%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP039-2 : TPTP v9.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.A4tpPt83xs true
% Computer : n023.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 : Thu Oct 2 04:35:30 PM UTC 2025
% Result : Unsatisfiable 1.18s 0.90s
% Output : Refutation 1.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : GRP039-2 : TPTP v9.2.0. Released v1.0.0.
% 0.09/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.A4tpPt83xs true
% 0.10/0.31 % Computer : n023.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Oct 1 14:07:23 EDT 2025
% 0.16/0.32 % CPUTime :
% 0.16/0.32 % Running portfolio for 300 s
% 0.16/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.32 % Number of cores: 8
% 0.16/0.32 % Python version: Python 3.6.8
% 0.16/0.32 % Running in FO mode
% 0.17/0.56 % Total configuration time : 435
% 0.17/0.56 % Estimated wc time : 1092
% 0.17/0.56 % Estimated cpu time (7 cpus) : 156.0
% 0.82/0.66 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.82/0.68 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.82/0.68 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.82/0.68 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.82/0.68 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.82/0.68 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.82/0.68 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.18/0.90 % Solved by fo/fo5.sh.
% 1.18/0.90 % done 216 iterations in 0.195s
% 1.18/0.90 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.18/0.90 % SZS output start Refutation
% 1.18/0.90 thf(element_in_O2_type, type, element_in_O2: $i > $i > $i).
% 1.18/0.90 thf(b_type, type, b: $i).
% 1.18/0.90 thf(subgroup_member_type, type, subgroup_member: $i > $o).
% 1.18/0.90 thf(c_type, type, c: $i).
% 1.18/0.90 thf(d_type, type, d: $i).
% 1.18/0.90 thf(identity_type, type, identity: $i).
% 1.18/0.90 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.18/0.90 thf(a_type, type, a: $i).
% 1.18/0.90 thf(inverse_type, type, inverse: $i > $i).
% 1.18/0.90 thf(closure_of_inverse, axiom,
% 1.18/0.90 (( ~( subgroup_member @ X ) ) | ( subgroup_member @ ( inverse @ X ) ))).
% 1.18/0.90 thf(zip_derived_cl3, plain,
% 1.18/0.90 (![X0 : $i]:
% 1.18/0.90 (~ (subgroup_member @ X0) | (subgroup_member @ (inverse @ X0)))),
% 1.18/0.90 inference('cnf', [status(esa)], [closure_of_inverse])).
% 1.18/0.90 thf(b_times_a_inverse_is_c, conjecture,
% 1.18/0.90 (( multiply @ b @ ( inverse @ a ) ) != ( c ))).
% 1.18/0.90 thf(zf_stmt_0, negated_conjecture,
% 1.18/0.90 (( multiply @ b @ ( inverse @ a ) ) = ( c )),
% 1.18/0.90 inference('cnf.neg', [status(esa)], [b_times_a_inverse_is_c])).
% 1.18/0.90 thf(zip_derived_cl10, plain, (((multiply @ b @ (inverse @ a)) = (c))),
% 1.18/0.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.18/0.90 thf(closure_of_multiply, axiom,
% 1.18/0.90 (( ~( subgroup_member @ X ) ) | ( ~( subgroup_member @ Y ) ) |
% 1.18/0.90 ( ( multiply @ X @ Y ) != ( Z ) ) | ( subgroup_member @ Z ))).
% 1.18/0.90 thf(zip_derived_cl4, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.18/0.90 (~ (subgroup_member @ X0)
% 1.18/0.90 | ~ (subgroup_member @ X1)
% 1.18/0.90 | ((multiply @ X0 @ X1) != (X2))
% 1.18/0.90 | (subgroup_member @ X2))),
% 1.18/0.90 inference('cnf', [status(esa)], [closure_of_multiply])).
% 1.18/0.90 thf(zip_derived_cl88, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 ( (subgroup_member @ (multiply @ X1 @ X0))
% 1.18/0.90 | ~ (subgroup_member @ X0)
% 1.18/0.90 | ~ (subgroup_member @ X1))),
% 1.18/0.90 inference('eq_res', [status(thm)], [zip_derived_cl4])).
% 1.18/0.90 thf(zip_derived_cl148, plain,
% 1.18/0.90 (( (subgroup_member @ c)
% 1.18/0.90 | ~ (subgroup_member @ b)
% 1.18/0.90 | ~ (subgroup_member @ (inverse @ a)))),
% 1.18/0.90 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl88])).
% 1.18/0.90 thf(b_in_O2, conjecture, (~( subgroup_member @ b ))).
% 1.18/0.90 thf(zf_stmt_1, negated_conjecture, (subgroup_member @ b),
% 1.18/0.90 inference('cnf.neg', [status(esa)], [b_in_O2])).
% 1.18/0.90 thf(zip_derived_cl9, plain, ( (subgroup_member @ b)),
% 1.18/0.90 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.18/0.90 thf(zip_derived_cl156, plain,
% 1.18/0.90 (( (subgroup_member @ c) | ~ (subgroup_member @ (inverse @ a)))),
% 1.18/0.90 inference('demod', [status(thm)], [zip_derived_cl148, zip_derived_cl9])).
% 1.18/0.90 thf(zip_derived_cl162, plain,
% 1.18/0.90 ((~ (subgroup_member @ a) | (subgroup_member @ c))),
% 1.18/0.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl156])).
% 1.18/0.90 thf(a_times_c_is_d, conjecture, (( multiply @ a @ c ) != ( d ))).
% 1.18/0.90 thf(zf_stmt_2, negated_conjecture, (( multiply @ a @ c ) = ( d )),
% 1.18/0.90 inference('cnf.neg', [status(esa)], [a_times_c_is_d])).
% 1.18/0.90 thf(zip_derived_cl11, plain, (((multiply @ a @ c) = (d))),
% 1.18/0.90 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.18/0.90 thf(zip_derived_cl88, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 ( (subgroup_member @ (multiply @ X1 @ X0))
% 1.18/0.90 | ~ (subgroup_member @ X0)
% 1.18/0.90 | ~ (subgroup_member @ X1))),
% 1.18/0.90 inference('eq_res', [status(thm)], [zip_derived_cl4])).
% 1.18/0.90 thf(zip_derived_cl149, plain,
% 1.18/0.90 (( (subgroup_member @ d)
% 1.18/0.90 | ~ (subgroup_member @ a)
% 1.18/0.90 | ~ (subgroup_member @ c))),
% 1.18/0.90 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl88])).
% 1.18/0.90 thf(prove_d_in_O2, conjecture, (subgroup_member @ d)).
% 1.18/0.90 thf(zf_stmt_3, negated_conjecture, (~( subgroup_member @ d )),
% 1.18/0.90 inference('cnf.neg', [status(esa)], [prove_d_in_O2])).
% 1.18/0.90 thf(zip_derived_cl12, plain, (~ (subgroup_member @ d)),
% 1.18/0.90 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.18/0.90 thf(zip_derived_cl157, plain,
% 1.18/0.90 ((~ (subgroup_member @ a) | ~ (subgroup_member @ c))),
% 1.18/0.90 inference('demod', [status(thm)], [zip_derived_cl149, zip_derived_cl12])).
% 1.18/0.90 thf(zip_derived_cl163, plain, (~ (subgroup_member @ a)),
% 1.18/0.90 inference('clc', [status(thm)], [zip_derived_cl162, zip_derived_cl157])).
% 1.18/0.90 thf(property_of_O2, axiom,
% 1.18/0.90 (( subgroup_member @ X ) | ( subgroup_member @ Y ) |
% 1.18/0.90 ( ( multiply @ X @ ( element_in_O2 @ X @ Y ) ) = ( Y ) ))).
% 1.18/0.90 thf(zip_derived_cl8, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 ( (subgroup_member @ X0)
% 1.18/0.90 | (subgroup_member @ X1)
% 1.18/0.90 | ((multiply @ X0 @ (element_in_O2 @ X0 @ X1)) = (X1)))),
% 1.18/0.90 inference('cnf', [status(esa)], [property_of_O2])).
% 1.18/0.90 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 1.18/0.90 thf(zip_derived_cl1, plain,
% 1.18/0.90 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.18/0.90 inference('cnf', [status(esa)], [left_inverse])).
% 1.18/0.90 thf(associativity, axiom,
% 1.18/0.90 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 1.18/0.90 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 1.18/0.90 thf(zip_derived_cl2, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.18/0.90 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.18/0.90 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.18/0.90 inference('cnf', [status(esa)], [associativity])).
% 1.18/0.90 thf(zip_derived_cl21, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 ((multiply @ identity @ X0)
% 1.18/0.90 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.18/0.90 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 1.18/0.90 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 1.18/0.90 thf(zip_derived_cl0, plain,
% 1.18/0.90 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.18/0.90 inference('cnf', [status(esa)], [left_identity])).
% 1.18/0.90 thf(zip_derived_cl27, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.18/0.90 inference('demod', [status(thm)], [zip_derived_cl21, zip_derived_cl0])).
% 1.18/0.90 thf(zip_derived_cl113, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 (((element_in_O2 @ X1 @ X0) = (multiply @ (inverse @ X1) @ X0))
% 1.18/0.90 | (subgroup_member @ X0)
% 1.18/0.90 | (subgroup_member @ X1))),
% 1.18/0.90 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl27])).
% 1.18/0.90 thf(zip_derived_cl11, plain, (((multiply @ a @ c) = (d))),
% 1.18/0.90 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.18/0.90 thf(zip_derived_cl27, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.18/0.90 inference('demod', [status(thm)], [zip_derived_cl21, zip_derived_cl0])).
% 1.18/0.90 thf(zip_derived_cl43, plain, (((c) = (multiply @ (inverse @ a) @ d))),
% 1.18/0.90 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl27])).
% 1.18/0.90 thf(zip_derived_cl1501, plain,
% 1.18/0.90 ((((c) = (element_in_O2 @ a @ d))
% 1.18/0.90 | (subgroup_member @ a)
% 1.18/0.90 | (subgroup_member @ d))),
% 1.18/0.90 inference('sup+', [status(thm)], [zip_derived_cl113, zip_derived_cl43])).
% 1.18/0.90 thf(zip_derived_cl163, plain, (~ (subgroup_member @ a)),
% 1.18/0.90 inference('clc', [status(thm)], [zip_derived_cl162, zip_derived_cl157])).
% 1.18/0.90 thf(zip_derived_cl12, plain, (~ (subgroup_member @ d)),
% 1.18/0.90 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.18/0.90 thf(zip_derived_cl1538, plain, (((c) = (element_in_O2 @ a @ d))),
% 1.18/0.90 inference('demod', [status(thm)],
% 1.18/0.90 [zip_derived_cl1501, zip_derived_cl163, zip_derived_cl12])).
% 1.18/0.90 thf(an_element_in_O2, axiom,
% 1.18/0.90 (( subgroup_member @ X ) | ( subgroup_member @ Y ) |
% 1.18/0.90 ( subgroup_member @ ( element_in_O2 @ X @ Y ) ))).
% 1.18/0.90 thf(zip_derived_cl7, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 ( (subgroup_member @ X0)
% 1.18/0.90 | (subgroup_member @ X1)
% 1.18/0.90 | (subgroup_member @ (element_in_O2 @ X0 @ X1)))),
% 1.18/0.90 inference('cnf', [status(esa)], [an_element_in_O2])).
% 1.18/0.90 thf(zip_derived_cl1539, plain,
% 1.18/0.90 (( (subgroup_member @ c)
% 1.18/0.90 | (subgroup_member @ d)
% 1.18/0.90 | (subgroup_member @ a))),
% 1.18/0.90 inference('sup+', [status(thm)], [zip_derived_cl1538, zip_derived_cl7])).
% 1.18/0.90 thf(right_inverse, axiom,
% 1.18/0.90 (( multiply @ X @ ( inverse @ X ) ) = ( identity ))).
% 1.18/0.90 thf(zip_derived_cl6, plain,
% 1.18/0.90 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.18/0.90 inference('cnf', [status(esa)], [right_inverse])).
% 1.18/0.90 thf(zip_derived_cl10, plain, (((multiply @ b @ (inverse @ a)) = (c))),
% 1.18/0.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.18/0.90 thf(zip_derived_cl2, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.18/0.90 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.18/0.90 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.18/0.90 inference('cnf', [status(esa)], [associativity])).
% 1.18/0.90 thf(zip_derived_cl22, plain,
% 1.18/0.90 (![X0 : $i]:
% 1.18/0.90 ((multiply @ c @ X0)
% 1.18/0.90 = (multiply @ b @ (multiply @ (inverse @ a) @ X0)))),
% 1.18/0.90 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl2])).
% 1.18/0.90 thf(zip_derived_cl229, plain,
% 1.18/0.90 (((multiply @ c @ (inverse @ (inverse @ a))) = (multiply @ b @ identity))),
% 1.18/0.90 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl22])).
% 1.18/0.90 thf(zip_derived_cl1, plain,
% 1.18/0.90 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.18/0.90 inference('cnf', [status(esa)], [left_inverse])).
% 1.18/0.90 thf(zip_derived_cl27, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.18/0.90 inference('demod', [status(thm)], [zip_derived_cl21, zip_derived_cl0])).
% 1.18/0.90 thf(zip_derived_cl40, plain,
% 1.18/0.90 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.18/0.90 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl27])).
% 1.18/0.90 thf(right_identity, axiom, (( multiply @ X @ identity ) = ( X ))).
% 1.18/0.90 thf(zip_derived_cl5, plain,
% 1.18/0.90 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.18/0.90 inference('cnf', [status(esa)], [right_identity])).
% 1.18/0.90 thf(zip_derived_cl50, plain,
% 1.18/0.90 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.18/0.90 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl5])).
% 1.18/0.90 thf(zip_derived_cl5, plain,
% 1.18/0.90 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.18/0.90 inference('cnf', [status(esa)], [right_identity])).
% 1.18/0.90 thf(zip_derived_cl236, plain, (((multiply @ c @ a) = (b))),
% 1.18/0.90 inference('demod', [status(thm)],
% 1.18/0.90 [zip_derived_cl229, zip_derived_cl50, zip_derived_cl5])).
% 1.18/0.90 thf(zip_derived_cl3, plain,
% 1.18/0.90 (![X0 : $i]:
% 1.18/0.90 (~ (subgroup_member @ X0) | (subgroup_member @ (inverse @ X0)))),
% 1.18/0.90 inference('cnf', [status(esa)], [closure_of_inverse])).
% 1.18/0.90 thf(zip_derived_cl27, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.18/0.90 inference('demod', [status(thm)], [zip_derived_cl21, zip_derived_cl0])).
% 1.18/0.90 thf(zip_derived_cl88, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 ( (subgroup_member @ (multiply @ X1 @ X0))
% 1.18/0.90 | ~ (subgroup_member @ X0)
% 1.18/0.90 | ~ (subgroup_member @ X1))),
% 1.18/0.90 inference('eq_res', [status(thm)], [zip_derived_cl4])).
% 1.18/0.90 thf(zip_derived_cl145, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 ( (subgroup_member @ X0)
% 1.18/0.90 | ~ (subgroup_member @ (inverse @ X1))
% 1.18/0.90 | ~ (subgroup_member @ (multiply @ X1 @ X0)))),
% 1.18/0.90 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl88])).
% 1.18/0.90 thf(zip_derived_cl158, plain,
% 1.18/0.90 (![X0 : $i, X1 : $i]:
% 1.18/0.90 (~ (subgroup_member @ X0)
% 1.18/0.90 | ~ (subgroup_member @ (multiply @ X0 @ X1))
% 1.18/0.90 | (subgroup_member @ X1))),
% 1.18/0.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl145])).
% 1.18/0.90 thf(zip_derived_cl304, plain,
% 1.18/0.90 ((~ (subgroup_member @ b)
% 1.18/0.90 | (subgroup_member @ a)
% 1.18/0.90 | ~ (subgroup_member @ c))),
% 1.18/0.90 inference('sup-', [status(thm)], [zip_derived_cl236, zip_derived_cl158])).
% 1.18/0.90 thf(zip_derived_cl9, plain, ( (subgroup_member @ b)),
% 1.18/0.90 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.18/0.90 thf(zip_derived_cl309, plain,
% 1.18/0.90 (( (subgroup_member @ a) | ~ (subgroup_member @ c))),
% 1.18/0.90 inference('demod', [status(thm)], [zip_derived_cl304, zip_derived_cl9])).
% 1.18/0.90 thf(zip_derived_cl163, plain, (~ (subgroup_member @ a)),
% 1.18/0.90 inference('clc', [status(thm)], [zip_derived_cl162, zip_derived_cl157])).
% 1.18/0.90 thf(zip_derived_cl378, plain, (~ (subgroup_member @ c)),
% 1.18/0.90 inference('clc', [status(thm)], [zip_derived_cl309, zip_derived_cl163])).
% 1.18/0.90 thf(zip_derived_cl12, plain, (~ (subgroup_member @ d)),
% 1.18/0.90 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.18/0.90 thf(zip_derived_cl1542, plain, ( (subgroup_member @ a)),
% 1.18/0.90 inference('demod', [status(thm)],
% 1.18/0.90 [zip_derived_cl1539, zip_derived_cl378, zip_derived_cl12])).
% 1.18/0.90 thf(zip_derived_cl1727, plain, ($false),
% 1.18/0.90 inference('demod', [status(thm)], [zip_derived_cl163, zip_derived_cl1542])).
% 1.18/0.90
% 1.18/0.90 % SZS output end Refutation
% 1.18/0.90
% 1.18/0.90
% 1.18/0.90 % Terminating...
% 1.41/1.00 % Runner terminated.
% 1.41/1.01 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------