0.07/0.15 % Problem : Vampire---4.8_14315 : TPTP v0.0.0. Released v0.0.0. 0.07/0.16 % Command : do_cvc5 %s %d 0.15/0.35 % Computer : n008.cluster.edu 0.15/0.35 % Model : x86_64 x86_64 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.35 % Memory : 8042.1875MB 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.35 % CPULimit : 1440 0.15/0.35 % WCLimit : 180 0.15/0.35 % DateTime : Mon Jul 3 13:09:34 EDT 2023 0.15/0.35 % CPUTime : 0.19/0.51 %----Proving TH0 0.19/0.51 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type, 0.19/0.51 set_real: $tType ). 0.19/0.51 0.19/0.51 thf(ty_n_t__Set__Oset_Itf__a_J,type, 0.19/0.51 set_a: $tType ). 0.19/0.51 0.19/0.51 thf(ty_n_t__Real__Oreal,type, 0.19/0.51 real: $tType ). 0.19/0.51 0.19/0.51 thf(ty_n_tf__a,type, 0.19/0.51 a: $tType ). 0.19/0.51 0.19/0.51 thf(sy_c_Elementary__Metric__Spaces_Oball_001t__Real__Oreal,type, 0.19/0.51 elemen341675809l_real: real > real > set_real ). 0.19/0.51 0.19/0.51 thf(sy_c_Elementary__Metric__Spaces_Oball_001tf__a,type, 0.19/0.51 elemen154694473ball_a: a > real > set_a ). 0.19/0.51 0.19/0.51 thf(sy_c_Flow_Oauto__ll__on__open_Oexistence__ivl0_001tf__a,type, 0.19/0.51 auto_l612940ivl0_a: ( a > a ) > set_a > a > set_real ). 0.19/0.51 0.19/0.51 thf(sy_c_Flow_Oauto__ll__on__open_Oflow0_001tf__a,type, 0.19/0.51 auto_ll_on_flow0_a: ( a > a ) > set_a > a > real > a ). 0.19/0.51 0.19/0.51 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type, 0.19/0.51 abs_abs_real: real > real ). 0.19/0.51 0.19/0.51 thf(sy_c_Groups_Oabs__class_Oabs_001tf__a,type, 0.19/0.51 abs_abs_a: a > a ). 0.19/0.51 0.19/0.51 thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type, 0.19/0.51 one_one_real: real ). 0.19/0.51 0.19/0.51 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type, 0.19/0.51 plus_plus_real: real > real > real ). 0.19/0.51 0.19/0.51 thf(sy_c_Groups_Oplus__class_Oplus_001tf__a,type, 0.19/0.51 plus_plus_a: a > a > a ). 0.19/0.51 0.19/0.51 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_Itf__a_Mtf__a_J,type, 0.19/0.51 uminus_uminus_a_a: ( a > a ) > a > a ). 0.19/0.51 0.19/0.51 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type, 0.19/0.51 uminus_uminus_real: real > real ). 0.19/0.51 0.19/0.51 thf(sy_c_Groups_Ouminus__class_Ouminus_001tf__a,type, 0.19/0.51 uminus_uminus_a: a > a ). 0.19/0.51 0.19/0.51 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type, 0.19/0.51 zero_zero_real: real ). 0.19/0.51 0.19/0.51 thf(sy_c_Groups_Ozero__class_Ozero_001tf__a,type, 0.19/0.51 zero_zero_a: a ). 0.19/0.51 0.19/0.51 thf(sy_c_If_001t__Real__Oreal,type, 0.19/0.51 if_real: $o > real > real > real ). 0.19/0.51 0.19/0.51 thf(sy_c_Initial__Value__Problem_Ointerval,type, 0.19/0.51 initia826609931terval: set_real > $o ). 0.19/0.51 0.19/0.51 thf(sy_c_Limit__Set_Oauto__ll__on__open_O_092_060alpha_062__limit__point_001tf__a,type, 0.19/0.51 limit_1865182413oint_a: ( a > a ) > set_a > a > a > $o ). 0.19/0.51 0.19/0.51 thf(sy_c_Limit__Set_Oauto__ll__on__open_O_092_060omega_062__limit__point_001tf__a,type, 0.19/0.51 limit_94460170oint_a: ( a > a ) > set_a > a > a > $o ). 0.19/0.51 0.19/0.51 thf(sy_c_Line__Segment_Oopen__segment_001tf__a,type, 0.19/0.51 line_open_segment_a: a > a > set_a ). 0.19/0.51 0.19/0.51 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type, 0.19/0.51 bot_bot_set_real: set_real ). 0.19/0.51 0.19/0.51 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type, 0.19/0.51 bot_bot_set_a: set_a ). 0.19/0.51 0.19/0.51 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type, 0.19/0.51 ord_less_real: real > real > $o ). 0.19/0.51 0.19/0.51 thf(sy_c_Orderings_Oord__class_Oless_001tf__a,type, 0.19/0.51 ord_less_a: a > a > $o ). 0.19/0.51 0.19/0.51 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type, 0.19/0.51 ord_less_eq_real: real > real > $o ). 0.19/0.51 0.19/0.51 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__a,type, 0.19/0.51 ord_less_eq_a: a > a > $o ). 0.19/0.51 0.19/0.51 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type, 0.19/0.51 top_top_set_real: set_real ). 0.19/0.51 0.19/0.51 thf(sy_c_Periodic__Orbit_Oauto__ll__on__open_Oclosed__orbit_001tf__a,type, 0.19/0.51 period720806154rbit_a: ( a > a ) > set_a > a > $o ). 0.19/0.51 0.19/0.51 thf(sy_c_Periodic__Orbit_Oauto__ll__on__open_Operiod_001tf__a,type, 0.19/0.51 period1305449585riod_a: ( a > a ) > set_a > a > real ). 0.19/0.51 0.19/0.51 thf(sy_c_Periodic__Orbit_Oauto__ll__on__open_Operiodic__orbit_001tf__a,type, 0.19/0.51 period138238489rbit_a: ( a > a ) > set_a > a > $o ). 0.19/0.51 0.19/0.51 thf(sy_c_Poincare__Bendixson__Mirabelle__pwkwpzhsyu_Oc1__on__open__R2_Otransversal__segment_001tf__a,type, 0.19/0.51 poinca522724647ment_a: ( a > a ) > set_a > a > a > $o ). 0.19/0.51 0.19/0.51 thf(sy_c_Set_OCollect_001t__Real__Oreal,type, 0.19/0.51 collect_real: ( real > $o ) > set_real ). 0.19/0.51 0.19/0.51 thf(sy_c_Set_OCollect_001tf__a,type, 0.19/0.51 collect_a: ( a > $o ) > set_a ). 0.19/0.51 0.19/0.51 thf(sy_c_Topological__Spaces_Ocontinuous__on_001tf__a_001t__Real__Oreal,type, 0.19/0.51 topolo1710226732a_real: set_a > ( a > real ) > $o ). 0.19/0.51 0.19/0.51 thf(sy_c_member_001t__Real__Oreal,type, 0.19/0.51 member_real: real > set_real > $o ). 0.19/0.51 0.19/0.51 thf(sy_c_member_001tf__a,type, 0.19/0.51 member_a: a > set_a > $o ). 0.19/0.51 0.19/0.51 thf(sy_v_X,type, 0.19/0.51 x: set_a ). 0.19/0.51 0.19/0.51 thf(sy_v_a,type, 0.19/0.51 a2: a ). 0.19/0.51 0.19/0.51 thf(sy_v_b,type, 0.19/0.51 b: a ). 0.19/0.51 0.19/0.51 thf(sy_v_f,type, 0.19/0.51 f: a > a ). 0.19/0.51 0.19/0.51 thf(sy_v_p,type, 0.19/0.51 p: a ). 0.19/0.51 0.19/0.51 thf(sy_v_thesisa____,type, 0.19/0.51 thesisa: $o ). 0.19/0.51 0.19/0.51 thf(sy_v_x,type, 0.19/0.51 x2: a ). 0.19/0.51 0.19/0.51 thf(fact_116_neg__less__0__iff__less,axiom, 0.19/0.51 ! [A: real] : 0.19/0.51 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real ) 0.19/0.51 = ( ord_less_real @ zero_zero_real @ A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_328_add__strict__increasing,axiom, 0.19/0.51 ! [A: a,B: a,C: a] : 0.19/0.51 ( ( ( ord_less_a @ B @ ( plus_plus_a @ A @ C ) ) 0.19/0.51 <= ( ord_less_eq_a @ B @ C ) ) 0.19/0.51 <= ( ord_less_a @ zero_zero_a @ A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_161_rev__eq__flow,axiom, 0.19/0.51 ! [Y: a,T2: real] : 0.19/0.51 ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T2 ) 0.19/0.51 = ( auto_ll_on_flow0_a @ f @ x @ Y @ ( uminus_uminus_real @ T2 ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_309_group__cancel_Oadd2,axiom, 0.19/0.51 ! [B4: real,K: real,B: real,A: real] : 0.19/0.51 ( ( B4 0.19/0.51 = ( plus_plus_real @ K @ B ) ) 0.19/0.51 => ( ( plus_plus_real @ A @ B4 ) 0.19/0.51 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_220_add__le__same__cancel2,axiom, 0.19/0.51 ! [A: a,B: a] : 0.19/0.51 ( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ B ) 0.19/0.51 = ( ord_less_eq_a @ A @ zero_zero_a ) ) ). 0.19/0.51 0.19/0.51 thf(fact_209_neg__0__le__iff__le,axiom, 0.19/0.51 ! [A: real] : 0.19/0.51 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) ) 0.19/0.51 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ). 0.19/0.51 0.19/0.51 thf(fact_321_add__mono__thms__linordered__field_I3_J,axiom, 0.19/0.51 ! [I: real,J: real,K: real,L: real] : 0.19/0.51 ( ( ( ord_less_real @ I @ J ) 0.19/0.51 & ( ord_less_eq_real @ K @ L ) ) 0.19/0.51 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_26_abs__abs,axiom, 0.19/0.51 ! [A: real] : 0.19/0.51 ( ( abs_abs_real @ ( abs_abs_real @ A ) ) 0.19/0.51 = ( abs_abs_real @ A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_303_add_Oright__cancel,axiom, 0.19/0.51 ! [B: real,A: real,C: real] : 0.19/0.51 ( ( ( plus_plus_real @ B @ A ) 0.19/0.51 = ( plus_plus_real @ C @ A ) ) 0.19/0.51 = ( B = C ) ) ). 0.19/0.51 0.19/0.51 thf(fact_242_abs__of__nonneg,axiom, 0.19/0.51 ! [A: a] : 0.19/0.51 ( ( ord_less_eq_a @ zero_zero_a @ A ) 0.19/0.51 => ( ( abs_abs_a @ A ) 0.19/0.51 = A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_40_abs__of__pos,axiom, 0.19/0.51 ! [A: real] : 0.19/0.51 ( ( ord_less_real @ zero_zero_real @ A ) 0.19/0.51 => ( ( abs_abs_real @ A ) 0.19/0.51 = A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_108_rev_Oclosed__orbit__period__zero__fixed__point,axiom, 0.19/0.51 ! [X: a] : 0.19/0.51 ( ( ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) 0.19/0.51 = zero_zero_real ) 0.19/0.51 => ( ( uminus_uminus_a_a @ f @ X ) 0.19/0.51 = zero_zero_a ) ) 0.19/0.51 <= ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ). 0.19/0.51 0.19/0.51 thf(fact_147_rev_Oclosed__orbitE,axiom, 0.19/0.51 ! [X: a] : 0.19/0.51 ( ~ ! [T4: real] : 0.19/0.51 ( ( ord_less_real @ zero_zero_real @ T4 ) 0.19/0.51 => ~ ! [T5: real] : 0.19/0.51 ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( plus_plus_real @ T5 @ T4 ) ) 0.19/0.51 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T5 ) ) ) 0.19/0.51 <= ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ). 0.19/0.51 0.19/0.51 thf(fact_36_not__one__less__zero,axiom, 0.19/0.51 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ). 0.19/0.51 0.19/0.51 thf(fact_131_minus__equation__iff,axiom, 0.19/0.51 ! [A: a,B: a] : 0.19/0.51 ( ( ( uminus_uminus_a @ A ) 0.19/0.51 = B ) 0.19/0.51 = ( ( uminus_uminus_a @ B ) 0.19/0.51 = A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_48_mem__Collect__eq,axiom, 0.19/0.51 ! [A: real,P: real > $o] : 0.19/0.51 ( ( member_real @ A @ ( collect_real @ P ) ) 0.19/0.51 = ( P @ A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_97_equal__neg__zero,axiom, 0.19/0.51 ! [A: real] : 0.19/0.51 ( ( A 0.19/0.51 = ( uminus_uminus_real @ A ) ) 0.19/0.51 = ( A = zero_zero_real ) ) ). 0.19/0.51 0.19/0.51 thf(fact_115_neg__less__0__iff__less,axiom, 0.19/0.51 ! [A: a] : 0.19/0.51 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ zero_zero_a ) 0.19/0.51 = ( ord_less_a @ zero_zero_a @ A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_275_add__nonneg__eq__0__iff,axiom, 0.19/0.51 ! [X: real,Y: real] : 0.19/0.51 ( ( ord_less_eq_real @ zero_zero_real @ X ) 0.19/0.51 => ( ( ord_less_eq_real @ zero_zero_real @ Y ) 0.19/0.51 => ( ( ( plus_plus_real @ X @ Y ) 0.19/0.51 = zero_zero_real ) 0.19/0.51 = ( ( Y = zero_zero_real ) 0.19/0.51 & ( X = zero_zero_real ) ) ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_122_local_Oexistence__ivl__initial__time__iff,axiom, 0.19/0.51 ! [X0: a] : 0.19/0.51 ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) 0.19/0.51 = ( ( member_a @ X0 @ x ) 0.19/0.51 & ( member_real @ zero_zero_real @ top_top_set_real ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_212_less__eq__neg__nonpos,axiom, 0.19/0.51 ! [A: real] : 0.19/0.51 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) ) 0.19/0.51 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ). 0.19/0.51 0.19/0.51 thf(fact_18_abs__zero,axiom, 0.19/0.51 ( ( abs_abs_real @ zero_zero_real ) 0.19/0.51 = zero_zero_real ) ). 0.19/0.51 0.19/0.51 thf(fact_180_add__cancel__right__left,axiom, 0.19/0.51 ! [A: a,B: a] : 0.19/0.51 ( ( A 0.19/0.51 = ( plus_plus_a @ B @ A ) ) 0.19/0.51 = ( B = zero_zero_a ) ) ). 0.19/0.51 0.19/0.51 thf(fact_342_add_Ocomm__neutral,axiom, 0.19/0.51 ! [A: real] : 0.19/0.51 ( ( plus_plus_real @ A @ zero_zero_real ) 0.19/0.51 = A ) ). 0.19/0.51 0.19/0.51 thf(fact_150_rev_Ovec__simps_I11_J,axiom, 0.19/0.51 ! [Ae: a,Be: a,Cd: a] : 0.19/0.51 ( ( plus_plus_a @ ( plus_plus_a @ Ae @ Be ) @ Cd ) 0.19/0.51 = ( plus_plus_a @ Ae @ ( plus_plus_a @ Be @ Cd ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_255_local_Oexistence__ivl__empty1,axiom, 0.19/0.51 ! [X0: a] : 0.19/0.51 ( ( ( auto_l612940ivl0_a @ f @ x @ X0 ) 0.19/0.51 = bot_bot_set_real ) 0.19/0.51 <= ~ ( member_real @ zero_zero_real @ top_top_set_real ) ) ). 0.19/0.51 0.19/0.51 thf(fact_301_add_Ocommute,axiom, 0.19/0.51 ( plus_plus_real 0.19/0.51 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ B3 @ A4 ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_279_add__nonneg__nonneg,axiom, 0.19/0.51 ! [A: real,B: real] : 0.19/0.51 ( ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) 0.19/0.51 <= ( ord_less_eq_real @ zero_zero_real @ B ) ) 0.19/0.51 <= ( ord_less_eq_real @ zero_zero_real @ A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_149_rev_Oclosed__orbit__period__nonneg,axiom, 0.19/0.51 ! [X: a] : 0.19/0.51 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) 0.19/0.51 => ( ord_less_eq_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_329_add__strict__increasing,axiom, 0.19/0.51 ! [A: real,B: real,C: real] : 0.19/0.51 ( ( ord_less_real @ zero_zero_real @ A ) 0.19/0.51 => ( ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) 0.19/0.51 <= ( ord_less_eq_real @ B @ C ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_87_periodic__orbit__period_I1_J,axiom, 0.19/0.51 ! [X: a] : 0.19/0.51 ( ( period138238489rbit_a @ f @ x @ X ) 0.19/0.51 => ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ X ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_158_add__right__cancel,axiom, 0.19/0.51 ! [B: real,A: real,C: real] : 0.19/0.51 ( ( ( plus_plus_real @ B @ A ) 0.19/0.51 = ( plus_plus_real @ C @ A ) ) 0.19/0.51 = ( B = C ) ) ). 0.19/0.51 0.19/0.51 thf(fact_93_neg__0__equal__iff__equal,axiom, 0.19/0.51 ! [A: a] : 0.19/0.51 ( ( zero_zero_a 0.19/0.51 = ( uminus_uminus_a @ A ) ) 0.19/0.51 = ( zero_zero_a = A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_159_add__left__cancel,axiom, 0.19/0.51 ! [A: a,B: a,C: a] : 0.19/0.51 ( ( ( plus_plus_a @ A @ B ) 0.19/0.51 = ( plus_plus_a @ A @ C ) ) 0.19/0.51 = ( B = C ) ) ). 0.19/0.51 0.19/0.51 thf(fact_112_neg__less__pos,axiom, 0.19/0.51 ! [A: real] : 0.19/0.51 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A ) 0.19/0.51 = ( ord_less_real @ zero_zero_real @ A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_233_add__less__same__cancel1,axiom, 0.19/0.51 ! [B: a,A: a] : 0.19/0.51 ( ( ord_less_a @ ( plus_plus_a @ B @ A ) @ B ) 0.19/0.51 = ( ord_less_a @ A @ zero_zero_a ) ) ). 0.19/0.51 0.19/0.51 thf(fact_153_rev_Ovec__simps_I12_J,axiom, 0.19/0.51 ( plus_plus_real 0.19/0.51 = ( ^ [Ag: real,Bg: real] : ( plus_plus_real @ Bg @ Ag ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_2_assms_I4_J,axiom, 0.19/0.51 member_a @ p @ ( line_open_segment_a @ a2 @ b ) ). 0.19/0.51 0.19/0.51 thf(fact_118_local_Orev_Omem__existence__ivl__iv__defined_I2_J,axiom, 0.19/0.51 ! [T2: real,X0: a] : 0.19/0.51 ( ( member_a @ X0 @ x ) 0.19/0.51 <= ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_264_add__le__imp__le__right,axiom, 0.19/0.51 ! [A: a,C: a,B: a] : 0.19/0.51 ( ( ord_less_eq_a @ A @ B ) 0.19/0.51 <= ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_260_abs__triangle__ineq,axiom, 0.19/0.51 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_21_gt__one__absI,axiom, 0.19/0.51 ! [K: real] : 0.19/0.51 ( ( ord_less_real @ K @ one_one_real ) 0.19/0.51 <= ( ord_less_real @ ( abs_abs_real @ K ) @ one_one_real ) ) ). 0.19/0.51 0.19/0.51 thf(fact_190_add_Oleft__neutral,axiom, 0.19/0.51 ! [A: a] : 0.19/0.51 ( ( plus_plus_a @ zero_zero_a @ A ) 0.19/0.51 = A ) ). 0.19/0.51 0.19/0.51 thf(fact_310_group__cancel_Oadd1,axiom, 0.19/0.51 ! [A3: a,K: a,A: a,B: a] : 0.19/0.51 ( ( A3 0.19/0.51 = ( plus_plus_a @ K @ A ) ) 0.19/0.51 => ( ( plus_plus_a @ A3 @ B ) 0.19/0.51 = ( plus_plus_a @ K @ ( plus_plus_a @ A @ B ) ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_80_local_Orev_Oflow__undefined0,axiom, 0.19/0.51 ! [T2: real,X: a] : 0.19/0.51 ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T2 ) 0.19/0.51 = zero_zero_a ) 0.19/0.51 <= ~ ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_334_add__nonneg__pos,axiom, 0.19/0.51 ! [A: a,B: a] : 0.19/0.51 ( ( ( ord_less_a @ zero_zero_a @ B ) 0.19/0.51 => ( ord_less_a @ zero_zero_a @ ( plus_plus_a @ A @ B ) ) ) 0.19/0.51 <= ( ord_less_eq_a @ zero_zero_a @ A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_156_interval__axioms,axiom, 0.19/0.51 initia826609931terval @ top_top_set_real ). 0.19/0.51 0.19/0.51 thf(fact_211_neg__le__0__iff__le,axiom, 0.19/0.51 ! [A: real] : 0.19/0.51 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real ) 0.19/0.51 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_183_add__cancel__left__left,axiom, 0.19/0.51 ! [B: real,A: real] : 0.19/0.51 ( ( ( plus_plus_real @ B @ A ) 0.19/0.51 = A ) 0.19/0.51 = ( B = zero_zero_real ) ) ). 0.19/0.51 0.19/0.51 thf(fact_73_closed__orbit__global__existence,axiom, 0.19/0.51 ! [X: a] : 0.19/0.51 ( ( ( auto_l612940ivl0_a @ f @ x @ X ) 0.19/0.51 = top_top_set_real ) 0.19/0.51 <= ( period720806154rbit_a @ f @ x @ X ) ) ). 0.19/0.51 0.19/0.51 thf(fact_213_neg__less__eq__nonneg,axiom, 0.19/0.51 ! [A: real] : 0.19/0.51 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A ) 0.19/0.51 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ). 0.19/0.51 0.19/0.51 thf(fact_267_add__le__imp__le__left,axiom, 0.19/0.51 ! [C: real,A: real,B: real] : 0.19/0.51 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) 0.19/0.51 => ( ord_less_eq_real @ A @ B ) ) ). 0.19/0.51 0.19/0.51 thf(fact_294_add__left__imp__eq,axiom, 0.19/0.51 ! [A: a,B: a,C: a] : 0.19/0.51 ( ( ( plus_plus_a @ A @ B ) 0.19/0.51 = ( plus_plus_a @ A @ C ) ) 0.19/0.51 => ( B = C ) ) ). 0.19/0.51 0.19/0.51 thf(fact_308_group__cancel_Oadd2,axiom, 0.19/0.51 ! [B4: a,K: a,B: a,A: a] : 0.19/0.51 ( ( ( plus_plus_a @ A @ B4 ) 0.19/0.51 = ( plus_plus_a @ K @ ( plus_plus_a @ A @ B ) ) ) 0.19/0.51 <= ( B4 0.19/0.51 = ( plus_plus_a @ K @ B ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_265_add__le__imp__le__right,axiom, 0.19/0.51 ! [A: real,C: real,B: real] : 0.19/0.51 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) 0.19/0.51 => ( ord_less_eq_real @ A @ B ) ) ). 0.19/0.51 0.19/0.51 thf(fact_300_add_Ocommute,axiom, 0.19/0.51 ( plus_plus_a 0.19/0.51 = ( ^ [A4: a,B3: a] : ( plus_plus_a @ B3 @ A4 ) ) ) ). 0.19/0.51 0.19/0.51 thf(conj_0,hypothesis, 0.19/0.51 ! [Delta2: real,Tau2: a > real] : 0.19/0.51 ( ( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ Delta2 ) @ Tau2 ) 0.19/0.51 => ( ( ( ! [Y3: a] : 0.19/0.51 ( ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ Y3 @ ( Tau2 @ Y3 ) ) @ ( line_open_segment_a @ a2 @ b ) ) 0.19/0.51 <= ( member_a @ Y3 @ ( elemen154694473ball_a @ p @ Delta2 ) ) ) 0.19/0.51 => thesisa ) 0.19/0.51 <= ! [Y3: a] : 0.19/0.51 ( ( ord_less_real @ ( abs_abs_real @ ( Tau2 @ Y3 ) ) @ one_one_real ) 0.19/0.51 <= ( member_a @ Y3 @ ( elemen154694473ball_a @ p @ Delta2 ) ) ) ) 0.19/0.51 <= ( ( Tau2 @ p ) 0.19/0.51 = zero_zero_real ) ) ) 0.19/0.51 <= ( ord_less_real @ zero_zero_real @ Delta2 ) ) ). 0.19/0.51 0.19/0.51 thf(fact_193_add__le__cancel__left,axiom, 0.19/0.51 ! [C: a,A: a,B: a] : 0.19/0.51 ( ( ord_less_eq_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) ) 0.19/0.51 = ( ord_less_eq_a @ A @ B ) ) ). 0.19/0.51 0.19/0.51 thf(fact_151_rev_Ovec__simps_I11_J,axiom, 0.19/0.51 ! [Ae: real,Be: real,Cd: real] : 0.19/0.51 ( ( plus_plus_real @ ( plus_plus_real @ Ae @ Be ) @ Cd ) 0.19/0.51 = ( plus_plus_real @ Ae @ ( plus_plus_real @ Be @ Cd ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_181_add__cancel__left__right,axiom, 0.19/0.51 ! [A: real,B: real] : 0.19/0.51 ( ( ( plus_plus_real @ A @ B ) 0.19/0.51 = A ) 0.19/0.51 = ( B = zero_zero_real ) ) ). 0.19/0.51 0.19/0.51 thf(fact_56_rev_Otransversal__segment__commute,axiom, 0.19/0.51 ! [X: a,Y: a] : 0.19/0.51 ( ( poinca522724647ment_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ Y ) 0.19/0.51 = ( poinca522724647ment_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ X ) ) ). 0.19/0.51 0.19/0.51 thf(fact_223_add__le__same__cancel1,axiom, 0.19/0.51 ! [B: real,A: real] : 0.19/0.51 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B ) 0.19/0.51 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ). 0.19/0.51 0.19/0.51 thf(fact_320_add__mono__thms__linordered__field_I3_J,axiom, 0.19/0.51 ! [I: a,J: a,K: a,L: a] : 0.19/0.51 ( ( ord_less_a @ ( plus_plus_a @ I @ K ) @ ( plus_plus_a @ J @ L ) ) 0.19/0.51 <= ( ( ord_less_a @ I @ J ) 0.19/0.51 & ( ord_less_eq_a @ K @ L ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_117_local_Omem__existence__ivl__iv__defined_I2_J,axiom, 0.19/0.51 ! [T2: real,X0: a] : 0.19/0.51 ( ( member_a @ X0 @ x ) 0.19/0.51 <= ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ). 0.19/0.51 0.19/0.51 thf(fact_16_abs__eq__0,axiom, 0.19/0.51 ! [A: real] : 0.19/0.51 ( ( ( abs_abs_real @ A ) 0.19/0.51 = zero_zero_real ) 0.19/0.51 = ( A = zero_zero_real ) ) ). 0.19/0.51 0.19/0.51 thf(fact_343_add_Ocomm__neutral,axiom, 0.19/0.51 ! [A: a] : 0.19/0.51 ( ( plus_plus_a @ A @ zero_zero_a ) 0.19/0.51 = A ) ). 0.19/0.51 0.19/0.51 thf(fact_114_neg__0__less__iff__less,axiom, 0.19/0.51 ! [A: real] : 0.19/0.51 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) ) 0.19/0.51 = ( ord_less_real @ A @ zero_zero_real ) ) ). 0.19/0.51 0.19/0.51 thf(fact_247_add__neg__numeral__special_I8_J,axiom, 0.19/0.51 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) 0.19/0.51 = zero_zero_real ) ). 0.19/0.51 0.19/0.51 thf(fact_196_add__less__cancel__right,axiom, 0.19/0.51 ! [A: a,C: a,B: a] : 0.19/0.51 ( ( ord_less_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) ) 0.19/0.52 = ( ord_less_a @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_154_rev_Ovec__simps_I13_J,axiom, 0.19/0.52 ! [Bg2: a,Ag2: a,Cf: a] : 0.19/0.52 ( ( plus_plus_a @ Bg2 @ ( plus_plus_a @ Ag2 @ Cf ) ) 0.19/0.52 = ( plus_plus_a @ Ag2 @ ( plus_plus_a @ Bg2 @ Cf ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_33_zero__neq__one,axiom, 0.19/0.52 zero_zero_real != one_one_real ). 0.19/0.52 0.19/0.52 thf(fact_224_linordered__ab__group__add__class_Ozero__less__double__add__iff__zero__less__single__add,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) ) 0.19/0.52 = ( ord_less_real @ zero_zero_real @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_236_add_Oright__inverse,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( plus_plus_a @ A @ ( uminus_uminus_a @ A ) ) 0.19/0.52 = zero_zero_a ) ). 0.19/0.52 0.19/0.52 thf(fact_228_less__add__same__cancel1,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) ) 0.19/0.52 = ( ord_less_real @ zero_zero_real @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_315_add__mono__thms__linordered__semiring_I2_J,axiom, 0.19/0.52 ! [I: real,J: real,K: real,L: real] : 0.19/0.52 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) 0.19/0.52 <= ( ( ord_less_eq_real @ K @ L ) 0.19/0.52 & ( I = J ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_280_add__increasing2,axiom, 0.19/0.52 ! [C: a,B: a,A: a] : 0.19/0.52 ( ( ord_less_eq_a @ zero_zero_a @ C ) 0.19/0.52 => ( ( ord_less_eq_a @ B @ ( plus_plus_a @ A @ C ) ) 0.19/0.52 <= ( ord_less_eq_a @ B @ A ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_1__092_060open_062p_A_092_060in_062_AX_092_060close_062,axiom, 0.19/0.52 member_a @ p @ x ). 0.19/0.52 0.19/0.52 thf(fact_38_abs__not__less__zero,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ). 0.19/0.52 0.19/0.52 thf(fact_283_add__decreasing2,axiom, 0.19/0.52 ! [C: real,A: real,B: real] : 0.19/0.52 ( ( ( ord_less_eq_real @ A @ B ) 0.19/0.52 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) 0.19/0.52 <= ( ord_less_eq_real @ C @ zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_191_add__le__cancel__right,axiom, 0.19/0.52 ! [A: a,C: a,B: a] : 0.19/0.52 ( ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) ) 0.19/0.52 = ( ord_less_eq_a @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_77_closed__orbit__periodic,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( period720806154rbit_a @ f @ x @ X ) 0.19/0.52 => ( ( period138238489rbit_a @ f @ x @ X ) 0.19/0.52 <= ( ( f @ X ) 0.19/0.52 != zero_zero_a ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_136_minus__less__iff,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) 0.19/0.52 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_19_abs__zero,axiom, 0.19/0.52 ( ( abs_abs_a @ zero_zero_a ) 0.19/0.52 = zero_zero_a ) ). 0.19/0.52 0.19/0.52 thf(fact_4_that,axiom, 0.19/0.52 ! [Delta: real,Tau: a > real] : 0.19/0.52 ( ( ord_less_real @ zero_zero_real @ Delta ) 0.19/0.52 => ( ( ( ! [Y3: a] : 0.19/0.52 ( ( ord_less_real @ ( abs_abs_real @ ( Tau @ Y3 ) ) @ one_one_real ) 0.19/0.52 <= ( member_a @ Y3 @ ( elemen154694473ball_a @ p @ Delta ) ) ) 0.19/0.52 => ( thesisa 0.19/0.52 <= ! [Y3: a] : 0.19/0.52 ( ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ Y3 @ ( Tau @ Y3 ) ) @ ( line_open_segment_a @ a2 @ b ) ) 0.19/0.52 <= ( member_a @ Y3 @ ( elemen154694473ball_a @ p @ Delta ) ) ) ) ) 0.19/0.52 <= ( ( Tau @ p ) 0.19/0.52 = zero_zero_real ) ) 0.19/0.52 <= ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ Delta ) @ Tau ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_254_local_Oexistence__ivl__empty__iff,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( ( auto_l612940ivl0_a @ f @ x @ X0 ) 0.19/0.52 = bot_bot_set_real ) 0.19/0.52 = ( ~ ( member_a @ X0 @ x ) 0.19/0.52 | ~ ( member_real @ zero_zero_real @ top_top_set_real ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_109_periodic__orbit__def,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( period138238489rbit_a @ f @ x @ X ) 0.19/0.52 = ( ( period720806154rbit_a @ f @ x @ X ) 0.19/0.52 & ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ X ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_231_add__less__same__cancel2,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ord_less_a @ ( plus_plus_a @ A @ B ) @ B ) 0.19/0.52 = ( ord_less_a @ A @ zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_230_add__less__same__cancel2,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B ) 0.19/0.52 = ( ord_less_real @ A @ zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_86_periodic__orbitI,axiom, 0.19/0.52 ! [T2: real,T3: real,Y: a] : 0.19/0.52 ( ( T2 != T3 ) 0.19/0.52 => ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ Y ) ) 0.19/0.52 => ( ( ( ( ( f @ Y ) 0.19/0.52 != zero_zero_a ) 0.19/0.52 => ( period138238489rbit_a @ f @ x @ Y ) ) 0.19/0.52 <= ( ( auto_ll_on_flow0_a @ f @ x @ Y @ T2 ) 0.19/0.52 = ( auto_ll_on_flow0_a @ f @ x @ Y @ T3 ) ) ) 0.19/0.52 <= ( member_real @ T3 @ ( auto_l612940ivl0_a @ f @ x @ Y ) ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom, 0.19/0.52 ! [X: real,Y: real] : 0.19/0.52 ( ( if_real @ $true @ X @ Y ) 0.19/0.52 = X ) ). 0.19/0.52 0.19/0.52 thf(fact_134_less__minus__iff,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) ) 0.19/0.52 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_206_abs__add__abs,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( abs_abs_a @ ( plus_plus_a @ ( abs_abs_a @ A ) @ ( abs_abs_a @ B ) ) ) 0.19/0.52 = ( plus_plus_a @ ( abs_abs_a @ A ) @ ( abs_abs_a @ B ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_49_Collect__mem__eq,axiom, 0.19/0.52 ! [A3: set_a] : 0.19/0.52 ( ( collect_a 0.19/0.52 @ ^ [X2: a] : ( member_a @ X2 @ A3 ) ) 0.19/0.52 = A3 ) ). 0.19/0.52 0.19/0.52 thf(fact_278_add__nonneg__nonneg,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ( ord_less_eq_a @ zero_zero_a @ B ) 0.19/0.52 => ( ord_less_eq_a @ zero_zero_a @ ( plus_plus_a @ A @ B ) ) ) 0.19/0.52 <= ( ord_less_eq_a @ zero_zero_a @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_297_add__mono,axiom, 0.19/0.52 ! [A: real,B: real,C: real,D2: real] : 0.19/0.52 ( ( ord_less_eq_real @ A @ B ) 0.19/0.52 => ( ( ord_less_eq_real @ C @ D2 ) 0.19/0.52 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_52_Collect__cong,axiom, 0.19/0.52 ! [P: a > $o,Q: a > $o] : 0.19/0.52 ( ( ( collect_a @ P ) 0.19/0.52 = ( collect_a @ Q ) ) 0.19/0.52 <= ! [X3: a] : 0.19/0.52 ( ( P @ X3 ) 0.19/0.52 = ( Q @ X3 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_81_closed__orbit__def,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( period720806154rbit_a @ f @ x @ X ) 0.19/0.52 = ( ? [X2: real] : 0.19/0.52 ( ( member_real @ X2 @ ( auto_l612940ivl0_a @ f @ x @ X ) ) 0.19/0.52 & ( ( auto_ll_on_flow0_a @ f @ x @ X @ X2 ) 0.19/0.52 = X ) 0.19/0.52 & ( X2 != zero_zero_real ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_324_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, 0.19/0.52 ! [A: a,B: a,C: a] : 0.19/0.52 ( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C ) 0.19/0.52 = ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_282_add__decreasing2,axiom, 0.19/0.52 ! [C: a,A: a,B: a] : 0.19/0.52 ( ( ( ord_less_eq_a @ A @ B ) 0.19/0.52 => ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ B ) ) 0.19/0.52 <= ( ord_less_eq_a @ C @ zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_244_ball__trivial,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( elemen154694473ball_a @ X @ zero_zero_real ) 0.19/0.52 = bot_bot_set_a ) ). 0.19/0.52 0.19/0.52 thf(fact_148_local_Orev_Oexistence__ivl__notempty,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) 0.19/0.52 != bot_bot_set_real ) 0.19/0.52 <= ( member_a @ X0 @ x ) ) 0.19/0.52 <= ( member_real @ zero_zero_real @ top_top_set_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_325_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, 0.19/0.52 ! [A: real,B: real,C: real] : 0.19/0.52 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C ) 0.19/0.52 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_62_neg__equal__iff__equal,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ( uminus_uminus_real @ A ) 0.19/0.52 = ( uminus_uminus_real @ B ) ) 0.19/0.52 = ( A = B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_272_add__nonpos__eq__0__iff,axiom, 0.19/0.52 ! [X: a,Y: a] : 0.19/0.52 ( ( ( ord_less_eq_a @ Y @ zero_zero_a ) 0.19/0.52 => ( ( ( plus_plus_a @ X @ Y ) 0.19/0.52 = zero_zero_a ) 0.19/0.52 = ( ( X = zero_zero_a ) 0.19/0.52 & ( Y = zero_zero_a ) ) ) ) 0.19/0.52 <= ( ord_less_eq_a @ X @ zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_146_abs__neg__one,axiom, 0.19/0.52 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) ) 0.19/0.52 = one_one_real ) ). 0.19/0.52 0.19/0.52 thf(fact_313_add__mono__thms__linordered__semiring_I1_J,axiom, 0.19/0.52 ! [I: real,J: real,K: real,L: real] : 0.19/0.52 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) 0.19/0.52 <= ( ( ord_less_eq_real @ K @ L ) 0.19/0.52 & ( ord_less_eq_real @ I @ J ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_333_add__nonpos__neg,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_eq_real @ A @ zero_zero_real ) 0.19/0.52 => ( ( ord_less_real @ B @ zero_zero_real ) 0.19/0.52 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_144_rev_Omvar_Ointerval__axioms,axiom, 0.19/0.52 ! [X0: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ). 0.19/0.52 0.19/0.52 thf(fact_27_transversal__segment__exists,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( member_a @ X @ x ) 0.19/0.52 => ( ~ ! [A2: a,B2: a] : 0.19/0.52 ( ( member_a @ X @ ( line_open_segment_a @ A2 @ B2 ) ) 0.19/0.52 => ~ ( poinca522724647ment_a @ f @ x @ A2 @ B2 ) ) 0.19/0.52 <= ( ( f @ X ) 0.19/0.52 != zero_zero_a ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_318_add__mono__thms__linordered__semiring_I4_J,axiom, 0.19/0.52 ! [I: a,J: a,K: a,L: a] : 0.19/0.52 ( ( ( I = J ) 0.19/0.52 & ( K = L ) ) 0.19/0.52 => ( ( plus_plus_a @ I @ K ) 0.19/0.52 = ( plus_plus_a @ J @ L ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_178_add__cancel__right__right,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( A 0.19/0.52 = ( plus_plus_a @ A @ B ) ) 0.19/0.52 = ( B = zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_204_add__minus__cancel,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( plus_plus_a @ A @ ( plus_plus_a @ ( uminus_uminus_a @ A ) @ B ) ) 0.19/0.52 = B ) ). 0.19/0.52 0.19/0.52 thf(fact_326_add__strict__increasing2,axiom, 0.19/0.52 ! [A: a,B: a,C: a] : 0.19/0.52 ( ( ( ord_less_a @ B @ C ) 0.19/0.52 => ( ord_less_a @ B @ ( plus_plus_a @ A @ C ) ) ) 0.19/0.52 <= ( ord_less_eq_a @ zero_zero_a @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_43_fixed__point__imp__closed__orbit__period__zero_I2_J,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( member_a @ X @ x ) 0.19/0.52 => ( ( ( period1305449585riod_a @ f @ x @ X ) 0.19/0.52 = zero_zero_real ) 0.19/0.52 <= ( ( f @ X ) 0.19/0.52 = zero_zero_a ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_42_periodic__orbit__imp__flow0__regular,axiom, 0.19/0.52 ! [X: a,T2: real] : 0.19/0.52 ( ( period138238489rbit_a @ f @ x @ X ) 0.19/0.52 => ( ( f @ ( auto_ll_on_flow0_a @ f @ x @ X @ T2 ) ) 0.19/0.52 != zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_145_mvar_Ointerval__axioms,axiom, 0.19/0.52 ! [X0: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ). 0.19/0.52 0.19/0.52 thf(fact_227_less__add__same__cancel2,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ord_less_a @ A @ ( plus_plus_a @ B @ A ) ) 0.19/0.52 = ( ord_less_a @ zero_zero_a @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_337_add__neg__nonpos,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_real @ A @ zero_zero_real ) 0.19/0.52 => ( ( ord_less_eq_real @ B @ zero_zero_real ) 0.19/0.52 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_132_minus__equation__iff,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ( uminus_uminus_real @ A ) 0.19/0.52 = B ) 0.19/0.52 = ( ( uminus_uminus_real @ B ) 0.19/0.52 = A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_60_add_Oinverse__inverse,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) ) 0.19/0.52 = A ) ). 0.19/0.52 0.19/0.52 thf(fact_143_rev_O_092_060alpha_062__limit__point__eq__rev,axiom, 0.19/0.52 ! [X: a,P2: a] : 0.19/0.52 ( ( limit_1865182413oint_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ P2 ) 0.19/0.52 = ( limit_94460170oint_a @ f @ x @ X @ P2 ) ) ). 0.19/0.52 0.19/0.52 thf(fact_82_rev_Oclosed__orbit__global__existence,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) 0.19/0.52 = top_top_set_real ) 0.19/0.52 <= ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ). 0.19/0.52 0.19/0.52 thf(fact_240_abs__le__self__iff,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( ord_less_eq_a @ ( abs_abs_a @ A ) @ A ) 0.19/0.52 = ( ord_less_eq_a @ zero_zero_a @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_319_add__mono__thms__linordered__semiring_I4_J,axiom, 0.19/0.52 ! [I: real,J: real,K: real,L: real] : 0.19/0.52 ( ( ( plus_plus_real @ I @ K ) 0.19/0.52 = ( plus_plus_real @ J @ L ) ) 0.19/0.52 <= ( ( K = L ) 0.19/0.52 & ( I = J ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_249_abs__of__nonpos,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ( abs_abs_real @ A ) 0.19/0.52 = ( uminus_uminus_real @ A ) ) 0.19/0.52 <= ( ord_less_eq_real @ A @ zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_74_closed__orbitI,axiom, 0.19/0.52 ! [T2: real,T3: real,Y: a] : 0.19/0.52 ( ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ Y ) ) 0.19/0.52 => ( ( member_real @ T3 @ ( auto_l612940ivl0_a @ f @ x @ Y ) ) 0.19/0.52 => ( ( period720806154rbit_a @ f @ x @ Y ) 0.19/0.52 <= ( ( auto_ll_on_flow0_a @ f @ x @ Y @ T2 ) 0.19/0.52 = ( auto_ll_on_flow0_a @ f @ x @ Y @ T3 ) ) ) ) ) 0.19/0.52 <= ( T2 != T3 ) ) ). 0.19/0.52 0.19/0.52 thf(fact_91_add_Oinverse__neutral,axiom, 0.19/0.52 ( ( uminus_uminus_a @ zero_zero_a ) 0.19/0.52 = zero_zero_a ) ). 0.19/0.52 0.19/0.52 thf(fact_306_add_Oassoc,axiom, 0.19/0.52 ! [A: a,B: a,C: a] : 0.19/0.52 ( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C ) 0.19/0.52 = ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_65_rev_Oclosed__orbit__eq__rev,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) 0.19/0.52 = ( period720806154rbit_a @ f @ x @ X ) ) ). 0.19/0.52 0.19/0.52 thf(fact_14_abs__0__eq,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( zero_zero_real 0.19/0.52 = ( abs_abs_real @ A ) ) 0.19/0.52 = ( A = zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(conj_1,conjecture, 0.19/0.52 thesisa ). 0.19/0.52 0.19/0.52 thf(fact_61_neg__equal__iff__equal,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ( uminus_uminus_a @ A ) 0.19/0.52 = ( uminus_uminus_a @ B ) ) 0.19/0.52 = ( A = B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_237_add_Oright__inverse,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) ) 0.19/0.52 = zero_zero_real ) ). 0.19/0.52 0.19/0.52 thf(fact_216_le__add__same__cancel2,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ord_less_eq_a @ A @ ( plus_plus_a @ B @ A ) ) 0.19/0.52 = ( ord_less_eq_a @ zero_zero_a @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_167_local_Oflow__trans,axiom, 0.19/0.52 ! [S: real,X0: a,T2: real] : 0.19/0.52 ( ( ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ ( plus_plus_real @ S @ T2 ) ) 0.19/0.52 = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ S ) @ T2 ) ) 0.19/0.52 <= ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ S ) ) ) ) 0.19/0.52 <= ( member_real @ S @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_257_local_Orev_Oexistence__ivl__empty1,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) 0.19/0.52 = bot_bot_set_real ) 0.19/0.52 <= ~ ( member_real @ zero_zero_real @ top_top_set_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_58_closed__orbit__in__domain,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( period720806154rbit_a @ f @ x @ X ) 0.19/0.52 => ( member_a @ X @ x ) ) ). 0.19/0.52 0.19/0.52 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom, 0.19/0.52 ! [X: real,Y: real] : 0.19/0.52 ( ( if_real @ $false @ X @ Y ) 0.19/0.52 = Y ) ). 0.19/0.52 0.19/0.52 thf(fact_71_fixpoint__sol_I1_J,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( ( ( auto_l612940ivl0_a @ f @ x @ X ) 0.19/0.52 = top_top_set_real ) 0.19/0.52 <= ( ( f @ X ) 0.19/0.52 = zero_zero_a ) ) 0.19/0.52 <= ( member_a @ X @ x ) ) ). 0.19/0.52 0.19/0.52 thf(fact_274_add__nonneg__eq__0__iff,axiom, 0.19/0.52 ! [X: a,Y: a] : 0.19/0.52 ( ( ord_less_eq_a @ zero_zero_a @ X ) 0.19/0.52 => ( ( ord_less_eq_a @ zero_zero_a @ Y ) 0.19/0.52 => ( ( ( plus_plus_a @ X @ Y ) 0.19/0.52 = zero_zero_a ) 0.19/0.52 = ( ( X = zero_zero_a ) 0.19/0.52 & ( Y = zero_zero_a ) ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(help_If_3_1_If_001t__Real__Oreal_T,axiom, 0.19/0.52 ! [P: $o] : 0.19/0.52 ( ( P = $true ) 0.19/0.52 | ( P = $false ) ) ). 0.19/0.52 0.19/0.52 thf(fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_At_O_A_092_060lbrakk_0620_A_060_Ad_059_Acontinuous__on_A_Iball_Ap_Ad_J_At_059_A_092_060And_062y_O_Ay_A_092_060in_062_Aball_Ap_Ad_A_092_060Longrightarrow_062_Aflow0_Ay_A_It_Ay_J_A_092_060in_062_A_123a_060_N_N_060b_125_059_A_092_060And_062y_O_Ay_A_092_060in_062_Aball_Ap_Ad_A_092_060Longrightarrow_062_A_092_060bar_062t_Ay_092_060bar_062_A_060_A1_059_Acontinuous__on_A_Iball_Ap_Ad_J_At_059_At_Ap_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom, 0.19/0.52 ~ ! [D: real] : 0.19/0.52 ( ( ord_less_real @ zero_zero_real @ D ) 0.19/0.52 => ! [T: a > real] : 0.19/0.52 ( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ D ) @ T ) 0.19/0.52 => ( ( ! [Y2: a] : 0.19/0.52 ( ( ord_less_real @ ( abs_abs_real @ ( T @ Y2 ) ) @ one_one_real ) 0.19/0.52 <= ( member_a @ Y2 @ ( elemen154694473ball_a @ p @ D ) ) ) 0.19/0.52 => ( ( ( T @ p ) 0.19/0.52 != zero_zero_real ) 0.19/0.52 <= ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ D ) @ T ) ) ) 0.19/0.52 <= ! [Y2: a] : 0.19/0.52 ( ( member_a @ Y2 @ ( elemen154694473ball_a @ p @ D ) ) 0.19/0.52 => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ Y2 @ ( T @ Y2 ) ) @ ( line_open_segment_a @ a2 @ b ) ) ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_292_add__right__imp__eq,axiom, 0.19/0.52 ! [B: a,A: a,C: a] : 0.19/0.52 ( ( ( plus_plus_a @ B @ A ) 0.19/0.52 = ( plus_plus_a @ C @ A ) ) 0.19/0.52 => ( B = C ) ) ). 0.19/0.52 0.19/0.52 thf(fact_207_abs__add__abs,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) 0.19/0.52 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_100_neg__less__iff__less,axiom, 0.19/0.52 ! [B: a,A: a] : 0.19/0.52 ( ( ord_less_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) ) 0.19/0.52 = ( ord_less_a @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_113_neg__0__less__iff__less,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( ord_less_a @ zero_zero_a @ ( uminus_uminus_a @ A ) ) 0.19/0.52 = ( ord_less_a @ A @ zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_135_minus__less__iff,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ B ) 0.19/0.52 = ( ord_less_a @ ( uminus_uminus_a @ B ) @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_287_add__increasing,axiom, 0.19/0.52 ! [A: real,B: real,C: real] : 0.19/0.52 ( ( ord_less_eq_real @ zero_zero_real @ A ) 0.19/0.52 => ( ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) 0.19/0.52 <= ( ord_less_eq_real @ B @ C ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_103_abs__minus,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) ) 0.19/0.52 = ( abs_abs_real @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_305_add_Oleft__cancel,axiom, 0.19/0.52 ! [A: real,B: real,C: real] : 0.19/0.52 ( ( ( plus_plus_real @ A @ B ) 0.19/0.52 = ( plus_plus_real @ A @ C ) ) 0.19/0.52 = ( B = C ) ) ). 0.19/0.52 0.19/0.52 thf(fact_99_local_Orev_Oflow__initial__time__if,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ zero_zero_real ) 0.19/0.52 = X0 ) 0.19/0.52 <= ( ( member_real @ zero_zero_real @ top_top_set_real ) 0.19/0.52 & ( member_a @ X0 @ x ) ) ) 0.19/0.52 & ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ zero_zero_real ) 0.19/0.52 = zero_zero_a ) 0.19/0.52 <= ~ ( ( member_a @ X0 @ x ) 0.19/0.52 & ( member_real @ zero_zero_real @ top_top_set_real ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_55_rev_Otransversal__segment__reverse,axiom, 0.19/0.52 ! [X: a,Y: a] : 0.19/0.52 ( ( poinca522724647ment_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ Y ) 0.19/0.52 => ( poinca522724647ment_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ X ) ) ). 0.19/0.52 0.19/0.52 thf(fact_35_abs__one,axiom, 0.19/0.52 ( ( abs_abs_real @ one_one_real ) 0.19/0.52 = one_one_real ) ). 0.19/0.52 0.19/0.52 thf(fact_235_add_Oleft__inverse,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) 0.19/0.52 = zero_zero_real ) ). 0.19/0.52 0.19/0.52 thf(fact_179_add__cancel__right__left,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( A 0.19/0.52 = ( plus_plus_real @ B @ A ) ) 0.19/0.52 = ( B = zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_90_rev_Oclosed__orbit__periodic,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( ( ( uminus_uminus_a_a @ f @ X ) 0.19/0.52 != zero_zero_a ) 0.19/0.52 => ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) 0.19/0.52 <= ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ). 0.19/0.52 0.19/0.52 thf(fact_37_zero__less__one,axiom, 0.19/0.52 ord_less_real @ zero_zero_real @ one_one_real ). 0.19/0.52 0.19/0.52 thf(fact_79_rev_Ofixpoint__sol_I1_J,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) 0.19/0.52 = top_top_set_real ) 0.19/0.52 <= ( ( uminus_uminus_a_a @ f @ X ) 0.19/0.52 = zero_zero_a ) ) 0.19/0.52 <= ( member_a @ X @ x ) ) ). 0.19/0.52 0.19/0.52 thf(fact_111_less__neg__neg,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) ) 0.19/0.52 = ( ord_less_real @ A @ zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_51_Collect__cong,axiom, 0.19/0.52 ! [P: real > $o,Q: real > $o] : 0.19/0.52 ( ( ( collect_real @ P ) 0.19/0.52 = ( collect_real @ Q ) ) 0.19/0.52 <= ! [X3: real] : 0.19/0.52 ( ( P @ X3 ) 0.19/0.52 = ( Q @ X3 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_202_minus__add__cancel,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( plus_plus_a @ ( uminus_uminus_a @ A ) @ ( plus_plus_a @ A @ B ) ) 0.19/0.52 = B ) ). 0.19/0.52 0.19/0.52 thf(fact_217_le__add__same__cancel2,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) ) 0.19/0.52 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_296_add__mono,axiom, 0.19/0.52 ! [A: a,B: a,C: a,D2: a] : 0.19/0.52 ( ( ord_less_eq_a @ A @ B ) 0.19/0.52 => ( ( ord_less_eq_a @ C @ D2 ) 0.19/0.52 => ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D2 ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_192_add__le__cancel__right,axiom, 0.19/0.52 ! [A: real,C: real,B: real] : 0.19/0.52 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) 0.19/0.52 = ( ord_less_eq_real @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_285_add__right__mono,axiom, 0.19/0.52 ! [A: real,B: real,C: real] : 0.19/0.52 ( ( ord_less_eq_real @ A @ B ) 0.19/0.52 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_162_rev_Orev__eq__flow,axiom, 0.19/0.52 ! [Y: a,T2: real] : 0.19/0.52 ( ( auto_ll_on_flow0_a @ f @ x @ Y @ T2 ) 0.19/0.52 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ ( uminus_uminus_real @ T2 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_238_abs__le__zero__iff,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( ord_less_eq_a @ ( abs_abs_a @ A ) @ zero_zero_a ) 0.19/0.52 = ( A = zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_312_add__mono__thms__linordered__semiring_I1_J,axiom, 0.19/0.52 ! [I: a,J: a,K: a,L: a] : 0.19/0.52 ( ( ( ord_less_eq_a @ I @ J ) 0.19/0.52 & ( ord_less_eq_a @ K @ L ) ) 0.19/0.52 => ( ord_less_eq_a @ ( plus_plus_a @ I @ K ) @ ( plus_plus_a @ J @ L ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_256_local_Orev_Oexistence__ivl__empty__iff,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) 0.19/0.52 = bot_bot_set_real ) 0.19/0.52 = ( ~ ( member_a @ X0 @ x ) 0.19/0.52 | ~ ( member_real @ zero_zero_real @ top_top_set_real ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_67_closed__orbit__flow0,axiom, 0.19/0.52 ! [X: a,T2: real] : 0.19/0.52 ( ( period720806154rbit_a @ f @ x @ X ) 0.19/0.52 => ( period720806154rbit_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X @ T2 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_63_existence__ivl__zero,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( member_a @ X0 @ x ) 0.19/0.52 => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_5_assms_I1_J,axiom, 0.19/0.52 poinca522724647ment_a @ f @ x @ a2 @ b ). 0.19/0.52 0.19/0.52 thf(fact_322_add__mono__thms__linordered__field_I4_J,axiom, 0.19/0.52 ! [I: a,J: a,K: a,L: a] : 0.19/0.52 ( ( ( ord_less_a @ K @ L ) 0.19/0.52 & ( ord_less_eq_a @ I @ J ) ) 0.19/0.52 => ( ord_less_a @ ( plus_plus_a @ I @ K ) @ ( plus_plus_a @ J @ L ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_0_rev_Oopen__segment__trichotomy,axiom, 0.19/0.52 ! [X: a,A: a,B: a,Y: a] : 0.19/0.52 ( ( ( member_a @ Y @ ( line_open_segment_a @ A @ B ) ) 0.19/0.52 => ( ( X = Y ) 0.19/0.52 | ( member_a @ Y @ ( line_open_segment_a @ A @ X ) ) 0.19/0.52 | ( member_a @ Y @ ( line_open_segment_a @ X @ B ) ) ) ) 0.19/0.52 <= ( member_a @ X @ ( line_open_segment_a @ A @ B ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_78_local_Orev_Oexistence__ivl__initial__time,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( member_real @ zero_zero_real @ top_top_set_real ) 0.19/0.52 => ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) 0.19/0.52 <= ( member_a @ X0 @ x ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_214_linordered__ab__group__add__class_Ozero__le__double__add__iff__zero__le__single__add,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) ) 0.19/0.52 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_304_add_Oleft__cancel,axiom, 0.19/0.52 ! [A: a,B: a,C: a] : 0.19/0.52 ( ( ( plus_plus_a @ A @ B ) 0.19/0.52 = ( plus_plus_a @ A @ C ) ) 0.19/0.52 = ( B = C ) ) ). 0.19/0.52 0.19/0.52 thf(fact_295_add__left__imp__eq,axiom, 0.19/0.52 ! [A: real,B: real,C: real] : 0.19/0.52 ( ( ( plus_plus_real @ A @ B ) 0.19/0.52 = ( plus_plus_real @ A @ C ) ) 0.19/0.52 => ( B = C ) ) ). 0.19/0.52 0.19/0.52 thf(fact_23_transversal__segment__commute,axiom, 0.19/0.52 ! [X: a,Y: a] : 0.19/0.52 ( ( poinca522724647ment_a @ f @ x @ X @ Y ) 0.19/0.52 = ( poinca522724647ment_a @ f @ x @ Y @ X ) ) ). 0.19/0.52 0.19/0.52 thf(fact_290_add__left__mono,axiom, 0.19/0.52 ! [A: a,B: a,C: a] : 0.19/0.52 ( ( ord_less_eq_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) ) 0.19/0.52 <= ( ord_less_eq_a @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_160_add__left__cancel,axiom, 0.19/0.52 ! [A: real,B: real,C: real] : 0.19/0.52 ( ( ( plus_plus_real @ A @ B ) 0.19/0.52 = ( plus_plus_real @ A @ C ) ) 0.19/0.52 = ( B = C ) ) ). 0.19/0.52 0.19/0.52 thf(fact_239_abs__le__zero__iff,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real ) 0.19/0.52 = ( A = zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_28_c1__on__open__R2_Otransversal__segment_Ocong,axiom, 0.19/0.52 poinca522724647ment_a = poinca522724647ment_a ). 0.19/0.52 0.19/0.52 thf(fact_234_add_Oleft__inverse,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( plus_plus_a @ ( uminus_uminus_a @ A ) @ A ) 0.19/0.52 = zero_zero_a ) ). 0.19/0.52 0.19/0.52 thf(fact_121_local_Omem__existence__ivl__iv__defined_I1_J,axiom, 0.19/0.52 ! [T2: real,X0: a] : 0.19/0.52 ( ( member_real @ zero_zero_real @ top_top_set_real ) 0.19/0.52 <= ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_8_centre__in__ball,axiom, 0.19/0.52 ! [X: a,E: real] : 0.19/0.52 ( ( member_a @ X @ ( elemen154694473ball_a @ X @ E ) ) 0.19/0.52 = ( ord_less_real @ zero_zero_real @ E ) ) ). 0.19/0.52 0.19/0.52 thf(fact_203_minus__add__cancel,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) ) 0.19/0.52 = B ) ). 0.19/0.52 0.19/0.52 thf(fact_269_add__less__le__mono,axiom, 0.19/0.52 ! [A: real,B: real,C: real,D2: real] : 0.19/0.52 ( ( ord_less_real @ A @ B ) 0.19/0.52 => ( ( ord_less_eq_real @ C @ D2 ) 0.19/0.52 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_252_local_Oexistence__ivl__undefined,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ~ ( member_a @ X0 @ x ) 0.19/0.52 => ( ( auto_l612940ivl0_a @ f @ x @ X0 ) 0.19/0.52 = bot_bot_set_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_293_add__right__imp__eq,axiom, 0.19/0.52 ! [B: real,A: real,C: real] : 0.19/0.52 ( ( B = C ) 0.19/0.52 <= ( ( plus_plus_real @ B @ A ) 0.19/0.52 = ( plus_plus_real @ C @ A ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_123_local_Oflow__initial__time,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ zero_zero_real ) 0.19/0.52 = X0 ) 0.19/0.52 <= ( member_a @ X0 @ x ) ) 0.19/0.52 <= ( member_real @ zero_zero_real @ top_top_set_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_119_flow0__defined,axiom, 0.19/0.52 ! [Xa: real,X0: a] : 0.19/0.52 ( ( member_real @ Xa @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) 0.19/0.52 => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ Xa ) @ x ) ) ). 0.19/0.52 0.19/0.52 thf(fact_92_add_Oinverse__neutral,axiom, 0.19/0.52 ( ( uminus_uminus_real @ zero_zero_real ) 0.19/0.52 = zero_zero_real ) ). 0.19/0.52 0.19/0.52 thf(fact_54_rev__transversal__segment,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( poinca522724647ment_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B ) 0.19/0.52 = ( poinca522724647ment_a @ f @ x @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_271_add__le__less__mono,axiom, 0.19/0.52 ! [A: real,B: real,C: real,D2: real] : 0.19/0.52 ( ( ord_less_eq_real @ A @ B ) 0.19/0.52 => ( ( ord_less_real @ C @ D2 ) 0.19/0.52 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_10_zero__less__abs__iff,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) ) 0.19/0.52 = ( A != zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_250_ball__eq__empty,axiom, 0.19/0.52 ! [X: a,E: real] : 0.19/0.52 ( ( ( elemen154694473ball_a @ X @ E ) 0.19/0.52 = bot_bot_set_a ) 0.19/0.52 = ( ord_less_eq_real @ E @ zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_70_local_Orev_Omem__existence__ivl__subset,axiom, 0.19/0.52 ! [T2: real,X0: a] : 0.19/0.52 ( ( member_real @ T2 @ top_top_set_real ) 0.19/0.52 <= ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_140_abs__of__neg,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( ( abs_abs_a @ A ) 0.19/0.52 = ( uminus_uminus_a @ A ) ) 0.19/0.52 <= ( ord_less_a @ A @ zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_276_add__nonpos__nonpos,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ zero_zero_a ) 0.19/0.52 <= ( ord_less_eq_a @ B @ zero_zero_a ) ) 0.19/0.52 <= ( ord_less_eq_a @ A @ zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_302_add_Oright__cancel,axiom, 0.19/0.52 ! [B: a,A: a,C: a] : 0.19/0.52 ( ( ( plus_plus_a @ B @ A ) 0.19/0.52 = ( plus_plus_a @ C @ A ) ) 0.19/0.52 = ( B = C ) ) ). 0.19/0.52 0.19/0.52 thf(fact_88_closed__orbit__period__zero__fixed__point,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( ( ( f @ X ) 0.19/0.52 = zero_zero_a ) 0.19/0.52 <= ( ( period1305449585riod_a @ f @ x @ X ) 0.19/0.52 = zero_zero_real ) ) 0.19/0.52 <= ( period720806154rbit_a @ f @ x @ X ) ) ). 0.19/0.52 0.19/0.52 thf(fact_126_local_Orev_Omem__existence__ivl__iv__defined_I1_J,axiom, 0.19/0.52 ! [T2: real,X0: a] : 0.19/0.52 ( ( member_real @ zero_zero_real @ top_top_set_real ) 0.19/0.52 <= ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_281_add__increasing2,axiom, 0.19/0.52 ! [C: real,B: real,A: real] : 0.19/0.52 ( ( ord_less_eq_real @ zero_zero_real @ C ) 0.19/0.52 => ( ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) 0.19/0.52 <= ( ord_less_eq_real @ B @ A ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_98_neg__equal__zero,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ( uminus_uminus_real @ A ) 0.19/0.52 = A ) 0.19/0.52 = ( A = zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_85_rev_Operiodic__orbit__imp__flow0__regular,axiom, 0.19/0.52 ! [X: a,T2: real] : 0.19/0.52 ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) 0.19/0.52 => ( ( uminus_uminus_a_a @ f @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T2 ) ) 0.19/0.52 != zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_172_local_Orev_Oexistence__ivl__trans,axiom, 0.19/0.52 ! [S: real,X0: a,T2: real] : 0.19/0.52 ( ( member_real @ S @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) 0.19/0.52 => ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ S ) ) ) 0.19/0.52 => ( member_real @ ( plus_plus_real @ S @ T2 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_251_ball__eq__empty,axiom, 0.19/0.52 ! [X: real,E: real] : 0.19/0.52 ( ( ( elemen341675809l_real @ X @ E ) 0.19/0.52 = bot_bot_set_real ) 0.19/0.52 = ( ord_less_eq_real @ E @ zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_177_add__cancel__right__right,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( A 0.19/0.52 = ( plus_plus_real @ A @ B ) ) 0.19/0.52 = ( B = zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_187_add_Oright__neutral,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( plus_plus_real @ A @ zero_zero_real ) 0.19/0.52 = A ) ). 0.19/0.52 0.19/0.52 thf(fact_32_one__reorient,axiom, 0.19/0.52 ! [X: real] : 0.19/0.52 ( ( one_one_real = X ) 0.19/0.52 = ( X = one_one_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_106_rev_Operiodic__orbitI,axiom, 0.19/0.52 ! [T2: real,T3: real,Y: a] : 0.19/0.52 ( ( T2 != T3 ) 0.19/0.52 => ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) ) 0.19/0.52 => ( ( member_real @ T3 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) ) 0.19/0.52 => ( ( ( ( uminus_uminus_a_a @ f @ Y ) 0.19/0.52 != zero_zero_a ) 0.19/0.52 => ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) ) 0.19/0.52 <= ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T2 ) 0.19/0.52 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T3 ) ) ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_299_add_Oleft__commute,axiom, 0.19/0.52 ! [B: real,A: real,C: real] : 0.19/0.52 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) 0.19/0.52 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_31_linorder__neqE__linordered__idom,axiom, 0.19/0.52 ! [X: real,Y: real] : 0.19/0.52 ( ( X != Y ) 0.19/0.52 => ( ~ ( ord_less_real @ X @ Y ) 0.19/0.52 => ( ord_less_real @ Y @ X ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_7_centre__in__ball,axiom, 0.19/0.52 ! [X: real,E: real] : 0.19/0.52 ( ( member_real @ X @ ( elemen341675809l_real @ X @ E ) ) 0.19/0.52 = ( ord_less_real @ zero_zero_real @ E ) ) ). 0.19/0.52 0.19/0.52 thf(fact_125_local_Orev_Oflow__in__domain,axiom, 0.19/0.52 ! [T2: real,X0: a] : 0.19/0.52 ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) 0.19/0.52 => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ T2 ) @ x ) ) ). 0.19/0.52 0.19/0.52 thf(fact_68_rev_Oexistence__ivl__zero,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) 0.19/0.52 <= ( member_a @ X0 @ x ) ) ). 0.19/0.52 0.19/0.52 thf(fact_137_abs__eq__iff,axiom, 0.19/0.52 ! [X: real,Y: real] : 0.19/0.52 ( ( ( abs_abs_real @ X ) 0.19/0.52 = ( abs_abs_real @ Y ) ) 0.19/0.52 = ( ( X 0.19/0.52 = ( uminus_uminus_real @ Y ) ) 0.19/0.52 | ( X = Y ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_157_add__right__cancel,axiom, 0.19/0.52 ! [B: a,A: a,C: a] : 0.19/0.52 ( ( ( plus_plus_a @ B @ A ) 0.19/0.52 = ( plus_plus_a @ C @ A ) ) 0.19/0.52 = ( B = C ) ) ). 0.19/0.52 0.19/0.52 thf(fact_69_local_Oexistence__ivl__initial__time,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) 0.19/0.52 <= ( member_a @ X0 @ x ) ) 0.19/0.52 <= ( member_real @ zero_zero_real @ top_top_set_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_215_linordered__ab__group__add__class_Odouble__add__le__zero__iff__single__add__le__zero,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real ) 0.19/0.52 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_323_add__mono__thms__linordered__field_I4_J,axiom, 0.19/0.52 ! [I: real,J: real,K: real,L: real] : 0.19/0.52 ( ( ( ord_less_eq_real @ I @ J ) 0.19/0.52 & ( ord_less_real @ K @ L ) ) 0.19/0.52 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_152_rev_Ovec__simps_I12_J,axiom, 0.19/0.52 ( plus_plus_a 0.19/0.52 = ( ^ [Ag: a,Bg: a] : ( plus_plus_a @ Bg @ Ag ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_22_transversal__segment__reverse,axiom, 0.19/0.52 ! [X: a,Y: a] : 0.19/0.52 ( ( poinca522724647ment_a @ f @ x @ Y @ X ) 0.19/0.52 <= ( poinca522724647ment_a @ f @ x @ X @ Y ) ) ). 0.19/0.52 0.19/0.52 thf(fact_76_periodic__orbit__period_I2_J,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( period1305449585riod_a @ f @ x @ X ) ) 0.19/0.52 = X ) 0.19/0.52 <= ( period138238489rbit_a @ f @ x @ X ) ) ). 0.19/0.52 0.19/0.52 thf(fact_166_rev_Orecurrence__time__flip__sign_I2_J,axiom, 0.19/0.52 ! [T6: real,X: a] : 0.19/0.52 ( ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T6 ) 0.19/0.52 = X ) 0.19/0.52 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( uminus_uminus_real @ T6 ) ) 0.19/0.52 = X ) ) 0.19/0.52 <= ( member_real @ T6 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_25_abs__idempotent,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( abs_abs_a @ ( abs_abs_a @ A ) ) 0.19/0.52 = ( abs_abs_a @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_245_ball__trivial,axiom, 0.19/0.52 ! [X: real] : 0.19/0.52 ( ( elemen341675809l_real @ X @ zero_zero_real ) 0.19/0.52 = bot_bot_set_real ) ). 0.19/0.52 0.19/0.52 thf(fact_30_zero__reorient,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( zero_zero_a = X ) 0.19/0.52 = ( X = zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_174_closed__orbit__period__nonneg,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( ord_less_eq_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ X ) ) 0.19/0.52 <= ( period720806154rbit_a @ f @ x @ X ) ) ). 0.19/0.52 0.19/0.52 thf(fact_96_neg__equal__0__iff__equal,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ( uminus_uminus_real @ A ) 0.19/0.52 = zero_zero_real ) 0.19/0.52 = ( A = zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_164_recurrence__time__flip__sign_I2_J,axiom, 0.19/0.52 ! [T6: real,X: a] : 0.19/0.52 ( ( member_real @ T6 @ ( auto_l612940ivl0_a @ f @ x @ X ) ) 0.19/0.52 => ( ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( uminus_uminus_real @ T6 ) ) 0.19/0.52 = X ) 0.19/0.52 <= ( ( auto_ll_on_flow0_a @ f @ x @ X @ T6 ) 0.19/0.52 = X ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_104_abs__minus__cancel,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( abs_abs_a @ ( uminus_uminus_a @ A ) ) 0.19/0.52 = ( abs_abs_a @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_311_group__cancel_Oadd1,axiom, 0.19/0.52 ! [A3: real,K: real,A: real,B: real] : 0.19/0.52 ( ( ( plus_plus_real @ A3 @ B ) 0.19/0.52 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) 0.19/0.52 <= ( A3 0.19/0.52 = ( plus_plus_real @ K @ A ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_44_local_Oflow__initial__time__if,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real ) 0.19/0.52 & ( member_a @ X0 @ x ) ) 0.19/0.52 => ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ zero_zero_real ) 0.19/0.52 = zero_zero_a ) ) 0.19/0.52 & ( ( ( auto_ll_on_flow0_a @ f @ x @ X0 @ zero_zero_real ) 0.19/0.52 = X0 ) 0.19/0.52 <= ( ( member_real @ zero_zero_real @ top_top_set_real ) 0.19/0.52 & ( member_a @ X0 @ x ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_142__092_060alpha_062__limit__point__eq__rev,axiom, 0.19/0.52 ! [X: a,P2: a] : 0.19/0.52 ( ( limit_1865182413oint_a @ f @ x @ X @ P2 ) 0.19/0.52 = ( limit_94460170oint_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ P2 ) ) ). 0.19/0.52 0.19/0.52 thf(fact_11_cross__time__continuous,axiom, 0.19/0.52 ! [A: a,B: a,X: a,E: real] : 0.19/0.52 ( ( ( member_a @ X @ ( line_open_segment_a @ A @ B ) ) 0.19/0.52 => ( ~ ! [D: real] : 0.19/0.52 ( ! [T: a > real] : 0.19/0.52 ( ( topolo1710226732a_real @ ( elemen154694473ball_a @ X @ D ) @ T ) 0.19/0.52 => ( ! [Y2: a] : 0.19/0.52 ( ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ Y2 @ ( T @ Y2 ) ) @ ( line_open_segment_a @ A @ B ) ) 0.19/0.52 <= ( member_a @ Y2 @ ( elemen154694473ball_a @ X @ D ) ) ) 0.19/0.52 => ( ( ( ( T @ X ) 0.19/0.52 != zero_zero_real ) 0.19/0.52 <= ( topolo1710226732a_real @ ( elemen154694473ball_a @ X @ D ) @ T ) ) 0.19/0.52 <= ! [Y2: a] : 0.19/0.52 ( ( member_a @ Y2 @ ( elemen154694473ball_a @ X @ D ) ) 0.19/0.52 => ( ord_less_real @ ( abs_abs_real @ ( T @ Y2 ) ) @ E ) ) ) ) ) 0.19/0.52 <= ( ord_less_real @ zero_zero_real @ D ) ) 0.19/0.52 <= ( ord_less_real @ zero_zero_real @ E ) ) ) 0.19/0.52 <= ( poinca522724647ment_a @ f @ x @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_41_abs__of__pos,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( ( abs_abs_a @ A ) 0.19/0.52 = A ) 0.19/0.52 <= ( ord_less_a @ zero_zero_a @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_208_neg__0__le__iff__le,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( ord_less_eq_a @ zero_zero_a @ ( uminus_uminus_a @ A ) ) 0.19/0.52 = ( ord_less_eq_a @ A @ zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_226_less__add__same__cancel2,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) ) 0.19/0.52 = ( ord_less_real @ zero_zero_real @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_197_add__less__cancel__left,axiom, 0.19/0.52 ! [C: real,A: real,B: real] : 0.19/0.52 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) 0.19/0.52 = ( ord_less_real @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_141_abs__of__neg,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ( abs_abs_real @ A ) 0.19/0.52 = ( uminus_uminus_real @ A ) ) 0.19/0.52 <= ( ord_less_real @ A @ zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_17_abs__eq__0,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( ( abs_abs_a @ A ) 0.19/0.52 = zero_zero_a ) 0.19/0.52 = ( A = zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_102_rev_Oclosed__orbit__def,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) 0.19/0.52 = ( ? [X2: real] : 0.19/0.52 ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ X2 ) 0.19/0.52 = X ) 0.19/0.52 & ( X2 != zero_zero_real ) 0.19/0.52 & ( member_real @ X2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_288_add__decreasing,axiom, 0.19/0.52 ! [A: a,C: a,B: a] : 0.19/0.52 ( ( ord_less_eq_a @ A @ zero_zero_a ) 0.19/0.52 => ( ( ord_less_eq_a @ C @ B ) 0.19/0.52 => ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ B ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_75_rev_Ofixed__point__imp__closed__orbit__period__zero_I1_J,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( member_a @ X @ x ) 0.19/0.52 => ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) 0.19/0.52 <= ( ( uminus_uminus_a_a @ f @ X ) 0.19/0.52 = zero_zero_a ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_34_abs__eq__0__iff,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ( abs_abs_real @ A ) 0.19/0.52 = zero_zero_real ) 0.19/0.52 = ( A = zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_332_add__nonpos__neg,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ord_less_eq_a @ A @ zero_zero_a ) 0.19/0.52 => ( ( ord_less_a @ ( plus_plus_a @ A @ B ) @ zero_zero_a ) 0.19/0.52 <= ( ord_less_a @ B @ zero_zero_a ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_66_rev_Oclosed__orbit__in__domain,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( member_a @ X @ x ) 0.19/0.52 <= ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ). 0.19/0.52 0.19/0.52 thf(fact_262_le__numeral__extra_I4_J,axiom, 0.19/0.52 ord_less_eq_real @ one_one_real @ one_one_real ). 0.19/0.52 0.19/0.52 thf(fact_129_equation__minus__iff,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( A 0.19/0.52 = ( uminus_uminus_a @ B ) ) 0.19/0.52 = ( B 0.19/0.52 = ( uminus_uminus_a @ A ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_286_add__increasing,axiom, 0.19/0.52 ! [A: a,B: a,C: a] : 0.19/0.52 ( ( ( ord_less_eq_a @ B @ C ) 0.19/0.52 => ( ord_less_eq_a @ B @ ( plus_plus_a @ A @ C ) ) ) 0.19/0.52 <= ( ord_less_eq_a @ zero_zero_a @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_107_rev_Operiodic__orbit__period_I1_J,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) 0.19/0.52 => ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_50_Collect__mem__eq,axiom, 0.19/0.52 ! [A3: set_real] : 0.19/0.52 ( ( collect_real 0.19/0.52 @ ^ [X2: real] : ( member_real @ X2 @ A3 ) ) 0.19/0.52 = A3 ) ). 0.19/0.52 0.19/0.52 thf(fact_316_add__mono__thms__linordered__semiring_I3_J,axiom, 0.19/0.52 ! [I: a,J: a,K: a,L: a] : 0.19/0.52 ( ( ( ord_less_eq_a @ I @ J ) 0.19/0.52 & ( K = L ) ) 0.19/0.52 => ( ord_less_eq_a @ ( plus_plus_a @ I @ K ) @ ( plus_plus_a @ J @ L ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_186_linordered__ab__group__add__class_Odouble__zero,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ( plus_plus_real @ A @ A ) 0.19/0.52 = zero_zero_real ) 0.19/0.52 = ( A = zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_188_add_Oright__neutral,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( plus_plus_a @ A @ zero_zero_a ) 0.19/0.52 = A ) ). 0.19/0.52 0.19/0.52 thf(fact_101_neg__less__iff__less,axiom, 0.19/0.52 ! [B: real,A: real] : 0.19/0.52 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) 0.19/0.52 = ( ord_less_real @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_94_neg__0__equal__iff__equal,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( zero_zero_real 0.19/0.52 = ( uminus_uminus_real @ A ) ) 0.19/0.52 = ( zero_zero_real = A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_128_local_Orev_Oflow__initial__time,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( member_real @ zero_zero_real @ top_top_set_real ) 0.19/0.52 => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ zero_zero_real ) 0.19/0.52 = X0 ) 0.19/0.52 <= ( member_a @ X0 @ x ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_270_add__le__less__mono,axiom, 0.19/0.52 ! [A: a,B: a,C: a,D2: a] : 0.19/0.52 ( ( ( ord_less_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D2 ) ) 0.19/0.52 <= ( ord_less_a @ C @ D2 ) ) 0.19/0.52 <= ( ord_less_eq_a @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_89_rev_Operiodic__orbit__period_I2_J,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) 0.19/0.52 = X ) 0.19/0.52 <= ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ). 0.19/0.52 0.19/0.52 thf(fact_59_add_Oinverse__inverse,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) ) 0.19/0.52 = A ) ). 0.19/0.52 0.19/0.52 thf(fact_335_add__nonneg__pos,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ( ord_less_real @ zero_zero_real @ B ) 0.19/0.52 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) 0.19/0.52 <= ( ord_less_eq_real @ zero_zero_real @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_298_add_Oleft__commute,axiom, 0.19/0.52 ! [B: a,A: a,C: a] : 0.19/0.52 ( ( plus_plus_a @ B @ ( plus_plus_a @ A @ C ) ) 0.19/0.52 = ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_314_add__mono__thms__linordered__semiring_I2_J,axiom, 0.19/0.52 ! [I: a,J: a,K: a,L: a] : 0.19/0.52 ( ( ord_less_eq_a @ ( plus_plus_a @ I @ K ) @ ( plus_plus_a @ J @ L ) ) 0.19/0.52 <= ( ( I = J ) 0.19/0.52 & ( ord_less_eq_a @ K @ L ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_46_rev_Ofixpoint__sol_I2_J,axiom, 0.19/0.52 ! [X: a,T2: real] : 0.19/0.52 ( ( member_a @ X @ x ) 0.19/0.52 => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T2 ) 0.19/0.52 = X ) 0.19/0.52 <= ( ( uminus_uminus_a_a @ f @ X ) 0.19/0.52 = zero_zero_a ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_268_add__less__le__mono,axiom, 0.19/0.52 ! [A: a,B: a,C: a,D2: a] : 0.19/0.52 ( ( ord_less_a @ A @ B ) 0.19/0.52 => ( ( ord_less_eq_a @ C @ D2 ) 0.19/0.52 => ( ord_less_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D2 ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_138_abs__less__iff,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B ) 0.19/0.52 = ( ( ord_less_real @ A @ B ) 0.19/0.52 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_241_abs__le__self__iff,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A ) 0.19/0.52 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_327_add__strict__increasing2,axiom, 0.19/0.52 ! [A: real,B: real,C: real] : 0.19/0.52 ( ( ord_less_eq_real @ zero_zero_real @ A ) 0.19/0.52 => ( ( ord_less_real @ B @ C ) 0.19/0.52 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_219_le__add__same__cancel1,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) ) 0.19/0.52 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_184_add__cancel__left__left,axiom, 0.19/0.52 ! [B: a,A: a] : 0.19/0.52 ( ( ( plus_plus_a @ B @ A ) 0.19/0.52 = A ) 0.19/0.52 = ( B = zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_72_rev_Oclosed__orbit__flow0,axiom, 0.19/0.52 ! [X: a,T2: real] : 0.19/0.52 ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T2 ) ) 0.19/0.52 <= ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ). 0.19/0.52 0.19/0.52 thf(fact_218_le__add__same__cancel1,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ord_less_eq_a @ A @ ( plus_plus_a @ A @ B ) ) 0.19/0.52 = ( ord_less_eq_a @ zero_zero_a @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_163_recurrence__time__flip__sign_I1_J,axiom, 0.19/0.52 ! [T6: real,X: a] : 0.19/0.52 ( ( ( member_real @ ( uminus_uminus_real @ T6 ) @ ( auto_l612940ivl0_a @ f @ x @ X ) ) 0.19/0.52 <= ( ( auto_ll_on_flow0_a @ f @ x @ X @ T6 ) 0.19/0.52 = X ) ) 0.19/0.52 <= ( member_real @ T6 @ ( auto_l612940ivl0_a @ f @ x @ X ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_307_add_Oassoc,axiom, 0.19/0.52 ! [A: real,B: real,C: real] : 0.19/0.52 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C ) 0.19/0.52 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_171_local_Orev_Oexistence__ivl__trans_H,axiom, 0.19/0.52 ! [T2: real,S: real,X0: a] : 0.19/0.52 ( ( ( member_real @ S @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ T2 ) ) ) 0.19/0.52 <= ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) 0.19/0.52 <= ( member_real @ ( plus_plus_real @ T2 @ S ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_317_add__mono__thms__linordered__semiring_I3_J,axiom, 0.19/0.52 ! [I: real,J: real,K: real,L: real] : 0.19/0.52 ( ( ( ord_less_eq_real @ I @ J ) 0.19/0.52 & ( K = L ) ) 0.19/0.52 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_340_add_Ogroup__left__neutral,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( plus_plus_real @ zero_zero_real @ A ) 0.19/0.52 = A ) ). 0.19/0.52 0.19/0.52 thf(fact_110_rev_Operiodic__orbit__def,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) 0.19/0.52 = ( ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) 0.19/0.52 & ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_47_mem__Collect__eq,axiom, 0.19/0.52 ! [A: a,P: a > $o] : 0.19/0.52 ( ( member_a @ A @ ( collect_a @ P ) ) 0.19/0.52 = ( P @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_53_local_Oflow__undefined0,axiom, 0.19/0.52 ! [T2: real,X: a] : 0.19/0.52 ( ~ ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ X ) ) 0.19/0.52 => ( ( auto_ll_on_flow0_a @ f @ x @ X @ T2 ) 0.19/0.52 = zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_182_add__cancel__left__right,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ( plus_plus_a @ A @ B ) 0.19/0.52 = A ) 0.19/0.52 = ( B = zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_84_rev_Ofixed__point__imp__closed__orbit__period__zero_I2_J,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) 0.19/0.52 = zero_zero_real ) 0.19/0.52 <= ( ( uminus_uminus_a_a @ f @ X ) 0.19/0.52 = zero_zero_a ) ) 0.19/0.52 <= ( member_a @ X @ x ) ) ). 0.19/0.52 0.19/0.52 thf(fact_259_abs__triangle__ineq,axiom, 0.19/0.52 ! [A: a,B: a] : ( ord_less_eq_a @ ( abs_abs_a @ ( plus_plus_a @ A @ B ) ) @ ( plus_plus_a @ ( abs_abs_a @ A ) @ ( abs_abs_a @ B ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_222_add__le__same__cancel1,axiom, 0.19/0.52 ! [B: a,A: a] : 0.19/0.52 ( ( ord_less_eq_a @ ( plus_plus_a @ B @ A ) @ B ) 0.19/0.52 = ( ord_less_eq_a @ A @ zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_39_abs__not__less__zero,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ~ ( ord_less_a @ ( abs_abs_a @ A ) @ zero_zero_a ) ). 0.19/0.52 0.19/0.52 thf(fact_6_assms_I3_J,axiom, 0.19/0.52 limit_94460170oint_a @ f @ x @ x2 @ p ). 0.19/0.52 0.19/0.52 thf(fact_248_abs__of__nonpos,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( ( abs_abs_a @ A ) 0.19/0.52 = ( uminus_uminus_a @ A ) ) 0.19/0.52 <= ( ord_less_eq_a @ A @ zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_289_add__decreasing,axiom, 0.19/0.52 ! [A: real,C: real,B: real] : 0.19/0.52 ( ( ord_less_eq_real @ A @ zero_zero_real ) 0.19/0.52 => ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) 0.19/0.52 <= ( ord_less_eq_real @ C @ B ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_261_le__numeral__extra_I3_J,axiom, 0.19/0.52 ord_less_eq_real @ zero_zero_real @ zero_zero_real ). 0.19/0.52 0.19/0.52 thf(fact_201_minus__add__distrib,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) ) 0.19/0.52 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_133_less__minus__iff,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ord_less_a @ A @ ( uminus_uminus_a @ B ) ) 0.19/0.52 = ( ord_less_a @ B @ ( uminus_uminus_a @ A ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_229_less__add__same__cancel1,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ord_less_a @ A @ ( plus_plus_a @ A @ B ) ) 0.19/0.52 = ( ord_less_a @ zero_zero_a @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_232_add__less__same__cancel1,axiom, 0.19/0.52 ! [B: real,A: real] : 0.19/0.52 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B ) 0.19/0.52 = ( ord_less_real @ A @ zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_95_neg__equal__0__iff__equal,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( ( uminus_uminus_a @ A ) 0.19/0.52 = zero_zero_a ) 0.19/0.52 = ( A = zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_24_abs__idempotent,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( abs_abs_real @ ( abs_abs_real @ A ) ) 0.19/0.52 = ( abs_abs_real @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_29_zero__reorient,axiom, 0.19/0.52 ! [X: real] : 0.19/0.52 ( ( zero_zero_real = X ) 0.19/0.52 = ( X = zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_168_local_Oexistence__ivl__trans_H,axiom, 0.19/0.52 ! [T2: real,S: real,X0: a] : 0.19/0.52 ( ( member_real @ ( plus_plus_real @ T2 @ S ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) 0.19/0.52 => ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) 0.19/0.52 => ( member_real @ S @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ T2 ) ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_246_add__neg__numeral__special_I7_J,axiom, 0.19/0.52 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) 0.19/0.52 = zero_zero_real ) ). 0.19/0.52 0.19/0.52 thf(fact_105_abs__minus__cancel,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) ) 0.19/0.52 = ( abs_abs_real @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_170_local_Orev_Oflow__trans,axiom, 0.19/0.52 ! [S: real,X0: a,T2: real] : 0.19/0.52 ( ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ S ) ) ) 0.19/0.52 => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ ( plus_plus_real @ S @ T2 ) ) 0.19/0.52 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ S ) @ T2 ) ) ) 0.19/0.52 <= ( member_real @ S @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_165_rev_Orecurrence__time__flip__sign_I1_J,axiom, 0.19/0.52 ! [T6: real,X: a] : 0.19/0.52 ( ( ( member_real @ ( uminus_uminus_real @ T6 ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) 0.19/0.52 <= ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X @ T6 ) 0.19/0.52 = X ) ) 0.19/0.52 <= ( member_real @ T6 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_284_add__right__mono,axiom, 0.19/0.52 ! [A: a,B: a,C: a] : 0.19/0.52 ( ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) ) 0.19/0.52 <= ( ord_less_eq_a @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_200_minus__add__distrib,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( uminus_uminus_a @ ( plus_plus_a @ A @ B ) ) 0.19/0.52 = ( plus_plus_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_9_zero__less__abs__iff,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( ord_less_a @ zero_zero_a @ ( abs_abs_a @ A ) ) 0.19/0.52 = ( A != zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_253_local_Orev_Oexistence__ivl__undefined,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ~ ( member_a @ X0 @ x ) 0.19/0.52 => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) 0.19/0.52 = bot_bot_set_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_120_local_Oflow__in__domain,axiom, 0.19/0.52 ! [T2: real,X0: a] : 0.19/0.52 ( ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ T2 ) @ x ) 0.19/0.52 <= ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_194_add__le__cancel__left,axiom, 0.19/0.52 ! [C: real,A: real,B: real] : 0.19/0.52 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) 0.19/0.52 = ( ord_less_eq_real @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_339_Elementary__Metric__Spaces_Oball__empty,axiom, 0.19/0.52 ! [E: real,X: real] : 0.19/0.52 ( ( ord_less_eq_real @ E @ zero_zero_real ) 0.19/0.52 => ( ( elemen341675809l_real @ X @ E ) 0.19/0.52 = bot_bot_set_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_45_rev_Otransversal__segment__exists,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( member_a @ X @ x ) 0.19/0.52 => ( ~ ! [A2: a,B2: a] : 0.19/0.52 ( ( member_a @ X @ ( line_open_segment_a @ A2 @ B2 ) ) 0.19/0.52 => ~ ( poinca522724647ment_a @ ( uminus_uminus_a_a @ f ) @ x @ A2 @ B2 ) ) 0.19/0.52 <= ( ( uminus_uminus_a_a @ f @ X ) 0.19/0.52 != zero_zero_a ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_205_add__minus__cancel,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) ) 0.19/0.52 = B ) ). 0.19/0.52 0.19/0.52 thf(fact_83_rev_Oclosed__orbitI,axiom, 0.19/0.52 ! [T2: real,T3: real,Y: a] : 0.19/0.52 ( ( T2 != T3 ) 0.19/0.52 => ( ( member_real @ T2 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) ) 0.19/0.52 => ( ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T2 ) 0.19/0.52 = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y @ T3 ) ) 0.19/0.52 => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) ) 0.19/0.52 <= ( member_real @ T3 @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ Y ) ) ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_225_double__add__less__zero__iff__single__add__less__zero,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real ) 0.19/0.52 = ( ord_less_real @ A @ zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_258_is__num__normalize_I8_J,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) ) 0.19/0.52 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_210_neg__le__0__iff__le,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( ord_less_eq_a @ ( uminus_uminus_a @ A ) @ zero_zero_a ) 0.19/0.52 = ( ord_less_eq_a @ zero_zero_a @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_12_abs__1,axiom, 0.19/0.52 ( ( abs_abs_real @ one_one_real ) 0.19/0.52 = one_one_real ) ). 0.19/0.52 0.19/0.52 thf(fact_221_add__le__same__cancel2,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B ) 0.19/0.52 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_336_add__neg__nonpos,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ( ord_less_a @ ( plus_plus_a @ A @ B ) @ zero_zero_a ) 0.19/0.52 <= ( ord_less_eq_a @ B @ zero_zero_a ) ) 0.19/0.52 <= ( ord_less_a @ A @ zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_195_add__less__cancel__right,axiom, 0.19/0.52 ! [A: real,C: real,B: real] : 0.19/0.52 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) 0.19/0.52 = ( ord_less_real @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_189_add_Oleft__neutral,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( plus_plus_real @ zero_zero_real @ A ) 0.19/0.52 = A ) ). 0.19/0.52 0.19/0.52 thf(fact_277_add__nonpos__nonpos,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_eq_real @ A @ zero_zero_real ) 0.19/0.52 => ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) 0.19/0.52 <= ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_341_add_Ogroup__left__neutral,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( plus_plus_a @ zero_zero_a @ A ) 0.19/0.52 = A ) ). 0.19/0.52 0.19/0.52 thf(fact_130_equation__minus__iff,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( A 0.19/0.52 = ( uminus_uminus_real @ B ) ) 0.19/0.52 = ( B 0.19/0.52 = ( uminus_uminus_real @ A ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_291_add__left__mono,axiom, 0.19/0.52 ! [A: real,B: real,C: real] : 0.19/0.52 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) 0.19/0.52 <= ( ord_less_eq_real @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_185_double__zero__sym,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( zero_zero_real 0.19/0.52 = ( plus_plus_real @ A @ A ) ) 0.19/0.52 = ( A = zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_13_abs__0,axiom, 0.19/0.52 ( ( abs_abs_real @ zero_zero_real ) 0.19/0.52 = zero_zero_real ) ). 0.19/0.52 0.19/0.52 thf(fact_139_abs__if,axiom, 0.19/0.52 ( abs_abs_real 0.19/0.52 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_266_add__le__imp__le__left,axiom, 0.19/0.52 ! [C: a,A: a,B: a] : 0.19/0.52 ( ( ord_less_eq_a @ A @ B ) 0.19/0.52 <= ( ord_less_eq_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_173_local_Oexistence__ivl__notempty,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( member_real @ zero_zero_real @ top_top_set_real ) 0.19/0.52 => ( ( member_a @ X0 @ x ) 0.19/0.52 => ( ( auto_l612940ivl0_a @ f @ x @ X0 ) 0.19/0.52 != bot_bot_set_real ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_175_neg__le__iff__le,axiom, 0.19/0.52 ! [B: a,A: a] : 0.19/0.52 ( ( ord_less_eq_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) ) 0.19/0.52 = ( ord_less_eq_a @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_57_fixed__point__imp__closed__orbit__period__zero_I1_J,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( ( period720806154rbit_a @ f @ x @ X ) 0.19/0.52 <= ( ( f @ X ) 0.19/0.52 = zero_zero_a ) ) 0.19/0.52 <= ( member_a @ X @ x ) ) ). 0.19/0.52 0.19/0.52 thf(fact_127_local_Orev_Oexistence__ivl__initial__time__iff,axiom, 0.19/0.52 ! [X0: a] : 0.19/0.52 ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) 0.19/0.52 = ( ( member_a @ X0 @ x ) 0.19/0.52 & ( member_real @ zero_zero_real @ top_top_set_real ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_330_add__pos__nonneg,axiom, 0.19/0.52 ! [A: a,B: a] : 0.19/0.52 ( ( ( ord_less_a @ zero_zero_a @ ( plus_plus_a @ A @ B ) ) 0.19/0.52 <= ( ord_less_eq_a @ zero_zero_a @ B ) ) 0.19/0.52 <= ( ord_less_a @ zero_zero_a @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_263_is__num__normalize_I1_J,axiom, 0.19/0.52 ! [A: real,B: real,C: real] : 0.19/0.52 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C ) 0.19/0.52 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_198_add__less__cancel__left,axiom, 0.19/0.52 ! [C: a,A: a,B: a] : 0.19/0.52 ( ( ord_less_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) ) 0.19/0.52 = ( ord_less_a @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_155_rev_Ovec__simps_I13_J,axiom, 0.19/0.52 ! [Bg2: real,Ag2: real,Cf: real] : 0.19/0.52 ( ( plus_plus_real @ Bg2 @ ( plus_plus_real @ Ag2 @ Cf ) ) 0.19/0.52 = ( plus_plus_real @ Ag2 @ ( plus_plus_real @ Bg2 @ Cf ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_243_abs__of__nonneg,axiom, 0.19/0.52 ! [A: real] : 0.19/0.52 ( ( ( abs_abs_real @ A ) 0.19/0.52 = A ) 0.19/0.52 <= ( ord_less_eq_real @ zero_zero_real @ A ) ) ). 0.19/0.52 0.19/0.52 thf(fact_338_Elementary__Metric__Spaces_Oball__empty,axiom, 0.19/0.52 ! [E: real,X: a] : 0.19/0.52 ( ( ( elemen154694473ball_a @ X @ E ) 0.19/0.52 = bot_bot_set_a ) 0.19/0.52 <= ( ord_less_eq_real @ E @ zero_zero_real ) ) ). 0.19/0.52 0.19/0.52 thf(fact_15_abs__0__eq,axiom, 0.19/0.52 ! [A: a] : 0.19/0.52 ( ( zero_zero_a 0.19/0.52 = ( abs_abs_a @ A ) ) 0.19/0.52 = ( A = zero_zero_a ) ) ). 0.19/0.52 0.19/0.52 thf(fact_273_add__nonpos__eq__0__iff,axiom, 0.19/0.52 ! [X: real,Y: real] : 0.19/0.52 ( ( ord_less_eq_real @ X @ zero_zero_real ) 0.19/0.52 => ( ( ( ( plus_plus_real @ X @ Y ) 0.19/0.52 = zero_zero_real ) 0.19/0.52 = ( ( Y = zero_zero_real ) 0.19/0.52 & ( X = zero_zero_real ) ) ) 0.19/0.52 <= ( ord_less_eq_real @ Y @ zero_zero_real ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_20_fixpoint__sol_I2_J,axiom, 0.19/0.52 ! [X: a,T2: real] : 0.19/0.52 ( ( member_a @ X @ x ) 0.19/0.52 => ( ( ( auto_ll_on_flow0_a @ f @ x @ X @ T2 ) 0.19/0.52 = X ) 0.19/0.52 <= ( ( f @ X ) 0.19/0.52 = zero_zero_a ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_64_local_Omem__existence__ivl__subset,axiom, 0.19/0.52 ! [T2: real,X0: a] : 0.19/0.52 ( ( member_real @ T2 @ top_top_set_real ) 0.19/0.52 <= ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_169_local_Oexistence__ivl__trans,axiom, 0.19/0.52 ! [S: real,X0: a,T2: real] : 0.19/0.52 ( ( ( member_real @ ( plus_plus_real @ S @ T2 ) @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) 0.19/0.52 <= ( member_real @ T2 @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ X0 @ S ) ) ) ) 0.19/0.52 <= ( member_real @ S @ ( auto_l612940ivl0_a @ f @ x @ X0 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_124_rev_Oflow0__defined,axiom, 0.19/0.52 ! [Xa: real,X0: a] : 0.19/0.52 ( ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 @ Xa ) @ x ) 0.19/0.52 <= ( member_real @ Xa @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ X0 ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_331_add__pos__nonneg,axiom, 0.19/0.52 ! [A: real,B: real] : 0.19/0.52 ( ( ord_less_real @ zero_zero_real @ A ) 0.19/0.52 => ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) 0.19/0.52 <= ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ). 0.19/0.52 0.19/0.52 thf(fact_176_neg__le__iff__le,axiom, 0.19/0.52 ! [B: real,A: real] : 0.19/0.52 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) 0.19/0.52 = ( ord_less_eq_real @ A @ B ) ) ). 0.19/0.52 0.19/0.52 thf(fact_199_closed__orbitE,axiom, 0.19/0.52 ! [X: a] : 0.19/0.52 ( ( period720806154rbit_a @ f @ x @ X ) 0.19/0.52 => ~ ! [T4: real] : 0.19/0.52 ( ~ ! [T5: real] : 0.19/0.52 ( ( auto_ll_on_flow0_a @ f @ x @ X @ ( plus_plus_real @ T5 @ T4 ) ) 0.19/0.52 = ( auto_ll_on_flow0_a @ f @ x @ X @ T5 ) ) 0.19/0.52 <= ( ord_less_real @ zero_zero_real @ T4 ) ) ) ). 0.19/0.58 0.19/0.58 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.EKvutMtyfE/cvc5---1.0.5_14416.p... 0.19/0.58 (declare-sort $$unsorted 0) 0.19/0.58 (declare-sort tptp.set_real 0) 0.19/0.58 (declare-sort tptp.set_a 0) 0.19/0.58 (declare-sort tptp.real 0) 0.19/0.58 (declare-sort tptp.a 0) 0.19/0.58 (declare-fun tptp.elemen341675809l_real (tptp.real tptp.real) tptp.set_real) 0.19/0.58 (declare-fun tptp.elemen154694473ball_a (tptp.a tptp.real) tptp.set_a) 0.19/0.58 (declare-fun tptp.auto_l612940ivl0_a ((-> tptp.a tptp.a) tptp.set_a tptp.a) tptp.set_real) 0.19/0.58 (declare-fun tptp.auto_ll_on_flow0_a ((-> tptp.a tptp.a) tptp.set_a tptp.a tptp.real) tptp.a) 0.19/0.58 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real) 0.19/0.58 (declare-fun tptp.abs_abs_a (tptp.a) tptp.a) 0.19/0.58 (declare-fun tptp.one_one_real () tptp.real) 0.19/0.58 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real) 0.19/0.58 (declare-fun tptp.plus_plus_a (tptp.a tptp.a) tptp.a) 0.19/0.58 (declare-fun tptp.uminus_uminus_a_a ((-> tptp.a tptp.a) tptp.a) tptp.a) 0.19/0.58 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real) 0.19/0.58 (declare-fun tptp.uminus_uminus_a (tptp.a) tptp.a) 0.19/0.58 (declare-fun tptp.zero_zero_real () tptp.real) 0.19/0.58 (declare-fun tptp.zero_zero_a () tptp.a) 0.19/0.58 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real) 0.19/0.58 (declare-fun tptp.initia826609931terval (tptp.set_real) Bool) 0.19/0.58 (declare-fun tptp.limit_1865182413oint_a ((-> tptp.a tptp.a) tptp.set_a tptp.a tptp.a) Bool) 0.19/0.58 (declare-fun tptp.limit_94460170oint_a ((-> tptp.a tptp.a) tptp.set_a tptp.a tptp.a) Bool) 0.19/0.58 (declare-fun tptp.line_open_segment_a (tptp.a tptp.a) tptp.set_a) 0.19/0.58 (declare-fun tptp.bot_bot_set_real () tptp.set_real) 0.19/0.58 (declare-fun tptp.bot_bot_set_a () tptp.set_a) 0.19/0.58 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool) 0.19/0.58 (declare-fun tptp.ord_less_a (tptp.a tptp.a) Bool) 0.19/0.58 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool) 0.19/0.58 (declare-fun tptp.ord_less_eq_a (tptp.a tptp.a) Bool) 0.19/0.58 (declare-fun tptp.top_top_set_real () tptp.set_real) 0.19/0.58 (declare-fun tptp.period720806154rbit_a ((-> tptp.a tptp.a) tptp.set_a tptp.a) Bool) 0.19/0.58 (declare-fun tptp.period1305449585riod_a ((-> tptp.a tptp.a) tptp.set_a tptp.a) tptp.real) 0.19/0.58 (declare-fun tptp.period138238489rbit_a ((-> tptp.a tptp.a) tptp.set_a tptp.a) Bool) 0.19/0.58 (declare-fun tptp.poinca522724647ment_a ((-> tptp.a tptp.a) tptp.set_a tptp.a tptp.a) Bool) 0.19/0.58 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real) 0.19/0.58 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a) 0.19/0.58 (declare-fun tptp.topolo1710226732a_real (tptp.set_a (-> tptp.a tptp.real)) Bool) 0.19/0.58 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool) 0.19/0.58 (declare-fun tptp.member_a (tptp.a tptp.set_a) Bool) 0.19/0.58 (declare-fun tptp.x () tptp.set_a) 0.19/0.58 (declare-fun tptp.a2 () tptp.a) 0.19/0.58 (declare-fun tptp.b () tptp.a) 0.19/0.58 (declare-fun tptp.f (tptp.a) tptp.a) 0.19/0.58 (declare-fun tptp.p () tptp.a) 0.19/0.58 (declare-fun tptp.thesisa () Bool) 0.19/0.58 (declare-fun tptp.x2 () tptp.a) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A)))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) A) (=> (@ (@ tptp.ord_less_eq_a B) C) (@ (@ tptp.ord_less_a B) (@ (@ tptp.plus_plus_a A) C)))))) 0.19/0.58 (assert (forall ((Y tptp.a) (T2 tptp.real)) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) Y) T2) (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y) (@ tptp.uminus_uminus_real T2))))) 0.19/0.58 (assert (forall ((B4 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B)))))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) B)) B) (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L))))) 0.19/0.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1)))) 0.19/0.58 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C)))) 0.19/0.58 (assert (forall ((A tptp.a)) (=> (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) A) (= (@ tptp.abs_abs_a A) A)))) 0.19/0.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A)))) 0.19/0.58 (assert (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) X) (=> (= (@ (@ (@ tptp.period1305449585riod_a _let_1) tptp.x) X) tptp.zero_zero_real) (= (@ _let_1 X) tptp.zero_zero_a)))))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (not (forall ((T5 tptp.real)) (let ((_let_1 (@ (@ (@ tptp.auto_ll_on_flow0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X))) (= (@ _let_1 (@ (@ tptp.plus_plus_real T5) T4)) (@ _let_1 T5))))))))))) 0.19/0.58 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (= (@ tptp.uminus_uminus_a A) B) (= (@ tptp.uminus_uminus_a B) A)))) 0.19/0.58 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A)))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a A)) tptp.zero_zero_a) (@ (@ tptp.ord_less_a tptp.zero_zero_a) A)))) 0.19/0.58 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= Y tptp.zero_zero_real) (= X tptp.zero_zero_real)))))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (let ((_let_1 (@ tptp.member_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)) (and (@ (@ tptp.member_a X0) tptp.x) (@ _let_1 tptp.top_top_set_real)))))) 0.19/0.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real))))) 0.19/0.58 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real)) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (= A (@ (@ tptp.plus_plus_a B) A)) (= B tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A))) 0.19/0.58 (assert (forall ((Ae tptp.a) (Be tptp.a) (Cd tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a Ae))) (= (@ (@ tptp.plus_plus_a (@ _let_1 Be)) Cd) (@ _let_1 (@ (@ tptp.plus_plus_a Be) Cd)))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (=> (not (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real)) (= (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0) tptp.bot_bot_set_real)))) 0.19/0.58 (assert (= tptp.plus_plus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real B3) A4)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B))))))) 0.19/0.58 (assert (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ (@ tptp.period1305449585riod_a _let_1) tptp.x) X)))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_real B) (@ (@ tptp.plus_plus_real A) C)))))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period138238489rbit_a tptp.f) tptp.x) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ (@ tptp.period1305449585riod_a tptp.f) tptp.x) X))))) 0.19/0.58 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C)))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (= tptp.zero_zero_a (@ tptp.uminus_uminus_a A)) (= tptp.zero_zero_a A)))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A)))) 0.19/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a B) A)) B) (@ (@ tptp.ord_less_a A) tptp.zero_zero_a)))) 0.19/0.58 (assert (= tptp.plus_plus_real (lambda ((Ag tptp.real) (Bg tptp.real)) (@ (@ tptp.plus_plus_real Bg) Ag)))) 0.19/0.58 (assert (@ (@ tptp.member_a tptp.p) (@ (@ tptp.line_open_segment_a tptp.a2) tptp.b))) 0.19/0.58 (assert (forall ((T2 tptp.real) (X0 tptp.a)) (=> (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0)) (@ (@ tptp.member_a X0) tptp.x)))) 0.19/0.58 (assert (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) C)) (@ (@ tptp.ord_less_eq_a A) B)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))) 0.19/0.58 (assert (forall ((K tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real K)) tptp.one_one_real) (@ (@ tptp.ord_less_real K) tptp.one_one_real)))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.plus_plus_a tptp.zero_zero_a) A) A))) 0.19/0.58 (assert (forall ((A3 tptp.a) (K tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_a A3) B) (@ _let_1 (@ (@ tptp.plus_plus_a A) B))))))) 0.19/0.58 (assert (forall ((T2 tptp.real) (X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (not (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X))) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) T2) tptp.zero_zero_a))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (=> (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_a A) B))))))) 0.19/0.58 (assert (@ tptp.initia826609931terval tptp.top_top_set_real)) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))) 0.19/0.58 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (= (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X) tptp.top_top_set_real)))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))) 0.19/0.58 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C))))) 0.19/0.58 (assert (forall ((B4 tptp.a) (K tptp.a) (B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a A))) (let ((_let_2 (@ tptp.plus_plus_a K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B)))))))) 0.19/0.58 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B)))) 0.19/0.58 (assert (= tptp.plus_plus_a (lambda ((A4 tptp.a) (B3 tptp.a)) (@ (@ tptp.plus_plus_a B3) A4)))) 0.19/0.58 (assert (forall ((Delta2 tptp.real) (Tau2 (-> tptp.a tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Delta2) (=> (@ (@ tptp.topolo1710226732a_real (@ (@ tptp.elemen154694473ball_a tptp.p) Delta2)) Tau2) (=> (= (@ Tau2 tptp.p) tptp.zero_zero_real) (=> (forall ((Y3 tptp.a)) (=> (@ (@ tptp.member_a Y3) (@ (@ tptp.elemen154694473ball_a tptp.p) Delta2)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ Tau2 Y3))) tptp.one_one_real))) (=> (forall ((Y3 tptp.a)) (=> (@ (@ tptp.member_a Y3) (@ (@ tptp.elemen154694473ball_a tptp.p) Delta2)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y3) (@ Tau2 Y3))) (@ (@ tptp.line_open_segment_a tptp.a2) tptp.b)))) tptp.thesisa))))))) 0.19/0.58 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a C))) (= (@ (@ tptp.ord_less_eq_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_a A) B))))) 0.19/0.58 (assert (forall ((Ae tptp.real) (Be tptp.real) (Cd tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real Ae))) (= (@ (@ tptp.plus_plus_real (@ _let_1 Be)) Cd) (@ _let_1 (@ (@ tptp.plus_plus_real Be) Cd)))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.poinca522724647ment_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x))) (= (@ (@ _let_1 X) Y) (@ (@ _let_1 Y) X))))) 0.19/0.58 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((I tptp.a) (J tptp.a) (K tptp.a) (L tptp.a)) (=> (and (@ (@ tptp.ord_less_a I) J) (@ (@ tptp.ord_less_eq_a K) L)) (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a I) K)) (@ (@ tptp.plus_plus_a J) L))))) 0.19/0.58 (assert (forall ((T2 tptp.real) (X0 tptp.a)) (=> (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)) (@ (@ tptp.member_a X0) tptp.x)))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.plus_plus_a A) tptp.zero_zero_a) A))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))) 0.19/0.58 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real)) 0.19/0.58 (assert (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) C)) (@ (@ tptp.ord_less_a A) B)))) 0.19/0.58 (assert (forall ((Bg2 tptp.a) (Ag2 tptp.a) (Cf tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a Bg2))) (let ((_let_2 (@ tptp.plus_plus_a Ag2))) (= (@ _let_1 (@ _let_2 Cf)) (@ _let_2 (@ _let_1 Cf))))))) 0.19/0.58 (assert (not (= tptp.zero_zero_real tptp.one_one_real))) 0.19/0.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A))))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.plus_plus_a A) (@ tptp.uminus_uminus_a A)) tptp.zero_zero_a))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B)))) 0.19/0.58 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real K) L) (= I J)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L))))) 0.19/0.58 (assert (forall ((C tptp.a) (B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a B))) (=> (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_a A) C))))))) 0.19/0.58 (assert (@ (@ tptp.member_a tptp.p) tptp.x)) 0.19/0.58 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B))))) 0.19/0.58 (assert (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) C)) (@ (@ tptp.ord_less_eq_a A) B)))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (=> (not (= (@ tptp.f X) tptp.zero_zero_a)) (@ (@ (@ tptp.period138238489rbit_a tptp.f) tptp.x) X))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) A)))) 0.19/0.58 (assert (= (@ tptp.abs_abs_a tptp.zero_zero_a) tptp.zero_zero_a)) 0.19/0.58 (assert (forall ((Delta tptp.real) (Tau (-> tptp.a tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Delta) (=> (@ (@ tptp.topolo1710226732a_real (@ (@ tptp.elemen154694473ball_a tptp.p) Delta)) Tau) (=> (= (@ Tau tptp.p) tptp.zero_zero_real) (=> (forall ((Y3 tptp.a)) (=> (@ (@ tptp.member_a Y3) (@ (@ tptp.elemen154694473ball_a tptp.p) Delta)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ Tau Y3))) tptp.one_one_real))) (=> (forall ((Y3 tptp.a)) (=> (@ (@ tptp.member_a Y3) (@ (@ tptp.elemen154694473ball_a tptp.p) Delta)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y3) (@ Tau Y3))) (@ (@ tptp.line_open_segment_a tptp.a2) tptp.b)))) tptp.thesisa))))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (= (= (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0) tptp.bot_bot_set_real) (or (not (@ (@ tptp.member_a X0) tptp.x)) (not (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real)))))) 0.19/0.58 (assert (forall ((X tptp.a)) (= (@ (@ (@ tptp.period138238489rbit_a tptp.f) tptp.x) X) (and (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ (@ tptp.period1305449585riod_a tptp.f) tptp.x) X)))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a A) B)) B) (@ (@ tptp.ord_less_a A) tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((T2 tptp.real) (T3 tptp.real) (Y tptp.a)) (let ((_let_1 (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y))) (let ((_let_2 (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) Y))) (=> (not (= T2 T3)) (=> (@ (@ tptp.member_real T2) _let_2) (=> (@ (@ tptp.member_real T3) _let_2) (=> (= (@ _let_1 T2) (@ _let_1 T3)) (=> (not (= (@ tptp.f Y) tptp.zero_zero_a)) (@ (@ (@ tptp.period138238489rbit_a tptp.f) tptp.x) Y)))))))))) 0.19/0.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y) X))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_real B) (@ tptp.uminus_uminus_real A))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.plus_plus_a (@ tptp.abs_abs_a A)) (@ tptp.abs_abs_a B)))) (= (@ tptp.abs_abs_a _let_1) _let_1)))) 0.19/0.58 (assert (forall ((A3 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) A3))) A3))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a tptp.zero_zero_a))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_a A) B))))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2)))))) 0.19/0.58 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_a P) (@ tptp.collect_a Q))))) 0.19/0.58 (assert (forall ((X tptp.a)) (= (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (exists ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X)) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) X2) X) (not (= X2 tptp.zero_zero_real))))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a A))) (= (@ (@ tptp.plus_plus_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_a B) C)))))) 0.19/0.58 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_eq_a C) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_eq_a A) B) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) C)) B))))) 0.19/0.58 (assert (forall ((X tptp.a)) (= (@ (@ tptp.elemen154694473ball_a X) tptp.zero_zero_real) tptp.bot_bot_set_a))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (=> (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real) (=> (@ (@ tptp.member_a X0) tptp.x) (not (= (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0) tptp.bot_bot_set_real)))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C)))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B)))) 0.19/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_eq_a Y) tptp.zero_zero_a) (= (= (@ (@ tptp.plus_plus_a X) Y) tptp.zero_zero_a) (and (= X tptp.zero_zero_a) (= Y tptp.zero_zero_a))))))) 0.19/0.58 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) 0.19/0.58 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real K) L) (@ (@ tptp.ord_less_eq_real I) J)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (@ tptp.initia826609931terval (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0)))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) tptp.x) (=> (not (= (@ tptp.f X) tptp.zero_zero_a)) (not (forall ((A2 tptp.a) (B2 tptp.a)) (=> (@ (@ tptp.member_a X) (@ (@ tptp.line_open_segment_a A2) B2)) (not (@ (@ (@ (@ tptp.poinca522724647ment_a tptp.f) tptp.x) A2) B2))))))))) 0.19/0.58 (assert (forall ((I tptp.a) (J tptp.a) (K tptp.a) (L tptp.a)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_a I) K) (@ (@ tptp.plus_plus_a J) L))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (= A (@ (@ tptp.plus_plus_a A) B)) (= B tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.plus_plus_a A) (@ (@ tptp.plus_plus_a (@ tptp.uminus_uminus_a A)) B)) B))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_a B))) (=> (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_a A) C))))))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ tptp.f X) tptp.zero_zero_a) (= (@ (@ (@ tptp.period1305449585riod_a tptp.f) tptp.x) X) tptp.zero_zero_real))))) 0.19/0.58 (assert (forall ((X tptp.a) (T2 tptp.real)) (=> (@ (@ (@ tptp.period138238489rbit_a tptp.f) tptp.x) X) (not (= (@ tptp.f (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) T2)) tptp.zero_zero_a))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (@ tptp.initia826609931terval (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a A) (@ (@ tptp.plus_plus_a B) A)) (@ (@ tptp.ord_less_a tptp.zero_zero_a) B)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A)))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A))) 0.19/0.58 (assert (forall ((X tptp.a) (P2 tptp.a)) (= (@ (@ (@ (@ tptp.limit_1865182413oint_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X) P2) (@ (@ (@ (@ tptp.limit_94460170oint_a tptp.f) tptp.x) X) P2)))) 0.19/0.58 (assert (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) X) (= (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X) tptp.top_top_set_real))))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ tptp.abs_abs_a A)) A) (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) A)))) 0.19/0.58 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= K L) (= I J)) (= (@ (@ tptp.plus_plus_real I) K) (@ (@ tptp.plus_plus_real J) L))))) 0.19/0.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A))))) 0.19/0.58 (assert (forall ((T2 tptp.real) (T3 tptp.real) (Y tptp.a)) (let ((_let_1 (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y))) (let ((_let_2 (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) Y))) (=> (not (= T2 T3)) (=> (@ (@ tptp.member_real T2) _let_2) (=> (@ (@ tptp.member_real T3) _let_2) (=> (= (@ _let_1 T2) (@ _let_1 T3)) (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) Y))))))))) 0.19/0.58 (assert (= (@ tptp.uminus_uminus_a tptp.zero_zero_a) tptp.zero_zero_a)) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a A))) (= (@ (@ tptp.plus_plus_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_a B) C)))))) 0.19/0.58 (assert (forall ((X tptp.a)) (= (@ (@ (@ tptp.period720806154rbit_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X) (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X)))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real)))) 0.19/0.58 (assert (not tptp.thesisa)) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (= (@ tptp.uminus_uminus_a A) (@ tptp.uminus_uminus_a B)) (= A B)))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_eq_a A) (@ (@ tptp.plus_plus_a B) A)) (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) B)))) 0.19/0.58 (assert (forall ((S tptp.real) (X0 tptp.a) (T2 tptp.real)) (let ((_let_1 (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x))) (let ((_let_2 (@ _let_1 X0))) (let ((_let_3 (@ _let_2 S))) (let ((_let_4 (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x))) (=> (@ (@ tptp.member_real S) (@ _let_4 X0)) (=> (@ (@ tptp.member_real T2) (@ _let_4 _let_3)) (= (@ _let_2 (@ (@ tptp.plus_plus_real S) T2)) (@ (@ _let_1 _let_3) T2)))))))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (=> (not (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real)) (= (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0) tptp.bot_bot_set_real)))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (@ (@ tptp.member_a X) tptp.x)))) 0.19/0.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y) Y))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ tptp.f X) tptp.zero_zero_a) (= (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X) tptp.top_top_set_real))))) 0.19/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a tptp.zero_zero_a))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_a X) Y) tptp.zero_zero_a) (and (= X tptp.zero_zero_a) (= Y tptp.zero_zero_a)))))))) 0.19/0.58 (assert (forall ((P Bool)) (or (= P true) (= P false)))) 0.19/0.58 (assert (not (forall ((D tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (forall ((T (-> tptp.a tptp.real))) (let ((_let_1 (@ (@ tptp.topolo1710226732a_real (@ (@ tptp.elemen154694473ball_a tptp.p) D)) T))) (=> _let_1 (=> (forall ((Y2 tptp.a)) (=> (@ (@ tptp.member_a Y2) (@ (@ tptp.elemen154694473ball_a tptp.p) D)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y2) (@ T Y2))) (@ (@ tptp.line_open_segment_a tptp.a2) tptp.b)))) (=> (forall ((Y2 tptp.a)) (=> (@ (@ tptp.member_a Y2) (@ (@ tptp.elemen154694473ball_a tptp.p) D)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ T Y2))) tptp.one_one_real))) (=> _let_1 (not (= (@ T tptp.p) tptp.zero_zero_real)))))))))))) 0.19/0.58 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (=> (= (@ (@ tptp.plus_plus_a B) A) (@ (@ tptp.plus_plus_a C) A)) (= B C)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (= (@ tptp.abs_abs_real _let_1) _let_1)))) 0.19/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a B)) (@ tptp.uminus_uminus_a A)) (@ (@ tptp.ord_less_a A) B)))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_a tptp.zero_zero_a) (@ tptp.uminus_uminus_a A)) (@ (@ tptp.ord_less_a A) tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a A)) B) (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a B)) A)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C))))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (let ((_let_1 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real))) (let ((_let_3 (@ (@ tptp.member_a X0) tptp.x))) (and (=> (and _let_2 _let_3) (= _let_1 X0)) (=> (not (and _let_3 _let_2)) (= _let_1 tptp.zero_zero_a)))))))) 0.19/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.poinca522724647ment_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x))) (=> (@ (@ _let_1 X) Y) (@ (@ _let_1 Y) X))))) 0.19/0.58 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real)) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) X) (=> (not (= (@ _let_1 X) tptp.zero_zero_a)) (@ (@ (@ tptp.period138238489rbit_a _let_1) tptp.x) X)))))) 0.19/0.58 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real)) 0.19/0.58 (assert (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ _let_1 X) tptp.zero_zero_a) (= (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X) tptp.top_top_set_real)))))) 0.19/0.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real))))) 0.19/0.58 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.plus_plus_a (@ tptp.uminus_uminus_a A)) (@ (@ tptp.plus_plus_a A) B)) B))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B)))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a) (D2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (@ (@ tptp.ord_less_eq_a C) D2) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) D2)))))) 0.19/0.58 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C))))) 0.19/0.58 (assert (forall ((Y tptp.a) (T2 tptp.real)) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y) T2) (@ (@ (@ (@ tptp.auto_ll_on_flow0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) Y) (@ tptp.uminus_uminus_real T2))))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ tptp.abs_abs_a A)) tptp.zero_zero_a) (= A tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((I tptp.a) (J tptp.a) (K tptp.a) (L tptp.a)) (=> (and (@ (@ tptp.ord_less_eq_a I) J) (@ (@ tptp.ord_less_eq_a K) L)) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a I) K)) (@ (@ tptp.plus_plus_a J) L))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (= (= (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0) tptp.bot_bot_set_real) (or (not (@ (@ tptp.member_a X0) tptp.x)) (not (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real)))))) 0.19/0.58 (assert (forall ((X tptp.a) (T2 tptp.real)) (let ((_let_1 (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x))) (=> (@ _let_1 X) (@ _let_1 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) T2)))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (=> (@ (@ tptp.member_a X0) tptp.x) (@ (@ tptp.member_real tptp.zero_zero_real) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0))))) 0.19/0.58 (assert (@ (@ (@ (@ tptp.poinca522724647ment_a tptp.f) tptp.x) tptp.a2) tptp.b)) 0.19/0.58 (assert (forall ((I tptp.a) (J tptp.a) (K tptp.a) (L tptp.a)) (=> (and (@ (@ tptp.ord_less_a K) L) (@ (@ tptp.ord_less_eq_a I) J)) (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a I) K)) (@ (@ tptp.plus_plus_a J) L))))) 0.19/0.58 (assert (forall ((X tptp.a) (A tptp.a) (B tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.member_a Y))) (let ((_let_2 (@ tptp.line_open_segment_a A))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.member_a X) _let_3) (=> (@ _let_1 _let_3) (or (= X Y) (@ _let_1 (@ _let_2 X)) (@ _let_1 (@ (@ tptp.line_open_segment_a X) B)))))))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (let ((_let_1 (@ tptp.member_real tptp.zero_zero_real))) (=> (@ _let_1 tptp.top_top_set_real) (=> (@ (@ tptp.member_a X0) tptp.x) (@ _let_1 (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0))))))) 0.19/0.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C))))) 0.19/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.poinca522724647ment_a tptp.f) tptp.x))) (= (@ (@ _let_1 X) Y) (@ (@ _let_1 Y) X))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a C))) (=> (@ (@ tptp.ord_less_eq_a A) B) (@ (@ tptp.ord_less_eq_a (@ _let_1 A)) (@ _let_1 B)))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real)))) 0.19/0.58 (assert (= tptp.poinca522724647ment_a tptp.poinca522724647ment_a)) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.plus_plus_a (@ tptp.uminus_uminus_a A)) A) tptp.zero_zero_a))) 0.19/0.58 (assert (forall ((T2 tptp.real) (X0 tptp.a)) (=> (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)) (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real)))) 0.19/0.58 (assert (forall ((X tptp.a) (E tptp.real)) (= (@ (@ tptp.member_a X) (@ (@ tptp.elemen154694473ball_a X) E)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) E)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2)))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (=> (not (@ (@ tptp.member_a X0) tptp.x)) (= (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0) tptp.bot_bot_set_real)))) 0.19/0.58 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C)))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (=> (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real) (=> (@ (@ tptp.member_a X0) tptp.x) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X0) tptp.zero_zero_real) X0))))) 0.19/0.58 (assert (forall ((Xa tptp.real) (X0 tptp.a)) (=> (@ (@ tptp.member_real Xa) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X0) Xa)) tptp.x)))) 0.19/0.58 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real)) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ (@ (@ tptp.poinca522724647ment_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) A) B) (@ (@ (@ (@ tptp.poinca522724647ment_a tptp.f) tptp.x) A) B)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2)))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real))))) 0.19/0.58 (assert (forall ((X tptp.a) (E tptp.real)) (= (= (@ (@ tptp.elemen154694473ball_a X) E) tptp.bot_bot_set_a) (@ (@ tptp.ord_less_eq_real E) tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((T2 tptp.real) (X0 tptp.a)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0)) (@ _let_1 tptp.top_top_set_real))))) 0.19/0.58 (assert (forall ((A tptp.a)) (=> (@ (@ tptp.ord_less_a A) tptp.zero_zero_a) (= (@ tptp.abs_abs_a A) (@ tptp.uminus_uminus_a A))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_eq_a B) tptp.zero_zero_a) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) B)) tptp.zero_zero_a))))) 0.19/0.58 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (= (= (@ (@ tptp.plus_plus_a B) A) (@ (@ tptp.plus_plus_a C) A)) (= B C)))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (=> (= (@ (@ (@ tptp.period1305449585riod_a tptp.f) tptp.x) X) tptp.zero_zero_real) (= (@ tptp.f X) tptp.zero_zero_a))))) 0.19/0.58 (assert (forall ((T2 tptp.real) (X0 tptp.a)) (=> (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0)) (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real)))) 0.19/0.58 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C))))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((X tptp.a) (T2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period138238489rbit_a _let_1) tptp.x) X) (not (= (@ _let_1 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) T2)) tptp.zero_zero_a)))))) 0.19/0.58 (assert (forall ((S tptp.real) (X0 tptp.a) (T2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x))) (let ((_let_3 (@ _let_2 X0))) (=> (@ (@ tptp.member_real S) _let_3) (=> (@ (@ tptp.member_real T2) (@ _let_2 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X0) S))) (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real S) T2)) _let_3)))))))) 0.19/0.58 (assert (forall ((X tptp.real) (E tptp.real)) (= (= (@ (@ tptp.elemen341675809l_real X) E) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_real E) tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A))) 0.19/0.58 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real)))) 0.19/0.58 (assert (forall ((T2 tptp.real) (T3 tptp.real) (Y tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) Y))) (let ((_let_3 (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) Y))) (=> (not (= T2 T3)) (=> (@ (@ tptp.member_real T2) _let_3) (=> (@ (@ tptp.member_real T3) _let_3) (=> (= (@ _let_2 T2) (@ _let_2 T3)) (=> (not (= (@ _let_1 Y) tptp.zero_zero_a)) (@ (@ (@ tptp.period138238489rbit_a _let_1) tptp.x) Y))))))))))) 0.19/0.58 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C))))))) 0.19/0.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X))))) 0.19/0.58 (assert (forall ((X tptp.real) (E tptp.real)) (= (@ (@ tptp.member_real X) (@ (@ tptp.elemen341675809l_real X) E)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) E)))) 0.19/0.58 (assert (forall ((T2 tptp.real) (X0 tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X0)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X0) T2)) tptp.x))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (=> (@ (@ tptp.member_a X0) tptp.x) (@ (@ tptp.member_real tptp.zero_zero_real) (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0))))) 0.19/0.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X) (@ tptp.abs_abs_real Y)) (or (= X (@ tptp.uminus_uminus_real Y)) (= X Y))))) 0.19/0.58 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (= (= (@ (@ tptp.plus_plus_a B) A) (@ (@ tptp.plus_plus_a C) A)) (= B C)))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (let ((_let_1 (@ tptp.member_real tptp.zero_zero_real))) (=> (@ _let_1 tptp.top_top_set_real) (=> (@ (@ tptp.member_a X0) tptp.x) (@ _let_1 (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0))))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L))))) 0.19/0.58 (assert (= tptp.plus_plus_a (lambda ((Ag tptp.a) (Bg tptp.a)) (@ (@ tptp.plus_plus_a Bg) Ag)))) 0.19/0.58 (assert (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.poinca522724647ment_a tptp.f) tptp.x))) (=> (@ (@ _let_1 X) Y) (@ (@ _let_1 Y) X))))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period138238489rbit_a tptp.f) tptp.x) X) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) (@ (@ (@ tptp.period1305449585riod_a tptp.f) tptp.x) X)) X)))) 0.19/0.58 (assert (forall ((T6 tptp.real) (X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X))) (=> (@ (@ tptp.member_real T6) (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X)) (=> (= (@ _let_2 T6) X) (= (@ _let_2 (@ tptp.uminus_uminus_real T6)) X))))))) 0.19/0.58 (assert (forall ((A tptp.a)) (let ((_let_1 (@ tptp.abs_abs_a A))) (= (@ tptp.abs_abs_a _let_1) _let_1)))) 0.19/0.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.elemen341675809l_real X) tptp.zero_zero_real) tptp.bot_bot_set_real))) 0.19/0.58 (assert (forall ((X tptp.a)) (= (= tptp.zero_zero_a X) (= X tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ (@ tptp.period1305449585riod_a tptp.f) tptp.x) X))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((T6 tptp.real) (X tptp.a)) (let ((_let_1 (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X))) (=> (@ (@ tptp.member_real T6) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X)) (=> (= (@ _let_1 T6) X) (= (@ _let_1 (@ tptp.uminus_uminus_real T6)) X)))))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ tptp.abs_abs_a (@ tptp.uminus_uminus_a A)) (@ tptp.abs_abs_a A)))) 0.19/0.58 (assert (forall ((A3 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A3) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B))))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (let ((_let_1 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X0) tptp.zero_zero_real))) (let ((_let_2 (and (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real) (@ (@ tptp.member_a X0) tptp.x)))) (and (=> (not _let_2) (= _let_1 tptp.zero_zero_a)) (=> _let_2 (= _let_1 X0))))))) 0.19/0.58 (assert (forall ((X tptp.a) (P2 tptp.a)) (= (@ (@ (@ (@ tptp.limit_1865182413oint_a tptp.f) tptp.x) X) P2) (@ (@ (@ (@ tptp.limit_94460170oint_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X) P2)))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (X tptp.a) (E tptp.real)) (=> (@ (@ (@ (@ tptp.poinca522724647ment_a tptp.f) tptp.x) A) B) (=> (@ (@ tptp.member_a X) (@ (@ tptp.line_open_segment_a A) B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((D tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (forall ((T (-> tptp.a tptp.real))) (let ((_let_1 (@ (@ tptp.topolo1710226732a_real (@ (@ tptp.elemen154694473ball_a X) D)) T))) (=> _let_1 (=> (forall ((Y2 tptp.a)) (=> (@ (@ tptp.member_a Y2) (@ (@ tptp.elemen154694473ball_a X) D)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y2) (@ T Y2))) (@ (@ tptp.line_open_segment_a A) B)))) (=> (forall ((Y2 tptp.a)) (=> (@ (@ tptp.member_a Y2) (@ (@ tptp.elemen154694473ball_a X) D)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ T Y2))) E))) (=> _let_1 (not (= (@ T X) tptp.zero_zero_real)))))))))))))))) 0.19/0.58 (assert (forall ((A tptp.a)) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) A) (= (@ tptp.abs_abs_a A) A)))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) (@ tptp.uminus_uminus_a A)) (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B)))) 0.19/0.58 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))) 0.19/0.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A))))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (= (@ tptp.abs_abs_a A) tptp.zero_zero_a) (= A tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((X tptp.a)) (= (@ (@ (@ tptp.period720806154rbit_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X) (exists ((X2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (and (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) X2) X) (not (= X2 tptp.zero_zero_real)) (@ (@ tptp.member_real X2) (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X)))))))) 0.19/0.58 (assert (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_eq_a C) B) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) C)) B))))) 0.19/0.58 (assert (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ _let_1 X) tptp.zero_zero_a) (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) X)))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_a B) tptp.zero_zero_a) (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a A) B)) tptp.zero_zero_a))))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X) (@ (@ tptp.member_a X) tptp.x)))) 0.19/0.58 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real)) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (= A (@ tptp.uminus_uminus_a B)) (= B (@ tptp.uminus_uminus_a A))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a B))) (=> (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_a A) C))))))) 0.19/0.58 (assert (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period138238489rbit_a _let_1) tptp.x) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ (@ tptp.period1305449585riod_a _let_1) tptp.x) X)))))) 0.19/0.58 (assert (forall ((A3 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A3))) A3))) 0.19/0.58 (assert (forall ((I tptp.a) (J tptp.a) (K tptp.a) (L tptp.a)) (=> (and (@ (@ tptp.ord_less_eq_a I) J) (= K L)) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a I) K)) (@ (@ tptp.plus_plus_a J) L))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.plus_plus_a A) tptp.zero_zero_a) A))) 0.19/0.58 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B)))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A)))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (=> (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real) (=> (@ (@ tptp.member_a X0) tptp.x) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0) tptp.zero_zero_real) X0))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a) (D2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (@ (@ tptp.ord_less_a C) D2) (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) D2)))))) 0.19/0.58 (assert (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period138238489rbit_a _let_1) tptp.x) X) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) (@ (@ (@ tptp.period1305449585riod_a _let_1) tptp.x) X)) X))))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ tptp.uminus_uminus_a (@ tptp.uminus_uminus_a A)) A))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B))))))) 0.19/0.58 (assert (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a B))) (let ((_let_2 (@ tptp.plus_plus_a A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C))))))) 0.19/0.58 (assert (forall ((I tptp.a) (J tptp.a) (K tptp.a) (L tptp.a)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_a K) L)) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a I) K)) (@ (@ tptp.plus_plus_a J) L))))) 0.19/0.58 (assert (forall ((X tptp.a) (T2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ _let_1 X) tptp.zero_zero_a) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) T2) X)))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a) (D2 tptp.a)) (=> (@ (@ tptp.ord_less_a A) B) (=> (@ (@ tptp.ord_less_eq_a C) D2) (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) D2)))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C))))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B)))) 0.19/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (= (= (@ (@ tptp.plus_plus_a B) A) A) (= B tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((X tptp.a) (T2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ tptp.period720806154rbit_a _let_1) tptp.x))) (=> (@ _let_2 X) (@ _let_2 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) T2))))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_eq_a A) (@ (@ tptp.plus_plus_a A) B)) (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) B)))) 0.19/0.58 (assert (forall ((T6 tptp.real) (X tptp.a)) (let ((_let_1 (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X))) (=> (@ (@ tptp.member_real T6) _let_1) (=> (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) T6) X) (@ (@ tptp.member_real (@ tptp.uminus_uminus_real T6)) _let_1)))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C)))))) 0.19/0.58 (assert (forall ((T2 tptp.real) (S tptp.real) (X0 tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x))) (let ((_let_3 (@ _let_2 X0))) (=> (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real T2) S)) _let_3) (=> (@ (@ tptp.member_real T2) _let_3) (@ (@ tptp.member_real S) (@ _let_2 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X0) T2)))))))))) 0.19/0.58 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (= K L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A))) 0.19/0.58 (assert (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (= (@ (@ (@ tptp.period138238489rbit_a _let_1) tptp.x) X) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ (@ tptp.period1305449585riod_a _let_1) tptp.x) X)) (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) X)))))) 0.19/0.58 (assert (forall ((A tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P)) (@ P A)))) 0.19/0.58 (assert (forall ((T2 tptp.real) (X tptp.a)) (=> (not (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X))) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) T2) tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (= (@ (@ tptp.plus_plus_a A) B) A) (= B tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ _let_1 X) tptp.zero_zero_a) (= (@ (@ (@ tptp.period1305449585riod_a _let_1) tptp.x) X) tptp.zero_zero_real)))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (@ (@ tptp.ord_less_eq_a (@ tptp.abs_abs_a (@ (@ tptp.plus_plus_a A) B))) (@ (@ tptp.plus_plus_a (@ tptp.abs_abs_a A)) (@ tptp.abs_abs_a B))))) 0.19/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a B) A)) B) (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((A tptp.a)) (not (@ (@ tptp.ord_less_a (@ tptp.abs_abs_a A)) tptp.zero_zero_a)))) 0.19/0.58 (assert (@ (@ (@ (@ tptp.limit_94460170oint_a tptp.f) tptp.x) tptp.x2) tptp.p)) 0.19/0.58 (assert (forall ((A tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a) (= (@ tptp.abs_abs_a A) (@ tptp.uminus_uminus_a A))))) 0.19/0.58 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B))))) 0.19/0.58 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real)) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a A) (@ tptp.uminus_uminus_a B)) (@ (@ tptp.ord_less_a B) (@ tptp.uminus_uminus_a A))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a A) (@ (@ tptp.plus_plus_a A) B)) (@ (@ tptp.ord_less_a tptp.zero_zero_a) B)))) 0.19/0.58 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (= (@ tptp.uminus_uminus_a A) tptp.zero_zero_a) (= A tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1)))) 0.19/0.58 (assert (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((T2 tptp.real) (S tptp.real) (X0 tptp.a)) (let ((_let_1 (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x))) (let ((_let_2 (@ _let_1 X0))) (=> (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real T2) S)) _let_2) (=> (@ (@ tptp.member_real T2) _let_2) (@ (@ tptp.member_real S) (@ _let_1 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X0) T2))))))))) 0.19/0.58 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real)) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A)))) 0.19/0.58 (assert (forall ((S tptp.real) (X0 tptp.a) (T2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x))) (let ((_let_3 (@ _let_2 X0))) (let ((_let_4 (@ _let_3 S))) (let ((_let_5 (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x))) (=> (@ (@ tptp.member_real S) (@ _let_5 X0)) (=> (@ (@ tptp.member_real T2) (@ _let_5 _let_4)) (= (@ _let_3 (@ (@ tptp.plus_plus_real S) T2)) (@ (@ _let_2 _let_4) T2))))))))))) 0.19/0.58 (assert (forall ((T6 tptp.real) (X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X))) (=> (@ (@ tptp.member_real T6) _let_2) (=> (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) T6) X) (@ (@ tptp.member_real (@ tptp.uminus_uminus_real T6)) _let_2))))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) C))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ tptp.uminus_uminus_a (@ (@ tptp.plus_plus_a A) B)) (@ (@ tptp.plus_plus_a (@ tptp.uminus_uminus_a A)) (@ tptp.uminus_uminus_a B))))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_a tptp.zero_zero_a) (@ tptp.abs_abs_a A)) (not (= A tptp.zero_zero_a))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (=> (not (@ (@ tptp.member_a X0) tptp.x)) (= (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0) tptp.bot_bot_set_real)))) 0.19/0.58 (assert (forall ((T2 tptp.real) (X0 tptp.a)) (=> (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X0) T2)) tptp.x)))) 0.19/0.58 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))) 0.19/0.58 (assert (forall ((E tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real E) tptp.zero_zero_real) (= (@ (@ tptp.elemen341675809l_real X) E) tptp.bot_bot_set_real)))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) tptp.x) (=> (not (= (@ (@ tptp.uminus_uminus_a_a tptp.f) X) tptp.zero_zero_a)) (not (forall ((A2 tptp.a) (B2 tptp.a)) (=> (@ (@ tptp.member_a X) (@ (@ tptp.line_open_segment_a A2) B2)) (not (@ (@ (@ (@ tptp.poinca522724647ment_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) A2) B2))))))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B))) 0.19/0.58 (assert (forall ((T2 tptp.real) (T3 tptp.real) (Y tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) Y))) (let ((_let_3 (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) Y))) (=> (not (= T2 T3)) (=> (@ (@ tptp.member_real T2) _let_3) (=> (@ (@ tptp.member_real T3) _let_3) (=> (= (@ _let_2 T2) (@ _let_2 T3)) (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) Y)))))))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A))))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ tptp.uminus_uminus_a A)) tptp.zero_zero_a) (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) A)))) 0.19/0.58 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real)) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_a A) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_eq_a B) tptp.zero_zero_a) (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a A) B)) tptp.zero_zero_a))))) 0.19/0.58 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B)))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real))))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (@ (@ tptp.plus_plus_a tptp.zero_zero_a) A) A))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))) 0.19/0.58 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real)))) 0.19/0.58 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real)) 0.19/0.58 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4)))) 0.19/0.58 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a C))) (=> (@ (@ tptp.ord_less_eq_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_a A) B))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (=> (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real) (=> (@ (@ tptp.member_a X0) tptp.x) (not (= (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0) tptp.bot_bot_set_real)))))) 0.19/0.58 (assert (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ tptp.uminus_uminus_a B)) (@ tptp.uminus_uminus_a A)) (@ (@ tptp.ord_less_eq_a A) B)))) 0.19/0.58 (assert (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ tptp.f X) tptp.zero_zero_a) (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X))))) 0.19/0.58 (assert (forall ((X0 tptp.a)) (let ((_let_1 (@ tptp.member_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0)) (and (@ (@ tptp.member_a X0) tptp.x) (@ _let_1 tptp.top_top_set_real)))))) 0.19/0.58 (assert (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) B) (@ _let_1 (@ (@ tptp.plus_plus_a A) B))))))) 0.19/0.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C)))))) 0.19/0.58 (assert (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a C))) (= (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_a A) B))))) 0.19/0.58 (assert (forall ((Bg2 tptp.real) (Ag2 tptp.real) (Cf tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real Bg2))) (let ((_let_2 (@ tptp.plus_plus_real Ag2))) (= (@ _let_1 (@ _let_2 Cf)) (@ _let_2 (@ _let_1 Cf))))))) 0.19/0.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A)))) 0.19/0.58 (assert (forall ((E tptp.real) (X tptp.a)) (=> (@ (@ tptp.ord_less_eq_real E) tptp.zero_zero_real) (= (@ (@ tptp.elemen154694473ball_a X) E) tptp.bot_bot_set_a)))) 0.19/0.58 (assert (forall ((A tptp.a)) (= (= tptp.zero_zero_a (@ tptp.abs_abs_a A)) (= A tptp.zero_zero_a)))) 0.19/0.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= Y tptp.zero_zero_real) (= X tptp.zero_zero_real))))))) 0.19/0.58 (assert (forall ((X tptp.a) (T2 tptp.real)) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ tptp.f X) tptp.zero_zero_a) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) T2) X))))) 0.19/0.58 (assert (forall ((T2 tptp.real) (X0 tptp.a)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)) (@ _let_1 tptp.top_top_set_real))))) 0.40/0.89 (assert (forall ((S tptp.real) (X0 tptp.a) (T2 tptp.real)) (let ((_let_1 (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x))) (let ((_let_2 (@ _let_1 X0))) (=> (@ (@ tptp.member_real S) _let_2) (=> (@ (@ tptp.member_real T2) (@ _let_1 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X0) S))) (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real S) T2)) _let_2))))))) 0.40/0.89 (assert (forall ((Xa tptp.real) (X0 tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ tptp.member_real Xa) (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X0)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X0) Xa)) tptp.x))))) 0.40/0.89 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B))))))) 0.40/0.89 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B)))) 0.40/0.89 (assert (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (not (forall ((T5 tptp.real)) (let ((_let_1 (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X))) (= (@ _let_1 (@ (@ tptp.plus_plus_real T5) T4)) (@ _let_1 T5))))))))))) 0.40/0.89 (set-info :filename cvc5---1.0.5_14416) 0.40/0.89 (check-sat-assuming ( true )) 0.40/0.89 ------- get file name : TPTP file name is 0.40/0.89 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14416.smt2... 0.40/0.89 --- Run --ho-elim --full-saturate-quant at 10... 0.40/0.89 % SZS status Theorem for 0.40/0.89 % SZS output start Proof for 0.40/0.89 ( 0.40/0.89 (let ((_let_1 (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))) (let ((_let_2 (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_3 (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_4 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_5 (not (forall ((D tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (forall ((T (-> tptp.a tptp.real))) (let ((_let_1 (@ (@ tptp.topolo1710226732a_real (@ (@ tptp.elemen154694473ball_a tptp.p) D)) T))) (=> _let_1 (=> (forall ((Y2 tptp.a)) (=> (@ (@ tptp.member_a Y2) (@ (@ tptp.elemen154694473ball_a tptp.p) D)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y2) (@ T Y2))) (@ (@ tptp.line_open_segment_a tptp.a2) tptp.b)))) (=> (forall ((Y2 tptp.a)) (=> (@ (@ tptp.member_a Y2) (@ (@ tptp.elemen154694473ball_a tptp.p) D)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ T Y2))) tptp.one_one_real))) (=> _let_1 (not (= (@ T tptp.p) tptp.zero_zero_real))))))))))))) (let ((_let_6 (not tptp.thesisa))) (let ((_let_7 (@ tptp.member_a tptp.p))) (let ((_let_8 (= (@ (@ tptp.plus_plus_real _let_4) tptp.one_one_real) tptp.zero_zero_real))) (let ((_let_9 (forall ((Delta2 tptp.real) (Tau2 (-> tptp.a tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Delta2) (=> (@ (@ tptp.topolo1710226732a_real (@ (@ tptp.elemen154694473ball_a tptp.p) Delta2)) Tau2) (=> (= (@ Tau2 tptp.p) tptp.zero_zero_real) (=> (forall ((Y3 tptp.a)) (=> (@ (@ tptp.member_a Y3) (@ (@ tptp.elemen154694473ball_a tptp.p) Delta2)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ Tau2 Y3))) tptp.one_one_real))) (=> (forall ((Y3 tptp.a)) (=> (@ (@ tptp.member_a Y3) (@ (@ tptp.elemen154694473ball_a tptp.p) Delta2)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y3) (@ Tau2 Y3))) (@ (@ tptp.line_open_segment_a tptp.a2) tptp.b)))) tptp.thesisa)))))))) (let ((_let_10 (ho_27 (ho_26 k_28 (ho_27 k_30 tptp.one_one_real)) tptp.one_one_real))) (let ((_let_11 (ho_10 (ho_32 k_31 _let_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82))) (let ((_let_12 (ho_67 k_66 tptp.p))) (let ((_let_13 (ho_71 (ho_70 k_69 (ho_68 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83))) (let ((_let_14 (= _let_10 (ho_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 tptp.p)))) (let ((_let_15 (forall ((Y3 tptp.a)) (or (not (ho_23 (ho_22 k_21 Y3) (ho_68 (ho_67 k_66 tptp.p) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82))) (ho_23 (ho_22 k_21 (ho_41 (ho_40 (ho_39 (ho_38 k_37 k_36) tptp.x) Y3) (ho_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 Y3))) (ho_64 (ho_63 k_62 tptp.a2) tptp.b)))))) (let ((_let_16 (not _let_15))) (let ((_let_17 (forall ((Y3 tptp.a)) (let ((_let_1 (ho_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 Y3))) (or (not (ho_23 (ho_22 k_21 Y3) (ho_68 (ho_67 k_66 tptp.p) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82))) (ho_10 (ho_32 k_31 (ho_27 (ho_26 (ho_46 k_45 (ho_10 (ho_32 k_31 _let_1) (ho_27 (ho_26 k_28 (ho_27 k_30 tptp.one_one_real)) tptp.one_one_real))) (ho_27 k_30 _let_1)) _let_1)) tptp.one_one_real)))))) (let ((_let_18 (not _let_17))) (let ((_let_19 (not _let_14))) (let ((_let_20 (not _let_13))) (let ((_let_21 (not _let_11))) (let ((_let_22 (or _let_21 _let_20 _let_19 _let_18 _let_16))) (let ((_let_23 (forall ((Y2 tptp.a)) (let ((_let_1 (ho_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 Y2))) (or (not (ho_23 (ho_22 k_21 Y2) (ho_68 (ho_67 k_66 tptp.p) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82))) (ho_10 (ho_32 k_31 (ho_27 (ho_26 (ho_46 k_45 (ho_10 (ho_32 k_31 _let_1) (ho_27 (ho_26 k_28 (ho_27 k_30 tptp.one_one_real)) tptp.one_one_real))) (ho_27 k_30 _let_1)) _let_1)) tptp.one_one_real)))))) (let ((_let_24 (not _let_23))) (let ((_let_25 (forall ((Y2 tptp.a)) (or (not (ho_23 (ho_22 k_21 Y2) (ho_68 (ho_67 k_66 tptp.p) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82))) (ho_23 (ho_22 k_21 (ho_41 (ho_40 (ho_39 (ho_38 k_37 k_36) tptp.x) Y2) (ho_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 Y2))) (ho_64 (ho_63 k_62 tptp.a2) tptp.b)))))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_21 _let_20 _let_26 _let_24 _let_19))) (let ((_let_28 (forall ((D tptp.real) (BOUND_VARIABLE_9057 |u_(-> tptp.a tptp.real)|)) (let ((_let_1 (ho_27 (ho_26 k_28 (ho_27 k_30 tptp.one_one_real)) tptp.one_one_real))) (or (not (ho_10 (ho_32 k_31 _let_1) D)) (not (ho_71 (ho_70 k_69 (ho_68 (ho_67 k_66 tptp.p) D)) BOUND_VARIABLE_9057)) (not (forall ((Y2 tptp.a)) (or (not (ho_23 (ho_22 k_21 Y2) (ho_68 (ho_67 k_66 tptp.p) D))) (ho_23 (ho_22 k_21 (ho_41 (ho_40 (ho_39 (ho_38 k_37 k_36) tptp.x) Y2) (ho_51 BOUND_VARIABLE_9057 Y2))) (ho_64 (ho_63 k_62 tptp.a2) tptp.b))))) (not (forall ((Y2 tptp.a)) (let ((_let_1 (ho_51 BOUND_VARIABLE_9057 Y2))) (or (not (ho_23 (ho_22 k_21 Y2) (ho_68 (ho_67 k_66 tptp.p) D))) (ho_10 (ho_32 k_31 (ho_27 (ho_26 (ho_46 k_45 (ho_10 (ho_32 k_31 _let_1) (ho_27 (ho_26 k_28 (ho_27 k_30 tptp.one_one_real)) tptp.one_one_real))) (ho_27 k_30 _let_1)) _let_1)) tptp.one_one_real))))) (not (= _let_1 (ho_51 BOUND_VARIABLE_9057 tptp.p)))))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (not _let_28))) (let ((_let_31 (SYMM (ASSUME :args (_let_8))))) (let ((_let_32 (AND_INTRO (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_6)) :args ((= tptp.thesisa false))) (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO _let_31 :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) _let_31))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_32 :args ((not (forall ((D tptp.real) (BOUND_VARIABLE_5129 (-> tptp.a tptp.real))) (or (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) D)) (not (@ (@ tptp.topolo1710226732a_real (@ (@ tptp.elemen154694473ball_a tptp.p) D)) BOUND_VARIABLE_5129)) (not (forall ((Y2 tptp.a)) (or (not (@ (@ tptp.member_a Y2) (@ (@ tptp.elemen154694473ball_a tptp.p) D))) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y2) (@ BOUND_VARIABLE_5129 Y2))) (@ (@ tptp.line_open_segment_a tptp.a2) tptp.b))))) (not (forall ((Y2 tptp.a)) (or (not (@ (@ tptp.member_a Y2) (@ (@ tptp.elemen154694473ball_a tptp.p) D))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ BOUND_VARIABLE_5129 Y2))) tptp.one_one_real)))) (not (= tptp.zero_zero_real (@ BOUND_VARIABLE_5129 tptp.p)))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((D tptp.real) (BOUND_VARIABLE_5129 (-> tptp.a tptp.real))) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))) (or (not (@ (@ tptp.ord_less_real _let_1) D)) (not (@ (@ tptp.topolo1710226732a_real (@ (@ tptp.elemen154694473ball_a tptp.p) D)) BOUND_VARIABLE_5129)) (not (forall ((Y2 tptp.a)) (or (not (@ (@ tptp.member_a Y2) (@ (@ tptp.elemen154694473ball_a tptp.p) D))) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y2) (@ BOUND_VARIABLE_5129 Y2))) (@ (@ tptp.line_open_segment_a tptp.a2) tptp.b))))) (not (forall ((Y2 tptp.a)) (let ((_let_1 (@ BOUND_VARIABLE_5129 Y2))) (or (not (@ (@ tptp.member_a Y2) (@ (@ tptp.elemen154694473ball_a tptp.p) D))) (@ (@ tptp.ord_less_real (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))) (@ tptp.uminus_uminus_real _let_1)) _let_1)) tptp.one_one_real))))) (not (= _let_1 (@ BOUND_VARIABLE_5129 tptp.p))))))) _let_30))))))) (let ((_let_34 (or))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_33) :args (_let_30))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_28))) (REFL :args (_let_29)) :args _let_34)) _let_33 :args (_let_29 true _let_28)))) (let ((_let_36 (REFL :args (_let_27)))) (let ((_let_37 (forall ((Delta2 tptp.real) (BOUND_VARIABLE_8118 |u_(-> tptp.a tptp.real)|)) (let ((_let_1 (ho_27 (ho_26 k_28 (ho_27 k_30 tptp.one_one_real)) tptp.one_one_real))) (or (not (ho_10 (ho_32 k_31 _let_1) Delta2)) (not (ho_71 (ho_70 k_69 (ho_68 (ho_67 k_66 tptp.p) Delta2)) BOUND_VARIABLE_8118)) (not (= _let_1 (ho_51 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(not (= tptp.zero_zero_real (@ Tau2 tptp.p))) (not (forall ((Y3 tptp.a)) (or (not (@ (@ tptp.member_a Y3) (@ (@ tptp.elemen154694473ball_a tptp.p) Delta2))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ Tau2 Y3))) tptp.one_one_real)))) (not (forall ((Y3 tptp.a)) (or (not (@ (@ tptp.member_a Y3) (@ (@ tptp.elemen154694473ball_a tptp.p) Delta2))) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y3) (@ Tau2 Y3))) (@ (@ tptp.line_open_segment_a tptp.a2) tptp.b)))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Delta2 tptp.real) (Tau2 (-> tptp.a tptp.real))) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))) (or (not (@ (@ tptp.ord_less_real _let_1) Delta2)) (not (@ (@ tptp.topolo1710226732a_real (@ (@ tptp.elemen154694473ball_a tptp.p) Delta2)) Tau2)) (not (= (@ Tau2 tptp.p) _let_1)) (not (forall ((Y3 tptp.a)) (let ((_let_1 (@ Tau2 Y3))) (or (not (@ (@ tptp.member_a Y3) (@ (@ tptp.elemen154694473ball_a tptp.p) Delta2))) (@ (@ tptp.ord_less_real (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))) (@ tptp.uminus_uminus_real _let_1)) _let_1)) tptp.one_one_real))))) (not (forall ((Y3 tptp.a)) (or (not (@ (@ tptp.member_a Y3) (@ (@ tptp.elemen154694473ball_a tptp.p) Delta2))) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y3) (@ Tau2 Y3))) (@ (@ tptp.line_open_segment_a tptp.a2) tptp.b)))))))) _let_37))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_21 _let_20 _let_19 _let_18 _let_16 (not _let_22)))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_25 (= Y2 Y3)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 2)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_34)) :args ((or _let_25 _let_27))) _let_35 :args (_let_25 true _let_27)) :args (_let_15 false _let_25)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_23 (= Y2 Y3)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 3)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_34)) :args ((or _let_23 _let_27))) _let_35 :args (_let_23 true _let_27)) :args (_let_17 false _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_71 (ho_70 k_69 (ho_68 _let_12 Delta2)) BOUND_VARIABLE_8118) false))))) :args (_let_37))) _let_38 :args (_let_22 false _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 4)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_14))) :args _let_34)) :args ((or _let_14 _let_27))) _let_35 :args (_let_14 true _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 1)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_13))) :args _let_34)) :args ((or _let_13 _let_27))) _let_35 :args (_let_13 true _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_11))) :args _let_34)) :args ((or _let_11 _let_27))) _let_35 :args (_let_11 true _let_27)) :args (false false _let_15 false _let_17 false _let_22 false _let_14 false _let_13 false _let_11)) :args ((forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) A) (=> (@ (@ tptp.ord_less_eq_a B) C) (@ (@ tptp.ord_less_a B) (@ (@ tptp.plus_plus_a A) C))))) (forall ((Y tptp.a) (T2 tptp.real)) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) Y) T2) (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y) (@ tptp.uminus_uminus_real T2)))) (forall ((B4 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) B)) B) (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))) (forall ((A tptp.a)) (=> (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) A) (= (@ tptp.abs_abs_a A) A))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))) (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) X) (=> (= (@ (@ (@ tptp.period1305449585riod_a _let_1) tptp.x) X) tptp.zero_zero_real) (= (@ _let_1 X) tptp.zero_zero_a))))) (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (not (forall ((T5 tptp.real)) (let ((_let_1 (@ (@ (@ tptp.auto_ll_on_flow0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X))) (= (@ _let_1 (@ (@ tptp.plus_plus_real T5) T4)) (@ _let_1 T5)))))))))) (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)) (forall ((A tptp.a) (B tptp.a)) (= (= (@ tptp.uminus_uminus_a A) B) (= (@ tptp.uminus_uminus_a B) A))) (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))) (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))) (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a A)) tptp.zero_zero_a) (@ (@ tptp.ord_less_a tptp.zero_zero_a) A))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= Y tptp.zero_zero_real) (= X tptp.zero_zero_real))))))) (forall ((X0 tptp.a)) (let ((_let_1 (@ tptp.member_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)) (and (@ (@ tptp.member_a X0) tptp.x) (@ _let_1 tptp.top_top_set_real))))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))) _let_2 (forall ((A tptp.a) (B tptp.a)) (= (= A (@ (@ tptp.plus_plus_a B) A)) (= B tptp.zero_zero_a))) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((Ae tptp.a) (Be tptp.a) (Cd tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a Ae))) (= (@ (@ tptp.plus_plus_a (@ _let_1 Be)) Cd) (@ _let_1 (@ (@ tptp.plus_plus_a Be) Cd))))) (forall ((X0 tptp.a)) (=> (not (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real)) (= (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0) tptp.bot_bot_set_real))) (= tptp.plus_plus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real B3) A4))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))) (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ (@ tptp.period1305449585riod_a _let_1) tptp.x) X))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_real B) (@ (@ tptp.plus_plus_real A) C))))) (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period138238489rbit_a tptp.f) tptp.x) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ (@ tptp.period1305449585riod_a tptp.f) tptp.x) X)))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))) (forall ((A tptp.a)) (= (= tptp.zero_zero_a (@ tptp.uminus_uminus_a A)) (= tptp.zero_zero_a A))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))) (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a B) A)) B) (@ (@ tptp.ord_less_a A) tptp.zero_zero_a))) (= tptp.plus_plus_real (lambda ((Ag tptp.real) (Bg tptp.real)) (@ (@ tptp.plus_plus_real Bg) Ag))) (@ _let_7 (@ (@ tptp.line_open_segment_a tptp.a2) tptp.b)) (forall ((T2 tptp.real) (X0 tptp.a)) (=> (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0)) (@ (@ tptp.member_a X0) tptp.x))) (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) C)) (@ (@ tptp.ord_less_eq_a A) B))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (forall ((K tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real K)) tptp.one_one_real) (@ (@ tptp.ord_less_real K) tptp.one_one_real))) (forall ((A tptp.a)) (= (@ (@ tptp.plus_plus_a tptp.zero_zero_a) A) A)) (forall ((A3 tptp.a) (K tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_a A3) B) (@ _let_1 (@ (@ tptp.plus_plus_a A) B)))))) (forall ((T2 tptp.real) (X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (not (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X))) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) T2) tptp.zero_zero_a)))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (=> (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_a A) B)))))) (@ tptp.initia826609931terval tptp.top_top_set_real) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))) (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))) (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (= (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X) tptp.top_top_set_real))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (forall ((B4 tptp.a) (K tptp.a) (B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a A))) (let ((_let_2 (@ tptp.plus_plus_a K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))) (= tptp.plus_plus_a (lambda ((A4 tptp.a) (B3 tptp.a)) (@ (@ tptp.plus_plus_a B3) A4))) _let_9 (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a C))) (= (@ (@ tptp.ord_less_eq_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_a A) B)))) (forall ((Ae tptp.real) (Be tptp.real) (Cd tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real Ae))) (= (@ (@ tptp.plus_plus_real (@ _let_1 Be)) Cd) (@ _let_1 (@ (@ tptp.plus_plus_real Be) Cd))))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))) (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.poinca522724647ment_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x))) (= (@ (@ _let_1 X) Y) (@ (@ _let_1 Y) X)))) (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))) (forall ((I tptp.a) (J tptp.a) (K tptp.a) (L tptp.a)) (=> (and (@ (@ tptp.ord_less_a I) J) (@ (@ tptp.ord_less_eq_a K) L)) (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a I) K)) (@ (@ tptp.plus_plus_a J) L)))) (forall ((T2 tptp.real) (X0 tptp.a)) (=> (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)) (@ (@ tptp.member_a X0) tptp.x))) (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.a)) (= (@ (@ tptp.plus_plus_a A) tptp.zero_zero_a) A)) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) _let_8 (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) C)) (@ (@ tptp.ord_less_a A) B))) (forall ((Bg2 tptp.a) (Ag2 tptp.a) (Cf tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a Bg2))) (let ((_let_2 (@ tptp.plus_plus_a Ag2))) (= (@ _let_1 (@ _let_2 Cf)) (@ _let_2 (@ _let_1 Cf)))))) (not (= tptp.zero_zero_real tptp.one_one_real)) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))) (forall ((A tptp.a)) (= (@ (@ tptp.plus_plus_a A) (@ tptp.uminus_uminus_a A)) tptp.zero_zero_a)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real K) L) (= I J)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((C tptp.a) (B tptp.a) (A tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a B))) (=> (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_a A) C)))))) (@ _let_7 tptp.x) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))) (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) C)) (@ (@ tptp.ord_less_eq_a A) B))) (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (=> (not (= (@ tptp.f X) tptp.zero_zero_a)) (@ (@ (@ tptp.period138238489rbit_a tptp.f) tptp.x) X)))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) A))) (= (@ tptp.abs_abs_a tptp.zero_zero_a) tptp.zero_zero_a) (forall ((Delta tptp.real) (Tau (-> tptp.a tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Delta) (=> (@ (@ tptp.topolo1710226732a_real (@ (@ tptp.elemen154694473ball_a tptp.p) Delta)) Tau) (=> (= (@ Tau tptp.p) tptp.zero_zero_real) (=> (forall ((Y3 tptp.a)) (=> (@ (@ tptp.member_a Y3) (@ (@ tptp.elemen154694473ball_a tptp.p) Delta)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ Tau Y3))) tptp.one_one_real))) (=> (forall ((Y3 tptp.a)) (=> (@ (@ tptp.member_a Y3) (@ (@ tptp.elemen154694473ball_a tptp.p) Delta)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y3) (@ Tau Y3))) (@ (@ tptp.line_open_segment_a tptp.a2) tptp.b)))) tptp.thesisa)))))) (forall ((X0 tptp.a)) (= (= (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0) tptp.bot_bot_set_real) (or (not (@ (@ tptp.member_a X0) tptp.x)) (not (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real))))) (forall ((X tptp.a)) (= (@ (@ (@ tptp.period138238489rbit_a tptp.f) tptp.x) X) (and (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ (@ tptp.period1305449585riod_a tptp.f) tptp.x) X))))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a A) B)) B) (@ (@ tptp.ord_less_a A) tptp.zero_zero_a))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((T2 tptp.real) (T3 tptp.real) (Y tptp.a)) (let ((_let_1 (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y))) (let ((_let_2 (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) Y))) (=> (not (= T2 T3)) (=> (@ (@ tptp.member_real T2) _let_2) (=> (@ (@ tptp.member_real T3) _let_2) (=> (= (@ _let_1 T2) (@ _let_1 T3)) (=> (not (= (@ tptp.f Y) tptp.zero_zero_a)) (@ (@ (@ tptp.period138238489rbit_a tptp.f) tptp.x) Y))))))))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y) X)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_real B) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ (@ tptp.plus_plus_a (@ tptp.abs_abs_a A)) (@ tptp.abs_abs_a B)))) (= (@ tptp.abs_abs_a _let_1) _let_1))) (forall ((A3 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X2 tptp.a)) (@ (@ tptp.member_a X2) A3))) A3)) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a tptp.zero_zero_a))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_a A) B)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))) (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_a P) (@ tptp.collect_a Q)))) (forall ((X tptp.a)) (= (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (exists ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X)) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) X2) X) (not (= X2 tptp.zero_zero_real)))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a A))) (= (@ (@ tptp.plus_plus_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_a B) C))))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_eq_a C) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_eq_a A) B) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) C)) B)))) (forall ((X tptp.a)) (= (@ (@ tptp.elemen154694473ball_a X) tptp.zero_zero_real) tptp.bot_bot_set_a)) (forall ((X0 tptp.a)) (=> (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real) (=> (@ (@ tptp.member_a X0) tptp.x) (not (= (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0) tptp.bot_bot_set_real))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))) (forall ((X tptp.a) (Y tptp.a)) (=> (@ (@ tptp.ord_less_eq_a X) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_eq_a Y) tptp.zero_zero_a) (= (= (@ (@ tptp.plus_plus_a X) Y) tptp.zero_zero_a) (and (= X tptp.zero_zero_a) (= Y tptp.zero_zero_a)))))) (= (@ tptp.abs_abs_real _let_4) tptp.one_one_real) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real K) L) (@ (@ tptp.ord_less_eq_real I) J)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))) (forall ((X0 tptp.a)) (@ tptp.initia826609931terval (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0))) (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) tptp.x) (=> (not (= (@ tptp.f X) tptp.zero_zero_a)) (not (forall ((A2 tptp.a) (B2 tptp.a)) (=> (@ (@ tptp.member_a X) (@ (@ tptp.line_open_segment_a A2) B2)) (not (@ (@ (@ (@ tptp.poinca522724647ment_a tptp.f) tptp.x) A2) B2)))))))) (forall ((I tptp.a) (J tptp.a) (K tptp.a) (L tptp.a)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_a I) K) (@ (@ tptp.plus_plus_a J) L)))) (forall ((A tptp.a) (B tptp.a)) (= (= A (@ (@ tptp.plus_plus_a A) B)) (= B tptp.zero_zero_a))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.plus_plus_a A) (@ (@ tptp.plus_plus_a (@ tptp.uminus_uminus_a A)) B)) B)) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_a B))) (=> (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_a A) C)))))) (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ tptp.f X) tptp.zero_zero_a) (= (@ (@ (@ tptp.period1305449585riod_a tptp.f) tptp.x) X) tptp.zero_zero_real)))) (forall ((X tptp.a) (T2 tptp.real)) (=> (@ (@ (@ tptp.period138238489rbit_a tptp.f) tptp.x) X) (not (= (@ tptp.f (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) T2)) tptp.zero_zero_a)))) (forall ((X0 tptp.a)) (@ tptp.initia826609931terval (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a A) (@ (@ tptp.plus_plus_a B) A)) (@ (@ tptp.ord_less_a tptp.zero_zero_a) B))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))) (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)) (forall ((X tptp.a) (P2 tptp.a)) (= (@ (@ (@ (@ tptp.limit_1865182413oint_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X) P2) (@ (@ (@ (@ tptp.limit_94460170oint_a tptp.f) tptp.x) X) P2))) (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) X) (= (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X) tptp.top_top_set_real)))) (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ tptp.abs_abs_a A)) A) (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) A))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= K L) (= I J)) (= (@ (@ tptp.plus_plus_real I) K) (@ (@ tptp.plus_plus_real J) L)))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))) (forall ((T2 tptp.real) (T3 tptp.real) (Y tptp.a)) (let ((_let_1 (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y))) (let ((_let_2 (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) Y))) (=> (not (= T2 T3)) (=> (@ (@ tptp.member_real T2) _let_2) (=> (@ (@ tptp.member_real T3) _let_2) (=> (= (@ _let_1 T2) (@ _let_1 T3)) (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) Y)))))))) (= (@ tptp.uminus_uminus_a tptp.zero_zero_a) tptp.zero_zero_a) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a A))) (= (@ (@ tptp.plus_plus_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_a B) C))))) (forall ((X tptp.a)) (= (@ (@ (@ tptp.period720806154rbit_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X) (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))) _let_6 (forall ((A tptp.a) (B tptp.a)) (= (= (@ tptp.uminus_uminus_a A) (@ tptp.uminus_uminus_a B)) (= A B))) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_eq_a A) (@ (@ tptp.plus_plus_a B) A)) (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) B))) (forall ((S tptp.real) (X0 tptp.a) (T2 tptp.real)) (let ((_let_1 (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x))) (let ((_let_2 (@ _let_1 X0))) (let ((_let_3 (@ _let_2 S))) (let ((_let_4 (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x))) (=> (@ (@ tptp.member_real S) (@ _let_4 X0)) (=> (@ (@ tptp.member_real T2) (@ _let_4 _let_3)) (= (@ _let_2 (@ (@ tptp.plus_plus_real S) T2)) (@ (@ _let_1 _let_3) T2))))))))) (forall ((X0 tptp.a)) (=> (not (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real)) (= (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0) tptp.bot_bot_set_real))) (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (@ (@ tptp.member_a X) tptp.x))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y) Y)) (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ tptp.f X) tptp.zero_zero_a) (= (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X) tptp.top_top_set_real)))) (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a tptp.zero_zero_a))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_a X) Y) tptp.zero_zero_a) (and (= X tptp.zero_zero_a) (= Y tptp.zero_zero_a))))))) (forall ((P Bool)) (or (= P true) (= P false))) _let_5 (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (=> (= (@ (@ tptp.plus_plus_a B) A) (@ (@ tptp.plus_plus_a C) A)) (= B C))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a B)) (@ tptp.uminus_uminus_a A)) (@ (@ tptp.ord_less_a A) B))) (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_a tptp.zero_zero_a) (@ tptp.uminus_uminus_a A)) (@ (@ tptp.ord_less_a A) tptp.zero_zero_a))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a A)) B) (@ (@ tptp.ord_less_a (@ tptp.uminus_uminus_a B)) A))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))) (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (forall ((X0 tptp.a)) (let ((_let_1 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real))) (let ((_let_3 (@ (@ tptp.member_a X0) tptp.x))) (and (=> (and _let_2 _let_3) (= _let_1 X0)) (=> (not (and _let_3 _let_2)) (= _let_1 tptp.zero_zero_a))))))) (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.poinca522724647ment_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x))) (=> (@ (@ _let_1 X) Y) (@ (@ _let_1 Y) X)))) _let_3 (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))) (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) X) (=> (not (= (@ _let_1 X) tptp.zero_zero_a)) (@ (@ (@ tptp.period138238489rbit_a _let_1) tptp.x) X))))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real) (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ _let_1 X) tptp.zero_zero_a) (= (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X) tptp.top_top_set_real))))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))) (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.plus_plus_a (@ tptp.uminus_uminus_a A)) (@ (@ tptp.plus_plus_a A) B)) B)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))) (forall ((A tptp.a) (B tptp.a) (C tptp.a) (D2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (@ (@ tptp.ord_less_eq_a C) D2) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) D2))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))) (forall ((Y tptp.a) (T2 tptp.real)) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y) T2) (@ (@ (@ (@ tptp.auto_ll_on_flow0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) Y) (@ tptp.uminus_uminus_real T2)))) (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ tptp.abs_abs_a A)) tptp.zero_zero_a) (= A tptp.zero_zero_a))) (forall ((I tptp.a) (J tptp.a) (K tptp.a) (L tptp.a)) (=> (and (@ (@ tptp.ord_less_eq_a I) J) (@ (@ tptp.ord_less_eq_a K) L)) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a I) K)) (@ (@ tptp.plus_plus_a J) L)))) (forall ((X0 tptp.a)) (= (= (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0) tptp.bot_bot_set_real) (or (not (@ (@ tptp.member_a X0) tptp.x)) (not (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real))))) (forall ((X tptp.a) (T2 tptp.real)) (let ((_let_1 (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x))) (=> (@ _let_1 X) (@ _let_1 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) T2))))) (forall ((X0 tptp.a)) (=> (@ (@ tptp.member_a X0) tptp.x) (@ (@ tptp.member_real tptp.zero_zero_real) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)))) (@ (@ (@ (@ tptp.poinca522724647ment_a tptp.f) tptp.x) tptp.a2) tptp.b) (forall ((I tptp.a) (J tptp.a) (K tptp.a) (L tptp.a)) (=> (and (@ (@ tptp.ord_less_a K) L) (@ (@ tptp.ord_less_eq_a I) J)) (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a I) K)) (@ (@ tptp.plus_plus_a J) L)))) (forall ((X tptp.a) (A tptp.a) (B tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.member_a Y))) (let ((_let_2 (@ tptp.line_open_segment_a A))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.member_a X) _let_3) (=> (@ _let_1 _let_3) (or (= X Y) (@ _let_1 (@ _let_2 X)) (@ _let_1 (@ (@ tptp.line_open_segment_a X) B))))))))) (forall ((X0 tptp.a)) (let ((_let_1 (@ tptp.member_real tptp.zero_zero_real))) (=> (@ _let_1 tptp.top_top_set_real) (=> (@ (@ tptp.member_a X0) tptp.x) (@ _let_1 (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0)))))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.poinca522724647ment_a tptp.f) tptp.x))) (= (@ (@ _let_1 X) Y) (@ (@ _let_1 Y) X)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a C))) (=> (@ (@ tptp.ord_less_eq_a A) B) (@ (@ tptp.ord_less_eq_a (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (= tptp.poinca522724647ment_a tptp.poinca522724647ment_a) (forall ((A tptp.a)) (= (@ (@ tptp.plus_plus_a (@ tptp.uminus_uminus_a A)) A) tptp.zero_zero_a)) (forall ((T2 tptp.real) (X0 tptp.a)) (=> (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)) (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real))) (forall ((X tptp.a) (E tptp.real)) (= (@ (@ tptp.member_a X) (@ (@ tptp.elemen154694473ball_a X) E)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) E))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))) (forall ((X0 tptp.a)) (=> (not (@ (@ tptp.member_a X0) tptp.x)) (= (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0) tptp.bot_bot_set_real))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))) (forall ((X0 tptp.a)) (=> (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real) (=> (@ (@ tptp.member_a X0) tptp.x) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X0) tptp.zero_zero_real) X0)))) (forall ((Xa tptp.real) (X0 tptp.a)) (=> (@ (@ tptp.member_real Xa) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X0) Xa)) tptp.x))) (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ (@ (@ tptp.poinca522724647ment_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) A) B) (@ (@ (@ (@ tptp.poinca522724647ment_a tptp.f) tptp.x) A) B))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))) (forall ((X 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(forall ((T2 tptp.real) (X0 tptp.a)) (=> (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0)) (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))) (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))) (forall ((X tptp.a) (T2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period138238489rbit_a _let_1) tptp.x) X) (not (= (@ _let_1 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) T2)) tptp.zero_zero_a))))) (forall ((S tptp.real) (X0 tptp.a) (T2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x))) (let ((_let_3 (@ _let_2 X0))) (=> (@ (@ tptp.member_real S) _let_3) (=> (@ (@ tptp.member_real T2) (@ _let_2 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X0) S))) (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real S) T2)) _let_3))))))) (forall ((X tptp.real) (E tptp.real)) (= (= (@ (@ tptp.elemen341675809l_real X) E) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_real E) tptp.zero_zero_real))) (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))) (forall ((T2 tptp.real) (T3 tptp.real) (Y tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) Y))) (let ((_let_3 (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) Y))) (=> (not (= T2 T3)) (=> (@ (@ tptp.member_real T2) _let_3) (=> (@ (@ tptp.member_real T3) _let_3) (=> (= (@ _let_2 T2) (@ _let_2 T3)) (=> (not (= (@ _let_1 Y) tptp.zero_zero_a)) (@ (@ (@ tptp.period138238489rbit_a _let_1) tptp.x) Y)))))))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))) (forall ((X tptp.real) (E tptp.real)) (= (@ (@ tptp.member_real X) (@ (@ tptp.elemen341675809l_real X) E)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) E))) (forall ((T2 tptp.real) (X0 tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X0)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X0) T2)) tptp.x)))) (forall ((X0 tptp.a)) (=> (@ (@ tptp.member_a X0) tptp.x) (@ (@ tptp.member_real tptp.zero_zero_real) (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0)))) (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X) (@ tptp.abs_abs_real Y)) (or (= X (@ tptp.uminus_uminus_real Y)) (= X Y)))) (forall ((B tptp.a) (A tptp.a) (C tptp.a)) (= (= (@ (@ tptp.plus_plus_a B) A) (@ (@ tptp.plus_plus_a C) A)) (= B C))) (forall ((X0 tptp.a)) (let ((_let_1 (@ tptp.member_real tptp.zero_zero_real))) (=> (@ _let_1 tptp.top_top_set_real) (=> (@ (@ tptp.member_a X0) tptp.x) (@ _let_1 (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)))))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))) (= tptp.plus_plus_a (lambda ((Ag tptp.a) (Bg tptp.a)) (@ (@ tptp.plus_plus_a Bg) Ag))) (forall ((X tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.poinca522724647ment_a tptp.f) tptp.x))) (=> (@ (@ _let_1 X) Y) (@ (@ _let_1 Y) X)))) (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period138238489rbit_a tptp.f) tptp.x) X) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) (@ (@ (@ tptp.period1305449585riod_a tptp.f) tptp.x) X)) X))) (forall ((T6 tptp.real) (X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X))) (=> (@ (@ tptp.member_real T6) (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X)) (=> (= (@ _let_2 T6) X) (= (@ _let_2 (@ tptp.uminus_uminus_real T6)) X)))))) (forall ((A tptp.a)) (let ((_let_1 (@ tptp.abs_abs_a A))) (= (@ tptp.abs_abs_a _let_1) _let_1))) (forall ((X tptp.real)) (= (@ (@ tptp.elemen341675809l_real X) tptp.zero_zero_real) tptp.bot_bot_set_real)) (forall ((X tptp.a)) (= (= tptp.zero_zero_a X) (= X tptp.zero_zero_a))) (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ (@ tptp.period1305449585riod_a tptp.f) tptp.x) X)))) (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((T6 tptp.real) (X tptp.a)) (let ((_let_1 (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X))) (=> (@ (@ tptp.member_real T6) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X)) (=> (= (@ _let_1 T6) X) (= (@ _let_1 (@ tptp.uminus_uminus_real T6)) X))))) (forall ((A tptp.a)) (= (@ tptp.abs_abs_a (@ tptp.uminus_uminus_a A)) (@ tptp.abs_abs_a A))) (forall ((A3 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A3) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))) (forall ((X0 tptp.a)) (let ((_let_1 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X0) tptp.zero_zero_real))) (let ((_let_2 (and (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real) (@ (@ tptp.member_a X0) tptp.x)))) (and (=> (not _let_2) (= _let_1 tptp.zero_zero_a)) (=> _let_2 (= _let_1 X0)))))) (forall ((X tptp.a) (P2 tptp.a)) (= (@ (@ (@ (@ tptp.limit_1865182413oint_a tptp.f) tptp.x) X) P2) (@ (@ (@ (@ tptp.limit_94460170oint_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X) P2))) (forall ((A tptp.a) (B tptp.a) (X tptp.a) (E tptp.real)) (=> (@ (@ (@ (@ tptp.poinca522724647ment_a tptp.f) tptp.x) A) B) (=> (@ (@ tptp.member_a X) (@ (@ tptp.line_open_segment_a A) B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((D tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (forall ((T (-> tptp.a tptp.real))) (let ((_let_1 (@ (@ tptp.topolo1710226732a_real (@ (@ tptp.elemen154694473ball_a X) D)) T))) (=> _let_1 (=> (forall ((Y2 tptp.a)) (=> (@ (@ tptp.member_a Y2) (@ (@ tptp.elemen154694473ball_a X) D)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) Y2) (@ T Y2))) (@ (@ tptp.line_open_segment_a A) B)))) (=> (forall ((Y2 tptp.a)) (=> (@ (@ tptp.member_a Y2) (@ (@ tptp.elemen154694473ball_a X) D)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ T Y2))) E))) (=> _let_1 (not (= (@ T X) tptp.zero_zero_real))))))))))))))) (forall ((A tptp.a)) (=> (@ (@ tptp.ord_less_a tptp.zero_zero_a) A) (= (@ tptp.abs_abs_a A) A))) (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) (@ tptp.uminus_uminus_a A)) (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.a)) (= (= (@ tptp.abs_abs_a A) tptp.zero_zero_a) (= A tptp.zero_zero_a))) (forall ((X tptp.a)) (= (@ (@ (@ tptp.period720806154rbit_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X) (exists ((X2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (and (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) X2) X) (not (= X2 tptp.zero_zero_real)) (@ (@ tptp.member_real X2) (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X))))))) (forall ((A tptp.a) (C tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_eq_a C) B) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) C)) B)))) (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ _let_1 X) tptp.zero_zero_a) (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) X))))) (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_a B) tptp.zero_zero_a) (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a A) B)) tptp.zero_zero_a)))) (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X) (@ (@ tptp.member_a X) tptp.x))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real) (forall ((A tptp.a) (B tptp.a)) (= (= A (@ tptp.uminus_uminus_a B)) (= B (@ tptp.uminus_uminus_a A)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.ord_less_eq_a B))) (=> (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_a A) C)))))) (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ (@ tptp.period138238489rbit_a _let_1) tptp.x) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ (@ tptp.period1305449585riod_a _let_1) tptp.x) X))))) (forall ((A3 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A3))) A3)) (forall ((I tptp.a) (J tptp.a) (K tptp.a) (L tptp.a)) (=> (and (@ (@ tptp.ord_less_eq_a I) J) (= K L)) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a I) K)) (@ (@ tptp.plus_plus_a J) L)))) (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.a)) (= (@ (@ tptp.plus_plus_a A) tptp.zero_zero_a) A)) (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))) (forall ((X0 tptp.a)) (=> (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real) (=> (@ (@ tptp.member_a X0) tptp.x) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0) tptp.zero_zero_real) X0)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a) (D2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (=> (@ (@ tptp.ord_less_a C) D2) (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a 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((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ _let_1 X) tptp.zero_zero_a) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) T2) X))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a) (D2 tptp.a)) (=> (@ (@ tptp.ord_less_a A) B) (=> (@ (@ tptp.ord_less_eq_a C) D2) (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) D2))))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B)))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))) (forall ((B tptp.a) (A tptp.a)) (= (= (@ (@ tptp.plus_plus_a B) A) A) (= B tptp.zero_zero_a))) (forall ((X tptp.a) (T2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ tptp.period720806154rbit_a _let_1) tptp.x))) (=> (@ _let_2 X) (@ _let_2 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) T2)))))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_eq_a A) (@ (@ tptp.plus_plus_a A) B)) (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) B))) (forall ((T6 tptp.real) (X tptp.a)) (let ((_let_1 (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X))) (=> (@ (@ tptp.member_real T6) _let_1) (=> (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) T6) X) (@ (@ tptp.member_real (@ tptp.uminus_uminus_real T6)) _let_1))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))) (forall ((T2 tptp.real) (S tptp.real) (X0 tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x))) (let ((_let_3 (@ _let_2 X0))) (=> (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real T2) S)) _let_3) (=> (@ (@ tptp.member_real T2) _let_3) (@ (@ tptp.member_real S) (@ _let_2 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X0) T2))))))))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (= K L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (= (@ (@ (@ tptp.period138238489rbit_a _let_1) tptp.x) X) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ (@ tptp.period1305449585riod_a _let_1) tptp.x) X)) (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) X))))) (forall ((A tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P)) (@ P A))) (forall ((T2 tptp.real) (X tptp.a)) (=> (not (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X))) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) T2) tptp.zero_zero_a))) (forall ((A tptp.a) (B tptp.a)) (= (= (@ (@ tptp.plus_plus_a A) B) A) (= B tptp.zero_zero_a))) (forall ((X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ _let_1 X) tptp.zero_zero_a) (= (@ (@ (@ tptp.period1305449585riod_a _let_1) tptp.x) X) tptp.zero_zero_real))))) (forall ((A tptp.a) (B tptp.a)) (@ (@ tptp.ord_less_eq_a (@ tptp.abs_abs_a (@ (@ tptp.plus_plus_a A) B))) (@ (@ tptp.plus_plus_a (@ tptp.abs_abs_a A)) (@ tptp.abs_abs_a B)))) (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a B) A)) B) (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a))) (forall ((A tptp.a)) (not (@ (@ tptp.ord_less_a (@ tptp.abs_abs_a A)) tptp.zero_zero_a))) (@ (@ (@ (@ tptp.limit_94460170oint_a tptp.f) tptp.x) tptp.x2) tptp.p) (forall ((A tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) tptp.zero_zero_a) (= (@ tptp.abs_abs_a A) (@ tptp.uminus_uminus_a A)))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a A) (@ tptp.uminus_uminus_a B)) (@ (@ tptp.ord_less_a B) (@ tptp.uminus_uminus_a A)))) (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.ord_less_a A) (@ (@ tptp.plus_plus_a A) B)) (@ (@ tptp.ord_less_a tptp.zero_zero_a) B))) (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((A tptp.a)) (= (= (@ tptp.uminus_uminus_a A) tptp.zero_zero_a) (= A tptp.zero_zero_a))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))) (forall ((T2 tptp.real) (S tptp.real) (X0 tptp.a)) (let ((_let_1 (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x))) (let ((_let_2 (@ _let_1 X0))) (=> (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real T2) S)) _let_2) (=> (@ (@ tptp.member_real T2) _let_2) (@ (@ tptp.member_real S) (@ _let_1 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X0) T2)))))))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_4) tptp.zero_zero_real) (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((S tptp.real) (X0 tptp.a) (T2 tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x))) (let ((_let_3 (@ _let_2 X0))) (let ((_let_4 (@ _let_3 S))) (let ((_let_5 (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x))) (=> (@ (@ tptp.member_real S) (@ _let_5 X0)) (=> (@ (@ tptp.member_real T2) (@ _let_5 _let_4)) (= (@ _let_3 (@ (@ tptp.plus_plus_real S) T2)) (@ (@ _let_2 _let_4) T2)))))))))) (forall ((T6 tptp.real) (X tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X))) (=> (@ (@ tptp.member_real T6) _let_2) (=> (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X) T6) X) (@ (@ tptp.member_real (@ tptp.uminus_uminus_real T6)) _let_2)))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (=> (@ (@ tptp.ord_less_eq_a A) B) (@ (@ tptp.ord_less_eq_a (@ (@ tptp.plus_plus_a A) C)) (@ (@ tptp.plus_plus_a B) C)))) (forall ((A tptp.a) (B tptp.a)) (= (@ tptp.uminus_uminus_a (@ (@ tptp.plus_plus_a A) B)) (@ (@ tptp.plus_plus_a (@ tptp.uminus_uminus_a A)) (@ tptp.uminus_uminus_a B)))) (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_a tptp.zero_zero_a) (@ tptp.abs_abs_a A)) (not (= A tptp.zero_zero_a)))) (forall ((X0 tptp.a)) (=> (not (@ (@ tptp.member_a X0) tptp.x)) (= (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0) tptp.bot_bot_set_real))) (forall ((T2 tptp.real) (X0 tptp.a)) (=> (@ (@ tptp.member_real T2) (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X0) T2)) tptp.x))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))) (forall ((E tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real E) tptp.zero_zero_real) (= (@ (@ tptp.elemen341675809l_real X) E) tptp.bot_bot_set_real))) (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) tptp.x) (=> (not (= (@ (@ tptp.uminus_uminus_a_a tptp.f) X) tptp.zero_zero_a)) (not (forall ((A2 tptp.a) (B2 tptp.a)) (=> (@ (@ tptp.member_a X) (@ (@ tptp.line_open_segment_a A2) B2)) (not (@ (@ (@ (@ tptp.poinca522724647ment_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) A2) B2)))))))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)) (forall ((T2 tptp.real) (T3 tptp.real) (Y tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (let ((_let_2 (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) Y))) (let ((_let_3 (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) Y))) (=> (not (= T2 T3)) (=> (@ (@ tptp.member_real T2) _let_3) (=> (@ (@ tptp.member_real T3) _let_3) (=> (= (@ _let_2 T2) (@ _let_2 T3)) (@ (@ (@ tptp.period720806154rbit_a _let_1) tptp.x) Y))))))))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ tptp.uminus_uminus_a A)) tptp.zero_zero_a) (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) A))) _let_3 (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))) (forall ((A tptp.a) (B tptp.a)) (=> (@ (@ tptp.ord_less_a A) tptp.zero_zero_a) (=> (@ (@ tptp.ord_less_eq_a B) tptp.zero_zero_a) (@ (@ tptp.ord_less_a (@ (@ tptp.plus_plus_a A) B)) tptp.zero_zero_a)))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.a)) (= (@ (@ tptp.plus_plus_a tptp.zero_zero_a) A) A)) (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))) _let_2 _let_1 (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a C))) (=> (@ (@ tptp.ord_less_eq_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_a A) B)))) (forall ((X0 tptp.a)) (=> (@ (@ tptp.member_real tptp.zero_zero_real) tptp.top_top_set_real) (=> (@ (@ tptp.member_a X0) tptp.x) (not (= (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0) tptp.bot_bot_set_real))))) (forall ((B tptp.a) (A tptp.a)) (= (@ (@ tptp.ord_less_eq_a (@ tptp.uminus_uminus_a B)) (@ tptp.uminus_uminus_a A)) (@ (@ tptp.ord_less_eq_a A) B))) (forall ((X tptp.a)) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ tptp.f X) tptp.zero_zero_a) (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X)))) (forall ((X0 tptp.a)) (let ((_let_1 (@ tptp.member_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ (@ tptp.auto_l612940ivl0_a (@ tptp.uminus_uminus_a_a tptp.f)) tptp.x) X0)) (and (@ (@ tptp.member_a X0) tptp.x) (@ _let_1 tptp.top_top_set_real))))) (forall ((A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.ord_less_a tptp.zero_zero_a))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_a tptp.zero_zero_a) B) (@ _let_1 (@ (@ tptp.plus_plus_a A) B)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))) (forall ((C tptp.a) (A tptp.a) (B tptp.a)) (let ((_let_1 (@ tptp.plus_plus_a C))) (= (@ (@ tptp.ord_less_a (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_a A) B)))) (forall ((Bg2 tptp.real) (Ag2 tptp.real) (Cf tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real Bg2))) (let ((_let_2 (@ tptp.plus_plus_real Ag2))) (= (@ _let_1 (@ _let_2 Cf)) (@ _let_2 (@ _let_1 Cf)))))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))) (forall ((E tptp.real) (X tptp.a)) (=> (@ (@ tptp.ord_less_eq_real E) tptp.zero_zero_real) (= (@ (@ tptp.elemen154694473ball_a X) E) tptp.bot_bot_set_a))) (forall ((A tptp.a)) (= (= tptp.zero_zero_a (@ tptp.abs_abs_a A)) (= A tptp.zero_zero_a))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= Y tptp.zero_zero_real) (= X tptp.zero_zero_real)))))) (forall ((X tptp.a) (T2 tptp.real)) (=> (@ (@ tptp.member_a X) tptp.x) (=> (= (@ tptp.f X) tptp.zero_zero_a) (= (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X) T2) X)))) (forall ((T2 tptp.real) (X0 tptp.a)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 (@ (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x) X0)) (@ _let_1 tptp.top_top_set_real)))) (forall ((S tptp.real) (X0 tptp.a) (T2 tptp.real)) (let ((_let_1 (@ (@ tptp.auto_l612940ivl0_a tptp.f) tptp.x))) (let ((_let_2 (@ _let_1 X0))) (=> (@ (@ tptp.member_real S) _let_2) (=> (@ (@ tptp.member_real T2) (@ _let_1 (@ (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X0) S))) (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real S) T2)) _let_2)))))) (forall ((Xa tptp.real) (X0 tptp.a)) (let ((_let_1 (@ tptp.uminus_uminus_a_a tptp.f))) (=> (@ (@ tptp.member_real Xa) (@ (@ (@ tptp.auto_l612940ivl0_a _let_1) tptp.x) X0)) (@ (@ tptp.member_a (@ (@ (@ (@ tptp.auto_ll_on_flow0_a _let_1) tptp.x) X0) Xa)) tptp.x)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))) (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B))) (forall ((X tptp.a)) (=> (@ (@ (@ tptp.period720806154rbit_a tptp.f) tptp.x) X) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (not (forall ((T5 tptp.real)) (let ((_let_1 (@ (@ (@ tptp.auto_ll_on_flow0_a tptp.f) tptp.x) X))) (= (@ _let_1 (@ (@ tptp.plus_plus_real T5) T4)) (@ _let_1 T5)))))))))) true))))))))))))))))))))))))))))))))))))))))) 0.40/0.89 ) 0.40/0.89 % SZS output end Proof for 0.40/0.89 % cvc5---1.0.5 exiting 0.40/0.89 % cvc5---1.0.5 exiting 0.40/0.89 EOF