assert (forall ((S tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n)) (=> (@ (@ tptp.member223413699real_n S) (@ tptp.sigma_1235138647real_n (@ tptp.comple230862828real_n M))) (@ (@ tptp.member223413699real_n (@ (@ tptp.comple1390568924real_n M) S)) (@ tptp.sigma_1235138647real_n M))))) 0.48/0.75 (assert (forall ((X2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n))) (=> (@ (@ tptp.member1746150050real_n X2) A2) (@ (@ tptp.member223413699real_n (@ F X2)) (@ (@ tptp.image_128879038real_n F) A2))))) 0.48/0.75 (assert (forall ((P (-> tptp.finite1489363574real_n Bool)) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (Q (-> tptp.finite1489363574real_n Bool))) (=> (forall ((X3 tptp.finite1489363574real_n)) (= (@ P (@ F X3)) (@ Q X3))) (= (@ (@ tptp.vimage1233683625real_n F) (@ tptp.collec321817931real_n P)) (@ tptp.collec321817931real_n Q))))) 0.48/0.75 (assert (forall ((C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (B2 tptp.set_Fi1326602817real_n)) (let ((_let_1 (@ tptp.member1746150050real_n C2))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.minus_725016986real_n A2) B2))))))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n)) (=> (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage2134951412real_n F) A2)) (@ (@ tptp.member1746150050real_n (@ F A)) A2)))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (P (-> tptp.finite1489363574real_n Bool)) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (N tptp.sigma_1466784463real_n)) (let ((_let_1 (@ tptp.sigma_346513458real_n M))) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (@ P X))))) (@ tptp.sigma_1235138647real_n M)) (= (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ (@ tptp.if_Fin127821360real_n (@ P X)) (@ F X)) (@ G X)))) (@ (@ tptp.sigma_439801790real_n M) N)) (and (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n (@ _let_1 (@ tptp.collec321817931real_n P))) N)) (@ (@ tptp.member1746150050real_n G) (@ (@ tptp.sigma_439801790real_n (@ _let_1 (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (not (@ P X)))))) N)))))))) 0.48/0.75 (assert (forall ((A tptp.finite964658038_int_n) (B tptp.finite964658038_int_n)) (= (= (@ tptp.minkow1134813771n_real A) (@ tptp.minkow1134813771n_real B)) (= A B)))) 0.48/0.75 (assert (forall ((X2 tptp.finite1489363574real_n) (Y3 tptp.finite1489363574real_n)) (= (= X2 (@ (@ tptp.plus_p585657087real_n X2) Y3)) (= Y3 tptp.zero_z200130687real_n)))) 0.48/0.75 (assert (forall ((A (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n)) (B2 tptp.set_se2111327970real_n)) (= (@ (@ tptp.member1746150050real_n A) (@ (@ tptp.vimage1910974324real_n F) B2)) (@ (@ tptp.member223413699real_n (@ F A)) B2)))) 0.48/0.75 (assert (= tptp.inf_in1974387902real_n (lambda ((A4 tptp.set_Fi1058188332real_n) (B3 tptp.set_Fi1058188332real_n)) (@ tptp.collec321817931real_n (@ (@ tptp.inf_in1620715847al_n_o (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n X) A4))) (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n X) B3))))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1422848389real_n) (P (-> tptp.set_Fi1058188332real_n Bool)) (Q (-> tptp.set_Fi1058188332real_n Bool))) (let ((_let_1 (@ tptp.sigma_433815053real_n M))) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ P X) (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)))))) _let_1) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)) (@ Q X))))) _let_1) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (=> (@ Q X) (@ P X)) (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)))))) _let_1)))))) 0.48/0.75 (assert (forall ((X2 tptp.nat) (Y3 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X2) Y3)) (and (= Y3 tptp.zero_zero_nat) (= X2 tptp.zero_zero_nat))))) 0.48/0.75 (assert (= (@ tptp.sigma_1235138647real_n tptp.lebesg260170249real_n) (@ tptp.sigma_1235138647real_n tptp.borel_676189912real_n))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (P (-> tptp.finite1489363574real_n Bool)) (Q (-> tptp.finite1489363574real_n Bool))) (let ((_let_1 (@ tptp.sigma_1235138647real_n M))) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (@ P X))))) _let_1) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ Q X) (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)))))) _let_1) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (or (@ Q X) (@ P X)) (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)))))) _let_1)))))) 0.48/0.75 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A) B))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (M2 tptp.sigma_1466784463real_n)) (=> (= (@ tptp.sigma_1235138647real_n M) (@ tptp.sigma_1235138647real_n M2)) (= (@ tptp.sigma_476185326real_n M) (@ tptp.sigma_476185326real_n M2))))) 0.48/0.75 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (P (-> tptp.finite1489363574real_n Bool)) (Q (-> tptp.finite1489363574real_n Bool))) (let ((_let_1 (@ tptp.sigma_1235138647real_n M))) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P X) (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)))))) _let_1) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (@ Q X))))) _let_1) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (@ P X) (@ Q X))))) _let_1)))))) 0.48/0.75 (assert (forall ((Y tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.vimage1233683625real_n (lambda ((X tptp.finite1489363574real_n)) X)) Y) Y))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (Omega tptp.set_Fi1058188332real_n)) (= (@ tptp.sigma_476185326real_n (@ (@ tptp.sigma_346513458real_n M) Omega)) (@ (@ tptp.inf_in1974387902real_n Omega) (@ tptp.sigma_476185326real_n M))))) 0.48/0.75 (assert (forall ((M tptp.sigma_107786596real_n) (Pb Bool)) (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)) Pb)))) (@ tptp.sigma_522684908real_n M)))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A tptp.set_Fi1058188332real_n) (A2 tptp.set_Fi1326602817real_n)) (=> (@ (@ tptp.member1746150050real_n (@ F A)) A2) (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage2134951412real_n F) A2))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (C tptp.set_Fi1058188332real_n) (B tptp.finite1489363574real_n) (D tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1352538125real_n A) C) (=> (@ (@ tptp.member1352538125real_n B) D) (@ (@ tptp.member1352538125real_n (@ (@ tptp.plus_p585657087real_n A) B)) (@ (@ tptp.plus_p1606848693real_n C) D)))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n)) (= (@ (@ tptp.minus_1037315151real_n A) tptp.zero_z200130687real_n) A))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n) (D2 tptp.finite1489363574real_n)) (=> (= (@ (@ tptp.minus_1037315151real_n A) B) (@ (@ tptp.minus_1037315151real_n C2) D2)) (= (= A B) (= C2 D2))))) 0.48/0.75 (assert (forall ((C2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_in632889204real_n A2) B2))))))) 0.48/0.75 (assert (forall ((X2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (Y3 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (= (@ (@ (@ tptp.if_Fin413489477real_n false) X2) Y3) Y3))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n) (C tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A2))) (let ((_let_2 (@ tptp.inf_in1974387902real_n B2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C))))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (Y3 tptp.set_Fi1058188332real_n) (Z tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n X2))) (let ((_let_2 (@ tptp.inf_in1974387902real_n Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z))))))) 0.48/0.75 (assert (forall ((B2 tptp.set_Fi1058188332real_n) (K tptp.set_Fi1058188332real_n) (B tptp.set_Fi1058188332real_n) (A tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A))) (let ((_let_2 (@ tptp.inf_in1974387902real_n K))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B)))))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (Y3 tptp.set_Fi1058188332real_n)) (= (@ (@ (@ tptp.if_set11487206real_n false) X2) Y3) Y3))) 0.48/0.75 (assert (forall ((C2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C2))) (=> (@ _let_1 (@ (@ tptp.inf_in632889204real_n A2) B2)) (@ _let_1 B2))))) 0.48/0.75 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n)) (A (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B tptp.set_Fi1058188332real_n) (B2 tptp.set_se2111327970real_n)) (=> (= (@ F A) B) (=> (@ (@ tptp.member223413699real_n B) B2) (@ (@ tptp.member1746150050real_n A) (@ (@ tptp.vimage1910974324real_n F) B2)))))) 0.48/0.75 (assert (= tptp.minus_1686442501real_n (lambda ((A4 tptp.set_Fi1058188332real_n) (B3 tptp.set_Fi1058188332real_n)) (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.member1352538125real_n X))) (and (not (@ _let_1 B3)) (@ _let_1 A4)))))))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n)) (M tptp.sigma_1422848389real_n) (N tptp.sigma_1466784463real_n) (P (-> tptp.finite1489363574real_n Bool))) (=> (@ (@ tptp.member1759501912real_n F) (@ (@ tptp.sigma_1333364596real_n M) N)) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P X) (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n N)))))) (@ tptp.sigma_1235138647real_n N)) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ P (@ F X)) (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)))))) (@ tptp.sigma_433815053real_n M)))))) 0.48/0.75 (assert (forall ((C2 tptp.finite1489363574real_n) (A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member1352538125real_n C2))) (=> (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A2) B2)) (@ _let_1 A2))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1058188332real_n) (P (-> tptp.finite1489363574real_n Bool))) (=> (forall ((X3 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X3) (@ (@ tptp.image_439535603real_n F) A2)) (@ P X3))) (forall ((X5 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X5) A2) (@ P (@ F X5))))))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n) (C tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.minus_1686442501real_n A2) B2)) C) (@ (@ tptp.minus_1686442501real_n (@ (@ tptp.inf_in1974387902real_n A2) C)) (@ (@ tptp.inf_in1974387902real_n B2) C))))) 0.48/0.75 (assert (forall ((B tptp.finite1489363574real_n) (A tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (= (= (@ (@ tptp.plus_p585657087real_n B) A) (@ (@ tptp.plus_p585657087real_n C2) A)) (= B C2)))) 0.48/0.75 (assert (= tptp.borel_1962407338real_n (lambda ((F2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M3 tptp.sigma_1466784463real_n)) (@ (@ tptp.member1746150050real_n F2) (@ (@ tptp.sigma_439801790real_n M3) tptp.borel_676189912real_n))))) 0.48/0.75 (assert (forall ((B tptp.finite1489363574real_n) (A tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n B))) (let ((_let_2 (@ tptp.plus_p585657087real_n A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2))))))) 0.48/0.75 (assert (forall ((C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (B2 tptp.set_Fi1326602817real_n)) (let ((_let_1 (@ tptp.member1746150050real_n C2))) (=> (@ _let_1 (@ (@ tptp.inf_in146441683real_n A2) B2)) (@ _let_1 B2))))) 0.48/0.75 (assert (forall ((C2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C2))) (=> (@ _let_1 (@ (@ tptp.inf_in632889204real_n A2) B2)) (@ _let_1 A2))))) 0.48/0.75 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A))) 0.48/0.75 (assert (= tptp.inf_in1974387902real_n (lambda ((A3 tptp.set_Fi1058188332real_n) (B4 tptp.set_Fi1058188332real_n)) (@ (@ tptp.inf_in1974387902real_n B4) A3)))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n)) (=> (@ (@ tptp.member223413699real_n X2) (@ tptp.sigma_1235138647real_n M)) (= (@ (@ tptp.inf_in1974387902real_n (@ tptp.sigma_476185326real_n M)) X2) X2)))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (= (@ (@ tptp.minus_1037315151real_n (@ (@ tptp.plus_p585657087real_n A) B)) B) A))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (F (-> tptp.finite1489363574real_n tptp.set_Fi1058188332real_n)) (N tptp.sigma_1422848389real_n)) (=> (forall ((X3 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X3) (@ tptp.sigma_476185326real_n M)) (@ (@ tptp.member223413699real_n (@ F X3)) (@ tptp.sigma_607186084real_n N)))) (=> (forall ((A6 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member1475136633real_n A6) (@ tptp.sigma_433815053real_n N)) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage207290975real_n F) A6)) (@ tptp.sigma_476185326real_n M))) (@ tptp.sigma_1235138647real_n M)))) (@ (@ tptp.member966061400real_n F) (@ (@ tptp.sigma_566919540real_n M) N)))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n)) (= (@ (@ tptp.plus_p585657087real_n A) tptp.zero_z200130687real_n) A))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n X2) (@ (@ tptp.plus_p565022571real_n A2) B2)) (not (forall ((A5 tptp.set_Fi1058188332real_n) (B5 tptp.set_Fi1058188332real_n)) (=> (= X2 (@ (@ tptp.plus_p1606848693real_n A5) B5)) (=> (@ (@ tptp.member223413699real_n A5) A2) (not (@ (@ tptp.member223413699real_n B5) B2))))))))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (X4 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n A2) (@ tptp.sigma_1235138647real_n M)) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage1233683625real_n F) A2)) X4)) (@ tptp.sigma_1235138647real_n (@ (@ (@ tptp.sigma_821351682real_n X4) F) M)))))) 0.48/0.75 (assert (forall ((X2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (B (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1746150050real_n X2) A2) (=> (= B (@ F X2)) (@ (@ tptp.member1746150050real_n B) (@ (@ tptp.image_1123376925real_n F) A2)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_107786596real_n) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n)) (N tptp.sigma_1466784463real_n)) (=> (forall ((X3 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1746150050real_n X3) (@ tptp.sigma_1483971331real_n M)) (@ (@ tptp.member1352538125real_n (@ F X3)) (@ tptp.sigma_476185326real_n N)))) (=> (forall ((A6 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n A6) (@ tptp.sigma_1235138647real_n N)) (@ (@ tptp.member2104752728real_n (@ (@ tptp.inf_in146441683real_n (@ (@ tptp.vimage1072397758real_n F) A6)) (@ tptp.sigma_1483971331real_n M))) (@ tptp.sigma_522684908real_n M)))) (@ (@ tptp.member1695588023real_n F) (@ (@ tptp.sigma_2028985427real_n M) N)))))) 0.48/0.75 (assert (forall ((A2 tptp.finite1489363574real_n) (K tptp.finite1489363574real_n) (A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_p585657087real_n A2) B) (@ _let_1 (@ (@ tptp.plus_p585657087real_n A) B))))))) 0.48/0.75 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat)))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n)) (let ((_let_1 (@ tptp.sigma_1235138647real_n M))) (=> (@ (@ tptp.member223413699real_n A) _let_1) (@ (@ tptp.member223413699real_n (@ (@ tptp.minus_1686442501real_n (@ tptp.sigma_476185326real_n M)) A)) _let_1))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (N tptp.sigma_1466784463real_n)) (=> (forall ((X3 tptp.finite1489363574real_n)) (=> (@ (@ tptp.member1352538125real_n X3) (@ tptp.sigma_476185326real_n M)) (@ (@ tptp.member1352538125real_n (@ F X3)) (@ tptp.sigma_476185326real_n N)))) (=> (forall ((A6 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member223413699real_n A6) (@ tptp.sigma_1235138647real_n N)) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage1233683625real_n F) A6)) (@ tptp.sigma_476185326real_n M))) (@ tptp.sigma_1235138647real_n M)))) (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n M) N)))))) 0.48/0.75 (assert (not (@ (@ tptp.member223413699real_n (@ (@ tptp.vimage1233683625real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.plus_p585657087real_n X) (@ tptp.minkow1134813771n_real tptp.a)))) (@ tptp.t2 tptp.a))) (@ tptp.sigma_1235138647real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n))))) 0.48/0.75 (assert (forall ((C2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C2))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.minus_1698615483real_n A2) B2))))))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (N tptp.sigma_1466784463real_n)) (=> (= A2 B2) (=> (= (@ tptp.sigma_1235138647real_n M) (@ tptp.sigma_1235138647real_n N)) (= (@ tptp.sigma_1235138647real_n (@ (@ tptp.sigma_346513458real_n M) A2)) (@ tptp.sigma_1235138647real_n (@ (@ tptp.sigma_346513458real_n N) B2))))))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (F (-> tptp.set_Fi1058188332real_n tptp.set_Fi1058188332real_n)) (A2 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage784510485real_n F) A2)) (@ (@ tptp.member223413699real_n (@ F A)) A2)))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (A tptp.finite1489363574real_n)) (let ((_let_1 (@ (@ tptp.sigma_439801790real_n M) tptp.borel_676189912real_n))) (=> (@ (@ tptp.member1746150050real_n F) _let_1) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.plus_p585657087real_n A) (@ F X)))) _let_1))))) 0.48/0.75 (assert (forall ((C2 tptp.finite1489363574real_n) (M tptp.sigma_1466784463real_n)) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) C2)) (@ (@ tptp.sigma_439801790real_n M) tptp.borel_676189912real_n)))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n) (C tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A2))) (= (@ (@ tptp.minus_1686442501real_n (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.minus_1686442501real_n B2) C)))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (S2 tptp.set_Fi1058188332real_n) (T3 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.image_439535603real_n (@ tptp.plus_p585657087real_n A)))) (= (@ _let_1 (@ (@ tptp.inf_in1974387902real_n S2) T3)) (@ (@ tptp.inf_in1974387902real_n (@ _let_1 S2)) (@ _let_1 T3)))))) 0.48/0.75 (assert (forall ((X2 tptp.set_Fi1058188332real_n) (Y3 tptp.set_Fi1058188332real_n) (Z tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n X2))) (let ((_let_2 (@ tptp.inf_in1974387902real_n Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z))))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A tptp.finite1489363574real_n) (A2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1352538125real_n (@ F A)) A2) (@ (@ tptp.member1352538125real_n A) (@ (@ tptp.vimage1233683625real_n F) A2))))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (B tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ (@ tptp.inf_in1974387902real_n A) B))) (= (@ (@ tptp.inf_in1974387902real_n _let_1) B) _let_1)))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n A))) (= (@ (@ tptp.plus_p585657087real_n (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_p585657087real_n B) C2)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (L2 tptp.sigma_1466784463real_n) (N tptp.sigma_1466784463real_n) (G (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n)) (let ((_let_1 (@ tptp.sigma_439801790real_n M))) (=> (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n L2) N)) (=> (@ (@ tptp.member1746150050real_n G) (@ _let_1 L2)) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) (@ F (@ G X)))) (@ _let_1 N))))))) 0.48/0.75 (assert (forall ((Omega tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n)) (=> (@ (@ tptp.member223413699real_n Omega) (@ tptp.sigma_1235138647real_n M)) (= (@ tptp.sigma_476185326real_n (@ (@ tptp.sigma_346513458real_n M) Omega)) Omega)))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (B tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.inf_in1974387902real_n A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2))))) 0.48/0.75 (assert (= tptp.inf_in1974387902real_n (lambda ((A4 tptp.set_Fi1058188332real_n) (B3 tptp.set_Fi1058188332real_n)) (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.member1352538125real_n X))) (and (@ _let_1 B3) (@ _let_1 A4)))))))) 0.48/0.75 (assert (forall ((A (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n)) (A2 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member1746150050real_n A) (@ (@ tptp.vimage1910974324real_n F) A2)) (@ (@ tptp.member223413699real_n (@ F A)) A2)))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1352538125real_n A) (@ (@ tptp.vimage1233683625real_n F) B2)) (@ (@ tptp.member1352538125real_n (@ F A)) B2)))) 0.48/0.75 (assert (forall ((C2 tptp.finite1489363574real_n) (A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member1352538125real_n C2))) (=> (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A2) B2)) (@ _let_1 B2))))) 0.48/0.75 (assert (forall ((X2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1746150050real_n X2) A2) (@ (@ tptp.member1746150050real_n (@ F X2)) (@ (@ tptp.image_1123376925real_n F) A2))))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1422848389real_n) (A2 tptp.sigma_107786596real_n) (X2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1764433517real_n F) (@ (@ tptp.sigma_588796041real_n M) A2)) (=> (@ (@ tptp.member223413699real_n X2) (@ tptp.sigma_607186084real_n M)) (@ (@ tptp.member1746150050real_n (@ F X2)) (@ tptp.sigma_1483971331real_n A2)))))) 0.48/0.75 (assert (forall ((A (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B2 tptp.set_Fi1326602817real_n)) (=> (@ (@ tptp.member1746150050real_n A) (@ (@ tptp.vimage180751827real_n F) B2)) (@ (@ tptp.member1746150050real_n (@ F A)) B2)))) 0.48/0.75 (assert (forall ((M tptp.sigma_107786596real_n) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n)) (N tptp.sigma_1422848389real_n)) (=> (forall ((X3 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1746150050real_n X3) (@ tptp.sigma_1483971331real_n M)) (@ (@ tptp.member223413699real_n (@ F X3)) (@ tptp.sigma_607186084real_n N)))) (=> (forall ((A6 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member1475136633real_n A6) (@ tptp.sigma_433815053real_n N)) (@ (@ tptp.member2104752728real_n (@ (@ tptp.inf_in146441683real_n (@ (@ tptp.vimage1910974324real_n F) A6)) (@ tptp.sigma_1483971331real_n M))) (@ tptp.sigma_522684908real_n M)))) (@ (@ tptp.member640587117real_n F) (@ (@ tptp.sigma_364818953real_n M) N)))))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.inf_in1974387902real_n A) A) A))) 0.48/0.75 (assert (forall ((C2 tptp.finite1489363574real_n) (A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member1352538125real_n C2))) (=> (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2)))))))) 0.48/0.75 (assert (= tptp.t2 (lambda ((A3 tptp.finite964658038_int_n)) (@ (@ tptp.inf_in1974387902real_n tptp.s) (@ tptp.r A3))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (= (@ (@ tptp.minus_1037315151real_n (@ (@ tptp.plus_p585657087real_n A) B)) A) B))) 0.48/0.75 (assert (forall ((Omega tptp.set_se2111327970real_n) (M tptp.sigma_1422848389real_n) (C2 tptp.finite1489363574real_n) (N tptp.sigma_1466784463real_n) (F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1475136633real_n (@ (@ tptp.inf_in632889204real_n Omega) (@ tptp.sigma_607186084real_n M))) (@ tptp.sigma_433815053real_n M)) (=> (@ (@ tptp.member1352538125real_n C2) (@ tptp.sigma_476185326real_n N)) (= (@ (@ tptp.member1759501912real_n F) (@ (@ tptp.sigma_1333364596real_n (@ (@ tptp.sigma_993999336real_n M) Omega)) N)) (@ (@ tptp.member1759501912real_n (lambda ((X tptp.set_Fi1058188332real_n)) (@ (@ (@ tptp.if_Fin127821360real_n (@ (@ tptp.member223413699real_n X) Omega)) (@ F X)) C2))) (@ (@ tptp.sigma_1333364596real_n M) N))))))) 0.48/0.75 (assert (= tptp.t (lambda ((A3 tptp.finite964658038_int_n)) (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n X) (@ tptp.minkow1134813771n_real A3)))) (@ tptp.t2 A3))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (= (= (@ (@ tptp.plus_p585657087real_n A) B) A) (= B tptp.zero_z200130687real_n)))) 0.48/0.75 (assert (= tptp.minus_725016986real_n (lambda ((A4 tptp.set_Fi1326602817real_n) (B3 tptp.set_Fi1326602817real_n)) (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (let ((_let_1 (@ tptp.member1746150050real_n X))) (and (not (@ _let_1 B3)) (@ _let_1 A4)))))))) 0.48/0.75 (assert (forall ((C2 tptp.finite1489363574real_n) (A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member1352538125real_n C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_in1974387902real_n A2) B2))))))) 0.48/0.75 (assert (forall ((X2 tptp.finite1489363574real_n) (Y3 tptp.finite1489363574real_n)) (= (@ (@ (@ tptp.if_Fin127821360real_n true) X2) Y3) X2))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (= (@ (@ tptp.plus_p585657087real_n (@ (@ tptp.minus_1037315151real_n A) B)) C2) (@ (@ tptp.minus_1037315151real_n (@ (@ tptp.plus_p585657087real_n A) C2)) B)))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1326602817real_n)) (= (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (@ (@ tptp.member1746150050real_n X) A2))) A2))) 0.48/0.75 (assert (forall ((A tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (B tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.sigma_1235138647real_n M))) (=> (@ (@ tptp.member223413699real_n A) _let_1) (=> (@ (@ tptp.member223413699real_n B) _let_1) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n A) B)) _let_1)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (Pb Bool)) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and Pb (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)))))) (@ tptp.sigma_1235138647real_n M)))) 0.48/0.75 (assert (forall ((R tptp.set_Fi1058188332real_n) (S tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.inf_in1620715847al_n_o (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n X) R))) (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n X) S))) (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n X) (@ (@ tptp.inf_in1974387902real_n R) S)))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (P (-> tptp.finite1489363574real_n Bool)) (Q (-> tptp.finite1489363574real_n Bool))) (let ((_let_1 (@ tptp.sigma_1235138647real_n M))) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P X) (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)))))) _let_1) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (@ Q X))))) _let_1) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)) (=> (@ Q X) (@ P X)))))) _let_1)))))) 0.48/0.75 (assert (forall ((B (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member1746150050real_n B) (@ (@ tptp.image_352856126real_n F) A2)) (not (forall ((X3 tptp.set_Fi1058188332real_n)) (=> (= B (@ F X3)) (not (@ (@ tptp.member223413699real_n X3) A2)))))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n) (P Bool)) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and P (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)))))) (@ tptp.sigma_1235138647real_n M)))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A tptp.set_Fi1058188332real_n) (B (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B2 tptp.set_Fi1326602817real_n)) (=> (= (@ F A) B) (=> (@ (@ tptp.member1746150050real_n B) B2) (@ (@ tptp.member223413699real_n A) (@ (@ tptp.vimage2134951412real_n F) B2)))))) 0.48/0.75 (assert (forall ((B (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (X2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n)) (=> (= B (@ F X2)) (=> (@ (@ tptp.member223413699real_n X2) A2) (@ (@ tptp.member1746150050real_n B) (@ (@ tptp.image_352856126real_n F) A2)))))) 0.48/0.75 (assert (forall ((C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (B2 tptp.set_Fi1326602817real_n)) (let ((_let_1 (@ tptp.member1746150050real_n C2))) (=> (@ _let_1 (@ (@ tptp.minus_725016986real_n A2) B2)) (not (=> (@ _let_1 A2) (@ _let_1 B2))))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1422848389real_n) (P (-> tptp.set_Fi1058188332real_n Bool)) (Q (-> tptp.set_Fi1058188332real_n Bool))) (let ((_let_1 (@ tptp.sigma_433815053real_n M))) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ P X) (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)))))) _let_1) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ Q X) (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)))))) _let_1) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)) (@ Q X) (@ P X))))) _let_1)))))) 0.48/0.75 (assert (forall ((Omega tptp.set_se2111327970real_n) (M tptp.sigma_1422848389real_n) (C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (N tptp.sigma_107786596real_n) (F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1475136633real_n (@ (@ tptp.inf_in632889204real_n Omega) (@ tptp.sigma_607186084real_n M))) (@ tptp.sigma_433815053real_n M)) (=> (@ (@ tptp.member1746150050real_n C2) (@ tptp.sigma_1483971331real_n N)) (= (@ (@ tptp.member1764433517real_n F) (@ (@ tptp.sigma_588796041real_n (@ (@ tptp.sigma_993999336real_n M) Omega)) N)) (@ (@ tptp.member1764433517real_n (lambda ((X tptp.set_Fi1058188332real_n) (__flatten_var_0 tptp.finite1489363574real_n)) (@ (@ (@ (@ tptp.if_Fin413489477real_n (@ (@ tptp.member223413699real_n X) Omega)) (@ F X)) C2) __flatten_var_0))) (@ (@ tptp.sigma_588796041real_n M) N))))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n)) (= (@ (@ tptp.minus_1037315151real_n A) A) tptp.zero_z200130687real_n))) 0.48/0.75 (assert (forall ((Omega tptp.set_Fi1058188332real_n) (M tptp.sigma_1466784463real_n) (C2 tptp.finite1489363574real_n) (N tptp.sigma_1466784463real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n Omega) (@ tptp.sigma_476185326real_n M))) (@ tptp.sigma_1235138647real_n M)) (=> (@ (@ tptp.member1352538125real_n C2) (@ tptp.sigma_476185326real_n N)) (= (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n (@ (@ tptp.sigma_346513458real_n M) Omega)) N)) (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ (@ tptp.if_Fin127821360real_n (@ (@ tptp.member1352538125real_n X) Omega)) (@ F X)) C2))) (@ (@ tptp.sigma_439801790real_n M) N))))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2))))) 0.48/0.75 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n)) (A2 tptp.set_Fi1326602817real_n)) (=> (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_128879038real_n F) A2)) (not (forall ((X3 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (= B (@ F X3)) (not (@ (@ tptp.member1746150050real_n X3) A2)))))))) 0.48/0.75 (assert (forall ((C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (B2 tptp.set_Fi1326602817real_n)) (let ((_let_1 (@ tptp.member1746150050real_n C2))) (=> (@ _let_1 (@ (@ tptp.inf_in146441683real_n A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2)))))))) 0.48/0.75 (assert (forall ((A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.minus_1686442501real_n A2))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.inf_in1974387902real_n A2) B2))))) 0.48/0.75 (assert (forall ((B tptp.set_Fi1058188332real_n) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n)) (X2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n)) (=> (= B (@ F X2)) (=> (@ (@ tptp.member1746150050real_n X2) A2) (@ (@ tptp.member223413699real_n B) (@ (@ tptp.image_128879038real_n F) A2)))))) 0.48/0.75 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat)))) 0.48/0.75 (assert (forall ((B tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (X2 tptp.finite1489363574real_n) (A2 tptp.set_Fi1058188332real_n)) (=> (= B (@ F X2)) (=> (@ (@ tptp.member1352538125real_n X2) A2) (@ (@ tptp.member1352538125real_n B) (@ (@ tptp.image_439535603real_n F) A2)))))) 0.48/0.75 (assert (forall ((P Bool)) (or (= P true) (= P false)))) 0.48/0.75 (assert (forall ((C2 tptp.set_Fi1058188332real_n) (A2 tptp.set_se2111327970real_n) (B2 tptp.set_se2111327970real_n)) (let ((_let_1 (@ tptp.member223413699real_n C2))) (= (@ _let_1 (@ (@ tptp.inf_in632889204real_n A2) B2)) (and (@ _let_1 A2) (@ _let_1 B2)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (T tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.comple230862828real_n tptp.lebesg260170249real_n))) (=> (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n _let_1) tptp.borel_676189912real_n)) (=> (@ (@ tptp.member223413699real_n T) (@ tptp.sigma_1235138647real_n tptp.borel_676189912real_n)) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n (@ F X)) T)))) (@ tptp.sigma_1235138647real_n _let_1))))))) 0.48/0.75 (assert (forall ((S tptp.set_Fi1058188332real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (let ((_let_1 (@ tptp.comple230862828real_n tptp.lebesg260170249real_n))) (=> (@ (@ tptp.member223413699real_n S) (@ tptp.sigma_1235138647real_n _let_1)) (= (@ (@ tptp.member1746150050real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ (@ tptp.if_Fin127821360real_n (@ (@ tptp.member1352538125real_n X) S)) (@ F X)) tptp.zero_z200130687real_n))) (@ (@ tptp.sigma_439801790real_n _let_1) tptp.borel_676189912real_n)) (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n (@ (@ tptp.sigma_346513458real_n _let_1) S)) tptp.borel_676189912real_n))))))) 0.48/0.75 (assert (= tptp.minus_1686442501real_n (lambda ((A4 tptp.set_Fi1058188332real_n) (B3 tptp.set_Fi1058188332real_n)) (@ tptp.collec321817931real_n (@ (@ tptp.minus_455231168al_n_o (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n X) A4))) (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n X) B3))))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1466784463real_n)) (@ (@ tptp.member223413699real_n (@ tptp.sigma_476185326real_n M)) (@ tptp.sigma_1235138647real_n M)))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (N tptp.sigma_1466784463real_n) (P (-> tptp.finite1489363574real_n Bool))) (=> (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n M) N)) (=> (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n N)) (@ P X))))) (@ tptp.sigma_1235138647real_n N)) (@ (@ tptp.member223413699real_n (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (and (@ P (@ F X)) (@ (@ tptp.member1352538125real_n X) (@ tptp.sigma_476185326real_n M)))))) (@ tptp.sigma_1235138647real_n M)))))) 0.48/0.75 (assert (forall ((C2 tptp.finite1489363574real_n) (A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n C2))) (= (@ (@ tptp.minus_1037315151real_n (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_1037315151real_n A) B))))) 0.48/0.75 (assert (forall ((A (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n)) (B2 tptp.set_se2111327970real_n)) (=> (@ (@ tptp.member1746150050real_n A) (@ (@ tptp.vimage1910974324real_n F) B2)) (@ (@ tptp.member223413699real_n (@ F A)) B2)))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n) (C2 tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.plus_p585657087real_n A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2))))) 0.48/0.75 (assert (forall ((M tptp.sigma_1422848389real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (let ((_let_1 (@ tptp.sigma_433815053real_n M))) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ P X) (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)))))) _let_1) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (not (@ P X)) (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)))))) _let_1))))) 0.48/0.75 (assert (= tptp.inf_in1974387902real_n (lambda ((X tptp.set_Fi1058188332real_n) (Y2 tptp.set_Fi1058188332real_n)) (@ (@ tptp.inf_in1974387902real_n Y2) X)))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1352538125real_n A) (@ (@ tptp.vimage1233683625real_n F) A2)) (@ (@ tptp.member1352538125real_n (@ F A)) A2)))) 0.48/0.75 (assert (forall ((M tptp.sigma_1422848389real_n) (P Bool)) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and P (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)))))) (@ tptp.sigma_433815053real_n M)))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.vimage1233683625real_n F))) (= (@ _let_1 (@ (@ tptp.minus_1686442501real_n A2) B2)) (@ (@ tptp.minus_1686442501real_n (@ _let_1 A2)) (@ _let_1 B2)))))) 0.48/0.75 (assert (= (@ tptp.sigma_476185326real_n tptp.lebesg260170249real_n) (@ tptp.sigma_476185326real_n tptp.borel_676189912real_n))) 0.48/0.75 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C2)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C2))))) 0.48/0.75 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n)) (M tptp.sigma_107786596real_n) (A2 tptp.sigma_1466784463real_n) (X2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (=> (@ (@ tptp.member1695588023real_n F) (@ (@ tptp.sigma_2028985427real_n M) A2)) (=> (@ (@ tptp.member1746150050real_n X2) (@ tptp.sigma_1483971331real_n M)) (@ (@ tptp.member1352538125real_n (@ F X2)) (@ tptp.sigma_476185326real_n A2)))))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (A2 tptp.sigma_1466784463real_n) (S tptp.set_Fi1058188332real_n)) (=> (@ (@ tptp.member1746150050real_n F) (@ (@ tptp.sigma_439801790real_n M) A2)) (=> (@ (@ tptp.member223413699real_n S) (@ tptp.sigma_1235138647real_n A2)) (@ (@ tptp.member223413699real_n (@ (@ tptp.inf_in1974387902real_n (@ (@ tptp.vimage1233683625real_n F) S)) (@ tptp.sigma_476185326real_n M))) (@ tptp.sigma_1235138647real_n M)))))) 0.48/0.75 (assert (forall ((A (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (= (@ (@ tptp.member1746150050real_n A) (@ tptp.collec1190264032real_n P)) (@ P A)))) 0.48/0.75 (assert (forall ((N3 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N3) tptp.zero_zero_nat))) 0.48/0.75 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n)) (=> (@ (@ tptp.member1746150050real_n (@ F A)) A2) (@ (@ tptp.member1746150050real_n A) (@ (@ tptp.vimage180751827real_n F) A2))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (A2 tptp.set_Fi1058188332real_n) (B2 tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.image_439535603real_n (@ tptp.plus_p585657087real_n A)))) (=> (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))) 0.48/0.75 (assert (forall ((S tptp.set_se2111327970real_n) (M tptp.sigma_1422848389real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (let ((_let_1 (@ tptp.sigma_433815053real_n M))) (=> (@ (@ tptp.member1475136633real_n S) _let_1) (= (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ P X) (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n (@ (@ tptp.sigma_993999336real_n M) S))))))) (@ tptp.sigma_433815053real_n (@ (@ tptp.sigma_993999336real_n M) S))) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member223413699real_n X))) (and (@ _let_1 (@ tptp.sigma_607186084real_n M)) (@ P X) (@ _let_1 S)))))) _let_1)))))) 0.48/0.75 (assert (forall ((F (-> tptp.set_Fi1058188332real_n tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1422848389real_n) (N tptp.sigma_107786596real_n) (P (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) Bool))) (=> (@ (@ tptp.member1764433517real_n F) (@ (@ tptp.sigma_588796041real_n M) N)) (=> (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ P X) (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n N)))))) (@ tptp.sigma_522684908real_n N)) (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ P (@ F X)) (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n M)))))) (@ tptp.sigma_433815053real_n M)))))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (B tptp.finite1489363574real_n)) (= (@ (@ tptp.minus_1037315151real_n (@ (@ tptp.plus_p585657087real_n A) B)) B) A))) 0.48/0.75 (assert (forall ((X2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (Y3 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (= (@ (@ (@ tptp.if_Fin413489477real_n true) X2) Y3) X2))) 0.48/0.75 (assert (forall ((A tptp.finite1489363574real_n) (S2 tptp.set_Fi1058188332real_n) (T3 tptp.set_Fi1058188332real_n)) (= (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n X) A))) (@ (@ tptp.minus_1686442501real_n S2) T3)) (@ (@ tptp.minus_1686442501real_n (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n X) A))) S2)) (@ (@ tptp.image_439535603real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.minus_1037315151real_n X) A))) T3))))) 0.48/0.75 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat)))) 0.48/0.75 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (M tptp.sigma_1466784463real_n) (N tptp.sigma_1466784463real_n) (Omega tptp.set_Fi1058188332real_n)) (let ((_let_1 (@ tptp.member1746150050real_n F))) (=> (@ _let_1 (@ (@ tptp.s/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 31133 Alarm clock ( read result; case "$result" in 179.52/180.02 unsat) 179.52/180.02 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0 179.52/180.02 ;; 179.52/180.02 sat) 179.52/180.02 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0 179.52/180.02 ;; 179.52/180.02 esac; exit 1 ) 179.52/180.03 igma_439801790real_n M) N)) (@ _let_1 (@ (@ tptp.sigma_439801790real_n (@ (@ tptp.sigma_346513458real_n M) Omega)) N)))))) 179.52/180.03 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat)))) 179.52/180.03 (assert (forall ((C2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (A2 tptp.set_Fi1326602817real_n) (B2 tptp.set_Fi1326602817real_n)) (let ((_let_1 (@ tptp.member1746150050real_n C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_in146441683real_n A2) B2))))))) 179.52/180.03 (assert (forall ((S tptp.set_Fi1058188332real_n) (A tptp.finite1489363574real_n)) (let ((_let_1 (@ tptp.sigma_1235138647real_n (@ tptp.comple230862828real_n tptp.lebesg260170249real_n)))) (=> (@ (@ tptp.member223413699real_n S) _let_1) (@ (@ tptp.member223413699real_n (@ (@ tptp.image_439535603real_n (@ tptp.plus_p585657087real_n A)) S)) _let_1))))) 179.52/180.03 (assert (forall ((F (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (P (-> tptp.finite1489363574real_n Bool))) (= (@ (@ tptp.vimage1233683625real_n F) (@ tptp.collec321817931real_n P)) (@ tptp.collec321817931real_n (lambda ((Y2 tptp.finite1489363574real_n)) (@ P (@ F Y2))))))) 179.52/180.03 (assert (= tptp.vimage1233683625real_n (lambda ((F2 (-> tptp.finite1489363574real_n tptp.finite1489363574real_n)) (B3 tptp.set_Fi1058188332real_n)) (@ tptp.collec321817931real_n (lambda ((X tptp.finite1489363574real_n)) (@ (@ tptp.member1352538125real_n (@ F2 X)) B3)))))) 179.52/180.03 (assert (forall ((F (-> (-> tptp.finite1489363574real_n tptp.finite1489363574real_n) tptp.set_Fi1058188332real_n)) (M tptp.sigma_107786596real_n) (N tptp.sigma_1422848389real_n) (P (-> tptp.set_Fi1058188332real_n Bool))) (=> (@ (@ tptp.member640587117real_n F) (@ (@ tptp.sigma_364818953real_n M) N)) (=> (@ (@ tptp.member1475136633real_n (@ tptp.collec452821761real_n (lambda ((X tptp.set_Fi1058188332real_n)) (and (@ (@ tptp.member223413699real_n X) (@ tptp.sigma_607186084real_n N)) (@ P X))))) (@ tptp.sigma_433815053real_n N)) (@ (@ tptp.member2104752728real_n (@ tptp.collec1190264032real_n (lambda ((X (-> tptp.finite1489363574real_n tptp.finite1489363574real_n))) (and (@ (@ tptp.member1746150050real_n X) (@ tptp.sigma_1483971331real_n M)) (@ P (@ F X)))))) (@ tptp.sigma_522684908real_n M)))))) 179.52/180.03 (assert (= tptp.minus_1698615483real_n (lambda ((A4 tptp.set_se2111327970real_n) (B3 tptp.set_se2111327970real_n)) (@ tptp.collec452821761real_n (@ (@ tptp.minus_1832115082al_n_o (lambda ((X tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n X) A4))) (lambda ((X tptp.set_Fi1058188332real_n)) (@ (@ tptp.member223413699real_n X) B3))))))) 179.52/180.03 (assert (forall ((M tptp.sigma_1466784463real_n)) (= (@ tptp.sigma_476185326real_n (@ tptp.comple230862828real_n M)) (@ tptp.sigma_476185326real_n M)))) 179.52/180.03 (set-info :filename cvc5---1.0.5_28121) 179.52/180.03 (check-sat-assuming ( true )) 179.52/180.03 ------- get file name : TPTP file name is 179.52/180.03 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28121.smt2... 179.52/180.03 --- Run --ho-elim --full-saturate-quant at 10... 179.52/180.03 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 179.52/180.03 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10... 179.52/180.03 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5... 179.52/180.03 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5... 179.52/180.03 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10... 179.52/180.03 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10... 179.52/180.03 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10... 179.52/180.03 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10... 179.52/180.03 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant... 179.52/180.03 Alarm clock 179.52/180.03 % cvc5---1.0.5 exiting 179.52/180.03 % cvc5---1.0.5 exiting 179.52/180.04 EOF