%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ANA003-4 : 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.nwN5w9BUvM true
% Computer : n003.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 04:28:48 PM UTC 2025
% Result : Unsatisfiable 0.59s 0.81s
% Output : Refutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ANA003-4 : TPTP v9.2.0. Released v1.0.0.
% 0.08/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.nwN5w9BUvM true
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 15:24:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.57/0.67 % Total configuration time : 435
% 0.57/0.67 % Estimated wc time : 1092
% 0.57/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.59/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.59/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.59/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.59/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.59/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.59/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.59/0.80 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.59/0.81 % Solved by fo/fo6_bce.sh.
% 0.59/0.81 % BCE start: 12
% 0.59/0.81 % BCE eliminated: 0
% 0.59/0.81 % PE start: 12
% 0.59/0.81 logic: neq
% 0.59/0.81 % PE eliminated: 0
% 0.59/0.81 % done 42 iterations in 0.058s
% 0.59/0.81 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.59/0.81 % SZS output start Refutation
% 0.59/0.81 thf(n0_type, type, n0: $i).
% 0.59/0.81 thf(a_real_number_type, type, a_real_number: $i).
% 0.59/0.81 thf(absolute_type, type, absolute: $i > $i).
% 0.59/0.81 thf(g_type, type, g: $i > $i).
% 0.59/0.81 thf(xs_type, type, xs: $i > $i).
% 0.59/0.81 thf(minimum_type, type, minimum: $i > $i > $i).
% 0.59/0.81 thf(negate_type, type, negate: $i > $i).
% 0.59/0.81 thf(half_type, type, half: $i > $i).
% 0.59/0.81 thf(f_type, type, f: $i > $i).
% 0.59/0.81 thf(delta_2_type, type, delta_2: $i > $i).
% 0.59/0.81 thf(delta_1_type, type, delta_1: $i > $i).
% 0.59/0.81 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 0.59/0.81 thf(add_type, type, add: $i > $i > $i).
% 0.59/0.81 thf(epsilon_0_type, type, epsilon_0: $i).
% 0.59/0.81 thf(clause_5, axiom, (~( less_or_equal @ epsilon_0 @ n0 ))).
% 0.59/0.81 thf(zip_derived_cl9, plain, (~ (less_or_equal @ epsilon_0 @ n0)),
% 0.59/0.81 inference('cnf', [status(esa)], [clause_5])).
% 0.59/0.81 thf(clause_6, axiom,
% 0.59/0.81 (( less_or_equal @ Delta @ n0 ) |
% 0.59/0.81 ( less_or_equal @
% 0.59/0.81 ( absolute @ ( add @ ( xs @ Delta ) @ ( negate @ a_real_number ) ) ) @
% 0.59/0.81 Delta ))).
% 0.59/0.81 thf(zip_derived_cl10, plain,
% 0.59/0.81 (![X0 : $i]:
% 0.59/0.81 ( (less_or_equal @ X0 @ n0)
% 0.59/0.81 | (less_or_equal @
% 0.59/0.81 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @ X0))),
% 0.59/0.81 inference('cnf', [status(esa)], [clause_6])).
% 0.59/0.81 thf(minimum7, axiom,
% 0.59/0.81 (( ~( less_or_equal @ Z @ ( minimum @ X @ Y ) ) ) |
% 0.59/0.81 ( less_or_equal @ Z @ Y ))).
% 0.59/0.81 thf(zip_derived_cl1, plain,
% 0.59/0.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.59/0.81 (~ (less_or_equal @ X0 @ (minimum @ X1 @ X2))
% 0.59/0.81 | (less_or_equal @ X0 @ X2))),
% 0.59/0.81 inference('cnf', [status(esa)], [minimum7])).
% 0.59/0.81 thf(zip_derived_cl13, plain,
% 0.59/0.81 (![X0 : $i, X1 : $i]:
% 0.59/0.81 ( (less_or_equal @ (minimum @ X1 @ X0) @ n0)
% 0.59/0.81 | (less_or_equal @
% 0.59/0.81 (absolute @
% 0.59/0.81 (add @ (xs @ (minimum @ X1 @ X0)) @ (negate @ a_real_number))) @
% 0.59/0.81 X0))),
% 0.59/0.81 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 0.59/0.81 thf(clause_4, axiom,
% 0.59/0.81 (( less_or_equal @ Epsilon @ n0 ) |
% 0.59/0.81 ( ~( less_or_equal @
% 0.59/0.81 ( absolute @ ( add @ Z @ ( negate @ a_real_number ) ) ) @
% 0.59/0.81 ( delta_2 @ Epsilon ) ) ) |
% 0.59/0.81 ( less_or_equal @
% 0.59/0.81 ( absolute @ ( add @ ( g @ Z ) @ ( negate @ ( g @ a_real_number ) ) ) ) @
% 0.59/0.81 Epsilon ))).
% 0.59/0.81 thf(zip_derived_cl8, plain,
% 0.59/0.81 (![X0 : $i, X1 : $i]:
% 0.59/0.81 ( (less_or_equal @ X0 @ n0)
% 0.59/0.81 | ~ (less_or_equal @
% 0.59/0.81 (absolute @ (add @ X1 @ (negate @ a_real_number))) @
% 0.59/0.81 (delta_2 @ X0))
% 0.59/0.81 | (less_or_equal @
% 0.59/0.81 (absolute @ (add @ (g @ X1) @ (negate @ (g @ a_real_number)))) @
% 0.59/0.81 X0))),
% 0.59/0.81 inference('cnf', [status(esa)], [clause_4])).
% 0.59/0.81 thf(zip_derived_cl10, plain,
% 0.59/0.81 (![X0 : $i]:
% 0.59/0.81 ( (less_or_equal @ X0 @ n0)
% 0.59/0.81 | (less_or_equal @
% 0.59/0.81 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @ X0))),
% 0.59/0.81 inference('cnf', [status(esa)], [clause_6])).
% 0.59/0.81 thf(minimum3, axiom,
% 0.59/0.81 (( ~( less_or_equal @ Z @ ( minimum @ X @ Y ) ) ) |
% 0.59/0.81 ( less_or_equal @ Z @ X ))).
% 0.59/0.81 thf(zip_derived_cl0, plain,
% 0.59/0.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.59/0.81 (~ (less_or_equal @ X0 @ (minimum @ X1 @ X2))
% 0.59/0.81 | (less_or_equal @ X0 @ X1))),
% 0.59/0.81 inference('cnf', [status(esa)], [minimum3])).
% 0.59/0.81 thf(zip_derived_cl12, plain,
% 0.59/0.81 (![X0 : $i, X1 : $i]:
% 0.59/0.81 ( (less_or_equal @ (minimum @ X1 @ X0) @ n0)
% 0.59/0.81 | (less_or_equal @
% 0.59/0.81 (absolute @
% 0.59/0.81 (add @ (xs @ (minimum @ X1 @ X0)) @ (negate @ a_real_number))) @
% 0.59/0.81 X1))),
% 0.59/0.81 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl0])).
% 0.59/0.81 thf(clause_3, axiom,
% 0.59/0.81 (( less_or_equal @ Epsilon @ n0 ) |
% 0.59/0.81 ( ~( less_or_equal @
% 0.59/0.81 ( absolute @ ( add @ Z @ ( negate @ a_real_number ) ) ) @
% 0.59/0.81 ( delta_1 @ Epsilon ) ) ) |
% 0.59/0.81 ( less_or_equal @
% 0.59/0.81 ( absolute @ ( add @ ( f @ Z ) @ ( negate @ ( f @ a_real_number ) ) ) ) @
% 0.59/0.81 Epsilon ))).
% 0.59/0.81 thf(zip_derived_cl7, plain,
% 0.59/0.81 (![X0 : $i, X1 : $i]:
% 0.59/0.81 ( (less_or_equal @ X0 @ n0)
% 0.59/0.81 | ~ (less_or_equal @
% 0.59/0.81 (absolute @ (add @ X1 @ (negate @ a_real_number))) @
% 0.59/0.81 (delta_1 @ X0))
% 0.59/0.81 | (less_or_equal @
% 0.59/0.81 (absolute @ (add @ (f @ X1) @ (negate @ (f @ a_real_number)))) @
% 0.59/0.81 X0))),
% 0.59/0.81 inference('cnf', [status(esa)], [clause_3])).
% 0.59/0.81 thf(less_or_equal_sum_of_halves, axiom,
% 0.59/0.81 (( ~( less_or_equal @ X @ ( half @ Z ) ) ) |
% 0.59/0.81 ( ~( less_or_equal @ Y @ ( half @ Z ) ) ) |
% 0.59/0.81 ( less_or_equal @ ( add @ X @ Y ) @ Z ))).
% 0.59/0.81 thf(zip_derived_cl3, plain,
% 0.59/0.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.59/0.81 (~ (less_or_equal @ X0 @ (half @ X1))
% 0.59/0.81 | ~ (less_or_equal @ X2 @ (half @ X1))
% 0.59/0.81 | (less_or_equal @ (add @ X0 @ X2) @ X1))),
% 0.59/0.81 inference('cnf', [status(esa)], [less_or_equal_sum_of_halves])).
% 0.59/0.81 thf(zip_derived_cl19, plain,
% 0.59/0.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.59/0.81 (~ (less_or_equal @
% 0.59/0.81 (absolute @ (add @ X1 @ (negate @ a_real_number))) @
% 0.59/0.81 (delta_1 @ (half @ X0)))
% 0.59/0.81 | (less_or_equal @ (half @ X0) @ n0)
% 0.59/0.81 | ~ (less_or_equal @ X2 @ (half @ X0))
% 0.59/0.81 | (less_or_equal @
% 0.59/0.81 (add @
% 0.59/0.81 (absolute @ (add @ (f @ X1) @ (negate @ (f @ a_real_number)))) @
% 0.59/0.81 X2) @
% 0.59/0.81 X0))),
% 0.59/0.81 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 0.59/0.81 thf(clause_7_2, conjecture,
% 0.59/0.81 (~( ( ~( less_or_equal @
% 0.59/0.81 ( add @
% 0.59/0.81 ( absolute @
% 0.59/0.81 ( add @
% 0.59/0.81 ( f @ ( xs @ Delta ) ) @ ( negate @ ( f @ a_real_number ) ) ) ) @
% 0.59/0.81 ( absolute @
% 0.59/0.81 ( add @
% 0.59/0.81 ( g @ ( xs @ Delta ) ) @ ( negate @ ( g @ a_real_number ) ) ) ) ) @
% 0.59/0.81 epsilon_0 ) ) |
% 0.59/0.81 ( less_or_equal @ Delta @ n0 ) ))).
% 0.59/0.81 thf(zf_stmt_0, negated_conjecture,
% 0.59/0.81 (( ~( less_or_equal @
% 0.59/0.81 ( add @
% 0.59/0.81 ( absolute @
% 0.59/0.81 ( add @
% 0.59/0.81 ( f @ ( xs @ Delta ) ) @ ( negate @ ( f @ a_real_number ) ) ) ) @
% 0.59/0.81 ( absolute @
% 0.59/0.81 ( add @
% 0.59/0.81 ( g @ ( xs @ Delta ) ) @ ( negate @ ( g @ a_real_number ) ) ) ) ) @
% 0.59/0.81 epsilon_0 ) ) |
% 0.59/0.81 ( less_or_equal @ Delta @ n0 )),
% 0.59/0.81 inference('cnf.neg', [status(esa)], [clause_7_2])).
% 0.59/0.81 thf(zip_derived_cl11, plain,
% 0.59/0.81 (![X0 : $i]:
% 0.59/0.81 (~ (less_or_equal @
% 0.59/0.81 (add @
% 0.59/0.81 (absolute @
% 0.59/0.81 (add @ (f @ (xs @ X0)) @ (negate @ (f @ a_real_number)))) @
% 0.59/0.81 (absolute @
% 0.59/0.81 (add @ (g @ (xs @ X0)) @ (negate @ (g @ a_real_number))))) @
% 0.59/0.81 epsilon_0)
% 0.59/0.81 | (less_or_equal @ X0 @ n0))),
% 0.59/0.81 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.59/0.81 thf(zip_derived_cl86, plain,
% 0.59/0.81 (![X0 : $i]:
% 0.59/0.81 (~ (less_or_equal @
% 0.59/0.81 (absolute @
% 0.59/0.81 (add @ (g @ (xs @ X0)) @ (negate @ (g @ a_real_number)))) @
% 0.59/0.81 (half @ epsilon_0))
% 0.59/0.81 | (less_or_equal @ (half @ epsilon_0) @ n0)
% 0.59/0.81 | ~ (less_or_equal @
% 0.59/0.81 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.59/0.81 (delta_1 @ (half @ epsilon_0)))
% 0.59/0.81 | (less_or_equal @ X0 @ n0))),
% 0.59/0.81 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl11])).
% 0.59/0.81 thf(zip_derived_cl103, plain,
% 0.59/0.81 (![X0 : $i]:
% 0.59/0.81 ( (less_or_equal @ (minimum @ (delta_1 @ (half @ epsilon_0)) @ X0) @
% 0.59/0.81 n0)
% 0.59/0.81 | ~ (less_or_equal @
% 0.59/0.81 (absolute @
% 0.59/0.81 (add @
% 0.59/0.81 (g @ (xs @ (minimum @ (delta_1 @ (half @ epsilon_0)) @ X0))) @
% 0.59/0.81 (negate @ (g @ a_real_number)))) @
% 0.59/0.81 (half @ epsilon_0))
% 0.59/0.81 | (less_or_equal @ (half @ epsilon_0) @ n0)
% 0.59/0.81 | (less_or_equal @
% 0.59/0.81 (minimum @ (delta_1 @ (half @ epsilon_0)) @ X0) @ n0))),
% 0.59/0.81 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl86])).
% 0.59/0.81 thf(zip_derived_cl109, plain,
% 0.59/0.81 (![X0 : $i]:
% 0.59/0.81 ( (less_or_equal @ (half @ epsilon_0) @ n0)
% 0.59/0.81 | ~ (less_or_equal @
% 0.59/0.81 (absolute @
% 0.59/0.81 (add @
% 0.59/0.81 (g @ (xs @ (minimum @ (delta_1 @ (half @ epsilon_0)) @ X0))) @
% 0.59/0.81 (negate @ (g @ a_real_number)))) @
% 0.59/0.81 (half @ epsilon_0))
% 0.59/0.81 | (less_or_equal @
% 0.59/0.81 (minimum @ (delta_1 @ (half @ epsilon_0)) @ X0) @ n0))),
% 0.59/0.81 inference('simplify', [status(thm)], [zip_derived_cl103])).
% 0.59/0.81 thf(zip_derived_cl117, plain,
% 0.59/0.81 (![X0 : $i]:
% 0.59/0.81 (~ (less_or_equal @
% 0.59/0.81 (absolute @
% 0.59/0.81 (add @ (xs @ (minimum @ (delta_1 @ (half @ epsilon_0)) @ X0)) @
% 0.59/0.81 (negate @ a_real_number))) @
% 0.59/0.81 (delta_2 @ (half @ epsilon_0)))
% 0.59/0.81 | (less_or_equal @ (half @ epsilon_0) @ n0)
% 0.59/0.81 | (less_or_equal @ (half @ epsilon_0) @ n0)
% 0.59/0.81 | (less_or_equal @
% 0.59/0.81 (minimum @ (delta_1 @ (half @ epsilon_0)) @ X0) @ n0))),
% 0.59/0.81 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl109])).
% 0.59/0.81 thf(zip_derived_cl118, plain,
% 0.59/0.81 (![X0 : $i]:
% 0.59/0.81 ( (less_or_equal @ (minimum @ (delta_1 @ (half @ epsilon_0)) @ X0) @
% 0.59/0.81 n0)
% 0.59/0.81 | (less_or_equal @ (half @ epsilon_0) @ n0)
% 0.59/0.81 | ~ (less_or_equal @
% 0.59/0.81 (absolute @
% 0.59/0.81 (add @
% 0.59/0.81 (xs @ (minimum @ (delta_1 @ (half @ epsilon_0)) @ X0)) @
% 0.59/0.81 (negate @ a_real_number))) @
% 0.59/0.81 (delta_2 @ (half @ epsilon_0))))),
% 0.59/0.81 inference('simplify', [status(thm)], [zip_derived_cl117])).
% 0.59/0.81 thf(zip_derived_cl135, plain,
% 0.59/0.81 (( (less_or_equal @
% 0.59/0.81 (minimum @ (delta_1 @ (half @ epsilon_0)) @
% 0.59/0.81 (delta_2 @ (half @ epsilon_0))) @
% 0.59/0.81 n0)
% 0.59/0.81 | (less_or_equal @
% 0.59/0.81 (minimum @ (delta_1 @ (half @ epsilon_0)) @
% 0.59/0.81 (delta_2 @ (half @ epsilon_0))) @
% 0.59/0.81 n0)
% 0.59/0.81 | (less_or_equal @ (half @ epsilon_0) @ n0))),
% 0.59/0.81 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl118])).
% 0.59/0.81 thf(zip_derived_cl138, plain,
% 0.59/0.81 (( (less_or_equal @ (half @ epsilon_0) @ n0)
% 0.59/0.81 | (less_or_equal @
% 0.59/0.81 (minimum @ (delta_1 @ (half @ epsilon_0)) @
% 0.59/0.81 (delta_2 @ (half @ epsilon_0))) @
% 0.59/0.81 n0))),
% 0.59/0.81 inference('simplify', [status(thm)], [zip_derived_cl135])).
% 0.59/0.81 thf(minimum9, axiom,
% 0.59/0.81 (( less_or_equal @ X @ n0 ) | ( less_or_equal @ Y @ n0 ) |
% 0.59/0.81 ( ~( less_or_equal @ ( minimum @ X @ Y ) @ n0 ) ))).
% 0.59/0.81 thf(zip_derived_cl2, plain,
% 0.59/0.81 (![X0 : $i, X1 : $i]:
% 0.59/0.81 ( (less_or_equal @ X0 @ n0)
% 0.59/0.81 | (less_or_equal @ X1 @ n0)
% 0.59/0.81 | ~ (less_or_equal @ (minimum @ X0 @ X1) @ n0))),
% 0.59/0.81 inference('cnf', [status(esa)], [minimum9])).
% 0.59/0.81 thf(zip_derived_cl143, plain,
% 0.59/0.81 (( (less_or_equal @ (half @ epsilon_0) @ n0)
% 0.59/0.81 | (less_or_equal @ (delta_1 @ (half @ epsilon_0)) @ n0)
% 0.59/0.81 | (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0))),
% 0.59/0.81 inference('s_sup-', [status(thm)], [zip_derived_cl138, zip_derived_cl2])).
% 0.59/0.81 thf(clause_1, axiom,
% 0.59/0.81 (( less_or_equal @ Epsilon @ n0 ) |
% 0.59/0.81 ( ~( less_or_equal @ ( delta_1 @ Epsilon ) @ n0 ) ))).
% 0.59/0.81 thf(zip_derived_cl5, plain,
% 0.59/0.81 (![X0 : $i]:
% 0.59/0.81 ( (less_or_equal @ X0 @ n0) | ~ (less_or_equal @ (delta_1 @ X0) @ n0))),
% 0.59/0.81 inference('cnf', [status(esa)], [clause_1])).
% 0.59/0.81 thf(zip_derived_cl144, plain,
% 0.59/0.81 (( (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0)
% 0.59/0.81 | (less_or_equal @ (half @ epsilon_0) @ n0))),
% 0.59/0.81 inference('clc', [status(thm)], [zip_derived_cl143, zip_derived_cl5])).
% 0.59/0.81 thf(clause_2, axiom,
% 0.59/0.81 (( less_or_equal @ Epsilon @ n0 ) |
% 0.59/0.81 ( ~( less_or_equal @ ( delta_2 @ Epsilon ) @ n0 ) ))).
% 0.59/0.81 thf(zip_derived_cl6, plain,
% 0.59/0.81 (![X0 : $i]:
% 0.59/0.81 ( (less_or_equal @ X0 @ n0) | ~ (less_or_equal @ (delta_2 @ X0) @ n0))),
% 0.59/0.81 inference('cnf', [status(esa)], [clause_2])).
% 0.59/0.81 thf(zip_derived_cl145, plain, ( (less_or_equal @ (half @ epsilon_0) @ n0)),
% 0.59/0.81 inference('clc', [status(thm)], [zip_derived_cl144, zip_derived_cl6])).
% 0.59/0.81 thf(zero_and_half, axiom,
% 0.59/0.81 (( less_or_equal @ X @ n0 ) | ( ~( less_or_equal @ ( half @ X ) @ n0 ) ))).
% 0.59/0.81 thf(zip_derived_cl4, plain,
% 0.59/0.81 (![X0 : $i]:
% 0.59/0.81 ( (less_or_equal @ X0 @ n0) | ~ (less_or_equal @ (half @ X0) @ n0))),
% 0.59/0.81 inference('cnf', [status(esa)], [zero_and_half])).
% 0.59/0.81 thf(zip_derived_cl146, plain, ( (less_or_equal @ epsilon_0 @ n0)),
% 0.59/0.81 inference('s_sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl4])).
% 0.59/0.81 thf(zip_derived_cl147, plain, ($false),
% 0.59/0.81 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl146])).
% 0.59/0.81
% 0.59/0.81 % SZS output end Refutation
% 0.59/0.81
% 0.59/0.81
% 0.59/0.81 % Terminating...
% 1.67/0.86 % Runner terminated.
% 1.67/0.87 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------