TSTP Solution File: ANA003-4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ANA003-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YYVqdFHrdK true
% Computer : n008.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 17:25:50 EDT 2023
% Result : Unsatisfiable 0.22s 0.82s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA003-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YYVqdFHrdK true
% 0.17/0.35 % Computer : n008.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.36 % DateTime : Fri Aug 25 18:15:17 EDT 2023
% 0.17/0.36 % CPUTime :
% 0.17/0.36 % Running portfolio for 300 s
% 0.17/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.36 % Number of cores: 8
% 0.17/0.36 % Python version: Python 3.6.8
% 0.17/0.36 % Running in FO mode
% 0.22/0.66 % Total configuration time : 435
% 0.22/0.66 % Estimated wc time : 1092
% 0.22/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.82 % Solved by fo/fo1_av.sh.
% 0.22/0.82 % done 48 iterations in 0.051s
% 0.22/0.82 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.22/0.82 % SZS output start Refutation
% 0.22/0.82 thf(n0_type, type, n0: $i).
% 0.22/0.82 thf(a_real_number_type, type, a_real_number: $i).
% 0.22/0.82 thf(absolute_type, type, absolute: $i > $i).
% 0.22/0.82 thf(g_type, type, g: $i > $i).
% 0.22/0.82 thf(xs_type, type, xs: $i > $i).
% 0.22/0.82 thf(minimum_type, type, minimum: $i > $i > $i).
% 0.22/0.82 thf(negate_type, type, negate: $i > $i).
% 0.22/0.82 thf(half_type, type, half: $i > $i).
% 0.22/0.82 thf(f_type, type, f: $i > $i).
% 0.22/0.82 thf(delta_2_type, type, delta_2: $i > $i).
% 0.22/0.82 thf(delta_1_type, type, delta_1: $i > $i).
% 0.22/0.82 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 0.22/0.82 thf(add_type, type, add: $i > $i > $i).
% 0.22/0.82 thf(epsilon_0_type, type, epsilon_0: $i).
% 0.22/0.82 thf(clause_5, axiom, (~( less_or_equal @ epsilon_0 @ n0 ))).
% 0.22/0.82 thf(zip_derived_cl9, plain, (~ (less_or_equal @ epsilon_0 @ n0)),
% 0.22/0.82 inference('cnf', [status(esa)], [clause_5])).
% 0.22/0.82 thf(clause_6, axiom,
% 0.22/0.82 (( less_or_equal @ Delta @ n0 ) |
% 0.22/0.82 ( less_or_equal @
% 0.22/0.82 ( absolute @ ( add @ ( xs @ Delta ) @ ( negate @ a_real_number ) ) ) @
% 0.22/0.82 Delta ))).
% 0.22/0.82 thf(zip_derived_cl10, plain,
% 0.22/0.82 (![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @ X0))),
% 0.22/0.82 inference('cnf', [status(esa)], [clause_6])).
% 0.22/0.82 thf(minimum7, axiom,
% 0.22/0.82 (( ~( less_or_equal @ Z @ ( minimum @ X @ Y ) ) ) |
% 0.22/0.82 ( less_or_equal @ Z @ Y ))).
% 0.22/0.82 thf(zip_derived_cl1, plain,
% 0.22/0.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.22/0.82 (~ (less_or_equal @ X0 @ (minimum @ X1 @ X2))
% 0.22/0.82 | (less_or_equal @ X0 @ X2))),
% 0.22/0.82 inference('cnf', [status(esa)], [minimum7])).
% 0.22/0.82 thf(zip_derived_cl14, plain,
% 0.22/0.82 (![X0 : $i, X1 : $i]:
% 0.22/0.82 ( (less_or_equal @ (minimum @ X1 @ X0) @ n0)
% 0.22/0.82 | (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (xs @ (minimum @ X1 @ X0)) @ (negate @ a_real_number))) @
% 0.22/0.82 X0))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 0.22/0.82 thf(zip_derived_cl10, plain,
% 0.22/0.82 (![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @ X0))),
% 0.22/0.82 inference('cnf', [status(esa)], [clause_6])).
% 0.22/0.82 thf(minimum3, axiom,
% 0.22/0.82 (( ~( less_or_equal @ Z @ ( minimum @ X @ Y ) ) ) |
% 0.22/0.82 ( less_or_equal @ Z @ X ))).
% 0.22/0.82 thf(zip_derived_cl0, plain,
% 0.22/0.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.22/0.82 (~ (less_or_equal @ X0 @ (minimum @ X1 @ X2))
% 0.22/0.82 | (less_or_equal @ X0 @ X1))),
% 0.22/0.82 inference('cnf', [status(esa)], [minimum3])).
% 0.22/0.82 thf(zip_derived_cl13, plain,
% 0.22/0.82 (![X0 : $i, X1 : $i]:
% 0.22/0.82 ( (less_or_equal @ (minimum @ X1 @ X0) @ n0)
% 0.22/0.82 | (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (xs @ (minimum @ X1 @ X0)) @ (negate @ a_real_number))) @
% 0.22/0.82 X1))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl0])).
% 0.22/0.82 thf(clause_3, axiom,
% 0.22/0.82 (( less_or_equal @ Epsilon @ n0 ) |
% 0.22/0.82 ( ~( less_or_equal @
% 0.22/0.82 ( absolute @ ( add @ Z @ ( negate @ a_real_number ) ) ) @
% 0.22/0.82 ( delta_1 @ Epsilon ) ) ) |
% 0.22/0.82 ( less_or_equal @
% 0.22/0.82 ( absolute @ ( add @ ( f @ Z ) @ ( negate @ ( f @ a_real_number ) ) ) ) @
% 0.22/0.82 Epsilon ))).
% 0.22/0.82 thf(zip_derived_cl7, plain,
% 0.22/0.82 (![X0 : $i, X1 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ X1 @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ X0))
% 0.22/0.82 | (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (f @ X1) @ (negate @ (f @ a_real_number)))) @
% 0.22/0.82 X0))),
% 0.22/0.82 inference('cnf', [status(esa)], [clause_3])).
% 0.22/0.82 thf(less_or_equal_sum_of_halves, axiom,
% 0.22/0.82 (( ~( less_or_equal @ X @ ( half @ Z ) ) ) |
% 0.22/0.82 ( ~( less_or_equal @ Y @ ( half @ Z ) ) ) |
% 0.22/0.82 ( less_or_equal @ ( add @ X @ Y ) @ Z ))).
% 0.22/0.82 thf(zip_derived_cl3, plain,
% 0.22/0.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.22/0.82 (~ (less_or_equal @ X0 @ (half @ X1))
% 0.22/0.82 | ~ (less_or_equal @ X2 @ (half @ X1))
% 0.22/0.82 | (less_or_equal @ (add @ X0 @ X2) @ X1))),
% 0.22/0.82 inference('cnf', [status(esa)], [less_or_equal_sum_of_halves])).
% 0.22/0.82 thf(zip_derived_cl19, plain,
% 0.22/0.82 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.22/0.82 (~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ X1 @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ X0)))
% 0.22/0.82 | (less_or_equal @ (half @ X0) @ n0)
% 0.22/0.82 | ~ (less_or_equal @ X2 @ (half @ X0))
% 0.22/0.82 | (less_or_equal @
% 0.22/0.82 (add @
% 0.22/0.82 (absolute @ (add @ (f @ X1) @ (negate @ (f @ a_real_number)))) @
% 0.22/0.82 X2) @
% 0.22/0.82 X0))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 0.22/0.82 thf(clause_7_2, conjecture,
% 0.22/0.82 (~( ( ~( less_or_equal @
% 0.22/0.82 ( add @
% 0.22/0.82 ( absolute @
% 0.22/0.82 ( add @
% 0.22/0.82 ( f @ ( xs @ Delta ) ) @ ( negate @ ( f @ a_real_number ) ) ) ) @
% 0.22/0.82 ( absolute @
% 0.22/0.82 ( add @
% 0.22/0.82 ( g @ ( xs @ Delta ) ) @ ( negate @ ( g @ a_real_number ) ) ) ) ) @
% 0.22/0.82 epsilon_0 ) ) |
% 0.22/0.82 ( less_or_equal @ Delta @ n0 ) ))).
% 0.22/0.82 thf(zf_stmt_0, negated_conjecture,
% 0.22/0.82 (( ~( less_or_equal @
% 0.22/0.82 ( add @
% 0.22/0.82 ( absolute @
% 0.22/0.82 ( add @
% 0.22/0.82 ( f @ ( xs @ Delta ) ) @ ( negate @ ( f @ a_real_number ) ) ) ) @
% 0.22/0.82 ( absolute @
% 0.22/0.82 ( add @
% 0.22/0.82 ( g @ ( xs @ Delta ) ) @ ( negate @ ( g @ a_real_number ) ) ) ) ) @
% 0.22/0.82 epsilon_0 ) ) |
% 0.22/0.82 ( less_or_equal @ Delta @ n0 )),
% 0.22/0.82 inference('cnf.neg', [status(esa)], [clause_7_2])).
% 0.22/0.82 thf(zip_derived_cl11, plain,
% 0.22/0.82 (![X0 : $i]:
% 0.22/0.82 (~ (less_or_equal @
% 0.22/0.82 (add @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (f @ (xs @ X0)) @ (negate @ (f @ a_real_number)))) @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (g @ (xs @ X0)) @ (negate @ (g @ a_real_number))))) @
% 0.22/0.82 epsilon_0)
% 0.22/0.82 | (less_or_equal @ X0 @ n0))),
% 0.22/0.82 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.22/0.82 thf(zip_derived_cl93, plain,
% 0.22/0.82 (![X0 : $i]:
% 0.22/0.82 (~ (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (g @ (xs @ X0)) @ (negate @ (g @ a_real_number)))) @
% 0.22/0.82 (half @ epsilon_0))
% 0.22/0.82 | (less_or_equal @ (half @ epsilon_0) @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | (less_or_equal @ X0 @ n0))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl11])).
% 0.22/0.82 thf(zip_derived_cl94, plain,
% 0.22/0.82 ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (g @ (xs @ X0)) @ (negate @ (g @ a_real_number)))) @
% 0.22/0.82 (half @ epsilon_0))))
% 0.22/0.82 <= ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (g @ (xs @ X0)) @ (negate @ (g @ a_real_number)))) @
% 0.22/0.82 (half @ epsilon_0)))))),
% 0.22/0.82 inference('split', [status(esa)], [zip_derived_cl93])).
% 0.22/0.82 thf(clause_4, axiom,
% 0.22/0.82 (( less_or_equal @ Epsilon @ n0 ) |
% 0.22/0.82 ( ~( less_or_equal @
% 0.22/0.82 ( absolute @ ( add @ Z @ ( negate @ a_real_number ) ) ) @
% 0.22/0.82 ( delta_2 @ Epsilon ) ) ) |
% 0.22/0.82 ( less_or_equal @
% 0.22/0.82 ( absolute @ ( add @ ( g @ Z ) @ ( negate @ ( g @ a_real_number ) ) ) ) @
% 0.22/0.82 Epsilon ))).
% 0.22/0.82 thf(zip_derived_cl8, plain,
% 0.22/0.82 (![X0 : $i, X1 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ X1 @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ X0))
% 0.22/0.82 | (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (g @ X1) @ (negate @ (g @ a_real_number)))) @
% 0.22/0.82 X0))),
% 0.22/0.82 inference('cnf', [status(esa)], [clause_4])).
% 0.22/0.82 thf(zip_derived_cl96, plain,
% 0.22/0.82 ((![X0 : $i]:
% 0.22/0.82 (~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | (less_or_equal @ X0 @ n0)
% 0.22/0.82 | (less_or_equal @ (half @ epsilon_0) @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0)))))
% 0.22/0.82 <= ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (g @ (xs @ X0)) @ (negate @ (g @ a_real_number)))) @
% 0.22/0.82 (half @ epsilon_0)))))),
% 0.22/0.82 inference('s_sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl8])).
% 0.22/0.82 thf(zip_derived_cl95, plain,
% 0.22/0.82 (( (less_or_equal @ (half @ epsilon_0) @ n0))
% 0.22/0.82 <= (( (less_or_equal @ (half @ epsilon_0) @ n0)))),
% 0.22/0.82 inference('split', [status(esa)], [zip_derived_cl93])).
% 0.22/0.82 thf(zero_and_half, axiom,
% 0.22/0.82 (( less_or_equal @ X @ n0 ) | ( ~( less_or_equal @ ( half @ X ) @ n0 ) ))).
% 0.22/0.82 thf(zip_derived_cl4, plain,
% 0.22/0.82 (![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0) | ~ (less_or_equal @ (half @ X0) @ n0))),
% 0.22/0.82 inference('cnf', [status(esa)], [zero_and_half])).
% 0.22/0.82 thf(zip_derived_cl102, plain,
% 0.22/0.82 (( (less_or_equal @ epsilon_0 @ n0))
% 0.22/0.82 <= (( (less_or_equal @ (half @ epsilon_0) @ n0)))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl95, zip_derived_cl4])).
% 0.22/0.82 thf(zip_derived_cl9, plain, (~ (less_or_equal @ epsilon_0 @ n0)),
% 0.22/0.82 inference('cnf', [status(esa)], [clause_5])).
% 0.22/0.82 thf('0', plain, (~ ( (less_or_equal @ (half @ epsilon_0) @ n0))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl102, zip_derived_cl9])).
% 0.22/0.82 thf('1', plain,
% 0.22/0.82 ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (g @ (xs @ X0)) @ (negate @ (g @ a_real_number)))) @
% 0.22/0.82 (half @ epsilon_0)))) |
% 0.22/0.82 ( (less_or_equal @ (half @ epsilon_0) @ n0))),
% 0.22/0.82 inference('split', [status(esa)], [zip_derived_cl93])).
% 0.22/0.82 thf('2', plain,
% 0.22/0.82 ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (g @ (xs @ X0)) @ (negate @ (g @ a_real_number)))) @
% 0.22/0.82 (half @ epsilon_0))))),
% 0.22/0.82 inference('sat_resolution*', [status(thm)], ['0', '1'])).
% 0.22/0.82 thf(zip_derived_cl104, plain,
% 0.22/0.82 (![X0 : $i]:
% 0.22/0.82 (~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | (less_or_equal @ X0 @ n0)
% 0.22/0.82 | (less_or_equal @ (half @ epsilon_0) @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0))))),
% 0.22/0.82 inference('simpl_trail', [status(thm)], [zip_derived_cl96, '2'])).
% 0.22/0.82 thf(zip_derived_cl105, plain,
% 0.22/0.82 ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0)))))
% 0.22/0.82 <= ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0))))))),
% 0.22/0.82 inference('split', [status(esa)], [zip_derived_cl104])).
% 0.22/0.82 thf(zip_derived_cl114, plain,
% 0.22/0.82 ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ (minimum @ (delta_2 @ (half @ epsilon_0)) @ X0) @
% 0.22/0.82 n0)
% 0.22/0.82 | (less_or_equal @
% 0.22/0.82 (minimum @ (delta_2 @ (half @ epsilon_0)) @ X0) @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @
% 0.22/0.82 (xs @ (minimum @ (delta_2 @ (half @ epsilon_0)) @ X0)) @
% 0.22/0.82 (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))))
% 0.22/0.82 <= ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0))))))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl105])).
% 0.22/0.82 thf(zip_derived_cl120, plain,
% 0.22/0.82 ((![X0 : $i]:
% 0.22/0.82 (~ (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (xs @ (minimum @ (delta_2 @ (half @ epsilon_0)) @ X0)) @
% 0.22/0.82 (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | (less_or_equal @
% 0.22/0.82 (minimum @ (delta_2 @ (half @ epsilon_0)) @ X0) @ n0)))
% 0.22/0.82 <= ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0))))))),
% 0.22/0.82 inference('simplify', [status(thm)], [zip_derived_cl114])).
% 0.22/0.82 thf('3', plain,
% 0.22/0.82 ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0))))) |
% 0.22/0.82 ( (less_or_equal @ (half @ epsilon_0) @ n0))),
% 0.22/0.82 inference('split', [status(esa)], [zip_derived_cl104])).
% 0.22/0.82 thf('4', plain,
% 0.22/0.82 ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0)))))),
% 0.22/0.82 inference('sat_resolution*', [status(thm)], ['0', '3'])).
% 0.22/0.82 thf(zip_derived_cl121, plain,
% 0.22/0.82 (![X0 : $i]:
% 0.22/0.82 (~ (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (xs @ (minimum @ (delta_2 @ (half @ epsilon_0)) @ X0)) @
% 0.22/0.82 (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | (less_or_equal @
% 0.22/0.82 (minimum @ (delta_2 @ (half @ epsilon_0)) @ X0) @ n0))),
% 0.22/0.82 inference('simpl_trail', [status(thm)], [zip_derived_cl120, '4'])).
% 0.22/0.82 thf(zip_derived_cl175, plain,
% 0.22/0.82 (( (less_or_equal @
% 0.22/0.82 (minimum @ (delta_2 @ (half @ epsilon_0)) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0))) @
% 0.22/0.82 n0)
% 0.22/0.82 | (less_or_equal @
% 0.22/0.82 (minimum @ (delta_2 @ (half @ epsilon_0)) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0))) @
% 0.22/0.82 n0))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl121])).
% 0.22/0.82 thf(zip_derived_cl176, plain,
% 0.22/0.82 ( (less_or_equal @
% 0.22/0.82 (minimum @ (delta_2 @ (half @ epsilon_0)) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0))) @
% 0.22/0.82 n0)),
% 0.22/0.82 inference('simplify', [status(thm)], [zip_derived_cl175])).
% 0.22/0.82 thf(minimum9, axiom,
% 0.22/0.82 (( less_or_equal @ X @ n0 ) | ( less_or_equal @ Y @ n0 ) |
% 0.22/0.82 ( ~( less_or_equal @ ( minimum @ X @ Y ) @ n0 ) ))).
% 0.22/0.82 thf(zip_derived_cl2, plain,
% 0.22/0.82 (![X0 : $i, X1 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | (less_or_equal @ X1 @ n0)
% 0.22/0.82 | ~ (less_or_equal @ (minimum @ X0 @ X1) @ n0))),
% 0.22/0.82 inference('cnf', [status(esa)], [minimum9])).
% 0.22/0.82 thf(zip_derived_cl178, plain,
% 0.22/0.82 (( (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0)
% 0.22/0.82 | (less_or_equal @ (delta_1 @ (half @ epsilon_0)) @ n0))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl176, zip_derived_cl2])).
% 0.22/0.82 thf(zip_derived_cl179, plain,
% 0.22/0.82 (( (less_or_equal @ (delta_1 @ (half @ epsilon_0)) @ n0))
% 0.22/0.82 <= (( (less_or_equal @ (delta_1 @ (half @ epsilon_0)) @ n0)))),
% 0.22/0.82 inference('split', [status(esa)], [zip_derived_cl178])).
% 0.22/0.82 thf(clause_1, axiom,
% 0.22/0.82 (( less_or_equal @ Epsilon @ n0 ) |
% 0.22/0.82 ( ~( less_or_equal @ ( delta_1 @ Epsilon ) @ n0 ) ))).
% 0.22/0.82 thf(zip_derived_cl5, plain,
% 0.22/0.82 (![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0) | ~ (less_or_equal @ (delta_1 @ X0) @ n0))),
% 0.22/0.82 inference('cnf', [status(esa)], [clause_1])).
% 0.22/0.82 thf(zip_derived_cl181, plain,
% 0.22/0.82 (( (less_or_equal @ (half @ epsilon_0) @ n0))
% 0.22/0.82 <= (( (less_or_equal @ (delta_1 @ (half @ epsilon_0)) @ n0)))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl179, zip_derived_cl5])).
% 0.22/0.82 thf(zip_derived_cl10, plain,
% 0.22/0.82 (![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @ X0))),
% 0.22/0.82 inference('cnf', [status(esa)], [clause_6])).
% 0.22/0.82 thf(zip_derived_cl105, plain,
% 0.22/0.82 ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0)))))
% 0.22/0.82 <= ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0))))))),
% 0.22/0.82 inference('split', [status(esa)], [zip_derived_cl104])).
% 0.22/0.82 thf(zip_derived_cl113, plain,
% 0.22/0.82 ((( (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0)
% 0.22/0.82 | (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (xs @ (delta_2 @ (half @ epsilon_0))) @
% 0.22/0.82 (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))))
% 0.22/0.82 <= ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0))))))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl105])).
% 0.22/0.82 thf(zip_derived_cl118, plain,
% 0.22/0.82 (((~ (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (xs @ (delta_2 @ (half @ epsilon_0))) @
% 0.22/0.82 (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0)))
% 0.22/0.82 <= ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0))))))),
% 0.22/0.82 inference('simplify', [status(thm)], [zip_derived_cl113])).
% 0.22/0.82 thf('5', plain,
% 0.22/0.82 ((![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0)
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | ~ (less_or_equal @
% 0.22/0.82 (absolute @ (add @ (xs @ X0) @ (negate @ a_real_number))) @
% 0.22/0.82 (delta_2 @ (half @ epsilon_0)))))),
% 0.22/0.82 inference('sat_resolution*', [status(thm)], ['0', '3'])).
% 0.22/0.82 thf(zip_derived_cl119, plain,
% 0.22/0.82 ((~ (less_or_equal @
% 0.22/0.82 (absolute @
% 0.22/0.82 (add @ (xs @ (delta_2 @ (half @ epsilon_0))) @
% 0.22/0.82 (negate @ a_real_number))) @
% 0.22/0.82 (delta_1 @ (half @ epsilon_0)))
% 0.22/0.82 | (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0))),
% 0.22/0.82 inference('simpl_trail', [status(thm)], [zip_derived_cl118, '5'])).
% 0.22/0.82 thf(zip_derived_cl139, plain,
% 0.22/0.82 (( (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0))
% 0.22/0.82 <= (( (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0)))),
% 0.22/0.82 inference('split', [status(esa)], [zip_derived_cl119])).
% 0.22/0.82 thf(clause_2, axiom,
% 0.22/0.82 (( less_or_equal @ Epsilon @ n0 ) |
% 0.22/0.82 ( ~( less_or_equal @ ( delta_2 @ Epsilon ) @ n0 ) ))).
% 0.22/0.82 thf(zip_derived_cl6, plain,
% 0.22/0.82 (![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0) | ~ (less_or_equal @ (delta_2 @ X0) @ n0))),
% 0.22/0.82 inference('cnf', [status(esa)], [clause_2])).
% 0.22/0.82 thf(zip_derived_cl141, plain,
% 0.22/0.82 (( (less_or_equal @ (half @ epsilon_0) @ n0))
% 0.22/0.82 <= (( (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0)))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl139, zip_derived_cl6])).
% 0.22/0.82 thf(zip_derived_cl4, plain,
% 0.22/0.82 (![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0) | ~ (less_or_equal @ (half @ X0) @ n0))),
% 0.22/0.82 inference('cnf', [status(esa)], [zero_and_half])).
% 0.22/0.82 thf(zip_derived_cl142, plain,
% 0.22/0.82 (( (less_or_equal @ epsilon_0 @ n0))
% 0.22/0.82 <= (( (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0)))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl4])).
% 0.22/0.82 thf(zip_derived_cl9, plain, (~ (less_or_equal @ epsilon_0 @ n0)),
% 0.22/0.82 inference('cnf', [status(esa)], [clause_5])).
% 0.22/0.82 thf('6', plain, (~ ( (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0))),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl9])).
% 0.22/0.82 thf('7', plain,
% 0.22/0.82 (( (less_or_equal @ (delta_1 @ (half @ epsilon_0)) @ n0)) |
% 0.22/0.82 ( (less_or_equal @ (delta_2 @ (half @ epsilon_0)) @ n0))),
% 0.22/0.82 inference('split', [status(esa)], [zip_derived_cl178])).
% 0.22/0.82 thf('8', plain, (( (less_or_equal @ (delta_1 @ (half @ epsilon_0)) @ n0))),
% 0.22/0.82 inference('sat_resolution*', [status(thm)], ['6', '7'])).
% 0.22/0.82 thf(zip_derived_cl182, plain, ( (less_or_equal @ (half @ epsilon_0) @ n0)),
% 0.22/0.82 inference('simpl_trail', [status(thm)], [zip_derived_cl181, '8'])).
% 0.22/0.82 thf(zip_derived_cl4, plain,
% 0.22/0.82 (![X0 : $i]:
% 0.22/0.82 ( (less_or_equal @ X0 @ n0) | ~ (less_or_equal @ (half @ X0) @ n0))),
% 0.22/0.82 inference('cnf', [status(esa)], [zero_and_half])).
% 0.22/0.82 thf(zip_derived_cl184, plain, ( (less_or_equal @ epsilon_0 @ n0)),
% 0.22/0.82 inference('s_sup-', [status(thm)], [zip_derived_cl182, zip_derived_cl4])).
% 0.22/0.82 thf(zip_derived_cl185, plain, ($false),
% 0.22/0.82 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl184])).
% 0.22/0.82
% 0.22/0.82 % SZS output end Refutation
% 0.22/0.82
% 0.22/0.82
% 0.22/0.82 % Terminating...
% 0.22/0.87 % Runner terminated.
% 0.22/0.88 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------