TSTP Solution File: ANA002-2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ANA002-2 : TPTP v8.1.2. Bugfixed v1.0.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.UHSGQGsfaj true
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 17:25:49 EDT 2023
% Result : Unsatisfiable 244.99s 35.61s
% Output : Refutation 244.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA002-2 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.UHSGQGsfaj true
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 18:35:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.20/0.65 % Total configuration time : 435
% 0.20/0.65 % Estimated wc time : 1092
% 0.20/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.20/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 244.99/35.61 % Solved by fo/fo6_bce.sh.
% 244.99/35.61 % BCE start: 18
% 244.99/35.61 % BCE eliminated: 0
% 244.99/35.61 % PE start: 18
% 244.99/35.61 logic: neq
% 244.99/35.61 % PE eliminated: 1
% 244.99/35.61 % done 8295 iterations in 34.861s
% 244.99/35.61 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 244.99/35.61 % SZS output start Refutation
% 244.99/35.61 thf(in_interval_type, type, in_interval: $i > $i > $i > $o).
% 244.99/35.61 thf(g_type, type, g: $i > $i).
% 244.99/35.61 thf(h_type, type, h: $i > $i).
% 244.99/35.61 thf(q_type, type, q: $i > $i > $i).
% 244.99/35.61 thf(k_type, type, k: $i > $i).
% 244.99/35.61 thf(f_type, type, f: $i > $i).
% 244.99/35.61 thf(lower_bound_type, type, lower_bound: $i).
% 244.99/35.61 thf(n0_type, type, n0: $i).
% 244.99/35.61 thf(l_type, type, l: $i).
% 244.99/35.61 thf(upper_bound_type, type, upper_bound: $i).
% 244.99/35.61 thf(less_than_or_equal_type, type, less_than_or_equal: $i > $i > $o).
% 244.99/35.61 thf(crossover2_and_g_function1, axiom,
% 244.99/35.61 (( less_than_or_equal @ ( g @ X ) @ upper_bound ) |
% 244.99/35.61 ( less_than_or_equal @ l @ X ))).
% 244.99/35.61 thf(zip_derived_cl11, plain,
% 244.99/35.61 (![X0 : $i]:
% 244.99/35.61 ( (less_than_or_equal @ (g @ X0) @ upper_bound)
% 244.99/35.61 | (less_than_or_equal @ l @ X0))),
% 244.99/35.61 inference('cnf', [status(esa)], [crossover2_and_g_function1])).
% 244.99/35.61 thf(crossover4_and_g_function3, axiom,
% 244.99/35.61 (( ~( less_than_or_equal @ ( g @ X ) @ X ) ) |
% 244.99/35.61 ( less_than_or_equal @ l @ X ))).
% 244.99/35.61 thf(zip_derived_cl13, plain,
% 244.99/35.61 (![X0 : $i]:
% 244.99/35.61 (~ (less_than_or_equal @ (g @ X0) @ X0)
% 244.99/35.61 | (less_than_or_equal @ l @ X0))),
% 244.99/35.61 inference('cnf', [status(esa)], [crossover4_and_g_function3])).
% 244.99/35.61 thf(zip_derived_cl58, plain,
% 244.99/35.61 (( (less_than_or_equal @ l @ upper_bound)
% 244.99/35.61 | (less_than_or_equal @ l @ upper_bound))),
% 244.99/35.61 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl13])).
% 244.99/35.61 thf(zip_derived_cl59, plain, ( (less_than_or_equal @ l @ upper_bound)),
% 244.99/35.61 inference('simplify', [status(thm)], [zip_derived_cl58])).
% 244.99/35.61 thf(transitivity_of_less, axiom,
% 244.99/35.61 (( less_than_or_equal @ X @ Z ) | ( ~( less_than_or_equal @ X @ Y ) ) |
% 244.99/35.61 ( ~( less_than_or_equal @ Y @ Z ) ))).
% 244.99/35.61 thf(zip_derived_cl3, plain,
% 244.99/35.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 244.99/35.61 ( (less_than_or_equal @ X0 @ X1)
% 244.99/35.61 | ~ (less_than_or_equal @ X0 @ X2)
% 244.99/35.61 | ~ (less_than_or_equal @ X2 @ X1))),
% 244.99/35.61 inference('cnf', [status(esa)], [transitivity_of_less])).
% 244.99/35.61 thf(zip_derived_cl60, plain,
% 244.99/35.61 (![X0 : $i]:
% 244.99/35.61 ( (less_than_or_equal @ l @ X0)
% 244.99/35.61 | ~ (less_than_or_equal @ upper_bound @ X0))),
% 244.99/35.61 inference('s_sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl3])).
% 244.99/35.61 thf(in_interval, axiom,
% 244.99/35.61 (( in_interval @ Lower @ X @ Upper ) |
% 244.99/35.61 ( ~( less_than_or_equal @ Lower @ X ) ) |
% 244.99/35.61 ( ~( less_than_or_equal @ X @ Upper ) ))).
% 244.99/35.61 thf(zip_derived_cl0, plain,
% 244.99/35.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 244.99/35.61 ( (in_interval @ X0 @ X1 @ X2)
% 244.99/35.61 | ~ (less_than_or_equal @ X0 @ X1)
% 244.99/35.61 | ~ (less_than_or_equal @ X1 @ X2))),
% 244.99/35.61 inference('cnf', [status(esa)], [in_interval])).
% 244.99/35.61 thf(continuity3, axiom,
% 244.99/35.61 (( less_than_or_equal @ n0 @ ( f @ X ) ) |
% 244.99/35.61 ( ~( less_than_or_equal @ ( k @ X ) @ X ) ) |
% 244.99/35.61 ( ~( in_interval @ lower_bound @ X @ upper_bound ) ))).
% 244.99/35.61 thf(zip_derived_cl8, plain,
% 244.99/35.61 (![X0 : $i]:
% 244.99/35.61 ( (less_than_or_equal @ n0 @ (f @ X0))
% 244.99/35.61 | ~ (less_than_or_equal @ (k @ X0) @ X0)
% 244.99/35.61 | ~ (in_interval @ lower_bound @ X0 @ upper_bound))),
% 244.99/35.61 inference('cnf', [status(esa)], [continuity3])).
% 244.99/35.61 thf(zip_derived_cl20, plain,
% 244.99/35.61 (![X0 : $i]:
% 244.99/35.61 (~ (less_than_or_equal @ X0 @ upper_bound)
% 244.99/35.61 | ~ (less_than_or_equal @ lower_bound @ X0)
% 244.99/35.61 | ~ (less_than_or_equal @ (k @ X0) @ X0)
% 244.99/35.61 | (less_than_or_equal @ n0 @ (f @ X0)))),
% 244.99/35.61 inference('dp-resolution', [status(thm)],
% 244.99/35.61 [zip_derived_cl0, zip_derived_cl8])).
% 244.99/35.61 thf(zip_derived_cl112, plain,
% 244.99/35.61 ((~ (less_than_or_equal @ upper_bound @ upper_bound)
% 244.99/35.61 | ~ (less_than_or_equal @ lower_bound @ l)
% 244.99/35.61 | ~ (less_than_or_equal @ (k @ l) @ l)
% 244.99/35.61 | (less_than_or_equal @ n0 @ (f @ l)))),
% 244.99/35.61 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl20])).
% 244.99/35.61 thf(reflexivity_of_less, axiom, (less_than_or_equal @ X @ X)).
% 244.99/35.61 thf(zip_derived_cl1, plain, (![X0 : $i]: (less_than_or_equal @ X0 @ X0)),
% 244.99/35.61 inference('cnf', [status(esa)], [reflexivity_of_less])).
% 244.99/35.61 thf(the_interval, axiom, (less_than_or_equal @ lower_bound @ upper_bound)).
% 244.99/35.61 thf(zip_derived_cl14, plain,
% 244.99/35.62 ( (less_than_or_equal @ lower_bound @ upper_bound)),
% 244.99/35.62 inference('cnf', [status(esa)], [the_interval])).
% 244.99/35.62 thf(crossover1, axiom,
% 244.99/35.62 (( less_than_or_equal @ X @ l ) |
% 244.99/35.62 ( ~( less_than_or_equal @ X @ upper_bound ) ) |
% 244.99/35.62 ( ~( less_than_or_equal @ ( f @ X ) @ n0 ) ))).
% 244.99/35.62 thf(zip_derived_cl10, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ X0 @ l)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ upper_bound)
% 244.99/35.62 | ~ (less_than_or_equal @ (f @ X0) @ n0))),
% 244.99/35.62 inference('cnf', [status(esa)], [crossover1])).
% 244.99/35.62 thf(zip_derived_cl47, plain,
% 244.99/35.62 (( (less_than_or_equal @ lower_bound @ l)
% 244.99/35.62 | ~ (less_than_or_equal @ (f @ lower_bound) @ n0))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl10])).
% 244.99/35.62 thf(lower_mapping, axiom, (less_than_or_equal @ ( f @ lower_bound ) @ n0)).
% 244.99/35.62 thf(zip_derived_cl15, plain,
% 244.99/35.62 ( (less_than_or_equal @ (f @ lower_bound) @ n0)),
% 244.99/35.62 inference('cnf', [status(esa)], [lower_mapping])).
% 244.99/35.62 thf(zip_derived_cl48, plain, ( (less_than_or_equal @ lower_bound @ l)),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl15])).
% 244.99/35.62 thf(zip_derived_cl117, plain,
% 244.99/35.62 ((~ (less_than_or_equal @ (k @ l) @ l)
% 244.99/35.62 | (less_than_or_equal @ n0 @ (f @ l)))),
% 244.99/35.62 inference('demod', [status(thm)],
% 244.99/35.62 [zip_derived_cl112, zip_derived_cl1, zip_derived_cl48])).
% 244.99/35.62 thf(zip_derived_cl0, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 244.99/35.62 ( (in_interval @ X0 @ X1 @ X2)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ X1)
% 244.99/35.62 | ~ (less_than_or_equal @ X1 @ X2))),
% 244.99/35.62 inference('cnf', [status(esa)], [in_interval])).
% 244.99/35.62 thf(prove_there_is_x_which_crosses, conjecture,
% 244.99/35.62 (in_interval @ ( f @ l ) @ n0 @ ( f @ l ))).
% 244.99/35.62 thf(zf_stmt_0, negated_conjecture,
% 244.99/35.62 (~( in_interval @ ( f @ l ) @ n0 @ ( f @ l ) )),
% 244.99/35.62 inference('cnf.neg', [status(esa)], [prove_there_is_x_which_crosses])).
% 244.99/35.62 thf(zip_derived_cl17, plain, (~ (in_interval @ (f @ l) @ n0 @ (f @ l))),
% 244.99/35.62 inference('cnf', [status(esa)], [zf_stmt_0])).
% 244.99/35.62 thf(zip_derived_cl22, plain,
% 244.99/35.62 ((~ (less_than_or_equal @ n0 @ (f @ l))
% 244.99/35.62 | ~ (less_than_or_equal @ (f @ l) @ n0))),
% 244.99/35.62 inference('dp-resolution', [status(thm)],
% 244.99/35.62 [zip_derived_cl0, zip_derived_cl17])).
% 244.99/35.62 thf(zip_derived_cl11, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ (g @ X0) @ upper_bound)
% 244.99/35.62 | (less_than_or_equal @ l @ X0))),
% 244.99/35.62 inference('cnf', [status(esa)], [crossover2_and_g_function1])).
% 244.99/35.62 thf(zip_derived_cl10, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ X0 @ l)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ upper_bound)
% 244.99/35.62 | ~ (less_than_or_equal @ (f @ X0) @ n0))),
% 244.99/35.62 inference('cnf', [status(esa)], [crossover1])).
% 244.99/35.62 thf(zip_derived_cl57, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ l @ X0)
% 244.99/35.62 | (less_than_or_equal @ (g @ X0) @ l)
% 244.99/35.62 | ~ (less_than_or_equal @ (f @ (g @ X0)) @ n0))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl10])).
% 244.99/35.62 thf(crossover3_and_g_function2, axiom,
% 244.99/35.62 (( less_than_or_equal @ ( f @ ( g @ X ) ) @ n0 ) |
% 244.99/35.62 ( less_than_or_equal @ l @ X ))).
% 244.99/35.62 thf(zip_derived_cl12, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ (f @ (g @ X0)) @ n0)
% 244.99/35.62 | (less_than_or_equal @ l @ X0))),
% 244.99/35.62 inference('cnf', [status(esa)], [crossover3_and_g_function2])).
% 244.99/35.62 thf(zip_derived_cl393, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ (g @ X0) @ l) | (less_than_or_equal @ l @ X0))),
% 244.99/35.62 inference('clc', [status(thm)], [zip_derived_cl57, zip_derived_cl12])).
% 244.99/35.62 thf(zip_derived_cl60, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ l @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ upper_bound @ X0))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl3])).
% 244.99/35.62 thf(zip_derived_cl0, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 244.99/35.62 ( (in_interval @ X0 @ X1 @ X2)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ X1)
% 244.99/35.62 | ~ (less_than_or_equal @ X1 @ X2))),
% 244.99/35.62 inference('cnf', [status(esa)], [in_interval])).
% 244.99/35.62 thf(continuity2, axiom,
% 244.99/35.62 (( less_than_or_equal @ ( f @ X ) @ n0 ) |
% 244.99/35.62 ( ~( less_than_or_equal @ Y @ X ) ) |
% 244.99/35.62 ( ~( less_than_or_equal @ ( f @ Y ) @ n0 ) ) |
% 244.99/35.62 ( less_than_or_equal @ Y @ ( h @ X ) ) |
% 244.99/35.62 ( ~( in_interval @ lower_bound @ X @ upper_bound ) ))).
% 244.99/35.62 thf(zip_derived_cl7, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ (f @ X0) @ n0)
% 244.99/35.62 | ~ (less_than_or_equal @ X1 @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ (f @ X1) @ n0)
% 244.99/35.62 | (less_than_or_equal @ X1 @ (h @ X0))
% 244.99/35.62 | ~ (in_interval @ lower_bound @ X0 @ upper_bound))),
% 244.99/35.62 inference('cnf', [status(esa)], [continuity2])).
% 244.99/35.62 thf(zip_derived_cl19, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ X0 @ upper_bound)
% 244.99/35.62 | ~ (less_than_or_equal @ lower_bound @ X0)
% 244.99/35.62 | (less_than_or_equal @ X1 @ (h @ X0))
% 244.99/35.62 | ~ (less_than_or_equal @ (f @ X1) @ n0)
% 244.99/35.62 | ~ (less_than_or_equal @ X1 @ X0)
% 244.99/35.62 | (less_than_or_equal @ (f @ X0) @ n0))),
% 244.99/35.62 inference('dp-resolution', [status(thm)],
% 244.99/35.62 [zip_derived_cl0, zip_derived_cl7])).
% 244.99/35.62 thf(zip_derived_cl13, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ (g @ X0) @ X0)
% 244.99/35.62 | (less_than_or_equal @ l @ X0))),
% 244.99/35.62 inference('cnf', [status(esa)], [crossover4_and_g_function3])).
% 244.99/35.62 thf(zip_derived_cl101, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ (f @ X0) @ n0)
% 244.99/35.62 | ~ (less_than_or_equal @ (g @ (h @ X0)) @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ (f @ (g @ (h @ X0))) @ n0)
% 244.99/35.62 | ~ (less_than_or_equal @ lower_bound @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ upper_bound)
% 244.99/35.62 | (less_than_or_equal @ l @ (h @ X0)))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl13])).
% 244.99/35.62 thf(zip_derived_cl12, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ (f @ (g @ X0)) @ n0)
% 244.99/35.62 | (less_than_or_equal @ l @ X0))),
% 244.99/35.62 inference('cnf', [status(esa)], [crossover3_and_g_function2])).
% 244.99/35.62 thf(zip_derived_cl855, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ l @ (h @ X0))
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ upper_bound)
% 244.99/35.62 | ~ (less_than_or_equal @ lower_bound @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ (g @ (h @ X0)) @ X0)
% 244.99/35.62 | (less_than_or_equal @ (f @ X0) @ n0))),
% 244.99/35.62 inference('clc', [status(thm)], [zip_derived_cl101, zip_derived_cl12])).
% 244.99/35.62 thf(zip_derived_cl874, plain,
% 244.99/35.62 ((~ (less_than_or_equal @ upper_bound @ upper_bound)
% 244.99/35.62 | (less_than_or_equal @ l @ (h @ l))
% 244.99/35.62 | ~ (less_than_or_equal @ lower_bound @ l)
% 244.99/35.62 | ~ (less_than_or_equal @ (g @ (h @ l)) @ l)
% 244.99/35.62 | (less_than_or_equal @ (f @ l) @ n0))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl855])).
% 244.99/35.62 thf(zip_derived_cl1, plain, (![X0 : $i]: (less_than_or_equal @ X0 @ X0)),
% 244.99/35.62 inference('cnf', [status(esa)], [reflexivity_of_less])).
% 244.99/35.62 thf(zip_derived_cl48, plain, ( (less_than_or_equal @ lower_bound @ l)),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl15])).
% 244.99/35.62 thf(zip_derived_cl886, plain,
% 244.99/35.62 (( (less_than_or_equal @ l @ (h @ l))
% 244.99/35.62 | ~ (less_than_or_equal @ (g @ (h @ l)) @ l)
% 244.99/35.62 | (less_than_or_equal @ (f @ l) @ n0))),
% 244.99/35.62 inference('demod', [status(thm)],
% 244.99/35.62 [zip_derived_cl874, zip_derived_cl1, zip_derived_cl48])).
% 244.99/35.62 thf(zip_derived_cl60, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ l @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ upper_bound @ X0))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl3])).
% 244.99/35.62 thf(zip_derived_cl0, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 244.99/35.62 ( (in_interval @ X0 @ X1 @ X2)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ X1)
% 244.99/35.62 | ~ (less_than_or_equal @ X1 @ X2))),
% 244.99/35.62 inference('cnf', [status(esa)], [in_interval])).
% 244.99/35.62 thf(continuity1, axiom,
% 244.99/35.62 (( less_than_or_equal @ ( f @ X ) @ n0 ) |
% 244.99/35.62 ( ~( less_than_or_equal @ X @ ( h @ X ) ) ) |
% 244.99/35.62 ( ~( in_interval @ lower_bound @ X @ upper_bound ) ))).
% 244.99/35.62 thf(zip_derived_cl6, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ (f @ X0) @ n0)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ (h @ X0))
% 244.99/35.62 | ~ (in_interval @ lower_bound @ X0 @ upper_bound))),
% 244.99/35.62 inference('cnf', [status(esa)], [continuity1])).
% 244.99/35.62 thf(zip_derived_cl18, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ X0 @ upper_bound)
% 244.99/35.62 | ~ (less_than_or_equal @ lower_bound @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ (h @ X0))
% 244.99/35.62 | (less_than_or_equal @ (f @ X0) @ n0))),
% 244.99/35.62 inference('dp-resolution', [status(thm)],
% 244.99/35.62 [zip_derived_cl0, zip_derived_cl6])).
% 244.99/35.62 thf(zip_derived_cl83, plain,
% 244.99/35.62 ((~ (less_than_or_equal @ upper_bound @ upper_bound)
% 244.99/35.62 | ~ (less_than_or_equal @ lower_bound @ l)
% 244.99/35.62 | ~ (less_than_or_equal @ l @ (h @ l))
% 244.99/35.62 | (less_than_or_equal @ (f @ l) @ n0))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl18])).
% 244.99/35.62 thf(zip_derived_cl1, plain, (![X0 : $i]: (less_than_or_equal @ X0 @ X0)),
% 244.99/35.62 inference('cnf', [status(esa)], [reflexivity_of_less])).
% 244.99/35.62 thf(zip_derived_cl48, plain, ( (less_than_or_equal @ lower_bound @ l)),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl15])).
% 244.99/35.62 thf(zip_derived_cl88, plain,
% 244.99/35.62 ((~ (less_than_or_equal @ l @ (h @ l))
% 244.99/35.62 | (less_than_or_equal @ (f @ l) @ n0))),
% 244.99/35.62 inference('demod', [status(thm)],
% 244.99/35.62 [zip_derived_cl83, zip_derived_cl1, zip_derived_cl48])).
% 244.99/35.62 thf(zip_derived_cl890, plain,
% 244.99/35.62 (( (less_than_or_equal @ (f @ l) @ n0)
% 244.99/35.62 | ~ (less_than_or_equal @ (g @ (h @ l)) @ l))),
% 244.99/35.62 inference('clc', [status(thm)], [zip_derived_cl886, zip_derived_cl88])).
% 244.99/35.62 thf(zip_derived_cl895, plain,
% 244.99/35.62 (( (less_than_or_equal @ l @ (h @ l))
% 244.99/35.62 | (less_than_or_equal @ (f @ l) @ n0))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl393, zip_derived_cl890])).
% 244.99/35.62 thf(zip_derived_cl88, plain,
% 244.99/35.62 ((~ (less_than_or_equal @ l @ (h @ l))
% 244.99/35.62 | (less_than_or_equal @ (f @ l) @ n0))),
% 244.99/35.62 inference('demod', [status(thm)],
% 244.99/35.62 [zip_derived_cl83, zip_derived_cl1, zip_derived_cl48])).
% 244.99/35.62 thf(zip_derived_cl896, plain, ( (less_than_or_equal @ (f @ l) @ n0)),
% 244.99/35.62 inference('clc', [status(thm)], [zip_derived_cl895, zip_derived_cl88])).
% 244.99/35.62 thf(zip_derived_cl897, plain, (~ (less_than_or_equal @ n0 @ (f @ l))),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl896])).
% 244.99/35.62 thf(zip_derived_cl905, plain, (~ (less_than_or_equal @ (k @ l) @ l)),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl897])).
% 244.99/35.62 thf(totality_of_less, axiom,
% 244.99/35.62 (( less_than_or_equal @ X @ Y ) | ( less_than_or_equal @ Y @ X ))).
% 244.99/35.62 thf(zip_derived_cl2, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ X0 @ X1) | (less_than_or_equal @ X1 @ X0))),
% 244.99/35.62 inference('cnf', [status(esa)], [totality_of_less])).
% 244.99/35.62 thf(zip_derived_cl2, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ X0 @ X1) | (less_than_or_equal @ X1 @ X0))),
% 244.99/35.62 inference('cnf', [status(esa)], [totality_of_less])).
% 244.99/35.62 thf(zip_derived_cl10, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ X0 @ l)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ upper_bound)
% 244.99/35.62 | ~ (less_than_or_equal @ (f @ X0) @ n0))),
% 244.99/35.62 inference('cnf', [status(esa)], [crossover1])).
% 244.99/35.62 thf(zip_derived_cl43, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ upper_bound @ X0)
% 244.99/35.62 | (less_than_or_equal @ X0 @ l)
% 244.99/35.62 | ~ (less_than_or_equal @ (f @ X0) @ n0))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl10])).
% 244.99/35.62 thf(zip_derived_cl264, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ n0 @ (f @ X0))
% 244.99/35.62 | (less_than_or_equal @ upper_bound @ X0)
% 244.99/35.62 | (less_than_or_equal @ X0 @ l))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl43])).
% 244.99/35.62 thf(zip_derived_cl2, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ X0 @ X1) | (less_than_or_equal @ X1 @ X0))),
% 244.99/35.62 inference('cnf', [status(esa)], [totality_of_less])).
% 244.99/35.62 thf(interpolation2, axiom,
% 244.99/35.62 (( ~( less_than_or_equal @ ( q @ X @ Y ) @ X ) ) |
% 244.99/35.62 ( less_than_or_equal @ Y @ X ))).
% 244.99/35.62 thf(zip_derived_cl5, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ (q @ X0 @ X1) @ X0)
% 244.99/35.62 | (less_than_or_equal @ X1 @ X0))),
% 244.99/35.62 inference('cnf', [status(esa)], [interpolation2])).
% 244.99/35.62 thf(zip_derived_cl49, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ X0 @ (q @ X0 @ X1))
% 244.99/35.62 | (less_than_or_equal @ X1 @ X0))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl5])).
% 244.99/35.62 thf(zip_derived_cl48, plain, ( (less_than_or_equal @ lower_bound @ l)),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl15])).
% 244.99/35.62 thf(zip_derived_cl0, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 244.99/35.62 ( (in_interval @ X0 @ X1 @ X2)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ X1)
% 244.99/35.62 | ~ (less_than_or_equal @ X1 @ X2))),
% 244.99/35.62 inference('cnf', [status(esa)], [in_interval])).
% 244.99/35.62 thf(continuity4, axiom,
% 244.99/35.62 (( less_than_or_equal @ n0 @ ( f @ X ) ) |
% 244.99/35.62 ( ~( less_than_or_equal @ X @ Y ) ) |
% 244.99/35.62 ( ~( less_than_or_equal @ n0 @ ( f @ Y ) ) ) |
% 244.99/35.62 ( less_than_or_equal @ ( k @ X ) @ Y ) |
% 244.99/35.62 ( ~( in_interval @ lower_bound @ X @ upper_bound ) ))).
% 244.99/35.62 thf(zip_derived_cl9, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ n0 @ (f @ X0))
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ X1)
% 244.99/35.62 | ~ (less_than_or_equal @ n0 @ (f @ X1))
% 244.99/35.62 | (less_than_or_equal @ (k @ X0) @ X1)
% 244.99/35.62 | ~ (in_interval @ lower_bound @ X0 @ upper_bound))),
% 244.99/35.62 inference('cnf', [status(esa)], [continuity4])).
% 244.99/35.62 thf(zip_derived_cl21, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ X1 @ upper_bound)
% 244.99/35.62 | ~ (less_than_or_equal @ lower_bound @ X1)
% 244.99/35.62 | (less_than_or_equal @ (k @ X1) @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ n0 @ (f @ X0))
% 244.99/35.62 | ~ (less_than_or_equal @ X1 @ X0)
% 244.99/35.62 | (less_than_or_equal @ n0 @ (f @ X1)))),
% 244.99/35.62 inference('dp-resolution', [status(thm)],
% 244.99/35.62 [zip_derived_cl0, zip_derived_cl9])).
% 244.99/35.62 thf(interpolation1, axiom,
% 244.99/35.62 (( ~( less_than_or_equal @ X @ ( q @ Y @ X ) ) ) |
% 244.99/35.62 ( less_than_or_equal @ X @ Y ))).
% 244.99/35.62 thf(zip_derived_cl4, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ X0 @ (q @ X1 @ X0))
% 244.99/35.62 | (less_than_or_equal @ X0 @ X1))),
% 244.99/35.62 inference('cnf', [status(esa)], [interpolation1])).
% 244.99/35.62 thf(zip_derived_cl124, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ n0 @ (f @ X0))
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ (q @ X1 @ (k @ X0)))
% 244.99/35.62 | ~ (less_than_or_equal @ n0 @ (f @ (q @ X1 @ (k @ X0))))
% 244.99/35.62 | ~ (less_than_or_equal @ lower_bound @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ upper_bound)
% 244.99/35.62 | (less_than_or_equal @ (k @ X0) @ X1))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl4])).
% 244.99/35.62 thf(zip_derived_cl151380, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ n0 @ (f @ l))
% 244.99/35.62 | ~ (less_than_or_equal @ l @ (q @ X0 @ (k @ l)))
% 244.99/35.62 | ~ (less_than_or_equal @ n0 @ (f @ (q @ X0 @ (k @ l))))
% 244.99/35.62 | ~ (less_than_or_equal @ l @ upper_bound)
% 244.99/35.62 | (less_than_or_equal @ (k @ l) @ X0))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl124])).
% 244.99/35.62 thf(zip_derived_cl897, plain, (~ (less_than_or_equal @ n0 @ (f @ l))),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl896])).
% 244.99/35.62 thf(zip_derived_cl59, plain, ( (less_than_or_equal @ l @ upper_bound)),
% 244.99/35.62 inference('simplify', [status(thm)], [zip_derived_cl58])).
% 244.99/35.62 thf(zip_derived_cl151447, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ l @ (q @ X0 @ (k @ l)))
% 244.99/35.62 | ~ (less_than_or_equal @ n0 @ (f @ (q @ X0 @ (k @ l))))
% 244.99/35.62 | (less_than_or_equal @ (k @ l) @ X0))),
% 244.99/35.62 inference('demod', [status(thm)],
% 244.99/35.62 [zip_derived_cl151380, zip_derived_cl897, zip_derived_cl59])).
% 244.99/35.62 thf(zip_derived_cl248796, plain,
% 244.99/35.62 (( (less_than_or_equal @ (k @ l) @ l)
% 244.99/35.62 | ~ (less_than_or_equal @ n0 @ (f @ (q @ l @ (k @ l))))
% 244.99/35.62 | (less_than_or_equal @ (k @ l) @ l))),
% 244.99/35.62 inference('s_sup-', [status(thm)],
% 244.99/35.62 [zip_derived_cl49, zip_derived_cl151447])).
% 244.99/35.62 thf(zip_derived_cl905, plain, (~ (less_than_or_equal @ (k @ l) @ l)),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl897])).
% 244.99/35.62 thf(zip_derived_cl905, plain, (~ (less_than_or_equal @ (k @ l) @ l)),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl897])).
% 244.99/35.62 thf(zip_derived_cl248865, plain,
% 244.99/35.62 (~ (less_than_or_equal @ n0 @ (f @ (q @ l @ (k @ l))))),
% 244.99/35.62 inference('demod', [status(thm)],
% 244.99/35.62 [zip_derived_cl248796, zip_derived_cl905, zip_derived_cl905])).
% 244.99/35.62 thf(zip_derived_cl248967, plain,
% 244.99/35.62 (( (less_than_or_equal @ (q @ l @ (k @ l)) @ l)
% 244.99/35.62 | (less_than_or_equal @ upper_bound @ (q @ l @ (k @ l))))),
% 244.99/35.62 inference('s_sup-', [status(thm)],
% 244.99/35.62 [zip_derived_cl264, zip_derived_cl248865])).
% 244.99/35.62 thf(zip_derived_cl5, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ (q @ X0 @ X1) @ X0)
% 244.99/35.62 | (less_than_or_equal @ X1 @ X0))),
% 244.99/35.62 inference('cnf', [status(esa)], [interpolation2])).
% 244.99/35.62 thf(zip_derived_cl249178, plain,
% 244.99/35.62 (( (less_than_or_equal @ upper_bound @ (q @ l @ (k @ l)))
% 244.99/35.62 | (less_than_or_equal @ (k @ l) @ l))),
% 244.99/35.62 inference('s_sup-', [status(thm)],
% 244.99/35.62 [zip_derived_cl248967, zip_derived_cl5])).
% 244.99/35.62 thf(zip_derived_cl905, plain, (~ (less_than_or_equal @ (k @ l) @ l)),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl897])).
% 244.99/35.62 thf(zip_derived_cl249215, plain,
% 244.99/35.62 ( (less_than_or_equal @ upper_bound @ (q @ l @ (k @ l)))),
% 244.99/35.62 inference('demod', [status(thm)],
% 244.99/35.62 [zip_derived_cl249178, zip_derived_cl905])).
% 244.99/35.62 thf(zip_derived_cl59, plain, ( (less_than_or_equal @ l @ upper_bound)),
% 244.99/35.62 inference('simplify', [status(thm)], [zip_derived_cl58])).
% 244.99/35.62 thf(zip_derived_cl48, plain, ( (less_than_or_equal @ lower_bound @ l)),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl15])).
% 244.99/35.62 thf(zip_derived_cl21, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ X1 @ upper_bound)
% 244.99/35.62 | ~ (less_than_or_equal @ lower_bound @ X1)
% 244.99/35.62 | (less_than_or_equal @ (k @ X1) @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ n0 @ (f @ X0))
% 244.99/35.62 | ~ (less_than_or_equal @ X1 @ X0)
% 244.99/35.62 | (less_than_or_equal @ n0 @ (f @ X1)))),
% 244.99/35.62 inference('dp-resolution', [status(thm)],
% 244.99/35.62 [zip_derived_cl0, zip_derived_cl9])).
% 244.99/35.62 thf(zip_derived_cl3, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ X0 @ X1)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ X2)
% 244.99/35.62 | ~ (less_than_or_equal @ X2 @ X1))),
% 244.99/35.62 inference('cnf', [status(esa)], [transitivity_of_less])).
% 244.99/35.62 thf(zip_derived_cl123, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i, X2 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ n0 @ (f @ X1))
% 244.99/35.62 | ~ (less_than_or_equal @ X1 @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ n0 @ (f @ X0))
% 244.99/35.62 | ~ (less_than_or_equal @ lower_bound @ X1)
% 244.99/35.62 | ~ (less_than_or_equal @ X1 @ upper_bound)
% 244.99/35.62 | (less_than_or_equal @ (k @ X1) @ X2)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ X2))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl3])).
% 244.99/35.62 thf(zip_derived_cl8158, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ n0 @ (f @ l))
% 244.99/35.62 | ~ (less_than_or_equal @ l @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ n0 @ (f @ X0))
% 244.99/35.62 | ~ (less_than_or_equal @ l @ upper_bound)
% 244.99/35.62 | (less_than_or_equal @ (k @ l) @ X1)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ X1))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl123])).
% 244.99/35.62 thf(zip_derived_cl897, plain, (~ (less_than_or_equal @ n0 @ (f @ l))),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl896])).
% 244.99/35.62 thf(zip_derived_cl59, plain, ( (less_than_or_equal @ l @ upper_bound)),
% 244.99/35.62 inference('simplify', [status(thm)], [zip_derived_cl58])).
% 244.99/35.62 thf(zip_derived_cl8168, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ l @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ n0 @ (f @ X0))
% 244.99/35.62 | (less_than_or_equal @ (k @ l) @ X1)
% 244.99/35.62 | ~ (less_than_or_equal @ X0 @ X1))),
% 244.99/35.62 inference('demod', [status(thm)],
% 244.99/35.62 [zip_derived_cl8158, zip_derived_cl897, zip_derived_cl59])).
% 244.99/35.62 thf(zip_derived_cl8222, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ n0 @ (f @ upper_bound))
% 244.99/35.62 | (less_than_or_equal @ (k @ l) @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ upper_bound @ X0))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl8168])).
% 244.99/35.62 thf(upper_mapping, axiom, (less_than_or_equal @ n0 @ ( f @ upper_bound ))).
% 244.99/35.62 thf(zip_derived_cl16, plain,
% 244.99/35.62 ( (less_than_or_equal @ n0 @ (f @ upper_bound))),
% 244.99/35.62 inference('cnf', [status(esa)], [upper_mapping])).
% 244.99/35.62 thf(zip_derived_cl8234, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 ( (less_than_or_equal @ (k @ l) @ X0)
% 244.99/35.62 | ~ (less_than_or_equal @ upper_bound @ X0))),
% 244.99/35.62 inference('demod', [status(thm)], [zip_derived_cl8222, zip_derived_cl16])).
% 244.99/35.62 thf(zip_derived_cl4, plain,
% 244.99/35.62 (![X0 : $i, X1 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ X0 @ (q @ X1 @ X0))
% 244.99/35.62 | (less_than_or_equal @ X0 @ X1))),
% 244.99/35.62 inference('cnf', [status(esa)], [interpolation1])).
% 244.99/35.62 thf(zip_derived_cl8305, plain,
% 244.99/35.62 (![X0 : $i]:
% 244.99/35.62 (~ (less_than_or_equal @ upper_bound @ (q @ X0 @ (k @ l)))
% 244.99/35.62 | (less_than_or_equal @ (k @ l) @ X0))),
% 244.99/35.62 inference('s_sup-', [status(thm)], [zip_derived_cl8234, zip_derived_cl4])).
% 244.99/35.62 thf(zip_derived_cl249336, plain, ( (less_than_or_equal @ (k @ l) @ l)),
% 244.99/35.62 inference('s_sup-', [status(thm)],
% 244.99/35.62 [zip_derived_cl249215, zip_derived_cl8305])).
% 244.99/35.62 thf(zip_derived_cl249349, plain, ($false),
% 244.99/35.62 inference('demod', [status(thm)],
% 244.99/35.62 [zip_derived_cl905, zip_derived_cl249336])).
% 244.99/35.62
% 244.99/35.62 % SZS output end Refutation
% 244.99/35.62
% 244.99/35.62
% 244.99/35.62 % Terminating...
% 245.68/35.74 % Runner terminated.
% 245.68/35.75 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------