0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.13	% Command    : do_cvc5 %s %d
0.13/0.34	% Computer   : n012.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1200
0.13/0.34	% WCLimit    : 120
0.13/0.34	% DateTime   : Tue Jul 13 12:49:31 EDT 2021
0.13/0.34	% CPUTime    : 
0.20/0.49	%----THF division
0.20/0.49	------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120...
0.20/0.49	--- Run --ho-elim --full-saturate-quant at 10...
10.38/10.55	--- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
12.76/12.98	% SZS status Theorem for theBenchmark
12.83/12.99	% SZS output start Proof for theBenchmark
12.83/12.99	(proof
12.83/12.99	(let ((_let_1 ((line_c1152468841ment_a a2) b))) (let ((_let_2 (member_a x2))) (let ((_let_3 (= ord_less_set_real (lambda ((A5 set_real) (B5 set_real)) (and ((ord_less_eq_set_real A5) B5) (not (= A5 B5))))))) (let ((_let_4 (= ord_less_real (lambda ((X3 real) (Y3 real)) (and (not ((ord_less_eq_real Y3) X3)) ((ord_less_eq_real X3) Y3)))))) (let ((_let_5 (ord_less_real zero_zero_real))) (let ((_let_6 (_let_5 d))) (let ((_let_7 (= uminus_uminus_a_a (lambda ((A5 (-> a a)) (X3 a)) (uminus_uminus_a (A5 X3)))))) (let ((_let_8 (forall ((X2 a)) (let ((_let_1 (poinca659159244_rot_a ((minus_minus_a a2) b)))) (=> ((member_a X2) ((elemen49976720ball_a x2) d)) ((ord_less_eq_real ((inner_1173012732nner_a (f s)) _let_1)) ((inner_1173012732nner_a (f X2)) _let_1))))))) (let ((_let_9 (forall ((Y a)) (let ((_let_1 (member_a Y))) (let ((_let_2 (f Y))) (=> (_let_1 ((elemen49976720ball_a x2) d)) (and ((ord_less_real zero_zero_real) ((inner_1173012732nner_a _let_2) (poinca659159244_rot_a ((minus_minus_a a2) b)))) (not (= _let_2 zero_zero_a)) (_let_1 x)))))))) (let ((_let_10 (poinca659159244_rot_a ((minus_minus_a a2) b)))) (let ((_let_11 (= ord_less_eq_set_a (lambda ((A5 set_a) (B5 set_a)) (forall ((X3 a)) (let ((_let_1 (member_a X3))) (=> (_let_1 A5) (_let_1 B5)))))))) (let ((_let_12 (f x2))) (let ((_let_13 (not (exists ((D3 real)) (and ((ord_less_real zero_zero_real) D3) (exists ((B7 real)) (and (forall ((X4 a)) (=> ((member_a X4) ((elemen49976720ball_a x2) D3)) ((ord_less_eq_real B7) ((inner_1173012732nner_a (f X4)) (poinca659159244_rot_a ((minus_minus_a a2) b)))))) ((ord_less_real zero_zero_real) B7)))))))) (let ((_let_14 (= ord_less_eq_set_real (lambda ((A5 set_real) (B5 set_real)) (forall ((X3 real)) (let ((_let_1 (member_real X3))) (=> (_let_1 A5) (_let_1 B5)))))))) (let ((_let_15 ((member_a s) ((elemen49976720ball_a x2) d)))) (let ((_let_16 (= ord_less_set_a (lambda ((A5 set_a) (B5 set_a)) (and (not ((ord_less_eq_set_a B5) A5)) ((ord_less_eq_set_a A5) B5)))))) (let ((_let_17 (ho_44 (ho_43 k_86 d) zero_zero_real))) (let ((_let_18 (ho_43 k_86 zero_zero_real))) (let ((_let_19 (ho_44 _let_18 d))) (let ((_let_20 (ho_58 k_102 s))) (let ((_let_21 (ho_40 (ho_39 k_41 _let_20) (ho_58 k_103 (ho_58 (ho_57 k_56 a2) b))))) (let ((_let_22 (ho_44 (ho_43 k_86 _let_21) zero_zero_real))) (let ((_let_23 (ho_44 _let_18 _let_21))) (let ((_let_24 (forall ((X4 a)) (let ((_let_1 (ho_58 k_103 (ho_58 (ho_57 k_56 a2) b)))) (or (not (ho_35 (ho_34 k_33 X4) (ho_134 (ho_133 k_132 x2) d))) (ho_44 (ho_43 k_86 (ho_40 (ho_39 k_41 (ho_58 k_102 s)) _let_1)) (ho_40 (ho_39 k_41 (ho_58 k_102 X4)) _let_1))))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (not _let_24))) (let ((_let_27 (not _let_19))) (let ((_let_28 (or _let_17 _let_27 _let_26 _let_22 _let_25))) (let ((_let_29 (ASSUME |:args| (_let_16)))) (let ((_let_30 (EQ_RESOLVE (ASSUME |:args| (_let_14)) (MACRO_SR_EQ_INTRO |:args| (_let_14 7 12))))) (let ((_let_31 (EQ_RESOLVE (ASSUME |:args| (_let_11)) (MACRO_SR_EQ_INTRO |:args| (_let_11 7 12))))) (let ((_let_32 (ASSUME |:args| (_let_7)))) (let ((_let_33 (ASSUME |:args| (_let_4)))) (let ((_let_34 (EQ_RESOLVE (ASSUME |:args| (_let_3)) (MACRO_SR_EQ_INTRO _let_33 _let_32 _let_31 _let_30 _let_29 |:args| (_let_3 7 12))))) (let ((_let_35 (EQ_RESOLVE (ASSUME |:args| (_let_6)) (TRANS (MACRO_SR_EQ_INTRO _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 |:args| (_let_6 7 12)) (PREPROCESS |:args| ((= (and (not ((ord_less_eq_real d) zero_zero_real)) ((ord_less_eq_real zero_zero_real) d)) (and (not _let_17) _let_19)))))))) (let ((_let_36 (not _let_22))) (let ((_let_37 (ho_34 k_33 s))) (let ((_let_38 (and (not (= zero_zero_a _let_20)) (ho_35 _let_37 x) _let_36 _let_23))) (let ((_let_39 (ho_35 _let_37 (ho_134 (ho_133 k_132 x2) d)))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38))) (let ((_let_42 (forall ((Y a)) (let ((_let_1 (ho_58 k_102 Y))) (let ((_let_2 (ho_40 (ho_39 k_41 _let_1) (ho_58 k_103 (ho_58 (ho_57 k_56 a2) b))))) (let ((_let_3 (ho_34 k_33 Y))) (or (not (ho_35 _let_3 (ho_134 (ho_133 k_132 x2) d))) (and (not (= zero_zero_a _let_1)) (ho_35 _let_3 x) (not (ho_44 (ho_43 k_86 _let_2) zero_zero_real)) (ho_44 (ho_43 k_86 zero_zero_real) _let_2))))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME |:args| (_let_9)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_9 7 12)) (MACRO_SR_EQ_INTRO _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 |:args| ((forall ((Y a)) (let ((_let_1 (member_a Y))) (let ((_let_2 (f Y))) (or (not (_let_1 ((elemen49976720ball_a x2) d))) (and ((ord_less_real zero_zero_real) ((inner_1173012732nner_a _let_2) (poinca659159244_rot_a ((minus_minus_a a2) b)))) (not (= zero_zero_a _let_2)) (_let_1 x)))))) 7 12)) (PREPROCESS |:args| ((= (forall ((Y a)) (let ((_let_1 (f Y))) (let ((_let_2 ((inner_1173012732nner_a _let_1) (poinca659159244_rot_a ((minus_minus_a a2) b))))) (let ((_let_3 (member_a Y))) (or (not (_let_3 ((elemen49976720ball_a x2) d))) (and (not (= zero_zero_a _let_1)) (_let_3 x) (not ((ord_less_eq_real _let_2) zero_zero_real)) ((ord_less_eq_real zero_zero_real) _let_2))))))) _let_42))))))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_41)) |:args| ((or _let_40 _let_38 (not _let_41)))) (EQ_RESOLVE (ASSUME |:args| (_let_15)) (PREPROCESS |:args| ((= _let_15 _let_39)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 |:args| (s)) |:args| (_let_42))) _let_43 |:args| (_let_41 false _let_42)) |:args| (_let_38 false _let_39 false _let_41)))) (let ((_let_45 (not _let_38))) (let ((_let_46 (forall ((X2 a)) (let ((_let_1 (ho_58 k_103 (ho_58 (ho_57 k_56 a2) b)))) (or (not (ho_35 (ho_34 k_33 X2) (ho_134 (ho_133 k_132 x2) d))) (ho_44 (ho_43 k_86 (ho_40 (ho_39 k_41 (ho_58 k_102 s)) _let_1)) (ho_40 (ho_39 k_41 (ho_58 k_102 X2)) _let_1))))))) (let ((_let_47 (forall ((D3 real) (BOUND_VARIABLE_5004 real)) (let ((_let_1 (ho_43 k_86 zero_zero_real))) (or (ho_44 (ho_43 k_86 D3) zero_zero_real) (not (ho_44 _let_1 D3)) (not (forall ((X4 a)) (or (not (ho_35 (ho_34 k_33 X4) (ho_134 (ho_133 k_132 x2) D3))) (ho_44 (ho_43 k_86 BOUND_VARIABLE_5004) (ho_40 (ho_39 k_41 (ho_58 k_102 X4)) (ho_58 k_103 (ho_58 (ho_57 k_56 a2) b))))))) (ho_44 (ho_43 k_86 BOUND_VARIABLE_5004) zero_zero_real) (not (ho_44 _let_1 BOUND_VARIABLE_5004))))))) (let ((_let_48 (EQ_RESOLVE (ASSUME |:args| (_let_13)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_13 7 12)) (MACRO_SR_EQ_INTRO _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 |:args| ((forall ((D3 real) (BOUND_VARIABLE_5004 real)) (let ((_let_1 (ord_less_real zero_zero_real))) (or (not (_let_1 D3)) (not (forall ((X4 a)) (or (not ((member_a X4) ((elemen49976720ball_a x2) D3))) ((ord_less_eq_real BOUND_VARIABLE_5004) ((inner_1173012732nner_a (f X4)) (poinca659159244_rot_a ((minus_minus_a a2) b))))))) (not (_let_1 BOUND_VARIABLE_5004))))) 7 12)) (PREPROCESS |:args| ((= (forall ((D3 real) (BOUND_VARIABLE_5004 real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (or ((ord_less_eq_real D3) zero_zero_real) (not (_let_1 D3)) (not (forall ((X4 a)) (or (not ((member_a X4) ((elemen49976720ball_a x2) D3))) ((ord_less_eq_real BOUND_VARIABLE_5004) ((inner_1173012732nner_a (f X4)) (poinca659159244_rot_a ((minus_minus_a a2) b))))))) ((ord_less_eq_real BOUND_VARIABLE_5004) zero_zero_real) (not (_let_1 BOUND_VARIABLE_5004))))) _let_47))))))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_28)) |:args| ((or _let_17 _let_27 _let_22 _let_25 _let_26 (not _let_28)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 |:args| (d _let_21)) |:args| (_let_47))) _let_48 |:args| (_let_28 false _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM2 (THEORY_LEMMA |:args| ((= _let_24 _let_46) 12))) |:args| ((or (not _let_46) _let_24))) (EQ_RESOLVE (ASSUME |:args| (_let_8)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_8 7 12)) (PREPROCESS |:args| ((= (forall ((X2 a)) (let ((_let_1 (poinca659159244_rot_a ((minus_minus_a a2) b)))) (or (not ((member_a X2) ((elemen49976720ball_a x2) d))) ((ord_less_eq_real ((inner_1173012732nner_a (f s)) _let_1)) ((inner_1173012732nner_a (f X2)) _let_1))))) _let_46))))) |:args| (_let_24 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS |:args| (_let_38 3)) |:args| ((or _let_23 _let_45))) _let_44 |:args| (_let_23 false _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS |:args| (_let_38 2)) |:args| ((or _let_36 _let_45))) _let_44 |:args| (_let_36 false _let_38)) (AND_ELIM _let_35 |:args| (1)) (AND_ELIM _let_35 |:args| (0)) |:args| (false false _let_28 false _let_24 false _let_23 true _let_22 false _let_19 true _let_17)) |:args| ((forall ((X a) (Y a)) (let ((_let_1 ((ord_less_eq_set_a ((line_c1152468841ment_a X) Y)) x))) (let ((_let_2 (not (= X Y)))) (=> ((((poinca522724647ment_a f) x) X) Y) (=> (=> _let_2 (=> _let_1 (not (forall ((Z2 a)) (=> ((member_a Z2) ((line_c1152468841ment_a X) Y)) ((ord_less_real zero_zero_real) ((inner_1173012732nner_a (f Z2)) (poinca659159244_rot_a ((minus_minus_a X) Y))))))))) (not (=> _let_2 (=> _let_1 (not (forall ((Z2 a)) (=> ((member_a Z2) ((line_c1152468841ment_a X) Y)) ((ord_less_real zero_zero_real) ((inner_1173012732nner_a (f Z2)) (poinca659159244_rot_a ((minus_minus_a Y) X))))))))))))))) (forall ((Y a) (X a) (E real)) (=> ((ord_less_real ((real_V1514887919dist_a Y) X)) E) ((ord_less_real ((real_V1514887919dist_a X) Y)) E))) (forall ((X real) (A real) (B real) (I real)) (=> ((member_real X) ((set_or656347191t_real A) B)) (=> ((ord_less_eq_real zero_zero_real) I) ((ord_less_eq_real ((inner_4346926r_real X) I)) ((inner_4346926r_real B) I))))) (forall ((A a)) (= ((ord_less_eq_a zero_zero_a) (uminus_uminus_a A)) ((ord_less_eq_a A) zero_zero_a))) (forall ((B a) (A a)) (= ((minus_minus_a (uminus_uminus_a B)) A) ((minus_minus_a (uminus_uminus_a A)) B))) (forall ((T2 real) (X0 a)) (let ((_let_1 (((auto_l612940ivl0_a (uminus_uminus_a_a f)) x) X0))) (=> ((member_real T2) _let_1) ((ord_less_eq_set_real ((set_or656347191t_real zero_zero_real) T2)) _let_1)))) (forall ((P (-> a Bool)) (Q (-> a Bool))) (= ((ord_less_eq_set_a (collect_a P)) (collect_a Q)) (forall ((X3 a)) (=> (P X3) (Q X3))))) (forall ((A real) (B real) (D2 real) (C real)) (=> ((ord_less_eq_real A) B) (=> ((ord_less_eq_real D2) C) ((ord_less_eq_real ((minus_minus_real A) C)) ((minus_minus_real B) D2))))) (forall ((A real)) (= (uminus_uminus_real (uminus_uminus_real A)) A)) (forall ((X a)) ((member_a X) top_top_set_a)) (initia826609931terval top_top_set_real) _let_16 (forall ((A real)) (= ((minus_minus_real zero_zero_real) A) (uminus_uminus_real A))) (forall ((A2 set_a) (B3 set_a)) (=> ((ord_less_set_a A2) B3) (exists ((B4 a)) ((member_a B4) ((minus_minus_set_a B3) A2))))) (forall ((C a) (A2 set_a) (B3 set_a)) (let ((_let_1 (member_a C))) (= (_let_1 ((minus_minus_set_a A2) B3)) (and (_let_1 A2) (not (_let_1 B3)))))) (forall ((A real) (B real)) (=> (= A B) (= (uminus_uminus_real A) (uminus_uminus_real B)))) (forall ((A a)) (= ((ord_less_a zero_zero_a) (uminus_uminus_a A)) ((ord_less_a A) zero_zero_a))) (forall ((A2 set_a) (B3 set_a)) (=> ((ord_less_eq_set_a A2) B3) (=> (not (= A2 B3)) ((ord_less_set_a A2) B3)))) (forall ((T0 real) (X0 a)) (=> ((member_real T0) top_top_set_real) (=> ((member_a X0) x) ((member_real ((minus_minus_real T0) T0)) (((auto_l612940ivl0_a f) x) X0))))) (forall ((X a)) (=> (((period720806154rbit_a f) x) X) (= (((auto_l612940ivl0_a f) x) X) top_top_set_real))) (forall ((A real) (B real)) (= (= A (uminus_uminus_real B)) (= B (uminus_uminus_real A)))) (forall ((A2 set_a)) ((ord_less_eq_set_a A2) A2)) (forall ((Y set_a) (X set_a)) (=> ((ord_less_eq_set_a (uminus_uminus_set_a Y)) X) ((ord_less_eq_set_a (uminus_uminus_set_a X)) Y))) (forall ((A a) (C a) (B a)) (let ((_let_1 (minus_minus_a A))) (= ((minus_minus_a (_let_1 C)) B) ((minus_minus_a (_let_1 B)) C)))) (forall ((A a) (B a)) (= (= (uminus_uminus_a A) (uminus_uminus_a B)) (= A B))) (forall ((A real)) (= ((minus_minus_real A) zero_zero_real) A)) (forall ((A a) (B a)) (= ((ord_less_a (uminus_uminus_a A)) B) ((ord_less_a (uminus_uminus_a B)) A))) (forall ((D2 real) (B3 real)) (let ((_let_1 (ord_less_real zero_zero_real))) (=> (_let_1 D2) (=> (_let_1 B3) (=> (forall ((X4 a) (Y5 a)) (=> ((member_a X4) ((line_c1152468841ment_a a2) b)) (=> ((ord_less_eq_real ((real_V1514887919dist_a X4) Y5)) D2) ((ord_less_eq_real B3) ((inner_1173012732nner_a (f Y5)) (poinca659159244_rot_a ((minus_minus_a a2) b))))))) thesis))))) (forall ((A2 set_a) (B3 set_a) (C a)) (let ((_let_1 (member_a C))) (=> ((ord_less_eq_set_a A2) B3) (=> (_let_1 A2) (_let_1 B3))))) (forall ((A a)) (= (uminus_uminus_a (uminus_uminus_a A)) A)) (forall ((A a) (P (-> a Bool))) (= ((member_a A) (collect_a P)) (P A))) (forall ((X a)) (let ((_let_1 (uminus_uminus_a_a f))) (= (((period138238489rbit_a _let_1) x) X) (and (((period720806154rbit_a _let_1) x) X) ((ord_less_real zero_zero_real) (((period1305449585riod_a _let_1) x) X)))))) (forall ((A2 set_a)) (= (collect_a (lambda ((X3 a)) ((member_a X3) A2))) A2)) (forall ((A real)) (= ((ord_less_eq_real zero_zero_real) (uminus_uminus_real A)) ((ord_less_eq_real A) zero_zero_real))) (forall ((X a) (Y a)) ((ord_less_eq_real zero_zero_real) ((real_V1514887919dist_a X) Y))) (not (= _let_12 zero_zero_a)) (forall ((C a) (A2 set_a) (B3 set_a)) (let ((_let_1 (member_a C))) (=> (_let_1 ((minus_minus_set_a A2) B3)) (not (=> (_let_1 A2) (_let_1 B3)))))) (forall ((A real)) (= ((ord_less_eq_real (uminus_uminus_real A)) zero_zero_real) ((ord_less_eq_real zero_zero_real) A))) _let_15 (forall ((A real) (B real)) (= ((ord_less_real zero_zero_real) ((minus_minus_real A) B)) ((ord_less_real B) A))) (= ord_less_real (lambda ((A3 real) (B2 real)) ((ord_less_real ((minus_minus_real A3) B2)) zero_zero_real))) (= (uminus_uminus_a zero_zero_a) zero_zero_a) (forall ((A2 set_a) (B3 set_a)) (=> ((ord_less_eq_set_a A2) B3) (=> ((ord_less_eq_set_a B3) A2) (= A2 B3)))) (forall ((A2 set_real) (B3 set_real) (C3 set_real)) (=> ((ord_less_eq_set_real A2) B3) (=> ((ord_less_eq_set_real B3) C3) (= ((minus_minus_set_real B3) ((minus_minus_set_real C3) A2)) A2)))) (forall ((B real) (A real) (C real)) (let ((_let_1 (minus_minus_real C))) (=> ((ord_less_real B) A) ((ord_less_real (_let_1 A)) (_let_1 B))))) (forall ((T2 real) (X0 a)) (let ((_let_1 (((auto_l612940ivl0_a (uminus_uminus_a_a f)) x) X0))) (=> ((member_real T2) _let_1) ((ord_less_eq_set_real ((set_or656347191t_real T2) zero_zero_real)) _let_1)))) (forall ((X set_a) (Y set_a)) (= ((ord_less_eq_set_a (uminus_uminus_set_a X)) (uminus_uminus_set_a Y)) ((ord_less_eq_set_a Y) X))) (forall ((A real) (B real) (C real) (D2 real)) (=> (= ((minus_minus_real A) B) ((minus_minus_real C) D2)) (= ((ord_less_real A) B) ((ord_less_real C) D2)))) (forall ((A a)) (= ((minus_minus_a A) zero_zero_a) A)) (forall ((I real) (L real) (U2 real)) (= ((member_real I) ((set_or656347191t_real L) U2)) (and ((ord_less_eq_real L) I) ((ord_less_eq_real I) U2)))) (forall ((A2 set_real) (B3 set_real) (X real)) (let ((_let_1 (member_real X))) (=> ((ord_less_eq_set_real A2) B3) (=> (_let_1 A2) (_let_1 B3))))) (forall ((X a)) (=> ((member_a X) x) (=> (= (f X) zero_zero_a) (= (((period1305449585riod_a f) x) X) zero_zero_real)))) (forall ((A2 set_real) (B3 set_real)) (=> (= A2 B3) (not (=> ((ord_less_eq_set_real A2) B3) (not ((ord_less_eq_set_real B3) A2)))))) (= ord_less_set_a (lambda ((A5 set_a) (B5 set_a)) (and ((ord_less_eq_set_a A5) B5) (not (= A5 B5))))) (forall ((B a) (A a)) (= ((ord_less_eq_a (uminus_uminus_a B)) (uminus_uminus_a A)) ((ord_less_eq_a A) B))) (forall ((T2 real) (T0 real) (X0 a)) (=> ((member_real ((minus_minus_real T2) T0)) (((auto_l612940ivl0_a (uminus_uminus_a_a f)) x) X0)) ((member_a X0) x))) (forall ((A2 set_a) (C3 set_a) (D4 set_a) (B3 set_a)) (=> ((ord_less_eq_set_a A2) C3) (=> ((ord_less_eq_set_a D4) B3) ((ord_less_eq_set_a ((minus_minus_set_a A2) B3)) ((minus_minus_set_a C3) D4))))) (forall ((A2 set_a) (B3 set_a)) (= ((ord_less_eq_set_a (uminus_uminus_set_a A2)) (uminus_uminus_set_a B3)) ((ord_less_eq_set_a B3) A2))) (forall ((X a) (A a) (B a) (I a)) (=> ((member_a X) ((set_or411607219Most_a A) B)) (=> ((ord_less_eq_a zero_zero_a) I) ((ord_less_eq_real ((inner_1173012732nner_a X) I)) ((inner_1173012732nner_a B) I))))) (forall ((X set_real) (Y set_real)) (= ((ord_less_eq_set_real (uminus773214379t_real X)) (uminus773214379t_real Y)) ((ord_less_eq_set_real Y) X))) (forall ((A2 set_a) (B3 set_a)) (=> (= A2 B3) ((ord_less_eq_set_a A2) B3))) (forall ((A2 set_real) (B3 set_real)) (= ((ord_less_eq_set_real (uminus773214379t_real A2)) (uminus773214379t_real B3)) ((ord_less_eq_set_real B3) A2))) (forall ((X a)) (let ((_let_1 (uminus_uminus_a_a f))) (=> ((member_a X) x) (=> (= (_let_1 X) zero_zero_a) (((period720806154rbit_a _let_1) x) X))))) (forall ((A real) (B real)) (= (= (uminus_uminus_real A) (uminus_uminus_real B)) (= A B))) (forall ((X a)) (= ((real_V1514887919dist_a X) X) zero_zero_real)) (forall ((X a)) (=> ((member_a X) x) (not (forall ((A4 real)) (=> ((ord_less_real zero_zero_real) A4) (not ((ord_less_eq_set_real ((set_or656347191t_real (uminus_uminus_real A4)) A4)) (((auto_l612940ivl0_a (uminus_uminus_a_a f)) x) X)))))))) (forall ((A2 set_set_real)) (= (collect_set_real (lambda ((X3 set_real)) ((member_set_real X3) A2))) A2)) (forall ((B real) (A real)) (= ((ord_less_real (uminus_uminus_real B)) (uminus_uminus_real A)) ((ord_less_real A) B))) (forall ((M set_a)) (= (((auto_l630715367iant_a (uminus_uminus_a_a f)) x) M) (forall ((X3 a)) (=> ((member_a X3) M) ((((oDE_au1996717075pped_a (uminus_uminus_a_a f)) x) X3) M))))) (forall ((T2 real) (S2 real) (X a)) (let ((_let_1 ((member_real ((minus_minus_real T2) S2)) (((auto_l612940ivl0_a f) x) X)))) (=> _let_1 (=> ((member_a X) x) (=> (forall ((S real) (T3 real) (X4 a)) (let ((_let_1 (f X4))) (=> ((member_a X4) x) (= _let_1 _let_1)))) (=> (= top_top_set_real top_top_set_real) _let_1)))))) (forall ((X a)) (= (((period720806154rbit_a (uminus_uminus_a_a f)) x) X) (((period720806154rbit_a f) x) X))) _let_14 (forall ((A a) (B a)) (= ((ord_less_a zero_zero_a) ((minus_minus_a A) B)) ((ord_less_a B) A))) (forall ((A a)) (= (= (uminus_uminus_a A) zero_zero_a) (= A zero_zero_a))) (forall ((C real) (A2 set_real)) (let ((_let_1 (member_real C))) (=> (not (_let_1 A2)) (_let_1 (uminus773214379t_real A2))))) (forall ((A2 set_real) (B3 set_real)) (=> ((ord_less_set_real A2) B3) (not (=> ((ord_less_eq_set_real A2) B3) ((ord_less_eq_set_real B3) A2))))) (forall ((X0 a)) (let ((_let_1 (member_real zero_zero_real))) (=> (_let_1 top_top_set_real) (=> ((member_a X0) x) (_let_1 (((auto_l612940ivl0_a f) x) X0)))))) (forall ((A2 set_a) (B3 set_a)) (=> ((ord_less_set_a A2) B3) ((ord_less_eq_set_a A2) B3))) (forall ((A set_real) (P (-> set_real Bool))) (= ((member_set_real A) (collect_set_real P)) (P A))) (forall ((C real) (A2 set_real)) (let ((_let_1 (member_real C))) (=> (_let_1 (uminus773214379t_real A2)) (not (_let_1 A2))))) (forall ((X a)) ((ord_less_eq_real zero_zero_real) ((inner_1173012732nner_a X) X))) (forall ((B real) (A real)) (= ((ord_less_eq_real (uminus_uminus_real B)) (uminus_uminus_real A)) ((ord_less_eq_real A) B))) (forall ((A a) (B a)) (= (= (uminus_uminus_a A) B) (= (uminus_uminus_a B) A))) _let_13 (forall ((A real) (B real)) (=> ((ord_less_real A) B) ((ord_less_real (uminus_uminus_real B)) (uminus_uminus_real A)))) (forall ((A a) (B a)) (= (= A (uminus_uminus_a B)) (= B (uminus_uminus_a A)))) (forall ((C real) (A2 set_real) (B3 set_real)) (let ((_let_1 (member_real C))) (=> (_let_1 ((minus_minus_set_real A2) B3)) (_let_1 A2)))) (forall ((A2 set_a) (B3 set_a)) (=> (forall ((X4 a)) (let ((_let_1 (member_a X4))) (=> (_let_1 A2) (_let_1 B3)))) ((ord_less_eq_set_a A2) B3))) (forall ((B real) (A real)) (= ((minus_minus_real (uminus_uminus_real B)) A) ((minus_minus_real (uminus_uminus_real A)) B))) (forall ((X real) (Y real) (Z real)) (let ((_let_1 (inner_4346926r_real X))) (= (_let_1 ((minus_minus_real Y) Z)) ((minus_minus_real (_let_1 Y)) (_let_1 Z))))) (forall ((A a)) (= ((minus_minus_a A) zero_zero_a) A)) (forall ((A a) (B a)) (=> ((ord_less_a A) B) ((ord_less_a (uminus_uminus_a B)) (uminus_uminus_a A)))) (forall ((A real)) (= ((ord_less_real (uminus_uminus_real A)) A) ((ord_less_real zero_zero_real) A))) (forall ((A a) (B a) (C a)) (=> ((ord_less_eq_a A) B) ((ord_less_eq_a ((minus_minus_a A) C)) ((minus_minus_a B) C)))) (forall ((A set_a) (P (-> set_a Bool))) (= ((member_set_a A) (collect_set_a P)) (P A))) (forall ((A real) (B real)) (= (uminus_uminus_real ((minus_minus_real A) B)) ((minus_minus_real B) A))) (forall ((A2 set_a) (B3 set_a) (C3 set_a)) (let ((_let_1 (ord_less_set_a A2))) (=> (_let_1 B3) (=> ((ord_less_eq_set_a B3) C3) (_let_1 C3))))) (forall ((X a) (Y a)) (=> (not (= X Y)) ((ord_less_real zero_zero_real) ((real_V1514887919dist_a X) Y)))) (= (lambda ((Y4 set_a) (Z3 set_a)) (= Y4 Z3)) (lambda ((A5 set_a) (B5 set_a)) (and ((ord_less_eq_set_a A5) B5) ((ord_less_eq_set_a B5) A5)))) (forall ((X a) (E real)) (= ((member_a X) ((elemen49976720ball_a X) E)) ((ord_less_eq_real zero_zero_real) E))) (forall ((A real) (B real)) (=> ((ord_less_eq_real A) B) ((ord_less_eq_real (uminus_uminus_real B)) (uminus_uminus_real A)))) ((member_a z) _let_1) (forall ((X real) (Y real) (Z real)) (= ((inner_4346926r_real ((minus_minus_real X) Y)) Z) ((minus_minus_real ((inner_4346926r_real X) Z)) ((inner_4346926r_real Y) Z)))) (forall ((X a)) (= (= (poinca659159244_rot_a X) zero_zero_a) (= X zero_zero_a))) (forall ((A2 set_a) (B3 set_a)) (=> ((ord_less_set_a A2) B3) (not (=> ((ord_less_eq_set_a A2) B3) ((ord_less_eq_set_a B3) A2))))) (forall ((X a) (Y a)) (let ((_let_1 ((poinca522724647ment_a f) x))) (=> ((_let_1 X) Y) ((_let_1 Y) X)))) (= ord_less_eq_real (lambda ((A3 real) (B2 real)) ((ord_less_eq_real ((minus_minus_real A3) B2)) zero_zero_real))) (forall ((X a) (Y a) (Z a)) (let ((_let_1 ((line_c1152468841ment_a X) Y))) (=> ((((poinca522724647ment_a f) x) X) Y) (=> ((member_a Z) _let_1) (=> ((ord_less_real zero_zero_real) ((inner_1173012732nner_a (f Z)) (poinca659159244_rot_a ((minus_minus_a X) Y)))) ((ord_less_eq_set_a _let_1) x)))))) (forall ((A2 set_a) (B3 set_a)) (=> (= A2 B3) (not (=> ((ord_less_eq_set_a A2) B3) (not ((ord_less_eq_set_a B3) A2)))))) (forall ((X real)) (= ((inner_4346926r_real zero_zero_real) X) zero_zero_real)) (forall ((X a) (Y a) (Za a) (Z a)) (let ((_let_1 (poinca659159244_rot_a ((minus_minus_a X) Y)))) (let ((_let_2 ((line_c1152468841ment_a X) Y))) (=> ((((poinca522724647ment_a f) x) X) Y) (=> ((member_a Za) _let_2) (=> ((ord_less_real ((inner_1173012732nner_a (f Za)) _let_1)) zero_zero_real) (=> ((member_a Z) _let_2) ((ord_less_real ((inner_1173012732nner_a (f Z)) _let_1)) zero_zero_real)))))))) (not (forall ((D real)) (=> ((ord_less_real zero_zero_real) D) (not (forall ((Y2 a)) (let ((_let_1 (member_a Y2))) (let ((_let_2 (f Y2))) (=> (_let_1 ((elemen49976720ball_a x2) D)) (and ((ord_less_real zero_zero_real) ((inner_1173012732nner_a _let_2) (poinca659159244_rot_a ((minus_minus_a a2) b)))) (not (= _let_2 zero_zero_a)) (_let_1 x)))))))))) (forall ((C real) (A2 set_real) (B3 set_real)) (let ((_let_1 (member_real C))) (= (_let_1 ((minus_minus_set_real A2) B3)) (and (not (_let_1 B3)) (_let_1 A2))))) (forall ((T2 real) (T0 real) (X0 a)) (=> ((member_real ((minus_minus_real T2) T0)) (((auto_l612940ivl0_a f) x) X0)) ((member_real T0) top_top_set_real))) (forall ((A real) (C real) (B real)) (let ((_let_1 (minus_minus_real A))) (= ((minus_minus_real (_let_1 C)) B) ((minus_minus_real (_let_1 B)) C)))) (forall ((A real) (P (-> real Bool))) (= ((member_real A) (collect_real P)) (P A))) (forall ((T2 real) (T0 real) (X0 a)) (=> ((member_real ((minus_minus_real T2) T0)) (((auto_l612940ivl0_a f) x) X0)) ((member_a X0) x))) (forall ((X real) (Y real)) (= ((inner_4346926r_real (uminus_uminus_real X)) Y) (uminus_uminus_real ((inner_4346926r_real X) Y)))) (forall ((A real) (B real) (C real)) (=> ((ord_less_real A) B) ((ord_less_real ((minus_minus_real A) C)) ((minus_minus_real B) C)))) (forall ((A2 set_a) (B3 set_a)) (let ((_let_1 ((minus_minus_set_a A2) B3))) (= ((minus_minus_set_a _let_1) B3) _let_1))) (forall ((X a)) (=> (((period720806154rbit_a f) x) X) (=> (= (((period1305449585riod_a f) x) X) zero_zero_real) (= (f X) zero_zero_a)))) (forall ((A a) (B a)) (= ((ord_less_eq_a A) (uminus_uminus_a B)) ((ord_less_eq_a B) (uminus_uminus_a A)))) (forall ((A real)) (= ((ord_less_eq_real (uminus_uminus_real A)) A) ((ord_less_eq_real zero_zero_real) A))) (forall ((Z a)) (=> ((member_a Z) ((line_c1152468841ment_a a2) b)) ((ord_less_real zero_zero_real) ((inner_1173012732nner_a (f Z)) (poinca659159244_rot_a ((minus_minus_a a2) b)))))) (forall ((X real)) (= (= zero_zero_real X) (= X zero_zero_real))) (forall ((C real) (A2 set_real)) (let ((_let_1 (member_real C))) (= (_let_1 (uminus773214379t_real A2)) (not (_let_1 A2))))) (forall ((X a)) (=> ((member_a X) x) (=> (not (= (f X) zero_zero_a)) (not (forall ((A4 a) (B4 a)) (=> ((member_a X) ((line_open_segment_a A4) B4)) (not ((((poinca522724647ment_a f) x) A4) B4)))))))) ((ord_less_eq_set_a _let_1) x) (forall ((T2 real) (X0 a)) (let ((_let_1 (member_real T2))) (=> (_let_1 (((auto_l612940ivl0_a (uminus_uminus_a_a f)) x) X0)) (_let_1 top_top_set_real)))) (_let_5 ((inner_1173012732nner_a _let_12) _let_10)) (forall ((A2 set_a) (B3 set_a) (C3 set_a)) (let ((_let_1 (ord_less_eq_set_a A2))) (=> (_let_1 B3) (=> ((ord_less_eq_set_a B3) C3) (_let_1 C3))))) (forall ((X0 a)) (=> ((member_a X0) x) ((member_real zero_zero_real) (((auto_l612940ivl0_a f) x) X0)))) _let_11 (forall ((C a) (A2 set_a)) (let ((_let_1 (member_a C))) (=> (_let_1 (uminus_uminus_set_a A2)) (not (_let_1 A2))))) (forall ((A2 set_real) (B3 set_real)) (=> ((ord_less_set_real A2) B3) ((ord_less_eq_set_real A2) B3))) (forall ((A2 set_a) (B3 set_a) (C3 set_a)) (=> ((ord_less_eq_set_a A2) B3) (=> ((ord_less_eq_set_a B3) C3) (= ((minus_minus_set_a B3) ((minus_minus_set_a C3) A2)) A2)))) (_let_5 ((inner_1173012732nner_a (f z)) _let_10)) (forall ((A a) (B a)) (= ((ord_less_eq_a zero_zero_a) ((minus_minus_a A) B)) ((ord_less_eq_a B) A))) (forall ((A a)) (= (= zero_zero_a (uminus_uminus_a A)) (= zero_zero_a A))) (forall ((B a)) (= ((minus_minus_a zero_zero_a) B) (uminus_uminus_a B))) (forall ((X0 a)) (=> ((member_a X0) x) ((member_real zero_zero_real) (((auto_l612940ivl0_a (uminus_uminus_a_a f)) x) X0)))) (forall ((X0 a)) ((ord_less_eq_set_real (((auto_l612940ivl0_a f) x) X0)) top_top_set_real)) (forall ((A real) (B real) (C real) (D2 real)) (=> (= ((minus_minus_real A) B) ((minus_minus_real C) D2)) (= (= A B) (= C D2)))) (forall ((X0 a)) (initia826609931terval (((auto_l612940ivl0_a (uminus_uminus_a_a f)) x) X0))) (= (poinca659159244_rot_a zero_zero_a) zero_zero_a) (forall ((A real)) (= (= zero_zero_real (uminus_uminus_real A)) (= zero_zero_real A))) (forall ((X a)) (=> (((period720806154rbit_a f) x) X) ((member_a X) x))) (forall ((X a) (Y a)) (not ((ord_less_real ((real_V1514887919dist_a X) Y)) zero_zero_real))) (forall ((A2 set_real)) (= (collect_real (lambda ((X3 real)) ((member_real X3) A2))) A2)) (not (forall ((S a)) (=> ((member_a S) ((elemen49976720ball_a x2) d)) (not (forall ((X2 a)) (let ((_let_1 (poinca659159244_rot_a ((minus_minus_a a2) b)))) (=> ((member_a X2) ((elemen49976720ball_a x2) d)) ((ord_less_eq_real ((inner_1173012732nner_a (f S)) _let_1)) ((inner_1173012732nner_a (f X2)) _let_1))))))))) (forall ((A real)) (= ((ord_less_real (uminus_uminus_real A)) zero_zero_real) ((ord_less_real zero_zero_real) A))) (forall ((A a) (B a) (D2 a) (C a)) (=> ((ord_less_eq_a A) B) (=> ((ord_less_eq_a D2) C) ((ord_less_eq_a ((minus_minus_a A) C)) ((minus_minus_a B) D2))))) (forall ((A2 set_real) (B3 set_real)) ((ord_less_eq_set_real ((minus_minus_set_real A2) B3)) A2)) (forall ((A real)) (= (= (uminus_uminus_real A) A) (= A zero_zero_real))) (forall ((A real) (B real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (_let_1 A) (=> (_let_1 B) (_let_1 ((inner_4346926r_real A) B)))))) (forall ((M set_a)) (= (((auto_l630715367iant_a f) x) M) (forall ((X3 a)) (=> ((member_a X3) M) ((((oDE_au1996717075pped_a f) x) X3) M))))) (forall ((X a)) (=> ((member_a X) x) (=> (= (f X) zero_zero_a) (((period720806154rbit_a f) x) X)))) (forall ((X a)) (=> ((member_a X) x) (exists ((A4 real) (B4 real)) (and ((ord_less_eq_set_real ((set_or656347191t_real A4) B4)) (((auto_l612940ivl0_a f) x) X)) ((ord_less_real zero_zero_real) B4) ((ord_less_real A4) zero_zero_real))))) (forall ((A2 set_a) (B3 set_a)) ((ord_less_eq_set_a ((minus_minus_set_a A2) B3)) A2)) (= ord_less_eq_set_real (lambda ((A5 set_real) (B5 set_real)) (forall ((T real)) (let ((_let_1 (member_real T))) (=> (_let_1 A5) (_let_1 B5)))))) (forall ((X real)) (= ((ord_less_real zero_zero_real) ((inner_4346926r_real X) X)) (not (= X zero_zero_real)))) (forall ((X a) (A a) (B a) (I a)) (=> ((member_a X) ((set_or411607219Most_a A) B)) (=> ((ord_less_eq_a zero_zero_a) I) ((ord_less_eq_real ((inner_1173012732nner_a A) I)) ((inner_1173012732nner_a X) I))))) (forall ((X a) (Y a) (Z a)) (let ((_let_1 ((line_c1152468841ment_a X) Y))) (=> ((((poinca522724647ment_a f) x) X) Y) (=> ((member_a Z) _let_1) (=> ((ord_less_real ((inner_1173012732nner_a (f Z)) (poinca659159244_rot_a ((minus_minus_a X) Y)))) zero_zero_real) ((ord_less_eq_set_a _let_1) x)))))) (forall ((Y set_real) (X set_real)) (=> ((ord_less_eq_set_real (uminus773214379t_real Y)) X) ((ord_less_eq_set_real (uminus773214379t_real X)) Y))) (forall ((R real) (X a)) (=> ((ord_less_real zero_zero_real) R) (exists ((A4 a)) (and ((ord_less_real ((real_V1514887919dist_a A4) X)) R) (not (= A4 X)))))) (forall ((P (-> real Bool)) (Q (-> real Bool))) (=> (forall ((X4 real)) (=> (P X4) (Q X4))) ((ord_less_eq_set_real (collect_real P)) (collect_real Q)))) (forall ((Y set_a) (X set_a)) (=> ((ord_less_eq_set_a Y) (uminus_uminus_set_a X)) ((ord_less_eq_set_a X) (uminus_uminus_set_a Y)))) (forall ((A2 set_real) (B3 set_real)) (=> ((ord_less_eq_set_real A2) B3) (=> (not (= A2 B3)) ((ord_less_set_real A2) B3)))) (forall ((A real)) (= (= (uminus_uminus_real A) zero_zero_real) (= A zero_zero_real))) (forall ((A real)) (let ((_let_1 (ord_less_real A))) (= (_let_1 (uminus_uminus_real A)) (_let_1 zero_zero_real)))) (forall ((C real) (A2 set_real) (B3 set_real)) (let ((_let_1 (member_real C))) (=> (_let_1 ((minus_minus_set_real A2) B3)) (not (_let_1 B3))))) (forall ((A2 set_a) (B3 set_a)) (=> (= A2 B3) ((ord_less_eq_set_a B3) A2))) (forall ((A a)) (= ((ord_less_eq_a (uminus_uminus_a A)) zero_zero_a) ((ord_less_eq_a zero_zero_a) A))) (forall ((X a) (A a) (B a)) (=> ((member_a X) ((line_c1152468841ment_a A) B)) (= ((inner_1173012732nner_a ((minus_minus_a X) A)) (poinca659159244_rot_a ((minus_minus_a B) A))) zero_zero_real))) (forall ((I a) (L a) (U2 a)) (= ((member_a I) ((set_or411607219Most_a L) U2)) (and ((ord_less_eq_a L) I) ((ord_less_eq_a I) U2)))) (forall ((C a) (A2 set_a) (B3 set_a)) (let ((_let_1 (member_a C))) (=> (_let_1 A2) (=> (not (_let_1 B3)) (_let_1 ((minus_minus_set_a A2) B3)))))) (forall ((A real) (B real)) (or (not ((ord_less_eq_real B) A)) (not ((ord_less_eq_real A) B)) (= A B))) (forall ((A2 set_real) (B3 set_real)) (=> (= A2 B3) ((ord_less_eq_set_real B3) A2))) (forall ((A real) (B real)) (= ((ord_less_eq_real zero_zero_real) ((minus_minus_real A) B)) ((ord_less_eq_real B) A))) (forall ((A2 set_real) (C3 set_real) (D4 set_real) (B3 set_real)) (=> ((ord_less_eq_set_real A2) C3) (=> ((ord_less_eq_set_real D4) B3) ((ord_less_eq_set_real ((minus_minus_set_real A2) B3)) ((minus_minus_set_real C3) D4))))) (forall ((A a) (X a) (Y a)) (= ((inner_1173012732nner_a A) (poinca659159244_rot_a ((minus_minus_a X) Y))) ((inner_1173012732nner_a (uminus_uminus_a A)) (poinca659159244_rot_a ((minus_minus_a Y) X))))) (= ord_less_eq_a (lambda ((A3 a) (B2 a)) ((ord_less_eq_a ((minus_minus_a A3) B2)) zero_zero_a))) (forall ((X a)) (= ((inner_1173012732nner_a X) zero_zero_a) zero_zero_real)) _let_9 (forall ((A2 set_real) (B3 set_real) (C real)) (let ((_let_1 (member_real C))) (=> ((ord_less_set_real A2) B3) (=> (_let_1 A2) (_let_1 B3))))) (forall ((A2 set_real) (B3 set_real)) (=> (forall ((X4 real)) (let ((_let_1 (member_real X4))) (=> (_let_1 A2) (_let_1 B3)))) ((ord_less_eq_set_real A2) B3))) (forall ((P (-> a Bool)) (Q (-> a Bool))) (=> (forall ((X4 a)) (=> (P X4) (Q X4))) ((ord_less_eq_set_a (collect_a P)) (collect_a Q)))) (forall ((A2 set_real)) ((ord_less_eq_set_real A2) A2)) (forall ((A set_real) (B set_real) (C set_real) (D2 set_real)) (= ((ord_le1733505144t_real ((set_or1619725421t_real A) B)) ((set_or1619725421t_real C) D2)) (or (and ((ord_less_eq_set_real C) A) ((ord_less_eq_set_real B) D2)) (not ((ord_less_eq_set_real A) B))))) (forall ((A real) (B real)) (= ((ord_less_eq_real (uminus_uminus_real A)) B) ((ord_less_eq_real (uminus_uminus_real B)) A))) (forall ((A a) (B a)) (=> ((ord_less_eq_a A) B) ((ord_less_eq_a (uminus_uminus_a B)) (uminus_uminus_a A)))) (forall ((A real) (B real) (C real) (D2 real)) (let ((_let_1 (ord_less_eq_real C))) (= ((ord_less_set_real ((set_or656347191t_real A) B)) ((set_or656347191t_real C) D2)) (and (or (and (or ((ord_less_real C) A) ((ord_less_real B) D2)) ((ord_less_eq_real B) D2) (_let_1 A)) (not ((ord_less_eq_real A) B))) (_let_1 D2))))) (forall ((A a)) (= ((minus_minus_a A) A) zero_zero_a)) (forall ((L set_real) (H set_real) (L2 set_real) (H2 set_real)) (= (= ((set_or1619725421t_real L) H) ((set_or1619725421t_real L2) H2)) (or (and (= H H2) (= L L2)) (and (not ((ord_less_eq_set_real L) H)) (not ((ord_less_eq_set_real L2) H2)))))) (forall ((X set_real) (Y set_real)) (=> ((ord_less_eq_set_real X) Y) ((ord_less_eq_set_real (uminus773214379t_real Y)) (uminus773214379t_real X)))) (= poinca522724647ment_a poinca522724647ment_a) (forall ((A a) (B a) (X a)) (let ((_let_1 ((minus_minus_a B) A))) (=> (not (= A B)) (= ((member_a X) ((line_c1152468841ment_a A) B)) (and (= ((inner_1173012732nner_a ((minus_minus_a X) A)) (poinca659159244_rot_a _let_1)) zero_zero_real) ((member_real ((inner_1173012732nner_a X) _let_1)) ((set_or656347191t_real ((inner_1173012732nner_a A) _let_1)) ((inner_1173012732nner_a B) _let_1)))))))) (= ord_less_eq_set_a (lambda ((A5 set_a) (B5 set_a)) (or ((ord_less_set_a A5) B5) (= A5 B5)))) _let_8 (forall ((X a) (D2 real) (Y a) (E real)) (= (= ((elemen49976720ball_a X) D2) ((elemen49976720ball_a Y) E)) (or (and (= X Y) (= D2 E)) (and ((ord_less_real D2) zero_zero_real) ((ord_less_real E) zero_zero_real))))) (forall ((A real)) (= (= A (uminus_uminus_real A)) (= A zero_zero_real))) (forall ((A a) (B a)) (= ((ord_less_eq_a (uminus_uminus_a A)) B) ((ord_less_eq_a (uminus_uminus_a B)) A))) (= real_V1514887919dist_a (lambda ((X3 a) (Y3 a)) ((real_V1514887919dist_a Y3) X3))) (forall ((A real)) (not ((ord_less_real A) A))) (forall ((S2 (-> a real)) (Ds (-> a bounde7994401a_real)) (S3 set_a)) (=> (((((reacha1191408304tion_a (uminus_uminus_a_a f)) x) S2) Ds) S3) ((ord_less_eq_set_a S3) x))) (forall ((D2 real) (E real) (X a)) (let ((_let_1 (elemen49976720ball_a X))) (=> ((ord_less_eq_real D2) E) ((ord_less_eq_set_a (_let_1 D2)) (_let_1 E))))) (forall ((A2 set_real) (B3 set_real)) (=> ((ord_less_eq_set_real A2) B3) ((ord_less_eq_set_real (uminus773214379t_real B3)) (uminus773214379t_real A2)))) (forall ((C a) (A2 set_a) (B3 set_a)) (let ((_let_1 (member_a C))) (=> (_let_1 ((minus_minus_set_a A2) B3)) (not (_let_1 B3))))) (forall ((T2 real) (T0 real) (X0 a)) (=> ((member_real ((minus_minus_real T2) T0)) (((auto_l612940ivl0_a f) x) X0)) ((member_real T2) top_top_set_real))) (forall ((X a)) (let ((_let_1 (uminus_uminus_a_a f))) (=> (((period720806154rbit_a _let_1) x) X) ((ord_less_eq_real zero_zero_real) (((period1305449585riod_a _let_1) x) X))))) (forall ((A2 set_real) (B3 set_real)) (=> ((ord_less_eq_set_real A2) B3) (=> ((ord_less_eq_set_real B3) A2) (= A2 B3)))) (forall ((B a) (A a)) (= (poinca659159244_rot_a ((minus_minus_a B) A)) (uminus_uminus_a (poinca659159244_rot_a ((minus_minus_a A) B))))) (= (lambda ((Y4 set_real) (Z3 set_real)) (= Y4 Z3)) (lambda ((A5 set_real) (B5 set_real)) (and ((ord_less_eq_set_real A5) B5) ((ord_less_eq_set_real B5) A5)))) (forall ((A a)) (= ((ord_less_a (uminus_uminus_a A)) zero_zero_a) ((ord_less_a zero_zero_a) A))) (forall ((A a) (B a) (C a) (D2 a)) (=> (= ((minus_minus_a A) B) ((minus_minus_a C) D2)) (= ((ord_less_a A) B) ((ord_less_a C) D2)))) (forall ((X real) (E real)) (= ((member_real X) ((elemen1140313242l_real X) E)) ((ord_less_eq_real zero_zero_real) E))) (forall ((A real) (B real) (C real) (D2 real)) (=> (= ((minus_minus_real A) B) ((minus_minus_real C) D2)) (= ((ord_less_eq_real A) B) ((ord_less_eq_real C) D2)))) (forall ((X a)) (=> (((period138238489rbit_a f) x) X) ((ord_less_real zero_zero_real) (((period1305449585riod_a f) x) X)))) (forall ((X a)) (let ((_let_1 (uminus_uminus_a_a f))) (=> ((member_a X) x) (=> (= (_let_1 X) zero_zero_a) (= (((period1305449585riod_a _let_1) x) X) zero_zero_real))))) (forall ((X real) (A real) (B real) (I real)) (=> ((member_real X) ((set_or656347191t_real A) B)) (=> ((ord_less_eq_real zero_zero_real) I) ((ord_less_eq_real ((inner_4346926r_real A) I)) ((inner_4346926r_real X) I))))) (forall ((A real)) (= ((minus_minus_real A) zero_zero_real) A)) _let_7 (forall ((P (-> real Bool)) (Q (-> real Bool))) (= ((ord_less_eq_set_real (collect_real P)) (collect_real Q)) (forall ((X3 real)) (=> (P X3) (Q X3))))) (forall ((A a) (B a) (C a)) (=> ((ord_less_a A) B) ((ord_less_a ((minus_minus_a A) C)) ((minus_minus_a B) C)))) (forall ((A2 set_real) (B3 set_real) (C3 set_real)) (let ((_let_1 (ord_less_eq_set_real A2))) (=> (_let_1 B3) (=> ((ord_less_eq_set_real B3) C3) (_let_1 C3))))) (forall ((Z a)) (=> ((member_a Z) ((line_c1152468841ment_a a2) b)) ((ord_less_real zero_zero_real) ((inner_1173012732nner_a (f Z)) (poinca659159244_rot_a ((minus_minus_a a2) b)))))) (forall ((A a) (B a)) (=> (= A B) (= (uminus_uminus_a A) (uminus_uminus_a B)))) (forall ((A a) (B a) (C a) (D2 a)) (= ((ord_less_eq_set_a ((set_or411607219Most_a A) B)) ((set_or411607219Most_a C) D2)) (or (and ((ord_less_eq_a C) A) ((ord_less_eq_a B) D2)) (not ((ord_less_eq_a A) B))))) (forall ((A real)) (let ((_let_1 (ord_less_eq_real A))) (= (_let_1 (uminus_uminus_real A)) (_let_1 zero_zero_real)))) (forall ((X a)) (let ((_let_1 (uminus_uminus_a_a f))) (=> (((period138238489rbit_a _let_1) x) X) ((ord_less_real zero_zero_real) (((period1305449585riod_a _let_1) x) X))))) (forall ((A real) (B real) (P (-> real real Bool))) (=> ((ord_less_eq_real A) B) (=> (forall ((A4 real) (B4 real) (C2 real)) (let ((_let_1 (P A4))) (=> (_let_1 B4) (=> ((P B4) C2) (=> ((ord_less_eq_real A4) B4) (=> ((ord_less_eq_real B4) C2) (_let_1 C2))))))) (=> (forall ((X4 real)) (=> ((ord_less_eq_real A) X4) (=> ((ord_less_eq_real X4) B) (exists ((D3 real)) (and ((ord_less_real zero_zero_real) D3) (forall ((A4 real) (B4 real)) (=> (and ((ord_less_eq_real X4) B4) ((ord_less_real ((minus_minus_real B4) A4)) D3) ((ord_less_eq_real A4) X4)) ((P A4) B4)))))))) ((P A) B))))) (forall ((A2 set_real) (B3 set_real) (C real)) (let ((_let_1 (member_real C))) (=> ((ord_less_eq_set_real A2) B3) (=> (_let_1 A2) (_let_1 B3))))) (forall ((X real)) ((member_real X) top_top_set_real)) (forall ((X a)) (let ((_let_1 (uminus_uminus_a_a f))) (=> (((period720806154rbit_a _let_1) x) X) (=> (= (((period1305449585riod_a _let_1) x) X) zero_zero_real) (= (_let_1 X) zero_zero_a))))) (forall ((W a) (Y a)) (=> ((((poinca522724647ment_a f) x) W) Y) (=> ((ord_less_real ((inner_1173012732nner_a (f W)) (poinca659159244_rot_a ((minus_minus_a W) Y)))) zero_zero_real) (forall ((X2 a)) (=> ((member_a X2) ((line_c1152468841ment_a W) Y)) ((ord_less_real ((inner_1173012732nner_a (f X2)) (poinca659159244_rot_a ((minus_minus_a W) Y)))) zero_zero_real)))))) (forall ((L real) (H real) (L2 real) (H2 real)) (= (= ((set_or656347191t_real L) H) ((set_or656347191t_real L2) H2)) (or (and (= L L2) (= H H2)) (and (not ((ord_less_eq_real L2) H2)) (not ((ord_less_eq_real L) H)))))) (forall ((T2 real) (X0 a)) (let ((_let_1 (((auto_l612940ivl0_a f) x) X0))) (=> ((member_real T2) _let_1) ((ord_less_eq_set_real ((set_or656347191t_real T2) zero_zero_real)) _let_1)))) _let_6 (_let_2 x) (= (lambda ((Y4 a) (Z3 a)) (= Y4 Z3)) (lambda ((A3 a) (B2 a)) (= ((minus_minus_a A3) B2) zero_zero_a))) (forall ((T2 real) (X0 a)) (=> ((member_real T2) (((auto_l612940ivl0_a f) x) X0)) ((member_a X0) x))) (= uminus_uminus_a_a (lambda ((A5 (-> a a)) (X3 a)) (uminus_uminus_a (A5 X3)))) (forall ((X a) (Y a) (Z a)) (= ((inner_1173012732nner_a ((minus_minus_a X) Y)) Z) ((minus_minus_real ((inner_1173012732nner_a X) Z)) ((inner_1173012732nner_a Y) Z)))) (forall ((X a)) (= (((period138238489rbit_a f) x) X) (and (((period720806154rbit_a f) x) X) ((ord_less_real zero_zero_real) (((period1305449585riod_a f) x) X))))) (forall ((B real)) (= (uminus_uminus_real (uminus_uminus_real B)) B)) (forall ((X real)) (= ((inner_4346926r_real X) zero_zero_real) zero_zero_real)) (forall ((A2 set_set_a)) (= (collect_set_a (lambda ((X3 set_a)) ((member_set_a X3) A2))) A2)) (= ord_less_a (lambda ((A3 a) (B2 a)) ((ord_less_a ((minus_minus_a A3) B2)) zero_zero_a))) (forall ((A2 set_a) (B3 set_a) (X a)) (let ((_let_1 (member_a X))) (=> ((ord_less_eq_set_a A2) B3) (=> (_let_1 A2) (_let_1 B3))))) (forall ((A real) (B real)) (= ((ord_less_real (uminus_uminus_real A)) B) ((ord_less_real (uminus_uminus_real B)) A))) (forall ((A real) (B real)) (= (= (uminus_uminus_real A) B) (= (uminus_uminus_real B) A))) (forall ((Y real) (X real) (E real)) (= ((member_real Y) ((elemen1140313242l_real X) E)) ((ord_less_eq_real ((real_V1934908667t_real X) Y)) E))) (= (uminus_uminus_real zero_zero_real) zero_zero_real) (not (= a2 b)) (forall ((A real)) (= ((minus_minus_real A) A) zero_zero_real)) (forall ((B a)) (= (uminus_uminus_a (uminus_uminus_a B)) B)) (forall ((A a) (B a) (C a) (D2 a)) (=> (= ((minus_minus_a A) B) ((minus_minus_a C) D2)) (= (= A B) (= C D2)))) (forall ((X a)) (let ((_let_1 (uminus_uminus_a_a f))) (=> (((period720806154rbit_a _let_1) x) X) (=> (not (= (_let_1 X) zero_zero_a)) (((period138238489rbit_a _let_1) x) X))))) (forall ((A a) (B a)) (= ((ord_less_a A) (uminus_uminus_a B)) ((ord_less_a B) (uminus_uminus_a A)))) (forall ((X a)) (= ((ord_less_real zero_zero_real) ((inner_1173012732nner_a X) X)) (not (= X zero_zero_a)))) (forall ((X a) (Y a) (W a)) (=> ((((poinca522724647ment_a f) x) X) Y) (=> ((member_a W) ((line_c1152468841ment_a X) Y)) (=> ((ord_less_real zero_zero_real) ((inner_1173012732nner_a (f W)) (poinca659159244_rot_a ((minus_minus_a X) Y)))) (forall ((X2 a)) (=> ((member_a X2) ((line_c1152468841ment_a X) Y)) ((ord_less_real zero_zero_real) ((inner_1173012732nner_a (f X2)) (poinca659159244_rot_a ((minus_minus_a X) Y)))))))))) (forall ((X a)) (=> ((member_a X) x) (=> (= (f X) zero_zero_a) (= (((auto_l612940ivl0_a f) x) X) top_top_set_real)))) (forall ((A2 set_real) (B3 set_real) (C3 set_real)) (let ((_let_1 (ord_less_set_real A2))) (=> (_let_1 B3) (=> ((ord_less_eq_set_real B3) C3) (_let_1 C3))))) (forall ((X a)) (= (= zero_zero_a X) (= X zero_zero_a))) (forall ((X0 a)) (initia826609931terval (((auto_l612940ivl0_a f) x) X0))) (forall ((B a) (A a)) (= ((ord_less_a (uminus_uminus_a B)) (uminus_uminus_a A)) ((ord_less_a A) B))) (= ord_less_eq_set_real (lambda ((A5 set_real) (B5 set_real)) (or ((ord_less_set_real A5) B5) (= A5 B5)))) (forall ((A real) (B real) (C real) (D2 real)) (= ((ord_less_eq_set_real ((set_or656347191t_real A) B)) ((set_or656347191t_real C) D2)) (or (and ((ord_less_eq_real B) D2) ((ord_less_eq_real C) A)) (not ((ord_less_eq_real A) B))))) (forall ((X a) (Y a) (Za a) (Z a)) (let ((_let_1 (poinca659159244_rot_a ((minus_minus_a X) Y)))) (let ((_let_2 (ord_less_real zero_zero_real))) (let ((_let_3 ((line_c1152468841ment_a X) Y))) (=> ((((poinca522724647ment_a f) x) X) Y) (=> ((member_a Za) _let_3) (=> (_let_2 ((inner_1173012732nner_a (f Za)) _let_1)) (=> ((member_a Z) _let_3) (_let_2 ((inner_1173012732nner_a (f Z)) _let_1)))))))))) _let_4 (forall ((X a) (Y a)) (let ((_let_1 (inner_1173012732nner_a X))) (= (_let_1 (uminus_uminus_a Y)) (uminus_uminus_real (_let_1 Y))))) (forall ((X real) (Y real) (E real) (F real)) (let ((_let_1 (elemen1140313242l_real Y))) (let ((_let_2 (member_real X))) (=> (_let_2 (_let_1 E)) (=> ((ord_less_eq_real E) F) (_let_2 (_let_1 F))))))) (forall ((C a) (A2 set_a) (B3 set_a)) (let ((_let_1 (member_a C))) (=> (_let_1 ((minus_minus_set_a A2) B3)) (_let_1 A2)))) (forall ((T2 real) (X0 a)) (=> ((member_real T2) (((auto_l612940ivl0_a (uminus_uminus_a_a f)) x) X0)) ((member_a X0) x))) (forall ((X a) (Y a)) (let ((_let_1 ((minus_minus_a X) Y))) (= ((inner_1173012732nner_a _let_1) (poinca659159244_rot_a _let_1)) zero_zero_real))) (forall ((X real) (Y real)) (let ((_let_1 (inner_4346926r_real X))) (= (_let_1 (uminus_uminus_real Y)) (uminus_uminus_real (_let_1 Y))))) ((((poinca522724647ment_a f) x) a2) b) (forall ((X a)) (= (= ((inner_1173012732nner_a X) X) zero_zero_real) (= X zero_zero_a))) (forall ((X a) (Y a)) (= ((ord_less_real zero_zero_real) ((real_V1514887919dist_a X) Y)) (not (= X Y)))) (forall ((X a) (Y a) (Z a)) (=> ((((poinca522724647ment_a f) x) X) Y) (=> ((member_a Z) ((line_c1152468841ment_a X) Y)) (=> ((ord_less_real zero_zero_real) ((inner_1173012732nner_a (f Z)) (poinca659159244_rot_a ((minus_minus_a X) Y)))) (not (= X Y)))))) (forall ((Y set_real) (X set_real)) (=> ((ord_less_eq_set_real Y) (uminus773214379t_real X)) ((ord_less_eq_set_real X) (uminus773214379t_real Y)))) (forall ((M set_a)) (let ((_let_1 ((auto_l630715367iant_a f) x))) (= (_let_1 M) (_let_1 ((minus_minus_set_a x) M))))) (forall ((B a) (A a) (C a)) (let ((_let_1 (minus_minus_a C))) (=> ((ord_less_eq_a B) A) ((ord_less_eq_a (_let_1 A)) (_let_1 B))))) (forall ((A2 set_a) (B3 set_a)) (=> ((ord_less_eq_set_a A2) B3) ((ord_less_eq_set_a (uminus_uminus_set_a B3)) (uminus_uminus_set_a A2)))) (forall ((M set_a)) (= (((auto_l630715367iant_a (uminus_uminus_a_a f)) x) M) (((auto_l630715367iant_a f) x) M))) _let_3 (forall ((C real) (A2 set_real) (B3 set_real)) (let ((_let_1 (member_real C))) (=> (_let_1 ((minus_minus_set_real A2) B3)) (not (=> (_let_1 A2) (_let_1 B3)))))) (forall ((X a)) (let ((_let_1 (uminus_uminus_a_a f))) (=> ((member_a X) x) (=> (= (_let_1 X) zero_zero_a) (= (((auto_l612940ivl0_a _let_1) x) X) top_top_set_real))))) (forall ((A set_a) (B set_a) (C set_a) (D2 set_a)) (let ((_let_1 (ord_less_eq_set_a C))) (= ((ord_less_set_set_a ((set_or2094724627_set_a A) B)) ((set_or2094724627_set_a C) D2)) (and (_let_1 D2) (or (not ((ord_less_eq_set_a A) B)) (and (_let_1 A) ((ord_less_eq_set_a B) D2) (or ((ord_less_set_a B) D2) ((ord_less_set_a C) A)))))))) (forall ((X a)) (=> ((member_a X) x) (not (forall ((A4 real)) (=> ((ord_less_real zero_zero_real) A4) (not ((ord_less_eq_set_real ((set_or656347191t_real (uminus_uminus_real A4)) A4)) (((auto_l612940ivl0_a f) x) X)))))))) (forall ((A2 set_real) (B3 set_real)) (=> (= A2 B3) ((ord_less_eq_set_real A2) B3))) (forall ((A real) (B real)) (= ((ord_less_real A) (uminus_uminus_real B)) ((ord_less_real B) (uminus_uminus_real A)))) (forall ((B real) (A real) (C real)) (let ((_let_1 (minus_minus_real C))) (=> ((ord_less_eq_real B) A) ((ord_less_eq_real (_let_1 A)) (_let_1 B))))) (forall ((A set_real) (B set_real) (C set_real) (D2 set_real)) (let ((_let_1 (ord_less_eq_set_real C))) (= ((ord_le861030508t_real ((set_or1619725421t_real A) B)) ((set_or1619725421t_real C) D2)) (and (or (not ((ord_less_eq_set_real A) B)) (and (_let_1 A) (or ((ord_less_set_real B) D2) ((ord_less_set_real C) A)) ((ord_less_eq_set_real B) D2))) (_let_1 D2))))) (forall ((X real)) (= (= ((inner_4346926r_real X) X) zero_zero_real) (= X zero_zero_real))) (forall ((A2 set_real) (B3 set_real) (C3 set_real)) (=> ((ord_less_eq_set_real A2) B3) (=> ((ord_less_set_real B3) C3) ((ord_less_set_real A2) C3)))) (forall ((X a)) (=> ((member_a X) x) (exists ((A4 real) (B4 real)) (and ((ord_less_eq_set_real ((set_or656347191t_real A4) B4)) (((auto_l612940ivl0_a (uminus_uminus_a_a f)) x) X)) ((ord_less_real zero_zero_real) B4) ((ord_less_real A4) zero_zero_real))))) (forall ((A real)) (= ((ord_less_real zero_zero_real) (uminus_uminus_real A)) ((ord_less_real A) zero_zero_real))) (forall ((X a) (Y a) (E real) (F real)) (let ((_let_1 (elemen49976720ball_a Y))) (let ((_let_2 (member_a X))) (=> (_let_2 (_let_1 E)) (=> ((ord_less_eq_real E) F) (_let_2 (_let_1 F))))))) (forall ((X set_a) (Y set_a)) (=> ((ord_less_eq_set_a X) Y) ((ord_less_eq_set_a (uminus_uminus_set_a Y)) (uminus_uminus_set_a X)))) (forall ((X a)) (=> (((period720806154rbit_a (uminus_uminus_a_a f)) x) X) ((member_a X) x))) (forall ((A2 set_a) (B3 set_a) (C3 set_a)) (=> ((ord_less_eq_set_a A2) B3) (=> ((ord_less_set_a B3) C3) ((ord_less_set_a A2) C3)))) (forall ((L set_a) (H set_a) (L2 set_a) (H2 set_a)) (= (= ((set_or2094724627_set_a L) H) ((set_or2094724627_set_a L2) H2)) (or (and (not ((ord_less_eq_set_a L2) H2)) (not ((ord_less_eq_set_a L) H))) (and (= L L2) (= H H2))))) (forall ((X a) (A a) (B a) (Y a)) (let ((_let_1 ((line_c1152468841ment_a A) B))) (=> ((member_a X) _let_1) (=> ((member_a Y) _let_1) (= ((inner_1173012732nner_a ((minus_minus_a X) Y)) (poinca659159244_rot_a ((minus_minus_a A) B))) zero_zero_real))))) (forall ((A a) (B a) (C a) (D2 a)) (=> (= ((minus_minus_a A) B) ((minus_minus_a C) D2)) (= ((ord_less_eq_a A) B) ((ord_less_eq_a C) D2)))) (forall ((I set_a) (L set_a) (U2 set_a)) (= ((member_set_a I) ((set_or2094724627_set_a L) U2)) (and ((ord_less_eq_set_a I) U2) ((ord_less_eq_set_a L) I)))) (forall ((X a) (Y a)) (= (= ((real_V1514887919dist_a X) Y) zero_zero_real) (= X Y))) (forall ((X a) (Y a)) (let ((_let_1 ((poinca522724647ment_a f) x))) (= ((_let_1 X) Y) ((_let_1 Y) X)))) (forall ((X a) (Y a) (Z a)) (=> ((((poinca522724647ment_a f) x) X) Y) (=> ((member_a Z) ((line_c1152468841ment_a X) Y)) (=> ((ord_less_real ((inner_1173012732nner_a (f Z)) (poinca659159244_rot_a ((minus_minus_a X) Y)))) zero_zero_real) (not (= X Y)))))) (forall ((A real)) (= ((minus_minus_real A) A) zero_zero_real)) (forall ((X a) (Y a)) (= ((inner_1173012732nner_a (uminus_uminus_a X)) Y) (uminus_uminus_real ((inner_1173012732nner_a X) Y)))) (forall ((A real) (B real) (D2 real) (C real)) (=> ((ord_less_real A) B) (=> ((ord_less_real D2) C) ((ord_less_real ((minus_minus_real A) C)) ((minus_minus_real B) D2))))) (forall ((X a) (Y a) (Z a)) (let ((_let_1 (inner_1173012732nner_a X))) (= (_let_1 ((minus_minus_a Y) Z)) ((minus_minus_real (_let_1 Y)) (_let_1 Z))))) (forall ((B6 real) (A6 real)) (= (not ((ord_less_eq_real B6) A6)) ((ord_less_real A6) B6))) (forall ((X a)) (= (forall ((U a)) (= ((inner_1173012732nner_a X) U) zero_zero_real)) (= X zero_zero_a))) (forall ((V a)) (= (poinca659159244_rot_a (poinca659159244_rot_a V)) (uminus_uminus_a V))) (forall ((X a)) (let ((_let_1 (uminus_uminus_a_a f))) (=> (((period720806154rbit_a _let_1) x) X) (= (((auto_l612940ivl0_a _let_1) x) X) top_top_set_real)))) (forall ((B real)) (= ((minus_minus_real zero_zero_real) B) (uminus_uminus_real B))) (forall ((A set_a) (B set_a) (C set_a) (D2 set_a)) (= ((ord_le318720350_set_a ((set_or2094724627_set_a A) B)) ((set_or2094724627_set_a C) D2)) (or (and ((ord_less_eq_set_a B) D2) ((ord_less_eq_set_a C) A)) (not ((ord_less_eq_set_a A) B))))) (= ord_less_set_real (lambda ((A5 set_real) (B5 set_real)) (and ((ord_less_eq_set_real A5) B5) (not ((ord_less_eq_set_real B5) A5))))) (forall ((X a) (Y a) (W a)) (=> ((((poinca522724647ment_a f) x) X) Y) (=> ((member_a W) ((line_c1152468841ment_a X) Y)) (=> ((ord_less_real ((inner_1173012732nner_a (f W)) (poinca659159244_rot_a ((minus_minus_a X) Y)))) zero_zero_real) (forall ((X2 a)) (=> ((member_a X2) ((line_c1152468841ment_a X) Y)) ((ord_less_real ((inner_1173012732nner_a (f X2)) (poinca659159244_rot_a ((minus_minus_a X) Y)))) zero_zero_real))))))) (_let_2 _let_1) (forall ((T2 real) (X0 a)) (let ((_let_1 (((auto_l612940ivl0_a f) x) X0))) (=> ((member_real T2) _let_1) ((ord_less_eq_set_real ((set_or656347191t_real zero_zero_real) T2)) _let_1)))) (= (lambda ((Y4 real) (Z3 real)) (= Y4 Z3)) (lambda ((A3 real) (B2 real)) (= ((minus_minus_real A3) B2) zero_zero_real))) (forall ((A real) (B real)) (= ((ord_less_eq_real A) (uminus_uminus_real B)) ((ord_less_eq_real B) (uminus_uminus_real A)))) (forall ((T2 real) (X0 a)) (let ((_let_1 (member_real T2))) (=> (_let_1 (((auto_l612940ivl0_a f) x) X0)) (_let_1 top_top_set_real)))) (= inner_1173012732nner_a (lambda ((X3 a) (Y3 a)) ((inner_1173012732nner_a Y3) X3))) (forall ((B a) (A a) (C a)) (let ((_let_1 (minus_minus_a C))) (=> ((ord_less_a B) A) ((ord_less_a (_let_1 A)) (_let_1 B))))) (forall ((X a)) (=> (((period720806154rbit_a f) x) X) ((ord_less_eq_real zero_zero_real) (((period1305449585riod_a f) x) X)))) (forall ((C real) (A2 set_real) (B3 set_real)) (let ((_let_1 (member_real C))) (=> (_let_1 A2) (=> (not (_let_1 B3)) (_let_1 ((minus_minus_set_real A2) B3)))))) (forall ((I set_real) (L set_real) (U2 set_real)) (= ((member_set_real I) ((set_or1619725421t_real L) U2)) (and ((ord_less_eq_set_real L) I) ((ord_less_eq_set_real I) U2)))) (forall ((X a)) (= ((inner_1173012732nner_a X) (poinca659159244_rot_a X)) zero_zero_real)) (forall ((A2 set_real) (B3 set_real)) (=> ((ord_less_set_real A2) B3) (exists ((B4 real)) ((member_real B4) ((minus_minus_set_real B3) A2))))) (forall ((A a) (B a) (D2 a) (C a)) (=> ((ord_less_a A) B) (=> ((ord_less_a D2) C) ((ord_less_a ((minus_minus_a A) C)) ((minus_minus_a B) D2))))) (forall ((X real)) (= (forall ((U real)) (= ((inner_4346926r_real X) U) zero_zero_real)) (= X zero_zero_real))) (forall ((A a) (B a)) (let ((_let_1 (ord_less_eq_a zero_zero_a))) (=> (_let_1 A) (=> (_let_1 B) ((ord_less_eq_real zero_zero_real) ((inner_1173012732nner_a A) B)))))) (forall ((S2 (-> a real)) (Ds (-> a bounde7994401a_real)) (S3 set_a)) (=> (((((reacha1191408304tion_a f) x) S2) Ds) S3) ((ord_less_eq_set_a S3) x))) (forall ((D2 real) (E real) (X real)) (let ((_let_1 (elemen1140313242l_real X))) (=> ((ord_less_eq_real D2) E) ((ord_less_eq_set_real (_let_1 D2)) (_let_1 E))))) (forall ((A a)) (= ((minus_minus_a A) A) zero_zero_a)) (forall ((M set_a)) (let ((_let_1 ((auto_l630715367iant_a (uminus_uminus_a_a f)) x))) (= (_let_1 M) (_let_1 ((minus_minus_set_a x) M))))) (forall ((A a) (B a)) (= (uminus_uminus_a ((minus_minus_a A) B)) ((minus_minus_a B) A))) (forall ((C a) (A2 set_a)) (let ((_let_1 (member_a C))) (= (_let_1 (uminus_uminus_set_a A2)) (not (_let_1 A2))))) (forall ((A real) (B real) (C real)) (=> ((ord_less_eq_real A) B) ((ord_less_eq_real ((minus_minus_real A) C)) ((minus_minus_real B) C)))) (forall ((A a)) (= ((minus_minus_a zero_zero_a) A) (uminus_uminus_a A))) (forall ((A2 set_a) (B3 set_a) (C a)) (let ((_let_1 (member_a C))) (=> ((ord_less_set_a A2) B3) (=> (_let_1 A2) (_let_1 B3))))) (= ord_less_eq_set_a (lambda ((A5 set_a) (B5 set_a)) (forall ((T a)) (let ((_let_1 (member_a T))) (=> (_let_1 A5) (_let_1 B5)))))) (forall ((X a)) (= ((inner_1173012732nner_a zero_zero_a) X) zero_zero_real)) (forall ((A a) (B a)) (= ((((poinca522724647ment_a f) x) A) B) (and (not (= A B)) (forall ((X3 a)) (=> ((member_a X3) ((line_c1152468841ment_a A) B)) (not (= ((inner_1173012732nner_a (f X3)) (poinca659159244_rot_a ((minus_minus_a A) B))) zero_zero_real)))) ((ord_less_eq_set_a ((line_c1152468841ment_a A) B)) x)))) (forall ((X a)) (=> (((period720806154rbit_a f) x) X) (=> (not (= (f X) zero_zero_a)) (((period138238489rbit_a f) x) X)))) (forall ((Y a) (X a) (E real)) (= ((member_a Y) ((elemen49976720ball_a X) E)) ((ord_less_eq_real ((real_V1514887919dist_a X) Y)) E))) (forall ((C a) (A2 set_a)) (let ((_let_1 (member_a C))) (=> (not (_let_1 A2)) (_let_1 (uminus_uminus_set_a A2))))) (forall ((X a) (Y a)) (= ((ord_less_eq_real ((real_V1514887919dist_a X) Y)) zero_zero_real) (= X Y))) (forall ((X0 a)) (let ((_let_1 (member_real zero_zero_real))) (=> (_let_1 top_top_set_real) (=> ((member_a X0) x) (_let_1 (((auto_l612940ivl0_a (uminus_uminus_a_a f)) x) X0)))))) (not false)))))))))))))))))))))))))))))))))))))))))))))))))))
12.83/13.00	)
12.83/13.00	% SZS output end Proof for theBenchmark
12.83/13.00	EOF