%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, set_real: $tType).
thf(type_def_6, type, set_a: $tType).
thf(type_def_7, type, real: $tType).
thf(type_def_8, type, a: $tType).
thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, elemen341675809l_real: (real > real > set_real)).
thf(func_def_1, type, elemen154694473ball_a: (a > real > set_a)).
thf(func_def_2, type, auto_l612940ivl0_a: ((a > a) > set_a > a > set_real)).
thf(func_def_3, type, auto_ll_on_flow0_a: ((a > a) > set_a > a > real > a)).
thf(func_def_4, type, abs_abs_real: (real > real)).
thf(func_def_5, type, abs_abs_a: (a > a)).
thf(func_def_6, type, one_one_real: real).
thf(func_def_7, type, plus_plus_real: (real > real > real)).
thf(func_def_8, type, plus_plus_a: (a > a > a)).
thf(func_def_9, type, uminus_uminus_a_a: ((a > a) > a > a)).
thf(func_def_10, type, uminus_uminus_real: (real > real)).
thf(func_def_11, type, uminus_uminus_a: (a > a)).
thf(func_def_12, type, zero_zero_real: real).
thf(func_def_13, type, zero_zero_a: a).
thf(func_def_14, type, if_real: ($o > real > real > real)).
thf(func_def_15, type, initia826609931terval: (set_real > $o)).
thf(func_def_16, type, limit_1865182413oint_a: ((a > a) > set_a > a > a > $o)).
thf(func_def_17, type, limit_94460170oint_a: ((a > a) > set_a > a > a > $o)).
thf(func_def_18, type, line_open_segment_a: (a > a > set_a)).
thf(func_def_19, type, bot_bot_set_real: set_real).
thf(func_def_20, type, bot_bot_set_a: set_a).
thf(func_def_21, type, ord_less_real: (real > real > $o)).
thf(func_def_22, type, ord_less_a: (a > a > $o)).
thf(func_def_23, type, ord_less_eq_real: (real > real > $o)).
thf(func_def_24, type, ord_less_eq_a: (a > a > $o)).
thf(func_def_25, type, top_top_set_real: set_real).
thf(func_def_26, type, period720806154rbit_a: ((a > a) > set_a > a > $o)).
thf(func_def_27, type, period1305449585riod_a: ((a > a) > set_a > a > real)).
thf(func_def_28, type, period138238489rbit_a: ((a > a) > set_a > a > $o)).
thf(func_def_29, type, poinca522724647ment_a: ((a > a) > set_a > a > a > $o)).
thf(func_def_30, type, collect_real: ((real > $o) > set_real)).
thf(func_def_31, type, collect_a: ((a > $o) > set_a)).
thf(func_def_32, type, topolo1710226732a_real: (set_a > (a > real) > $o)).
thf(func_def_33, type, member_real: (real > set_real > $o)).
thf(func_def_34, type, member_a: (a > set_a > $o)).
thf(func_def_35, type, x: set_a).
thf(func_def_36, type, a2: a).
thf(func_def_37, type, b: a).
thf(func_def_38, type, f: (a > a)).
thf(func_def_39, type, p: a).
thf(func_def_40, type, thesisa: $o).
thf(func_def_41, type, x2: a).
thf(func_def_43, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_44, type, vNOT: ($o > $o)).
thf(func_def_47, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_48, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_49, type, vAND: ($o > $o > $o)).
thf(func_def_50, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_51, type, vOR: ($o > $o > $o)).
thf(func_def_52, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_53, type, sK0: (a > a)).
thf(func_def_54, type, sK1: (a > a)).
thf(func_def_55, type, sK2: (a > a)).
thf(func_def_56, type, sK3: (a > a)).
thf(func_def_57, type, sK4: (a > real)).
thf(func_def_58, type, sK5: (a > a > real > a > real)).
thf(func_def_59, type, sK6: (a > a > real > a > a > real)).
thf(func_def_60, type, sK7: (real > (a > real) > a)).
thf(func_def_61, type, sK8: (real > (a > real) > a)).
thf(func_def_62, type, sK9: (a > real)).
thf(func_def_63, type, sK10: real).
thf(func_def_64, type, sK11: (a > real)).
thf(func_def_65, type, sK12: (real > (a > real) > a)).
thf(func_def_66, type, sK13: (real > (a > real) > a)).
thf(f29,axiom,(
  ! [X1 : real,X0 : real] : (((ord_less_real @ (uminus_uminus_real @ X0) @ (uminus_uminus_real @ X1))) = ((ord_less_real @ X1 @ X0)))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_neg__less__iff__less)).
thf(f42,axiom,(
  ! [X0 : real,X1 : (a > real)] : ((ord_less_real @ zero_zero_real @ X0) => ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1) => ((((X1 @ p)) = zero_zero_real) => (! [X2 : a] : ((member_a @ X2 @ (elemen154694473ball_a @ p @ X0)) => (ord_less_real @ (abs_abs_real @ (X1 @ X2)) @ one_one_real)) => (! [X2 : a] : ((member_a @ X2 @ (elemen154694473ball_a @ p @ X0)) => (member_a @ (auto_ll_on_flow0_a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment_a @ a2 @ b))) => thesisa)))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
thf(f325,axiom,(
  ~ ! [X0 : real] : ((ord_less_real @ zero_zero_real @ X0) => ! [X1 : (a > real)] : ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1) => (! [X2 : a] : ((member_a @ X2 @ (elemen154694473ball_a @ p @ X0)) => (member_a @ (auto_ll_on_flow0_a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment_a @ a2 @ b))) => (! [X2 : a] : ((member_a @ X2 @ (elemen154694473ball_a @ p @ X0)) => (ord_less_real @ (abs_abs_real @ (X1 @ X2)) @ one_one_real)) => ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1) => (((X1 @ p)) != zero_zero_real))))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',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)).
thf(f349,conjecture,(
  thesisa),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
thf(f350,negated_conjecture,(
  ~thesisa),
  inference(negated_conjecture,[status(cth)],[f349])).
thf(f434,plain,(
  ! [X0 : real,X1 : (a > real)] : ((ord_less_real @ zero_zero_real @ X0) => ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1) => ((((X1 @ p)) = zero_zero_real) => (! [X2 : a] : ((member_a @ X2 @ (elemen154694473ball_a @ p @ X0)) => (ord_less_real @ (abs_abs_real @ (X1 @ X2)) @ one_one_real)) => (! [X3 : a] : ((member_a @ X3 @ (elemen154694473ball_a @ p @ X0)) => (member_a @ (auto_ll_on_flow0_a @ f @ x @ X3 @ (X1 @ X3)) @ (line_open_segment_a @ a2 @ b))) => thesisa)))))),
  inference(rectify,[],[f42])).
thf(f435,plain,(
  ! [X0 : real,X1 : (a > real)] : ((((ord_less_real @ zero_zero_real @ X0)) = $true) => ((((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1)) = $true) => ((zero_zero_real = ((X1 @ p))) => (! [X2 : a] : ((((member_a @ X2 @ (elemen154694473ball_a @ p @ X0))) = $true) => (((ord_less_real @ (abs_abs_real @ (X1 @ X2)) @ one_one_real)) = $true)) => (! [X3 : a] : ((((member_a @ X3 @ (elemen154694473ball_a @ p @ X0))) = $true) => (((member_a @ (auto_ll_on_flow0_a @ f @ x @ X3 @ (X1 @ X3)) @ (line_open_segment_a @ a2 @ b))) = $true)) => (thesisa = $true))))))),
  inference(fool_elimination,[],[f434])).
thf(f544,plain,(
  ~thesisa),
  inference(rectify,[],[f350])).
thf(f545,plain,(
  ~ (thesisa = $true)),
  inference(fool_elimination,[],[f544])).
thf(f609,plain,(
  ~ ! [X0 : real] : ((ord_less_real @ zero_zero_real @ X0) => ! [X1 : (a > real)] : ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1) => (! [X2 : a] : ((member_a @ X2 @ (elemen154694473ball_a @ p @ X0)) => (member_a @ (auto_ll_on_flow0_a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment_a @ a2 @ b))) => (! [X3 : a] : ((member_a @ X3 @ (elemen154694473ball_a @ p @ X0)) => (ord_less_real @ (abs_abs_real @ (X1 @ X3)) @ one_one_real)) => ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1) => (((X1 @ p)) != zero_zero_real))))))),
  inference(rectify,[],[f325])).
thf(f610,plain,(
  ~ ! [X0 : real] : ((((ord_less_real @ zero_zero_real @ X0)) = $true) => ! [X1 : (a > real)] : ((((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1)) = $true) => (! [X2 : a] : ((((member_a @ X2 @ (elemen154694473ball_a @ p @ X0))) = $true) => (((member_a @ (auto_ll_on_flow0_a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment_a @ a2 @ b))) = $true)) => (! [X3 : a] : ((((member_a @ X3 @ (elemen154694473ball_a @ p @ X0))) = $true) => (((ord_less_real @ (abs_abs_real @ (X1 @ X3)) @ one_one_real)) = $true)) => ((((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1)) = $true) => (zero_zero_real != ((X1 @ p))))))))),
  inference(fool_elimination,[],[f609])).
thf(f757,plain,(
  (thesisa != $true)),
  inference(flattening,[],[f545])).
thf(f812,plain,(
  ! [X0 : real,X1 : (a > real)] : ((((((thesisa = $true) | ? [X3 : a] : ((((member_a @ X3 @ (elemen154694473ball_a @ p @ X0))) = $true) & (((member_a @ (auto_ll_on_flow0_a @ f @ x @ X3 @ (X1 @ X3)) @ (line_open_segment_a @ a2 @ b))) != $true))) | ? [X2 : a] : ((((ord_less_real @ (abs_abs_real @ (X1 @ X2)) @ one_one_real)) != $true) & (((member_a @ X2 @ (elemen154694473ball_a @ p @ X0))) = $true))) | (zero_zero_real != ((X1 @ p)))) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1)) != $true)) | (((ord_less_real @ zero_zero_real @ X0)) != $true))),
  inference(ennf_transformation,[],[f435])).
thf(f813,plain,(
  ! [X1 : (a > real),X0 : real] : ((thesisa = $true) | (((ord_less_real @ zero_zero_real @ X0)) != $true) | ? [X2 : a] : ((((ord_less_real @ (abs_abs_real @ (X1 @ X2)) @ one_one_real)) != $true) & (((member_a @ X2 @ (elemen154694473ball_a @ p @ X0))) = $true)) | (zero_zero_real != ((X1 @ p))) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1)) != $true) | ? [X3 : a] : ((((member_a @ X3 @ (elemen154694473ball_a @ p @ X0))) = $true) & (((member_a @ (auto_ll_on_flow0_a @ f @ x @ X3 @ (X1 @ X3)) @ (line_open_segment_a @ a2 @ b))) != $true)))),
  inference(flattening,[],[f812])).
thf(f877,plain,(
  ? [X0 : real] : (? [X1 : (a > real)] : (((((zero_zero_real = ((X1 @ p))) & (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1)) = $true)) & ! [X3 : a] : ((((member_a @ X3 @ (elemen154694473ball_a @ p @ X0))) != $true) | (((ord_less_real @ (abs_abs_real @ (X1 @ X3)) @ one_one_real)) = $true))) & ! [X2 : a] : ((((member_a @ X2 @ (elemen154694473ball_a @ p @ X0))) != $true) | (((member_a @ (auto_ll_on_flow0_a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment_a @ a2 @ b))) = $true))) & (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1)) = $true)) & (((ord_less_real @ zero_zero_real @ X0)) = $true))),
  inference(ennf_transformation,[],[f610])).
thf(f878,plain,(
  ? [X0 : real] : (? [X1 : (a > real)] : (! [X3 : a] : ((((member_a @ X3 @ (elemen154694473ball_a @ p @ X0))) != $true) | (((ord_less_real @ (abs_abs_real @ (X1 @ X3)) @ one_one_real)) = $true)) & ! [X2 : a] : ((((member_a @ X2 @ (elemen154694473ball_a @ p @ X0))) != $true) | (((member_a @ (auto_ll_on_flow0_a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment_a @ a2 @ b))) = $true)) & (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1)) = $true) & (zero_zero_real = ((X1 @ p))) & (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1)) = $true)) & (((ord_less_real @ zero_zero_real @ X0)) = $true))),
  inference(flattening,[],[f877])).
thf(f889,plain,(
  ! [X0 : (a > real),X1 : real] : ((thesisa = $true) | (((ord_less_real @ zero_zero_real @ X1)) != $true) | ? [X2 : a] : ((((ord_less_real @ (abs_abs_real @ (X0 @ X2)) @ one_one_real)) != $true) & (((member_a @ X2 @ (elemen154694473ball_a @ p @ X1))) = $true)) | (zero_zero_real != ((X0 @ p))) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true) | ? [X3 : a] : ((((member_a @ X3 @ (elemen154694473ball_a @ p @ X1))) = $true) & (((member_a @ (auto_ll_on_flow0_a @ f @ x @ X3 @ (X0 @ X3)) @ (line_open_segment_a @ a2 @ b))) != $true)))),
  inference(rectify,[],[f813])).
thf(f890,plain,(
  ! [X0 : (a > real),X1 : real] : ((thesisa = $true) | (((ord_less_real @ zero_zero_real @ X1)) != $true) | ((((ord_less_real @ (abs_abs_real @ (X0 @ (sK7 @ X1 @ X0))) @ one_one_real)) != $true) & (((member_a @ (sK7 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true)) | (zero_zero_real != ((X0 @ p))) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true) | ((((member_a @ (sK8 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true) & (((member_a @ (auto_ll_on_flow0_a @ f @ x @ (sK8 @ X1 @ X0) @ (X0 @ (sK8 @ X1 @ X0))) @ (line_open_segment_a @ a2 @ b))) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,$thf(sK1 @ X0)),skolemize(X2,$thf(sK1 @ X0))],[f889])).
thf(f896,plain,(
  ! [X0 : real,X1 : real] : (((ord_less_real @ X0 @ X1)) = ((ord_less_real @ (uminus_uminus_real @ X1) @ (uminus_uminus_real @ X0))))),
  inference(rectify,[],[f29])).
thf(f909,plain,(
  ? [X0 : real] : (? [X1 : (a > real)] : (! [X2 : a] : ((((member_a @ X2 @ (elemen154694473ball_a @ p @ X0))) != $true) | (((ord_less_real @ (abs_abs_real @ (X1 @ X2)) @ one_one_real)) = $true)) & ! [X3 : a] : ((((member_a @ X3 @ (elemen154694473ball_a @ p @ X0))) != $true) | (((member_a @ (auto_ll_on_flow0_a @ f @ x @ X3 @ (X1 @ X3)) @ (line_open_segment_a @ a2 @ b))) = $true)) & (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1)) = $true) & (zero_zero_real = ((X1 @ p))) & (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ X1)) = $true)) & (((ord_less_real @ zero_zero_real @ X0)) = $true))),
  inference(rectify,[],[f878])).
thf(f910,plain,(
  (! [X2 : a] : ((((member_a @ X2 @ (elemen154694473ball_a @ p @ sK10))) != $true) | (((ord_less_real @ (abs_abs_real @ (sK11 @ X2)) @ one_one_real)) = $true)) & ! [X3 : a] : ((((member_a @ X3 @ (elemen154694473ball_a @ p @ sK10))) != $true) | (((member_a @ (auto_ll_on_flow0_a @ f @ x @ X3 @ (sK11 @ X3)) @ (line_open_segment_a @ a2 @ b))) = $true)) & ($true = ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11))) & (zero_zero_real = ((sK11 @ p))) & ($true = ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11)))) & (((ord_less_real @ zero_zero_real @ sK10)) = $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,$thf(sK10)),skolemize(X1,$thf(sK11))],[f909])).
thf(f950,plain,(
  ( ! [X0 : (a > real),X1 : real] : ((((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true) | (((member_a @ (auto_ll_on_flow0_a @ f @ x @ (sK8 @ X1 @ X0) @ (X0 @ (sK8 @ X1 @ X0))) @ (line_open_segment_a @ a2 @ b))) != $true) | (((ord_less_real @ zero_zero_real @ X1)) != $true) | (((member_a @ (sK7 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true) | (thesisa = $true) | (zero_zero_real != ((X0 @ p)))) )),
  inference(cnf_transformation,[],[f890])).
thf(f951,plain,(
  ( ! [X0 : (a > real),X1 : real] : ((((member_a @ (sK7 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true) | (((member_a @ (sK8 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true) | (zero_zero_real != ((X0 @ p))) | (((ord_less_real @ zero_zero_real @ X1)) != $true) | (thesisa = $true)) )),
  inference(cnf_transformation,[],[f890])).
thf(f952,plain,(
  ( ! [X0 : (a > real),X1 : real] : ((thesisa = $true) | (((ord_less_real @ zero_zero_real @ X1)) != $true) | (((member_a @ (auto_ll_on_flow0_a @ f @ x @ (sK8 @ X1 @ X0) @ (X0 @ (sK8 @ X1 @ X0))) @ (line_open_segment_a @ a2 @ b))) != $true) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true) | (zero_zero_real != ((X0 @ p))) | (((ord_less_real @ (abs_abs_real @ (X0 @ (sK7 @ X1 @ X0))) @ one_one_real)) != $true)) )),
  inference(cnf_transformation,[],[f890])).
thf(f953,plain,(
  ( ! [X0 : (a > real),X1 : real] : ((((ord_less_real @ zero_zero_real @ X1)) != $true) | (((member_a @ (sK8 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true) | (thesisa = $true) | (((ord_less_real @ (abs_abs_real @ (X0 @ (sK7 @ X1 @ X0))) @ one_one_real)) != $true) | (zero_zero_real != ((X0 @ p))) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f890])).
thf(f967,plain,(
  ( ! [X0 : real,X1 : real] : ((((ord_less_real @ X0 @ X1)) = ((ord_less_real @ (uminus_uminus_real @ X1) @ (uminus_uminus_real @ X0))))) )),
  inference(cnf_transformation,[],[f896])).
thf(f1015,plain,(
  (((ord_less_real @ zero_zero_real @ sK10)) = $true)),
  inference(cnf_transformation,[],[f910])).
thf(f1017,plain,(
  (zero_zero_real = ((sK11 @ p)))),
  inference(cnf_transformation,[],[f910])).
thf(f1018,plain,(
  ($true = ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11)))),
  inference(cnf_transformation,[],[f910])).
thf(f1019,plain,(
  ( ! [X3 : a] : ((((member_a @ (auto_ll_on_flow0_a @ f @ x @ X3 @ (sK11 @ X3)) @ (line_open_segment_a @ a2 @ b))) = $true) | (((member_a @ X3 @ (elemen154694473ball_a @ p @ sK10))) != $true)) )),
  inference(cnf_transformation,[],[f910])).
thf(f1020,plain,(
  ( ! [X2 : a] : ((((member_a @ X2 @ (elemen154694473ball_a @ p @ sK10))) != $true) | (((ord_less_real @ (abs_abs_real @ (sK11 @ X2)) @ one_one_real)) = $true)) )),
  inference(cnf_transformation,[],[f910])).
thf(f1035,plain,(
  (thesisa != $true)),
  inference(cnf_transformation,[],[f757])).
thf(f1064,definition,(
  spl14_1 <=> ! [X0 : (a > real),X1 : real] : ((((member_a @ (sK7 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true) | (((ord_less_real @ zero_zero_real @ X1)) != $true) | (zero_zero_real != ((X0 @ p))) | (((member_a @ (sK8 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true))),
  introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition])).
thf(f1065,plain,(
  ( ! [X0 : (a > real),X1 : real] : ((((member_a @ (sK8 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true) | (((ord_less_real @ zero_zero_real @ X1)) != $true) | (zero_zero_real != ((X0 @ p))) | (((member_a @ (sK7 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true)) ) | ~spl14_1),
  inference(avatar_component_clause,[],[f1064])).
thf(f1067,definition,(
  spl14_2 <=> (thesisa = $true)),
  introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition])).
thf(f1070,plain,(
  spl14_1 | spl14_2),
  inference(avatar_split_clause,[],[f951,f1067,f1064])).
thf(f1072,definition,(
  spl14_3 <=> ! [X0 : (a > real),X1 : real] : ((((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true) | (zero_zero_real != ((X0 @ p))) | (((member_a @ (sK7 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true) | (((ord_less_real @ zero_zero_real @ X1)) != $true) | (((member_a @ (auto_ll_on_flow0_a @ f @ x @ (sK8 @ X1 @ X0) @ (X0 @ (sK8 @ X1 @ X0))) @ (line_open_segment_a @ a2 @ b))) != $true))),
  introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition])).
thf(f1073,plain,(
  ( ! [X0 : (a > real),X1 : real] : ((((member_a @ (auto_ll_on_flow0_a @ f @ x @ (sK8 @ X1 @ X0) @ (X0 @ (sK8 @ X1 @ X0))) @ (line_open_segment_a @ a2 @ b))) != $true) | (zero_zero_real != ((X0 @ p))) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true) | (((ord_less_real @ zero_zero_real @ X1)) != $true) | (((member_a @ (sK7 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true)) ) | ~spl14_3),
  inference(avatar_component_clause,[],[f1072])).
thf(f1074,plain,(
  spl14_3 | spl14_2),
  inference(avatar_split_clause,[],[f950,f1067,f1072])).
thf(f1076,definition,(
  spl14_4 <=> ! [X0 : (a > real),X1 : real] : ((((ord_less_real @ zero_zero_real @ X1)) != $true) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true) | (zero_zero_real != ((X0 @ p))) | (((ord_less_real @ (abs_abs_real @ (X0 @ (sK7 @ X1 @ X0))) @ one_one_real)) != $true) | (((member_a @ (sK8 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true))),
  introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition])).
thf(f1077,plain,(
  ( ! [X0 : (a > real),X1 : real] : ((((member_a @ (sK8 @ X1 @ X0) @ (elemen154694473ball_a @ p @ X1))) = $true) | (zero_zero_real != ((X0 @ p))) | (((ord_less_real @ (abs_abs_real @ (X0 @ (sK7 @ X1 @ X0))) @ one_one_real)) != $true) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true) | (((ord_less_real @ zero_zero_real @ X1)) != $true)) ) | ~spl14_4),
  inference(avatar_component_clause,[],[f1076])).
thf(f1078,plain,(
  spl14_4 | spl14_2),
  inference(avatar_split_clause,[],[f953,f1067,f1076])).
thf(f1079,plain,(
  ~spl14_2),
  inference(avatar_split_clause,[],[f1035,f1067])).
thf(f1081,definition,(
  spl14_5 <=> ! [X0 : (a > real),X1 : real] : ((((ord_less_real @ zero_zero_real @ X1)) != $true) | (((ord_less_real @ (abs_abs_real @ (X0 @ (sK7 @ X1 @ X0))) @ one_one_real)) != $true) | (zero_zero_real != ((X0 @ p))) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true) | (((member_a @ (auto_ll_on_flow0_a @ f @ x @ (sK8 @ X1 @ X0) @ (X0 @ (sK8 @ X1 @ X0))) @ (line_open_segment_a @ a2 @ b))) != $true))),
  introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition])).
thf(f1082,plain,(
  ( ! [X0 : (a > real),X1 : real] : ((((member_a @ (auto_ll_on_flow0_a @ f @ x @ (sK8 @ X1 @ X0) @ (X0 @ (sK8 @ X1 @ X0))) @ (line_open_segment_a @ a2 @ b))) != $true) | (((ord_less_real @ (abs_abs_real @ (X0 @ (sK7 @ X1 @ X0))) @ one_one_real)) != $true) | (((ord_less_real @ zero_zero_real @ X1)) != $true) | (zero_zero_real != ((X0 @ p))) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X1) @ X0)) != $true)) ) | ~spl14_5),
  inference(avatar_component_clause,[],[f1081])).
thf(f1083,plain,(
  spl14_5 | spl14_2),
  inference(avatar_split_clause,[],[f952,f1067,f1081])).
thf(f1101,plain,(
  ( ! [X0 : real] : ((((ord_less_real @ zero_zero_real @ X0)) != $true) | ($true != $true) | (zero_zero_real != ((sK11 @ p))) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ sK11)) != $true) | (((member_a @ (sK8 @ X0 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | ($true != ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ X0 @ sK11))) @ one_one_real)))) ) | ~spl14_5),
  inference(superposition,[],[f1082,f1019])).
thf(f1106,plain,(
  ( ! [X0 : real] : ((((member_a @ (sK8 @ X0 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | (((ord_less_real @ zero_zero_real @ X0)) != $true) | ($true != ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ X0 @ sK11))) @ one_one_real))) | (zero_zero_real != ((sK11 @ p))) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ sK11)) != $true)) ) | ~spl14_5),
  inference(trivial_inequality_removal,[],[f1101])).
thf(f1109,plain,(
  ( ! [X0 : real] : ((((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ sK11)) != $true) | (((member_a @ (sK8 @ X0 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | (((ord_less_real @ zero_zero_real @ X0)) != $true) | ($true != ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ X0 @ sK11))) @ one_one_real)))) ) | ~spl14_5),
  inference(forward_subsumption_resolution,[],[f1106,f1017])).
thf(f1119,plain,(
  ( ! [X0 : real] : ((((ord_less_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (abs_abs_real @ (sK11 @ (sK7 @ X0 @ sK11)))))) != $true) | (((ord_less_real @ zero_zero_real @ X0)) != $true) | (((member_a @ (sK8 @ X0 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ sK11)) != $true)) ) | ~spl14_5),
  inference(forward_demodulation,[],[f1109,f967])).
thf(f1135,plain,(
  ( ! [X0 : real] : ((zero_zero_real != ((sK11 @ p))) | (((ord_less_real @ zero_zero_real @ X0)) != $true) | (((member_a @ (sK7 @ X0 @ sK11) @ (elemen154694473ball_a @ p @ X0))) = $true) | (((member_a @ (sK8 @ X0 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | ($true != $true) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ sK11)) != $true)) ) | ~spl14_3),
  inference(superposition,[],[f1073,f1019])).
thf(f1140,plain,(
  ( ! [X0 : real] : ((((ord_less_real @ zero_zero_real @ X0)) != $true) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ sK11)) != $true) | (((member_a @ (sK8 @ X0 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | (zero_zero_real != ((sK11 @ p))) | (((member_a @ (sK7 @ X0 @ sK11) @ (elemen154694473ball_a @ p @ X0))) = $true)) ) | ~spl14_3),
  inference(trivial_inequality_removal,[],[f1135])).
thf(f1143,plain,(
  ( ! [X0 : real] : ((((member_a @ (sK7 @ X0 @ sK11) @ (elemen154694473ball_a @ p @ X0))) = $true) | (((ord_less_real @ zero_zero_real @ X0)) != $true) | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X0) @ sK11)) != $true) | (((member_a @ (sK8 @ X0 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true)) ) | ~spl14_3),
  inference(forward_subsumption_resolution,[],[f1140,f1017])).
thf(f1151,plain,(
  ($true != $true) | ($true = ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11))) @ one_one_real))) | (((ord_less_real @ zero_zero_real @ sK10)) != $true) | (((member_a @ (sK8 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | ($true != ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11))) | ~spl14_3),
  inference(superposition,[],[f1020,f1143])).
thf(f1152,plain,(
  ($true != ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11))) | (((ord_less_real @ zero_zero_real @ sK10)) != $true) | (((member_a @ (sK8 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | ($true = ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11))) @ one_one_real))) | ~spl14_3),
  inference(trivial_inequality_removal,[],[f1151])).
thf(f1153,plain,(
  ($true = ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11))) @ one_one_real))) | (((member_a @ (sK8 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | (((ord_less_real @ zero_zero_real @ sK10)) != $true) | ~spl14_3),
  inference(forward_subsumption_resolution,[],[f1152,f1018])).
thf(f1154,plain,(
  ($true = ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11))) @ one_one_real))) | (((member_a @ (sK8 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | ~spl14_3),
  inference(forward_subsumption_resolution,[],[f1153,f1015])).
thf(f1155,plain,(
  (((member_a @ (sK8 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | (((ord_less_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11)))))) = $true) | ~spl14_3),
  inference(forward_demodulation,[],[f1154,f967])).
thf(f1157,definition,(
  spl14_10 <=> (((member_a @ (sK8 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) = $true)),
  introduced(definition,[new_symbols(definition,[spl14_10])],[avatar_definition])).
thf(f1158,plain,(
  (((member_a @ (sK8 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) = $true) | ~spl14_10),
  inference(avatar_component_clause,[],[f1157])).
thf(f1159,plain,(
  (((member_a @ (sK8 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | spl14_10),
  inference(avatar_component_clause,[],[f1157])).
thf(f1161,definition,(
  spl14_11 <=> (((ord_less_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11)))))) = $true)),
  introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition])).
thf(f1162,plain,(
  (((ord_less_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11)))))) != $true) | spl14_11),
  inference(avatar_component_clause,[],[f1161])).
thf(f1163,plain,(
  (((ord_less_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11)))))) = $true) | ~spl14_11),
  inference(avatar_component_clause,[],[f1161])).
thf(f1164,plain,(
  ~spl14_10 | spl14_11 | ~spl14_3),
  inference(avatar_split_clause,[],[f1155,f1072,f1161,f1157])).
thf(f1165,plain,(
  (((ord_less_real @ zero_zero_real @ sK10)) != $true) | (zero_zero_real != ((sK11 @ p))) | ($true != ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11))) | (((member_a @ (sK7 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) = $true) | ($true != $true) | (~spl14_1 | spl14_10)),
  inference(superposition,[],[f1159,f1065])).
thf(f1166,plain,(
  ($true != ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11))) | (zero_zero_real != ((sK11 @ p))) | ($true != $true) | ($true != ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11))) @ one_one_real))) | (((ord_less_real @ zero_zero_real @ sK10)) != $true) | (~spl14_4 | spl14_10)),
  inference(superposition,[],[f1159,f1077])).
thf(f1169,plain,(
  (((ord_less_real @ zero_zero_real @ sK10)) != $true) | ($true != ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11))) | (zero_zero_real != ((sK11 @ p))) | ($true != ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11))) @ one_one_real))) | (~spl14_4 | spl14_10)),
  inference(trivial_inequality_removal,[],[f1166])).
thf(f1170,plain,(
  (zero_zero_real != ((sK11 @ p))) | (((member_a @ (sK7 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) = $true) | (((ord_less_real @ zero_zero_real @ sK10)) != $true) | ($true != ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11))) | (~spl14_1 | spl14_10)),
  inference(trivial_inequality_removal,[],[f1165])).
thf(f1171,plain,(
  (zero_zero_real != ((sK11 @ p))) | ($true != ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11))) @ one_one_real))) | ($true != ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11))) | (~spl14_4 | spl14_10)),
  inference(forward_subsumption_resolution,[],[f1169,f1015])).
thf(f1172,plain,(
  ($true != ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11))) | (((ord_less_real @ zero_zero_real @ sK10)) != $true) | (((member_a @ (sK7 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) = $true) | (~spl14_1 | spl14_10)),
  inference(forward_subsumption_resolution,[],[f1170,f1017])).
thf(f1173,plain,(
  ($true != ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11))) | ($true != ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11))) @ one_one_real))) | (~spl14_4 | spl14_10)),
  inference(forward_subsumption_resolution,[],[f1171,f1017])).
thf(f1174,plain,(
  (((member_a @ (sK7 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) = $true) | (((ord_less_real @ zero_zero_real @ sK10)) != $true) | (~spl14_1 | spl14_10)),
  inference(forward_subsumption_resolution,[],[f1172,f1018])).
thf(f1175,plain,(
  ($true != ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11))) @ one_one_real))) | (~spl14_4 | spl14_10)),
  inference(forward_subsumption_resolution,[],[f1173,f1018])).
thf(f1176,plain,(
  (((member_a @ (sK7 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) = $true) | (~spl14_1 | spl14_10)),
  inference(forward_subsumption_resolution,[],[f1174,f1015])).
thf(f1177,plain,(
  (((ord_less_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11)))))) != $true) | (~spl14_4 | spl14_10)),
  inference(forward_demodulation,[],[f1175,f967])).
thf(f1178,plain,(
  ~spl14_11 | ~spl14_4 | spl14_10),
  inference(avatar_split_clause,[],[f1177,f1157,f1076,f1161])).
thf(f1204,plain,(
  ($true != $true) | ($true = ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11))) @ one_one_real))) | (~spl14_1 | spl14_10)),
  inference(superposition,[],[f1020,f1176])).
thf(f1205,plain,(
  ($true = ((ord_less_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11))) @ one_one_real))) | (~spl14_1 | spl14_10)),
  inference(trivial_inequality_removal,[],[f1204])).
thf(f1206,plain,(
  (((ord_less_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (abs_abs_real @ (sK11 @ (sK7 @ sK10 @ sK11)))))) = $true) | (~spl14_1 | spl14_10)),
  inference(forward_demodulation,[],[f1205,f967])).
thf(f1207,plain,(
  $false | (~spl14_1 | spl14_10 | spl14_11)),
  inference(forward_subsumption_resolution,[],[f1206,f1162])).
thf(f1208,plain,(
  ~spl14_1 | spl14_10 | spl14_11),
  inference(avatar_contradiction_clause,[],[f1207])).
thf(f1244,plain,(
  ($true != $true) | (((member_a @ (sK8 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | ($true != ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11))) | (((ord_less_real @ zero_zero_real @ sK10)) != $true) | (~spl14_5 | ~spl14_11)),
  inference(superposition,[],[f1119,f1163])).
thf(f1245,plain,(
  ($true != ((topolo1710226732a_real @ (elemen154694473ball_a @ p @ sK10) @ sK11))) | (((member_a @ (sK8 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | (((ord_less_real @ zero_zero_real @ sK10)) != $true) | (~spl14_5 | ~spl14_11)),
  inference(trivial_inequality_removal,[],[f1244])).
thf(f1246,plain,(
  (((member_a @ (sK8 @ sK10 @ sK11) @ (elemen154694473ball_a @ p @ sK10))) != $true) | (((ord_less_real @ zero_zero_real @ sK10)) != $true) | (~spl14_5 | ~spl14_11)),
  inference(forward_subsumption_resolution,[],[f1245,f1018])).
thf(f1247,plain,(
  (((ord_less_real @ zero_zero_real @ sK10)) != $true) | (~spl14_5 | ~spl14_10 | ~spl14_11)),
  inference(forward_subsumption_resolution,[],[f1246,f1158])).
thf(f1248,plain,(
  $false | (~spl14_5 | ~spl14_10 | ~spl14_11)),
  inference(forward_subsumption_resolution,[],[f1247,f1015])).
thf(f1249,plain,(
  ~spl14_5 | ~spl14_10 | ~spl14_11),
  inference(avatar_contradiction_clause,[],[f1248])).
cnf(s1, plain, spl14_1 | spl14_2, inference(sat_conversion,[],[f1070])).
cnf(s2, plain, spl14_2 | spl14_3, inference(sat_conversion,[],[f1074])).
cnf(s3, plain, spl14_2 | spl14_4, inference(sat_conversion,[],[f1078])).
cnf(s4, plain, ~spl14_2, inference(sat_conversion,[],[f1079])).
cnf(s5, plain, spl14_2 | spl14_5, inference(sat_conversion,[],[f1083])).
cnf(s8, plain, ~spl14_3 | ~spl14_10 | spl14_11, inference(sat_conversion,[],[f1164])).
cnf(s9, plain, ~spl14_4 | spl14_10 | ~spl14_11, inference(sat_conversion,[],[f1178])).
cnf(s10, plain, ~spl14_1 | spl14_10 | spl14_11, inference(sat_conversion,[],[f1208])).
cnf(s11, plain, ~spl14_5 | ~spl14_10 | ~spl14_11, inference(sat_conversion,[],[f1249])).
cnf(s12, plain, spl14_5, inference(rat,[],[s5,s4])).
cnf(s13, plain, spl14_4, inference(rat,[],[s3,s4])).
cnf(s14, plain, spl14_3, inference(rat,[],[s2,s4])).
cnf(s15, plain, spl14_1, inference(rat,[],[s1,s4])).
cnf(s16, plain, spl14_10, inference(rat,[],[s9,s10,s13,s15])).
cnf(s17, plain, ~spl14_11, inference(rat,[],[s11,s12,s16])).
cnf(s18, plain, $false, inference(rat,[],[s8,s14,s17,s16])).
thf(f1250,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s18])).
% SZS output end Proof for theBenchmark