0.02/0.08 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.10 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.jFPV31lyGt true 0.10/0.30 % Computer : n008.cluster.edu 0.10/0.30 % Model : x86_64 x86_64 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.30 % Memory : 8042.1875MB 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.30 % CPULimit : 960 0.10/0.30 % WCLimit : 120 0.10/0.30 % DateTime : Tue Aug 9 05:18:38 EDT 2022 0.10/0.30 % CPUTime : 0.10/0.30 % Running portfolio for 960 s 0.10/0.30 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.10/0.30 % Number of cores: 8 0.10/0.30 % Python version: Python 3.6.8 0.10/0.30 % Running in HO mode 0.15/0.52 % Total configuration time : 828 0.15/0.52 % Estimated wc time : 1656 0.15/0.52 % Estimated cpu time (8 cpus) : 207.0 0.98/0.59 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.98/0.59 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.98/0.59 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.98/0.59 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.98/0.59 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.98/0.59 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.98/0.59 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.98/0.61 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 1.10/0.64 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 1.10/0.65 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 115.85/15.10 % Solved by lams/30_b.l.sh. 115.85/15.10 % done 1390 iterations in 14.396s 115.85/15.10 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 115.85/15.10 % SZS output start Refutation 115.85/15.10 thf(real_type, type, real: $tType). 115.85/15.10 thf(set_a_type, type, set_a: $tType). 115.85/15.10 thf(a_type, type, a: $tType). 115.85/15.10 thf(abs_abs_real_type, type, abs_abs_real: real > real). 115.85/15.10 thf('#sk7_type', type, '#sk7': a > real). 115.85/15.10 thf(b_type, type, b: a). 115.85/15.10 thf('#sk32_type', type, '#sk32': real > (a > real) > a). 115.85/15.10 thf(zero_zero_real_type, type, zero_zero_real: real). 115.85/15.10 thf(auto_ll_on_flow0_a_type, type, auto_ll_on_flow0_a: (a > a) > set_a > a > 115.85/15.10 real > a). 115.85/15.10 thf(topolo1710226732a_real_type, type, topolo1710226732a_real: set_a > 115.85/15.10 (a > real) > $o). 115.85/15.10 thf('#sk41_type', type, '#sk41': real > (a > real) > a). 115.85/15.10 thf(elemen154694473ball_a_type, type, elemen154694473ball_a: a > real > set_a). 115.85/15.10 thf(line_open_segment_a_type, type, line_open_segment_a: a > a > set_a). 115.85/15.10 thf(a2_type, type, a2: a). 115.85/15.10 thf(p_type, type, p: a). 115.85/15.10 thf(one_one_real_type, type, one_one_real: real). 115.85/15.10 thf(member_a_type, type, member_a: a > set_a > $o). 115.85/15.10 thf(thesisa_type, type, thesisa: $o). 115.85/15.10 thf(ord_less_real_type, type, ord_less_real: real > real > $o). 115.85/15.10 thf(f_type, type, f: a > a). 115.85/15.10 thf('#form40_type', type, '#form40': real > (a > real) > $o). 115.85/15.10 thf('#form96_type', type, '#form96': real > (a > real) > $o). 115.85/15.10 thf('#sk6_type', type, '#sk6': real). 115.85/15.10 thf(x_type, type, x: set_a). 115.85/15.10 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, 115.85/15.10 (~( ![D:real]: 115.85/15.10 ( ( ord_less_real @ zero_zero_real @ D ) => 115.85/15.10 ( ![T:( a > real )]: 115.85/15.10 ( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ D ) @ T ) => 115.85/15.10 ( ( ![Y2:a]: 115.85/15.10 ( ( member_a @ Y2 @ ( elemen154694473ball_a @ p @ D ) ) => 115.85/15.10 ( member_a @ 115.85/15.10 ( auto_ll_on_flow0_a @ f @ x @ Y2 @ ( T @ Y2 ) ) @ 115.85/15.10 ( line_open_segment_a @ a2 @ b ) ) ) ) => 115.85/15.10 ( ( ![Y2:a]: 115.85/15.10 ( ( member_a @ Y2 @ ( elemen154694473ball_a @ p @ D ) ) => 115.85/15.10 ( ord_less_real @ 115.85/15.10 ( abs_abs_real @ ( T @ Y2 ) ) @ one_one_real ) ) ) => 115.85/15.10 ( ( topolo1710226732a_real @ 115.85/15.10 ( elemen154694473ball_a @ p @ D ) @ T ) => 115.85/15.10 ( ( T @ p ) != ( zero_zero_real ) ) ) ) ) ) ) ) ))). 115.85/15.10 thf(zip_derived_cl177, plain, 115.85/15.10 (~ (((!!) @ (^[Y0 : real]: 115.85/15.10 (((ord_less_real @ zero_zero_real @ Y0) => 115.85/15.10 (((!!) @ (^[Y1 : a > real]: 115.85/15.10 (((topolo1710226732a_real @ 115.85/15.10 (elemen154694473ball_a @ p @ Y0) @ Y1) => 115.85/15.10 (((((!!) @ (^[Y2 : a]: 115.85/15.10 (((member_a @ Y2 @ 115.85/15.10 (elemen154694473ball_a @ 115.85/15.10 p @ Y0)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ 115.85/15.10 x @ Y2 @ (Y1 @ Y2)) @ 115.85/15.10 (line_open_segment_a @ 115.85/15.10 a2 @ b))))))) => 115.85/15.10 (((((!!) @ (^[Y2 : a]: 115.85/15.10 (((member_a @ Y2 @ 115.85/15.10 (elemen154694473ball_a @ 115.85/15.10 p @ Y0)) => 115.85/15.10 (ord_less_real @ 115.85/15.10 (abs_abs_real @ 115.85/15.10 (Y1 @ Y2)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((topolo1710226732a_real @ 115.85/15.10 (elemen154694473ball_a @ p @ Y0) @ 115.85/15.10 Y1) => 115.85/15.10 (((Y1 @ p) != (zero_zero_real)))))))))))))))))))), 115.85/15.10 inference('cnf', [status(esa)], 115.85/15.10 [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])). 115.85/15.10 thf(zip_derived_cl1376, plain, 115.85/15.10 (~ (((ord_less_real @ zero_zero_real @ '#sk6') => 115.85/15.10 (((!!) @ (^[Y0 : a > real]: 115.85/15.10 (((topolo1710226732a_real @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6') @ Y0) => 115.85/15.10 (((((!!) @ (^[Y1 : a]: 115.85/15.10 (((member_a @ Y1 @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6')) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y1 @ 115.85/15.10 (Y0 @ Y1)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) => 115.85/15.10 (((((!!) @ (^[Y1 : a]: 115.85/15.10 (((member_a @ Y1 @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6')) => 115.85/15.10 (ord_less_real @ 115.85/15.10 (abs_abs_real @ (Y0 @ Y1)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((topolo1710226732a_real @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6') @ Y0) => 115.85/15.10 (((Y0 @ p) != (zero_zero_real))))))))))))))))), 115.85/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl177])). 115.85/15.10 thf(zip_derived_cl1378, plain, 115.85/15.10 (~ (((!!) @ (^[Y0 : a > real]: 115.85/15.10 (((topolo1710226732a_real @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6') @ Y0) => 115.85/15.10 (((((!!) @ (^[Y1 : a]: 115.85/15.10 (((member_a @ Y1 @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6')) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y1 @ 115.85/15.10 (Y0 @ Y1)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) => 115.85/15.10 (((((!!) @ (^[Y1 : a]: 115.85/15.10 (((member_a @ Y1 @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6')) => 115.85/15.10 (ord_less_real @ 115.85/15.10 (abs_abs_real @ (Y0 @ Y1)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((topolo1710226732a_real @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6') @ Y0) => 115.85/15.10 (((Y0 @ p) != (zero_zero_real))))))))))))))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1376])). 115.85/15.10 thf(zip_derived_cl1379, plain, 115.85/15.10 (~ (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ '#sk6') @ 115.85/15.10 '#sk7') => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6')) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ ('#sk7' @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6')) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ ('#sk7' @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((topolo1710226732a_real @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6') @ '#sk7') => 115.85/15.10 ((('#sk7' @ p) != (zero_zero_real)))))))))))), 115.85/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1378])). 115.85/15.10 thf(zip_derived_cl1380, plain, 115.85/15.10 ( (topolo1710226732a_real @ (elemen154694473ball_a @ p @ '#sk6') @ '#sk7')), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1379])). 115.85/15.10 thf(fact_4_that, axiom, 115.85/15.10 (![Delta:real,Tau:( a > real )]: 115.85/15.10 ( ( ord_less_real @ zero_zero_real @ Delta ) => 115.85/15.10 ( ( topolo1710226732a_real @ ( elemen154694473ball_a @ p @ Delta ) @ Tau ) => 115.85/15.10 ( ( ( Tau @ p ) = ( zero_zero_real ) ) => 115.85/15.10 ( ( ![Y3:a]: 115.85/15.10 ( ( member_a @ Y3 @ ( elemen154694473ball_a @ p @ Delta ) ) => 115.85/15.10 ( ord_less_real @ 115.85/15.10 ( abs_abs_real @ ( Tau @ Y3 ) ) @ one_one_real ) ) ) => 115.85/15.10 ( ( ![Y3:a]: 115.85/15.10 ( ( member_a @ Y3 @ ( elemen154694473ball_a @ p @ Delta ) ) => 115.85/15.10 ( member_a @ 115.85/15.10 ( auto_ll_on_flow0_a @ f @ x @ Y3 @ ( Tau @ Y3 ) ) @ 115.85/15.10 ( line_open_segment_a @ a2 @ b ) ) ) ) => 115.85/15.10 ( thesisa ) ) ) ) ) ))). 115.85/15.10 thf(zip_derived_cl145, plain, 115.85/15.10 ( (((!!) @ (^[Y0 : real]: 115.85/15.10 (((!!) @ (^[Y1 : a > real]: 115.85/15.10 (((ord_less_real @ zero_zero_real @ Y0) => 115.85/15.10 (((topolo1710226732a_real @ 115.85/15.10 (elemen154694473ball_a @ p @ Y0) @ Y1) => 115.85/15.10 (((((Y1 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y2 : a]: 115.85/15.10 (((member_a @ Y2 @ 115.85/15.10 (elemen154694473ball_a @ 115.85/15.10 p @ Y0)) => 115.85/15.10 (ord_less_real @ 115.85/15.10 (abs_abs_real @ (Y1 @ Y2)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((((!!) @ (^[Y2 : a]: 115.85/15.10 (((member_a @ Y2 @ 115.85/15.10 (elemen154694473ball_a @ 115.85/15.10 p @ Y0)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ 115.85/15.10 f @ x @ Y2 @ ( 115.85/15.10 Y1 @ Y2)) @ 115.85/15.10 (line_open_segment_a @ 115.85/15.10 a2 @ b))))))) => 115.85/15.10 (thesisa)))))))))))))))))), 115.85/15.10 inference('cnf', [status(esa)], [fact_4_that])). 115.85/15.10 thf(zip_derived_cl1515, plain, 115.85/15.10 (![X2 : real]: 115.85/15.10 (((!!) @ (^[Y0 : a > real]: 115.85/15.10 (((ord_less_real @ zero_zero_real @ X2) => 115.85/15.10 (((topolo1710226732a_real @ 115.85/15.10 (elemen154694473ball_a @ p @ X2) @ Y0) => 115.85/15.10 (((((Y0 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y1 : a]: 115.85/15.10 (((member_a @ Y1 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ 115.85/15.10 (abs_abs_real @ (Y0 @ Y1)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((((!!) @ (^[Y1 : a]: 115.85/15.10 (((member_a @ Y1 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ 115.85/15.10 Y1 @ (Y0 @ Y1)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) => 115.85/15.10 (thesisa))))))))))))))), 115.85/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl145])). 115.85/15.10 thf(zip_derived_cl1516, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (((ord_less_real @ zero_zero_real @ X2) => 115.85/15.10 (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ 115.85/15.10 X4) => 115.85/15.10 (((((X4 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) => 115.85/15.10 (thesisa)))))))))))), 115.85/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1515])). 115.85/15.10 thf(conj_1, conjecture, (thesisa)). 115.85/15.10 thf(zf_stmt_0, negated_conjecture, (~( thesisa )), 115.85/15.10 inference('cnf.neg', [status(esa)], [conj_1])). 115.85/15.10 thf(zip_derived_cl326, plain, (~ (thesisa)), 115.85/15.10 inference('cnf', [status(esa)], [zf_stmt_0])). 115.85/15.10 thf(zip_derived_cl1517, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (((ord_less_real @ zero_zero_real @ X2) => 115.85/15.10 (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ 115.85/15.10 X4) => 115.85/15.10 (((((X4 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) => 115.85/15.10 ($false)))))))))))), 115.85/15.10 inference('demod', [status(thm)], [zip_derived_cl1516, zip_derived_cl326])). 115.85/15.10 thf(zip_derived_cl1518, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (((ord_less_real @ zero_zero_real @ X2) => 115.85/15.10 (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ 115.85/15.10 X4) => 115.85/15.10 (((((X4 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b)))))))))))))))))), 115.85/15.10 inference('simplify boolean subterms', [status(thm)], 115.85/15.10 [zip_derived_cl1517])). 115.85/15.10 thf(zip_derived_cl1519, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (ord_less_real @ zero_zero_real @ X2) 115.85/15.10 | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ 115.85/15.10 X4) => 115.85/15.10 (((((X4 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))))))))))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1518])). 115.85/15.10 thf(zip_derived_cl1520, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ X4) 115.85/15.10 | (((((X4 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))))))) 115.85/15.10 | ~ (ord_less_real @ zero_zero_real @ X2))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1519])). 115.85/15.10 thf(zip_derived_cl1521, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (((X4 @ p) = (zero_zero_real))) 115.85/15.10 | (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))))) 115.85/15.10 | ~ (ord_less_real @ zero_zero_real @ X2) 115.85/15.10 | ~ (topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ X4))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1520])). 115.85/15.10 thf(zip_derived_cl1522, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (((X4 @ p) != (zero_zero_real)) 115.85/15.10 | (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))))) 115.85/15.10 | ~ (ord_less_real @ zero_zero_real @ X2) 115.85/15.10 | ~ (topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ X4))), 115.85/15.10 inference('simplify nested equalities', [status(thm)], 115.85/15.10 [zip_derived_cl1521])). 115.85/15.10 thf(zip_derived_cl1522, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (((X4 @ p) != (zero_zero_real)) 115.85/15.10 | (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))))) 115.85/15.10 | ~ (ord_less_real @ zero_zero_real @ X2) 115.85/15.10 | ~ (topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ X4))), 115.85/15.10 inference('simplify nested equalities', [status(thm)], 115.85/15.10 [zip_derived_cl1521])). 115.85/15.10 thf(zip_derived_cl1523, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ ('#form96' @ X2 @ X4) 115.85/15.10 | (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))))))), 115.85/15.10 define([status(thm)])). 115.85/15.10 thf(zip_derived_cl1525, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 ( ('#form96' @ X2 @ X4) 115.85/15.10 | ~ (topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ X4) 115.85/15.10 | ~ (ord_less_real @ zero_zero_real @ X2) 115.85/15.10 | ((X4 @ p) != (zero_zero_real)))), 115.85/15.10 inference('renaming', [status(thm)], 115.85/15.10 [zip_derived_cl1522, zip_derived_cl1523])). 115.85/15.10 thf(zip_derived_cl18396, plain, 115.85/15.10 (((('#sk7' @ p) != (zero_zero_real)) 115.85/15.10 | ~ (ord_less_real @ zero_zero_real @ '#sk6') 115.85/15.10 | ('#form96' @ '#sk6' @ '#sk7'))), 115.85/15.10 inference('sup-', [status(thm)], [zip_derived_cl1380, zip_derived_cl1525])). 115.85/15.10 thf(zip_derived_cl1381, plain, 115.85/15.10 (~ (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6')) => (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ ('#sk7' @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6')) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ ('#sk7' @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((topolo1710226732a_real @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6') @ '#sk7') => 115.85/15.10 ((('#sk7' @ p) != (zero_zero_real)))))))))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1379])). 115.85/15.10 thf(zip_derived_cl1383, plain, 115.85/15.10 (~ (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ '#sk6')) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ ('#sk7' @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ '#sk6') @ 115.85/15.10 '#sk7') => ((('#sk7' @ p) != (zero_zero_real)))))))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1381])). 115.85/15.10 thf(zip_derived_cl1386, plain, 115.85/15.10 (~ (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ '#sk6') @ 115.85/15.10 '#sk7') => ((('#sk7' @ p) != (zero_zero_real)))))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1383])). 115.85/15.10 thf(zip_derived_cl1390, plain, (~ ((('#sk7' @ p) != (zero_zero_real)))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1386])). 115.85/15.10 thf(zip_derived_cl1392, plain, ((('#sk7' @ p) = (zero_zero_real))), 115.85/15.10 inference('simplify nested equalities', [status(thm)], 115.85/15.10 [zip_derived_cl1390])). 115.85/15.10 thf(zip_derived_cl1377, plain, ( (ord_less_real @ zero_zero_real @ '#sk6')), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1376])). 115.85/15.10 thf(zip_derived_cl18402, plain, 115.85/15.10 ((((zero_zero_real) != (zero_zero_real)) | ('#form96' @ '#sk6' @ '#sk7'))), 115.85/15.10 inference('demod', [status(thm)], 115.85/15.10 [zip_derived_cl18396, zip_derived_cl1392, zip_derived_cl1377])). 115.85/15.10 thf(zip_derived_cl18403, plain, ( ('#form96' @ '#sk6' @ '#sk7')), 115.85/15.10 inference('simplify', [status(thm)], [zip_derived_cl18402])). 115.85/15.10 thf(conj_0, axiom, 115.85/15.10 (![Delta2:real,Tau2:( a > real )]: 115.85/15.10 ( ( ord_less_real @ zero_zero_real @ Delta2 ) => 115.85/15.10 ( ( topolo1710226732a_real @ 115.85/15.10 ( elemen154694473ball_a @ p @ Delta2 ) @ Tau2 ) => 115.85/15.10 ( ( ( Tau2 @ p ) = ( zero_zero_real ) ) => 115.85/15.10 ( ( ![Y3:a]: 115.85/15.10 ( ( member_a @ Y3 @ ( elemen154694473ball_a @ p @ Delta2 ) ) => 115.85/15.10 ( ord_less_real @ 115.85/15.10 ( abs_abs_real @ ( Tau2 @ Y3 ) ) @ one_one_real ) ) ) => 115.85/15.10 ( ( ![Y3:a]: 115.85/15.10 ( ( member_a @ Y3 @ ( elemen154694473ball_a @ p @ Delta2 ) ) => 115.85/15.10 ( member_a @ 115.85/15.10 ( auto_ll_on_flow0_a @ f @ x @ Y3 @ ( Tau2 @ Y3 ) ) @ 115.85/15.10 ( line_open_segment_a @ a2 @ b ) ) ) ) => 115.85/15.10 ( thesisa ) ) ) ) ) ))). 115.85/15.10 thf(zip_derived_cl119, plain, 115.85/15.10 ( (((!!) @ (^[Y0 : real]: 115.85/15.10 (((!!) @ (^[Y1 : a > real]: 115.85/15.10 (((ord_less_real @ zero_zero_real @ Y0) => 115.85/15.10 (((topolo1710226732a_real @ 115.85/15.10 (elemen154694473ball_a @ p @ Y0) @ Y1) => 115.85/15.10 (((((Y1 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y2 : a]: 115.85/15.10 (((member_a @ Y2 @ 115.85/15.10 (elemen154694473ball_a @ 115.85/15.10 p @ Y0)) => 115.85/15.10 (ord_less_real @ 115.85/15.10 (abs_abs_real @ (Y1 @ Y2)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((((!!) @ (^[Y2 : a]: 115.85/15.10 (((member_a @ Y2 @ 115.85/15.10 (elemen154694473ball_a @ 115.85/15.10 p @ Y0)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ 115.85/15.10 f @ x @ Y2 @ ( 115.85/15.10 Y1 @ Y2)) @ 115.85/15.10 (line_open_segment_a @ 115.85/15.10 a2 @ b))))))) => 115.85/15.10 (thesisa)))))))))))))))))), 115.85/15.10 inference('cnf', [status(esa)], [conj_0])). 115.85/15.10 thf(zip_derived_cl1396, plain, 115.85/15.10 (![X2 : real]: 115.85/15.10 (((!!) @ (^[Y0 : a > real]: 115.85/15.10 (((ord_less_real @ zero_zero_real @ X2) => 115.85/15.10 (((topolo1710226732a_real @ 115.85/15.10 (elemen154694473ball_a @ p @ X2) @ Y0) => 115.85/15.10 (((((Y0 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y1 : a]: 115.85/15.10 (((member_a @ Y1 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ 115.85/15.10 (abs_abs_real @ (Y0 @ Y1)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((((!!) @ (^[Y1 : a]: 115.85/15.10 (((member_a @ Y1 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ 115.85/15.10 Y1 @ (Y0 @ Y1)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) => 115.85/15.10 (thesisa))))))))))))))), 115.85/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl119])). 115.85/15.10 thf(zip_derived_cl1397, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (((ord_less_real @ zero_zero_real @ X2) => 115.85/15.10 (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ 115.85/15.10 X4) => 115.85/15.10 (((((X4 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) => 115.85/15.10 (thesisa)))))))))))), 115.85/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1396])). 115.85/15.10 thf(zip_derived_cl326, plain, (~ (thesisa)), 115.85/15.10 inference('cnf', [status(esa)], [zf_stmt_0])). 115.85/15.10 thf(zip_derived_cl1398, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (((ord_less_real @ zero_zero_real @ X2) => 115.85/15.10 (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ 115.85/15.10 X4) => 115.85/15.10 (((((X4 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) => 115.85/15.10 ($false)))))))))))), 115.85/15.10 inference('demod', [status(thm)], [zip_derived_cl1397, zip_derived_cl326])). 115.85/15.10 thf(zip_derived_cl1399, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (((ord_less_real @ zero_zero_real @ X2) => 115.85/15.10 (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ 115.85/15.10 X4) => 115.85/15.10 (((((X4 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b)))))))))))))))))), 115.85/15.10 inference('simplify boolean subterms', [status(thm)], 115.85/15.10 [zip_derived_cl1398])). 115.85/15.10 thf(zip_derived_cl1400, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (ord_less_real @ zero_zero_real @ X2) 115.85/15.10 | (((topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ 115.85/15.10 X4) => 115.85/15.10 (((((X4 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))))))))))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1399])). 115.85/15.10 thf(zip_derived_cl1401, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ X4) 115.85/15.10 | (((((X4 @ p) = (zero_zero_real))) => 115.85/15.10 (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))))))) 115.85/15.10 | ~ (ord_less_real @ zero_zero_real @ X2))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1400])). 115.85/15.10 thf(zip_derived_cl1402, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (((X4 @ p) = (zero_zero_real))) 115.85/15.10 | (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))))) 115.85/15.10 | ~ (ord_less_real @ zero_zero_real @ X2) 115.85/15.10 | ~ (topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ X4))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1401])). 115.85/15.10 thf(zip_derived_cl1403, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (((X4 @ p) != (zero_zero_real)) 115.85/15.10 | (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))))) 115.85/15.10 | ~ (ord_less_real @ zero_zero_real @ X2) 115.85/15.10 | ~ (topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ X4))), 115.85/15.10 inference('simplify nested equalities', [status(thm)], 115.85/15.10 [zip_derived_cl1402])). 115.85/15.10 thf(zip_derived_cl1404, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) 115.85/15.10 | ~ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) 115.85/15.10 | ~ (topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ X4) 115.85/15.10 | ~ (ord_less_real @ zero_zero_real @ X2) 115.85/15.10 | ((X4 @ p) != (zero_zero_real)))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1403])). 115.85/15.10 thf(zip_derived_cl1405, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (((member_a @ ('#sk32' @ X2 @ X4) @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => (ord_less_real @ 115.85/15.10 (abs_abs_real @ (X4 @ ('#sk32' @ X2 @ X4))) @ one_one_real))) 115.85/15.10 | ((X4 @ p) != (zero_zero_real)) 115.85/15.10 | ~ (ord_less_real @ zero_zero_real @ X2) 115.85/15.10 | ~ (topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ X4) 115.85/15.10 | ~ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))), 115.85/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1404])). 115.85/15.10 thf(zip_derived_cl1406, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 ( (member_a @ ('#sk32' @ X2 @ X4) @ (elemen154694473ball_a @ p @ X2)) 115.85/15.10 | ~ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) 115.85/15.10 | ~ (topolo1710226732a_real @ (elemen154694473ball_a @ p @ X2) @ X4) 115.85/15.10 | ~ (ord_less_real @ zero_zero_real @ X2) 115.85/15.10 | ((X4 @ p) != (zero_zero_real)))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1405])). 115.85/15.10 thf(zip_derived_cl1408, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 ( ('#form40' @ X2 @ X4) 115.85/15.10 | ~ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))), 115.85/15.10 define([status(thm)])). 115.85/15.10 thf(zip_derived_cl1409, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (((member_a @ ('#sk41' @ X2 @ X4) @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ ('#sk41' @ X2 @ X4) @ 115.85/15.10 (X4 @ ('#sk41' @ X2 @ X4))) @ 115.85/15.10 (line_open_segment_a @ a2 @ b)))) 115.85/15.10 | ('#form40' @ X2 @ X4))), 115.85/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1408])). 115.85/15.10 thf(zip_derived_cl1412, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 ( (member_a @ ('#sk41' @ X2 @ X4) @ (elemen154694473ball_a @ p @ X2)) 115.85/15.10 | ('#form40' @ X2 @ X4))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1409])). 115.85/15.10 thf(zip_derived_cl1523, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ ('#form96' @ X2 @ X4) 115.85/15.10 | (((((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) => 115.85/15.10 (((~) @ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ 115.85/15.10 (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))))))), 115.85/15.10 define([status(thm)])). 115.85/15.10 thf(zip_derived_cl1524, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))) 115.85/15.10 | ~ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))) 115.85/15.10 | ~ ('#form96' @ X2 @ X4))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1523])). 115.85/15.10 thf(zip_derived_cl1408, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 ( ('#form40' @ X2 @ X4) 115.85/15.10 | ~ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ (X4 @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))))))), 115.85/15.10 define([status(thm)])). 115.85/15.10 thf(zip_derived_cl1526, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ ('#form40' @ X2 @ (^[Y0 : a]: (X4 @ Y0))) 115.85/15.10 | ~ ('#form96' @ X2 @ X4) 115.85/15.10 | ~ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))))), 115.85/15.10 inference('renaming', [status(thm)], 115.85/15.10 [zip_derived_cl1524, zip_derived_cl1408])). 115.85/15.10 thf(zip_derived_cl1527, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ ('#form40' @ X2 @ X4) 115.85/15.10 | ~ ('#form96' @ X2 @ X4) 115.85/15.10 | ~ (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ (X4 @ Y0)) @ 115.85/15.10 one_one_real)))))))), 115.85/15.10 inference('ho_norm', [status(thm)], [zip_derived_cl1526])). 115.85/15.10 thf(zip_derived_cl1528, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (((member_a @ ('#sk32' @ X2 @ X4) @ 115.85/15.10 (elemen154694473ball_a @ p @ X2)) => (ord_less_real @ 115.85/15.10 (abs_abs_real @ (X4 @ ('#sk32' @ X2 @ X4))) @ one_one_real))) 115.85/15.10 | ~ ('#form96' @ X2 @ X4) 115.85/15.10 | ~ ('#form40' @ X2 @ X4))), 115.85/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1527])). 115.85/15.10 thf(zip_derived_cl1529, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 ( (member_a @ ('#sk32' @ X2 @ X4) @ (elemen154694473ball_a @ p @ X2)) 115.85/15.10 | ~ ('#form40' @ X2 @ X4) 115.85/15.10 | ~ ('#form96' @ X2 @ X4))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1528])). 115.85/15.10 thf(zip_derived_cl1382, plain, 115.85/15.10 ( (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ (elemen154694473ball_a @ p @ '#sk6')) => 115.85/15.10 (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ Y0 @ ('#sk7' @ Y0)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b)))))))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1381])). 115.85/15.10 thf(zip_derived_cl1384, plain, 115.85/15.10 (![X2 : a]: 115.85/15.10 (((member_a @ X2 @ (elemen154694473ball_a @ p @ '#sk6')) => 115.85/15.10 (member_a @ (auto_ll_on_flow0_a @ f @ x @ X2 @ ('#sk7' @ X2)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b))))), 115.85/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1382])). 115.85/15.10 thf(zip_derived_cl1387, plain, 115.85/15.10 (![X2 : a]: 115.85/15.10 (~ (member_a @ X2 @ (elemen154694473ball_a @ p @ '#sk6')) 115.85/15.10 | (member_a @ (auto_ll_on_flow0_a @ f @ x @ X2 @ ('#sk7' @ X2)) @ 115.85/15.10 (line_open_segment_a @ a2 @ b)))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1384])). 115.85/15.10 thf(zip_derived_cl1413, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (member_a @ 115.85/15.10 (auto_ll_on_flow0_a @ f @ x @ ('#sk41' @ X2 @ X4) @ 115.85/15.10 (X4 @ ('#sk41' @ X2 @ X4))) @ 115.85/15.10 (line_open_segment_a @ a2 @ b)) 115.85/15.10 | ('#form40' @ X2 @ X4))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1409])). 115.85/15.10 thf(zip_derived_cl1385, plain, 115.85/15.10 ( (((!!) @ (^[Y0 : a]: 115.85/15.10 (((member_a @ Y0 @ (elemen154694473ball_a @ p @ '#sk6')) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ ('#sk7' @ Y0)) @ 115.85/15.10 one_one_real))))))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1383])). 115.85/15.10 thf(zip_derived_cl1388, plain, 115.85/15.10 (![X2 : a]: 115.85/15.10 (((member_a @ X2 @ (elemen154694473ball_a @ p @ '#sk6')) => 115.85/15.10 (ord_less_real @ (abs_abs_real @ ('#sk7' @ X2)) @ one_one_real)))), 115.85/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1385])). 115.85/15.10 thf(zip_derived_cl1391, plain, 115.85/15.10 (![X2 : a]: 115.85/15.10 (~ (member_a @ X2 @ (elemen154694473ball_a @ p @ '#sk6')) 115.85/15.10 | (ord_less_real @ (abs_abs_real @ ('#sk7' @ X2)) @ one_one_real))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1388])). 115.85/15.10 thf(zip_derived_cl1530, plain, 115.85/15.10 (![X2 : real, X4 : a > real]: 115.85/15.10 (~ (ord_less_real @ (abs_abs_real @ (X4 @ ('#sk32' @ X2 @ X4))) @ 115.85/15.10 one_one_real) 115.85/15.10 | ~ ('#form40' @ X2 @ X4) 115.85/15.10 | ~ ('#form96' @ X2 @ X4))), 115.85/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1528])). 115.85/15.10 thf(zip_derived_cl30057, plain, ($false), 115.85/15.10 inference('eprover', [status(thm)], 115.85/15.10 [zip_derived_cl18403, zip_derived_cl1412, zip_derived_cl1529, 115.85/15.10 zip_derived_cl1387, zip_derived_cl1413, zip_derived_cl1391, 115.85/15.10 zip_derived_cl1530])). 115.85/15.10 115.85/15.10 % SZS output end Refutation 115.85/15.10 115.85/15.10 115.85/15.10 % Terminating... 115.86/15.19 % Runner terminated. 115.86/15.20 % Zipperpin 1.5 exiting 115.86/15.21 EOF