%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : COM003+1 : TPTP v9.2.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VQYx4eZ8De true
% Computer : n018.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 04:30:31 PM UTC 2025
% Result : Theorem 4.18s 2.31s
% Output : Refutation 4.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.52 % Problem : COM003+1 : TPTP v9.2.0. Released v2.0.0.
% 0.05/0.57 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VQYx4eZ8De true
% 0.11/0.85 % Computer : n018.cluster.edu
% 0.11/0.85 % Model : x86_64 x86_64
% 0.11/0.85 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.85 % Memory : 8042.1875MB
% 0.11/0.85 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.85 % CPULimit : 300
% 0.11/0.85 % WCLimit : 300
% 0.11/0.85 % DateTime : Wed Oct 1 13:47:23 EDT 2025
% 0.11/0.86 % CPUTime :
% 0.11/0.86 % Running portfolio for 300 s
% 0.11/0.86 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.86 % Number of cores: 8
% 0.11/0.86 % Python version: Python 3.6.8
% 0.11/0.86 % Running in FO mode
% 0.33/1.14 % Total configuration time : 435
% 0.33/1.14 % Estimated wc time : 1092
% 0.33/1.14 % Estimated cpu time (7 cpus) : 156.0
% 0.35/1.26 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.35/1.37 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.35/1.39 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.35/1.42 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.35/1.44 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.35/1.44 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.35/1.46 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 4.18/2.31 % Solved by fo/fo5.sh.
% 4.18/2.31 % done 610 iterations in 0.718s
% 4.18/2.31 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.18/2.31 % SZS output start Refutation
% 4.18/2.31 thf(algorithm_type, type, algorithm: $i > $o).
% 4.18/2.31 thf(zip_tseitin_16_type, type, zip_tseitin_16: $i > $o).
% 4.18/2.31 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $o).
% 4.18/2.31 thf(zip_tseitin_9_type, type, zip_tseitin_9: $i > $i > $o).
% 4.18/2.31 thf(halts3_type, type, halts3: $i > $i > $i > $o).
% 4.18/2.31 thf(decides_type, type, decides: $i > $i > $i > $o).
% 4.18/2.31 thf(zip_tseitin_14_type, type, zip_tseitin_14: $i > $o).
% 4.18/2.31 thf(good_type, type, good: $i).
% 4.18/2.31 thf(zip_tseitin_7_type, type, zip_tseitin_7: $i > $i > $o).
% 4.18/2.31 thf(sk__1_type, type, sk__1: $i).
% 4.18/2.31 thf(program_type, type, program: $i > $o).
% 4.18/2.31 thf(zip_tseitin_6_type, type, zip_tseitin_6: $i > $o).
% 4.18/2.31 thf(halts2_type, type, halts2: $i > $i > $o).
% 4.18/2.31 thf(sk__9_type, type, sk__9: $i).
% 4.18/2.31 thf(zip_tseitin_11_type, type, zip_tseitin_11: $i > $i > $o).
% 4.18/2.31 thf(zip_tseitin_17_type, type, zip_tseitin_17: $i > $i > $o).
% 4.18/2.31 thf(sk__8_type, type, sk__8: $i > $i).
% 4.18/2.31 thf(sk__5_type, type, sk__5: $i).
% 4.18/2.31 thf(sk__2_type, type, sk__2: $i > $i).
% 4.18/2.31 thf(zip_tseitin_13_type, type, zip_tseitin_13: $i > $o).
% 4.18/2.31 thf(zip_tseitin_5_type, type, zip_tseitin_5: $i > $i > $i > $o).
% 4.18/2.31 thf(zip_tseitin_15_type, type, zip_tseitin_15: $i > $i > $o).
% 4.18/2.31 thf(sk__6_type, type, sk__6: $i > $i).
% 4.18/2.31 thf(zip_tseitin_19_type, type, zip_tseitin_19: $i > $i > $o).
% 4.18/2.31 thf(outputs_type, type, outputs: $i > $i > $o).
% 4.18/2.31 thf(sk__4_type, type, sk__4: $i > $i).
% 4.18/2.31 thf(bad_type, type, bad: $i).
% 4.18/2.31 thf(zip_tseitin_18_type, type, zip_tseitin_18: $i > $i > $o).
% 4.18/2.31 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $o).
% 4.18/2.31 thf(zip_tseitin_12_type, type, zip_tseitin_12: $i > $i > $o).
% 4.18/2.31 thf(sk__7_type, type, sk__7: $i).
% 4.18/2.31 thf(zip_tseitin_8_type, type, zip_tseitin_8: $i > $o).
% 4.18/2.31 thf(zip_tseitin_20_type, type, zip_tseitin_20: $i > $o).
% 4.18/2.31 thf(zip_tseitin_4_type, type, zip_tseitin_4: $i > $i > $i > $o).
% 4.18/2.31 thf(sk__type, type, sk_: $i > $i > $i).
% 4.18/2.31 thf(zip_tseitin_10_type, type, zip_tseitin_10: $i > $i > $o).
% 4.18/2.31 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $i > $o).
% 4.18/2.31 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $o).
% 4.18/2.31 thf(sk__3_type, type, sk__3: $i > $i > $i).
% 4.18/2.31 thf(p3, axiom,
% 4.18/2.31 (( ?[W:$i]:
% 4.18/2.31 ( ( program @ W ) &
% 4.18/2.31 ( ![Y:$i]:
% 4.18/2.31 ( ( ( ( halts2 @ Y @ Y ) & ( program @ Y ) ) =>
% 4.18/2.31 ( ( outputs @ W @ good ) & ( halts3 @ W @ Y @ Y ) ) ) &
% 4.18/2.31 ( ( ( ~( halts2 @ Y @ Y ) ) & ( program @ Y ) ) =>
% 4.18/2.31 ( ( outputs @ W @ bad ) & ( halts3 @ W @ Y @ Y ) ) ) ) ) ) ) =>
% 4.18/2.31 ( ?[V:$i]:
% 4.18/2.31 ( ( program @ V ) &
% 4.18/2.31 ( ![Y:$i]:
% 4.18/2.31 ( ( ( ( halts2 @ Y @ Y ) & ( program @ Y ) ) =>
% 4.18/2.31 ( ( outputs @ V @ good ) & ( halts2 @ V @ Y ) ) ) &
% 4.18/2.31 ( ( ( ~( halts2 @ Y @ Y ) ) & ( program @ Y ) ) =>
% 4.18/2.31 ( ( outputs @ V @ bad ) & ( halts2 @ V @ Y ) ) ) ) ) ) ))).
% 4.18/2.31 thf(zf_stmt_0, axiom,
% 4.18/2.31 (![Y:$i]:
% 4.18/2.31 ( ( zip_tseitin_6 @ Y ) => ( ( program @ Y ) & ( halts2 @ Y @ Y ) ) ))).
% 4.18/2.31 thf(zip_derived_cl15, plain,
% 4.18/2.31 (![X0 : $i]: ( (halts2 @ X0 @ X0) | ~ (zip_tseitin_6 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.18/2.31 thf(p1, axiom,
% 4.18/2.31 (( ?[X:$i]:
% 4.18/2.31 ( ( algorithm @ X ) &
% 4.18/2.31 ( ![Y:$i]: ( ( program @ Y ) => ( ![Z:$i]: ( decides @ X @ Y @ Z ) ) ) ) ) ) =>
% 4.18/2.31 ( ?[W:$i]:
% 4.18/2.31 ( ( program @ W ) &
% 4.18/2.31 ( ![Y:$i]: ( ( program @ Y ) => ( ![Z:$i]: ( decides @ W @ Y @ Z ) ) ) ) ) ))).
% 4.18/2.31 thf(zf_stmt_1, axiom,
% 4.18/2.31 (![W:$i]:
% 4.18/2.31 ( ( zip_tseitin_1 @ W ) =>
% 4.18/2.31 ( ( ![Y:$i]: ( ( program @ Y ) => ( ![Z:$i]: ( decides @ W @ Y @ Z ) ) ) ) &
% 4.18/2.31 ( program @ W ) ) ))).
% 4.18/2.31 thf(zip_derived_cl2, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 (~ (program @ X0) | (decides @ X1 @ X0 @ X2) | ~ (zip_tseitin_1 @ X1))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_1])).
% 4.18/2.31 thf(p2, axiom,
% 4.18/2.31 (![W:$i]:
% 4.18/2.31 ( ( ( ![Y:$i]: ( ( program @ Y ) => ( ![Z:$i]: ( decides @ W @ Y @ Z ) ) ) ) &
% 4.18/2.31 ( program @ W ) ) =>
% 4.18/2.31 ( ![Y:$i,Z:$i]:
% 4.18/2.31 ( ( ( ( halts2 @ Y @ Z ) & ( program @ Y ) ) =>
% 4.18/2.31 ( ( outputs @ W @ good ) & ( halts3 @ W @ Y @ Z ) ) ) &
% 4.18/2.31 ( ( ( ~( halts2 @ Y @ Z ) ) & ( program @ Y ) ) =>
% 4.18/2.31 ( ( outputs @ W @ bad ) & ( halts3 @ W @ Y @ Z ) ) ) ) ) ))).
% 4.18/2.31 thf(zf_stmt_2, axiom,
% 4.18/2.31 (![Y:$i,W:$i]:
% 4.18/2.31 ( ( ( program @ Y ) => ( ![Z:$i]: ( decides @ W @ Y @ Z ) ) ) =>
% 4.18/2.31 ( zip_tseitin_2 @ Y @ W ) ))).
% 4.18/2.31 thf(zip_derived_cl5, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_2 @ X0 @ X1)
% 4.18/2.31 | ~ (decides @ X1 @ X0 @ (sk__3 @ X1 @ X0)))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_2])).
% 4.18/2.31 thf(zip_derived_cl83, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X1)
% 4.18/2.31 | ~ (program @ X0)
% 4.18/2.31 | (zip_tseitin_2 @ X0 @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl5])).
% 4.18/2.31 thf(zip_derived_cl6, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]: ( (zip_tseitin_2 @ X0 @ X1) | (program @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_2])).
% 4.18/2.31 thf(zip_derived_cl93, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_2 @ X0 @ X1) | ~ (zip_tseitin_1 @ X1))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl83, zip_derived_cl6])).
% 4.18/2.31 thf(zf_stmt_3, type, zip_tseitin_5 : $i > $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_4, axiom,
% 4.18/2.31 (![Z:$i,Y:$i,W:$i]:
% 4.18/2.31 ( ( zip_tseitin_5 @ Z @ Y @ W ) =>
% 4.18/2.31 ( ( ( ( program @ Y ) & ( ~( halts2 @ Y @ Z ) ) ) =>
% 4.18/2.31 ( zip_tseitin_4 @ Z @ Y @ W ) ) &
% 4.18/2.31 ( ( ( program @ Y ) & ( halts2 @ Y @ Z ) ) =>
% 4.18/2.31 ( zip_tseitin_3 @ Z @ Y @ W ) ) ) ))).
% 4.18/2.31 thf(zf_stmt_5, type, zip_tseitin_4 : $i > $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_6, axiom,
% 4.18/2.31 (![Z:$i,Y:$i,W:$i]:
% 4.18/2.31 ( ( zip_tseitin_4 @ Z @ Y @ W ) =>
% 4.18/2.31 ( ( halts3 @ W @ Y @ Z ) & ( outputs @ W @ bad ) ) ))).
% 4.18/2.31 thf(zf_stmt_7, type, zip_tseitin_3 : $i > $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_8, axiom,
% 4.18/2.31 (![Z:$i,Y:$i,W:$i]:
% 4.18/2.31 ( ( zip_tseitin_3 @ Z @ Y @ W ) =>
% 4.18/2.31 ( ( halts3 @ W @ Y @ Z ) & ( outputs @ W @ good ) ) ))).
% 4.18/2.31 thf(zf_stmt_9, type, zip_tseitin_2 : $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_10, axiom,
% 4.18/2.31 (![W:$i]:
% 4.18/2.31 ( ( ( program @ W ) & ( ![Y:$i]: ( zip_tseitin_2 @ Y @ W ) ) ) =>
% 4.18/2.31 ( ![Y:$i,Z:$i]: ( zip_tseitin_5 @ Z @ Y @ W ) ) ))).
% 4.18/2.31 thf(zip_derived_cl13, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 ( (zip_tseitin_5 @ X0 @ X1 @ X2)
% 4.18/2.31 | ~ (zip_tseitin_2 @ (sk__4 @ X2) @ X2)
% 4.18/2.31 | ~ (program @ X2))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_10])).
% 4.18/2.31 thf(zip_derived_cl117, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X0)
% 4.18/2.31 | ~ (program @ X0)
% 4.18/2.31 | (zip_tseitin_5 @ X2 @ X1 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl13])).
% 4.18/2.31 thf(zip_derived_cl3, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_1 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_1])).
% 4.18/2.31 thf(zip_derived_cl351, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 ( (zip_tseitin_5 @ X2 @ X1 @ X0) | ~ (zip_tseitin_1 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl117, zip_derived_cl3])).
% 4.18/2.31 thf(zip_derived_cl12, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 (~ (program @ X0)
% 4.18/2.31 | ~ (halts2 @ X0 @ X1)
% 4.18/2.31 | (zip_tseitin_3 @ X1 @ X0 @ X2)
% 4.18/2.31 | ~ (zip_tseitin_5 @ X1 @ X0 @ X2))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.18/2.31 thf(zip_derived_cl353, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X0)
% 4.18/2.31 | (zip_tseitin_3 @ X2 @ X1 @ X0)
% 4.18/2.31 | ~ (halts2 @ X1 @ X2)
% 4.18/2.31 | ~ (program @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl351, zip_derived_cl12])).
% 4.18/2.31 thf(zip_derived_cl439, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_6 @ X0)
% 4.18/2.31 | ~ (program @ X0)
% 4.18/2.31 | (zip_tseitin_3 @ X0 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl353])).
% 4.18/2.31 thf(zip_derived_cl14, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_6 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.18/2.31 thf(zip_derived_cl1876, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X1)
% 4.18/2.31 | (zip_tseitin_3 @ X0 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_6 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl439, zip_derived_cl14])).
% 4.18/2.31 thf(zip_derived_cl7, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 ( (halts3 @ X0 @ X1 @ X2) | ~ (zip_tseitin_3 @ X2 @ X1 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_8])).
% 4.18/2.31 thf(zip_derived_cl1877, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_6 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X0)
% 4.18/2.31 | (halts3 @ X0 @ X1 @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1876, zip_derived_cl7])).
% 4.18/2.31 thf(zip_derived_cl1876, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X1)
% 4.18/2.31 | (zip_tseitin_3 @ X0 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_6 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl439, zip_derived_cl14])).
% 4.18/2.31 thf(zip_derived_cl8, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 ( (outputs @ X0 @ good) | ~ (zip_tseitin_3 @ X1 @ X2 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_8])).
% 4.18/2.31 thf(zip_derived_cl1878, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_6 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X0)
% 4.18/2.31 | (outputs @ X0 @ good))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1876, zip_derived_cl8])).
% 4.18/2.31 thf(zf_stmt_11, axiom,
% 4.18/2.31 (![Y:$i,W:$i]:
% 4.18/2.31 ( ( ( zip_tseitin_6 @ Y ) =>
% 4.18/2.31 ( ( halts3 @ W @ Y @ Y ) & ( outputs @ W @ good ) ) ) =>
% 4.18/2.31 ( zip_tseitin_7 @ Y @ W ) ))).
% 4.18/2.31 thf(zip_derived_cl17, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_7 @ X0 @ X1) | (zip_tseitin_6 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_11])).
% 4.18/2.31 thf(zip_derived_cl351, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 ( (zip_tseitin_5 @ X2 @ X1 @ X0) | ~ (zip_tseitin_1 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl117, zip_derived_cl3])).
% 4.18/2.31 thf(zip_derived_cl11, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 (~ (program @ X0)
% 4.18/2.31 | (halts2 @ X0 @ X1)
% 4.18/2.31 | (zip_tseitin_4 @ X1 @ X0 @ X2)
% 4.18/2.31 | ~ (zip_tseitin_5 @ X1 @ X0 @ X2))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.18/2.31 thf(zip_derived_cl352, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X0)
% 4.18/2.31 | (zip_tseitin_4 @ X2 @ X1 @ X0)
% 4.18/2.31 | (halts2 @ X1 @ X2)
% 4.18/2.31 | ~ (program @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl351, zip_derived_cl11])).
% 4.18/2.31 thf(zf_stmt_12, axiom,
% 4.18/2.31 (![Y:$i]:
% 4.18/2.31 ( ( zip_tseitin_8 @ Y ) => ( ( program @ Y ) & ( ~( halts2 @ Y @ Y ) ) ) ))).
% 4.18/2.31 thf(zip_derived_cl19, plain,
% 4.18/2.31 (![X0 : $i]: (~ (halts2 @ X0 @ X0) | ~ (zip_tseitin_8 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_12])).
% 4.18/2.31 thf(zip_derived_cl360, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (program @ X0)
% 4.18/2.31 | (zip_tseitin_4 @ X0 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_8 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl352, zip_derived_cl19])).
% 4.18/2.31 thf(zip_derived_cl18, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_8 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_12])).
% 4.18/2.31 thf(zip_derived_cl1790, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_8 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X1)
% 4.18/2.31 | (zip_tseitin_4 @ X0 @ X0 @ X1))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl360, zip_derived_cl18])).
% 4.18/2.31 thf(zip_derived_cl9, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 ( (halts3 @ X0 @ X1 @ X2) | ~ (zip_tseitin_4 @ X2 @ X1 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_6])).
% 4.18/2.31 thf(zip_derived_cl1791, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_8 @ X1)
% 4.18/2.31 | (halts3 @ X0 @ X1 @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1790, zip_derived_cl9])).
% 4.18/2.31 thf(zip_derived_cl352, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X0)
% 4.18/2.31 | (zip_tseitin_4 @ X2 @ X1 @ X0)
% 4.18/2.31 | (halts2 @ X1 @ X2)
% 4.18/2.31 | ~ (program @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl351, zip_derived_cl11])).
% 4.18/2.31 thf(zip_derived_cl10, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 ( (outputs @ X0 @ bad) | ~ (zip_tseitin_4 @ X1 @ X2 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_6])).
% 4.18/2.31 thf(zip_derived_cl355, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 (~ (program @ X1)
% 4.18/2.31 | (halts2 @ X1 @ X2)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X0)
% 4.18/2.31 | (outputs @ X0 @ bad))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl352, zip_derived_cl10])).
% 4.18/2.31 thf(zip_derived_cl19, plain,
% 4.18/2.31 (![X0 : $i]: (~ (halts2 @ X0 @ X0) | ~ (zip_tseitin_8 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_12])).
% 4.18/2.31 thf(zip_derived_cl379, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (outputs @ X1 @ bad)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X1)
% 4.18/2.31 | ~ (program @ X0)
% 4.18/2.31 | ~ (zip_tseitin_8 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl355, zip_derived_cl19])).
% 4.18/2.31 thf(zip_derived_cl18, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_8 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_12])).
% 4.18/2.31 thf(zip_derived_cl419, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_8 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X1)
% 4.18/2.31 | (outputs @ X1 @ bad))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl379, zip_derived_cl18])).
% 4.18/2.31 thf(zf_stmt_13, axiom,
% 4.18/2.31 (![Y:$i,W:$i]:
% 4.18/2.31 ( ( ( zip_tseitin_8 @ Y ) =>
% 4.18/2.31 ( ( halts3 @ W @ Y @ Y ) & ( outputs @ W @ bad ) ) ) =>
% 4.18/2.31 ( zip_tseitin_9 @ Y @ W ) ))).
% 4.18/2.31 thf(zip_derived_cl20, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_9 @ X0 @ X1)
% 4.18/2.31 | ~ (halts3 @ X1 @ X0 @ X0)
% 4.18/2.31 | ~ (outputs @ X1 @ bad))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_13])).
% 4.18/2.31 thf(zip_derived_cl420, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_8 @ X2)
% 4.18/2.31 | ~ (halts3 @ X0 @ X1 @ X1)
% 4.18/2.31 | (zip_tseitin_9 @ X1 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl419, zip_derived_cl20])).
% 4.18/2.31 thf(zip_derived_cl1793, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 (~ (zip_tseitin_8 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X1)
% 4.18/2.31 | (zip_tseitin_9 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_8 @ X2)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1791, zip_derived_cl420])).
% 4.18/2.31 thf(zip_derived_cl1797, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.18/2.31 (~ (zip_tseitin_8 @ X2)
% 4.18/2.31 | (zip_tseitin_9 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_8 @ X0))),
% 4.18/2.31 inference('simplify', [status(thm)], [zip_derived_cl1793])).
% 4.18/2.31 thf(zip_derived_cl1843, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_8 @ X0)
% 4.18/2.31 | (zip_tseitin_9 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X1))),
% 4.18/2.31 inference('condensation', [status(thm)], [zip_derived_cl1797])).
% 4.18/2.31 thf(zip_derived_cl21, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_9 @ X0 @ X1) | (zip_tseitin_8 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_13])).
% 4.18/2.31 thf(zip_derived_cl1844, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X1) | (zip_tseitin_9 @ X0 @ X1))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl1843, zip_derived_cl21])).
% 4.18/2.31 thf(zf_stmt_14, type, zip_tseitin_13 : $i > $o).
% 4.18/2.31 thf(zf_stmt_15, axiom,
% 4.18/2.31 (![V:$i]:
% 4.18/2.31 ( ( zip_tseitin_13 @ V ) =>
% 4.18/2.31 ( ( ![Y:$i]: ( zip_tseitin_12 @ Y @ V ) ) & ( program @ V ) ) ))).
% 4.18/2.31 thf(zf_stmt_16, type, zip_tseitin_12 : $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_17, axiom,
% 4.18/2.31 (![Y:$i,V:$i]:
% 4.18/2.31 ( ( zip_tseitin_12 @ Y @ V ) =>
% 4.18/2.31 ( ( ( ( program @ Y ) & ( ~( halts2 @ Y @ Y ) ) ) =>
% 4.18/2.31 ( zip_tseitin_11 @ Y @ V ) ) &
% 4.18/2.31 ( ( ( program @ Y ) & ( halts2 @ Y @ Y ) ) =>
% 4.18/2.31 ( zip_tseitin_10 @ Y @ V ) ) ) ))).
% 4.18/2.31 thf(zf_stmt_18, type, zip_tseitin_11 : $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_19, axiom,
% 4.18/2.31 (![Y:$i,V:$i]:
% 4.18/2.31 ( ( zip_tseitin_11 @ Y @ V ) =>
% 4.18/2.31 ( ( halts2 @ V @ Y ) & ( outputs @ V @ bad ) ) ))).
% 4.18/2.31 thf(zf_stmt_20, type, zip_tseitin_10 : $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_21, axiom,
% 4.18/2.31 (![Y:$i,V:$i]:
% 4.18/2.31 ( ( zip_tseitin_10 @ Y @ V ) =>
% 4.18/2.31 ( ( halts2 @ V @ Y ) & ( outputs @ V @ good ) ) ))).
% 4.18/2.31 thf(zf_stmt_22, type, zip_tseitin_9 : $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_23, type, zip_tseitin_8 : $i > $o).
% 4.18/2.31 thf(zf_stmt_24, type, zip_tseitin_7 : $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_25, type, zip_tseitin_6 : $i > $o).
% 4.18/2.31 thf(zf_stmt_26, axiom,
% 4.18/2.31 (( ?[W:$i]:
% 4.18/2.31 ( ( ![Y:$i]: ( ( zip_tseitin_9 @ Y @ W ) & ( zip_tseitin_7 @ Y @ W ) ) ) &
% 4.18/2.31 ( program @ W ) ) ) =>
% 4.18/2.31 ( ?[V:$i]: ( zip_tseitin_13 @ V ) ))).
% 4.18/2.31 thf(zip_derived_cl30, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 ( (zip_tseitin_13 @ sk__5)
% 4.18/2.31 | ~ (program @ X0)
% 4.18/2.31 | ~ (zip_tseitin_9 @ (sk__6 @ X0) @ X0)
% 4.18/2.31 | ~ (zip_tseitin_7 @ (sk__6 @ X0) @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_26])).
% 4.18/2.31 thf(zip_derived_cl1845, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_7 @ (sk__6 @ X0) @ X0)
% 4.18/2.31 | ~ (program @ X0)
% 4.18/2.31 | (zip_tseitin_13 @ sk__5))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1844, zip_derived_cl30])).
% 4.18/2.31 thf(zip_derived_cl3, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_1 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_1])).
% 4.18/2.31 thf(zip_derived_cl1846, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 ( (zip_tseitin_13 @ sk__5)
% 4.18/2.31 | ~ (zip_tseitin_7 @ (sk__6 @ X0) @ X0)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl1845, zip_derived_cl3])).
% 4.18/2.31 thf(zip_derived_cl28, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_12 @ X0 @ X1) | ~ (zip_tseitin_13 @ X1))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_15])).
% 4.18/2.31 thf(zip_derived_cl26, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (program @ X0)
% 4.18/2.31 | (halts2 @ X0 @ X0)
% 4.18/2.31 | (zip_tseitin_11 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_12 @ X0 @ X1))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_17])).
% 4.18/2.31 thf(zip_derived_cl137, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | (zip_tseitin_11 @ X1 @ X0)
% 4.18/2.31 | (halts2 @ X1 @ X1)
% 4.18/2.31 | ~ (program @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl26])).
% 4.18/2.31 thf(zip_derived_cl24, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (halts2 @ X0 @ X1) | ~ (zip_tseitin_11 @ X1 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_19])).
% 4.18/2.31 thf(zip_derived_cl566, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (program @ X1)
% 4.18/2.31 | (halts2 @ X1 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | (halts2 @ X0 @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl24])).
% 4.18/2.31 thf(p4, axiom,
% 4.18/2.31 (( ?[V:$i]:
% 4.18/2.31 ( ( program @ V ) &
% 4.18/2.31 ( ![Y:$i]:
% 4.18/2.31 ( ( ( ( halts2 @ Y @ Y ) & ( program @ Y ) ) =>
% 4.18/2.31 ( ( outputs @ V @ good ) & ( halts2 @ V @ Y ) ) ) &
% 4.18/2.31 ( ( ( ~( halts2 @ Y @ Y ) ) & ( program @ Y ) ) =>
% 4.18/2.31 ( ( outputs @ V @ bad ) & ( halts2 @ V @ Y ) ) ) ) ) ) ) =>
% 4.18/2.31 ( ?[U:$i]:
% 4.18/2.31 ( ( program @ U ) &
% 4.18/2.31 ( ![Y:$i]:
% 4.18/2.31 ( ( ( ( halts2 @ Y @ Y ) & ( program @ Y ) ) =>
% 4.18/2.31 ( ~( halts2 @ U @ Y ) ) ) &
% 4.18/2.31 ( ( ( ~( halts2 @ Y @ Y ) ) & ( program @ Y ) ) =>
% 4.18/2.31 ( ( outputs @ U @ bad ) & ( halts2 @ U @ Y ) ) ) ) ) ) ))).
% 4.18/2.31 thf(zf_stmt_27, axiom,
% 4.18/2.31 (![Y:$i]:
% 4.18/2.31 ( ( zip_tseitin_16 @ Y ) => ( ( program @ Y ) & ( ~( halts2 @ Y @ Y ) ) ) ))).
% 4.18/2.31 thf(zip_derived_cl36, plain,
% 4.18/2.31 (![X0 : $i]: (~ (halts2 @ X0 @ X0) | ~ (zip_tseitin_16 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_27])).
% 4.18/2.31 thf(zip_derived_cl741, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (halts2 @ X1 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X1)
% 4.18/2.31 | ~ (program @ X0)
% 4.18/2.31 | ~ (zip_tseitin_16 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl566, zip_derived_cl36])).
% 4.18/2.31 thf(zip_derived_cl35, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_16 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_27])).
% 4.18/2.31 thf(zip_derived_cl1123, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_16 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X1)
% 4.18/2.31 | (halts2 @ X1 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl741, zip_derived_cl35])).
% 4.18/2.31 thf(zip_derived_cl137, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | (zip_tseitin_11 @ X1 @ X0)
% 4.18/2.31 | (halts2 @ X1 @ X1)
% 4.18/2.31 | ~ (program @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl26])).
% 4.18/2.31 thf(zip_derived_cl25, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (outputs @ X0 @ bad) | ~ (zip_tseitin_11 @ X1 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_19])).
% 4.18/2.31 thf(zip_derived_cl567, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (program @ X1)
% 4.18/2.31 | (halts2 @ X1 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | (outputs @ X0 @ bad))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl25])).
% 4.18/2.31 thf(zip_derived_cl36, plain,
% 4.18/2.31 (![X0 : $i]: (~ (halts2 @ X0 @ X0) | ~ (zip_tseitin_16 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_27])).
% 4.18/2.31 thf(zip_derived_cl861, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (outputs @ X1 @ bad)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X1)
% 4.18/2.31 | ~ (program @ X0)
% 4.18/2.31 | ~ (zip_tseitin_16 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl567, zip_derived_cl36])).
% 4.18/2.31 thf(zip_derived_cl35, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_16 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_27])).
% 4.18/2.31 thf(zip_derived_cl1460, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_16 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X1)
% 4.18/2.31 | (outputs @ X1 @ bad))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl861, zip_derived_cl35])).
% 4.18/2.31 thf(zip_derived_cl28, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_12 @ X0 @ X1) | ~ (zip_tseitin_13 @ X1))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_15])).
% 4.18/2.31 thf(zf_stmt_28, axiom,
% 4.18/2.31 (![Y:$i]:
% 4.18/2.31 ( ( zip_tseitin_14 @ Y ) => ( ( program @ Y ) & ( halts2 @ Y @ Y ) ) ))).
% 4.18/2.31 thf(zip_derived_cl32, plain,
% 4.18/2.31 (![X0 : $i]: ( (halts2 @ X0 @ X0) | ~ (zip_tseitin_14 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_28])).
% 4.18/2.31 thf(zip_derived_cl27, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (program @ X0)
% 4.18/2.31 | ~ (halts2 @ X0 @ X0)
% 4.18/2.31 | (zip_tseitin_10 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_12 @ X0 @ X1))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_17])).
% 4.18/2.31 thf(zip_derived_cl114, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_14 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_12 @ X0 @ X1)
% 4.18/2.31 | (zip_tseitin_10 @ X0 @ X1)
% 4.18/2.31 | ~ (program @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl27])).
% 4.18/2.31 thf(zip_derived_cl31, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_14 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_28])).
% 4.18/2.31 thf(zip_derived_cl152, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_10 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_12 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_14 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl114, zip_derived_cl31])).
% 4.18/2.31 thf(zip_derived_cl153, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_14 @ X1)
% 4.18/2.31 | (zip_tseitin_10 @ X1 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl152])).
% 4.18/2.31 thf(zip_derived_cl22, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (halts2 @ X0 @ X1) | ~ (zip_tseitin_10 @ X1 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_21])).
% 4.18/2.31 thf(zip_derived_cl245, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_14 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | (halts2 @ X0 @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl153, zip_derived_cl22])).
% 4.18/2.31 thf(zip_derived_cl28, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_12 @ X0 @ X1) | ~ (zip_tseitin_13 @ X1))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_15])).
% 4.18/2.31 thf(zip_derived_cl566, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (program @ X1)
% 4.18/2.31 | (halts2 @ X1 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | (halts2 @ X0 @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl24])).
% 4.18/2.31 thf(zip_derived_cl773, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 ( (halts2 @ X0 @ X0) | ~ (zip_tseitin_13 @ X0) | ~ (program @ X0))),
% 4.18/2.31 inference('eq_fact', [status(thm)], [zip_derived_cl566])).
% 4.18/2.31 thf(zip_derived_cl29, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_13 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_15])).
% 4.18/2.31 thf(zip_derived_cl785, plain,
% 4.18/2.31 (![X0 : $i]: (~ (zip_tseitin_13 @ X0) | (halts2 @ X0 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl773, zip_derived_cl29])).
% 4.18/2.31 thf(zip_derived_cl27, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (program @ X0)
% 4.18/2.31 | ~ (halts2 @ X0 @ X0)
% 4.18/2.31 | (zip_tseitin_10 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_12 @ X0 @ X1))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_17])).
% 4.18/2.31 thf(zip_derived_cl795, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_12 @ X0 @ X1)
% 4.18/2.31 | (zip_tseitin_10 @ X0 @ X1)
% 4.18/2.31 | ~ (program @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl785, zip_derived_cl27])).
% 4.18/2.31 thf(zip_derived_cl29, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_13 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_15])).
% 4.18/2.31 thf(zip_derived_cl1035, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_10 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_12 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl795, zip_derived_cl29])).
% 4.18/2.31 thf(zip_derived_cl1036, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X1)
% 4.18/2.31 | (zip_tseitin_10 @ X1 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl1035])).
% 4.18/2.31 thf(zip_derived_cl1202, plain,
% 4.18/2.31 (![X0 : $i]: ( (zip_tseitin_10 @ X0 @ X0) | ~ (zip_tseitin_13 @ X0))),
% 4.18/2.31 inference('eq_fact', [status(thm)], [zip_derived_cl1036])).
% 4.18/2.31 thf(zip_derived_cl23, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (outputs @ X0 @ good) | ~ (zip_tseitin_10 @ X1 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_21])).
% 4.18/2.31 thf(zip_derived_cl1205, plain,
% 4.18/2.31 (![X0 : $i]: (~ (zip_tseitin_13 @ X0) | (outputs @ X0 @ good))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1202, zip_derived_cl23])).
% 4.18/2.31 thf(zf_stmt_29, axiom,
% 4.18/2.31 (![Y:$i,V:$i]:
% 4.18/2.31 ( ( ( zip_tseitin_14 @ Y ) =>
% 4.18/2.31 ( ( halts2 @ V @ Y ) & ( outputs @ V @ good ) ) ) =>
% 4.18/2.31 ( zip_tseitin_15 @ Y @ V ) ))).
% 4.18/2.31 thf(zip_derived_cl33, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_15 @ X0 @ X1)
% 4.18/2.31 | ~ (halts2 @ X1 @ X0)
% 4.18/2.31 | ~ (outputs @ X1 @ good))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_29])).
% 4.18/2.31 thf(zip_derived_cl1207, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | ~ (halts2 @ X0 @ X1)
% 4.18/2.31 | (zip_tseitin_15 @ X1 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1205, zip_derived_cl33])).
% 4.18/2.31 thf(zip_derived_cl1211, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_14 @ X0)
% 4.18/2.31 | (zip_tseitin_15 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl245, zip_derived_cl1207])).
% 4.18/2.31 thf(zip_derived_cl1226, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_15 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_14 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X1))),
% 4.18/2.31 inference('simplify', [status(thm)], [zip_derived_cl1211])).
% 4.18/2.31 thf(zip_derived_cl34, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_15 @ X0 @ X1) | (zip_tseitin_14 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_29])).
% 4.18/2.31 thf(zip_derived_cl1297, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X1) | (zip_tseitin_15 @ X0 @ X1))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl1226, zip_derived_cl34])).
% 4.18/2.31 thf(zf_stmt_30, axiom,
% 4.18/2.31 (![Y:$i,V:$i]:
% 4.18/2.31 ( ( ( zip_tseitin_16 @ Y ) =>
% 4.18/2.31 ( ( halts2 @ V @ Y ) & ( outputs @ V @ bad ) ) ) =>
% 4.18/2.31 ( zip_tseitin_17 @ Y @ V ) ))).
% 4.18/2.31 thf(zip_derived_cl38, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_17 @ X0 @ X1) | (zip_tseitin_16 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_30])).
% 4.18/2.31 thf(zf_stmt_31, type, zip_tseitin_20 : $i > $o).
% 4.18/2.31 thf(zf_stmt_32, axiom,
% 4.18/2.31 (![U:$i]:
% 4.18/2.31 ( ( zip_tseitin_20 @ U ) =>
% 4.18/2.31 ( ( ![Y:$i]: ( zip_tseitin_19 @ Y @ U ) ) & ( program @ U ) ) ))).
% 4.18/2.31 thf(zf_stmt_33, type, zip_tseitin_19 : $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_34, axiom,
% 4.18/2.31 (![Y:$i,U:$i]:
% 4.18/2.31 ( ( zip_tseitin_19 @ Y @ U ) =>
% 4.18/2.31 ( ( ( ( program @ Y ) & ( ~( halts2 @ Y @ Y ) ) ) =>
% 4.18/2.31 ( zip_tseitin_18 @ Y @ U ) ) &
% 4.18/2.31 ( ( ( program @ Y ) & ( halts2 @ Y @ Y ) ) => ( ~( halts2 @ U @ Y ) ) ) ) ))).
% 4.18/2.31 thf(zf_stmt_35, type, zip_tseitin_18 : $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_36, axiom,
% 4.18/2.31 (![Y:$i,U:$i]:
% 4.18/2.31 ( ( zip_tseitin_18 @ Y @ U ) =>
% 4.18/2.31 ( ( halts2 @ U @ Y ) & ( outputs @ U @ bad ) ) ))).
% 4.18/2.31 thf(zf_stmt_37, type, zip_tseitin_17 : $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_38, type, zip_tseitin_16 : $i > $o).
% 4.18/2.31 thf(zf_stmt_39, type, zip_tseitin_15 : $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_40, type, zip_tseitin_14 : $i > $o).
% 4.18/2.31 thf(zf_stmt_41, axiom,
% 4.18/2.31 (( ?[V:$i]:
% 4.18/2.31 ( ( ![Y:$i]: ( ( zip_tseitin_17 @ Y @ V ) & ( zip_tseitin_15 @ Y @ V ) ) ) &
% 4.18/2.31 ( program @ V ) ) ) =>
% 4.18/2.31 ( ?[U:$i]: ( zip_tseitin_20 @ U ) ))).
% 4.18/2.31 thf(zip_derived_cl45, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 ( (zip_tseitin_20 @ sk__7)
% 4.18/2.31 | ~ (program @ X0)
% 4.18/2.31 | ~ (zip_tseitin_17 @ (sk__8 @ X0) @ X0)
% 4.18/2.31 | ~ (zip_tseitin_15 @ (sk__8 @ X0) @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_41])).
% 4.18/2.31 thf(zip_derived_cl43, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_19 @ X0 @ X1) | ~ (zip_tseitin_20 @ X1))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_32])).
% 4.18/2.31 thf(zip_derived_cl41, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (program @ X0)
% 4.18/2.31 | (halts2 @ X0 @ X0)
% 4.18/2.31 | (zip_tseitin_18 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_19 @ X0 @ X1))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_34])).
% 4.18/2.31 thf(zip_derived_cl138, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_20 @ X0)
% 4.18/2.31 | (zip_tseitin_18 @ X1 @ X0)
% 4.18/2.31 | (halts2 @ X1 @ X1)
% 4.18/2.31 | ~ (program @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl41])).
% 4.18/2.31 thf(zip_derived_cl39, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (halts2 @ X0 @ X1) | ~ (zip_tseitin_18 @ X1 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_36])).
% 4.18/2.31 thf(zip_derived_cl661, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (program @ X1)
% 4.18/2.31 | (halts2 @ X1 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_20 @ X0)
% 4.18/2.31 | (halts2 @ X0 @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl138, zip_derived_cl39])).
% 4.18/2.31 thf(zip_derived_cl993, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 ( (halts2 @ X0 @ X0) | ~ (zip_tseitin_20 @ X0) | ~ (program @ X0))),
% 4.18/2.31 inference('eq_fact', [status(thm)], [zip_derived_cl661])).
% 4.18/2.31 thf(zip_derived_cl43, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_19 @ X0 @ X1) | ~ (zip_tseitin_20 @ X1))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_32])).
% 4.18/2.31 thf(zip_derived_cl42, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (program @ X0)
% 4.18/2.31 | ~ (halts2 @ X0 @ X0)
% 4.18/2.31 | ~ (halts2 @ X1 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_19 @ X0 @ X1))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_34])).
% 4.18/2.31 thf(zip_derived_cl101, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 (~ (zip_tseitin_19 @ X0 @ X0)
% 4.18/2.31 | ~ (halts2 @ X0 @ X0)
% 4.18/2.31 | ~ (program @ X0))),
% 4.18/2.31 inference('eq_fact', [status(thm)], [zip_derived_cl42])).
% 4.18/2.31 thf(zip_derived_cl104, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 (~ (zip_tseitin_20 @ X0) | ~ (program @ X0) | ~ (halts2 @ X0 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl101])).
% 4.18/2.31 thf(zip_derived_cl44, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_20 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_32])).
% 4.18/2.31 thf(zip_derived_cl105, plain,
% 4.18/2.31 (![X0 : $i]: (~ (halts2 @ X0 @ X0) | ~ (zip_tseitin_20 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl104, zip_derived_cl44])).
% 4.18/2.31 thf(zip_derived_cl1003, plain,
% 4.18/2.31 (![X0 : $i]: (~ (program @ X0) | ~ (zip_tseitin_20 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl993, zip_derived_cl105])).
% 4.18/2.31 thf(zip_derived_cl44, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_20 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_32])).
% 4.18/2.31 thf(zip_derived_cl1004, plain, (![X0 : $i]: ~ (zip_tseitin_20 @ X0)),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl1003, zip_derived_cl44])).
% 4.18/2.31 thf(zip_derived_cl1005, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 (~ (program @ X0)
% 4.18/2.31 | ~ (zip_tseitin_17 @ (sk__8 @ X0) @ X0)
% 4.18/2.31 | ~ (zip_tseitin_15 @ (sk__8 @ X0) @ X0))),
% 4.18/2.31 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl1004])).
% 4.18/2.31 thf(zip_derived_cl1034, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 ( (zip_tseitin_16 @ (sk__8 @ X0))
% 4.18/2.31 | ~ (zip_tseitin_15 @ (sk__8 @ X0) @ X0)
% 4.18/2.31 | ~ (program @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl1005])).
% 4.18/2.31 thf(zip_derived_cl1298, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | ~ (program @ X0)
% 4.18/2.31 | (zip_tseitin_16 @ (sk__8 @ X0)))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1297, zip_derived_cl1034])).
% 4.18/2.31 thf(zip_derived_cl29, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_13 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_15])).
% 4.18/2.31 thf(zip_derived_cl1301, plain,
% 4.18/2.31 (![X0 : $i]: ( (zip_tseitin_16 @ (sk__8 @ X0)) | ~ (zip_tseitin_13 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl1298, zip_derived_cl29])).
% 4.18/2.31 thf(zip_derived_cl1462, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (outputs @ X1 @ bad)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X0))),
% 4.18/2.31 inference('sup+', [status(thm)], [zip_derived_cl1460, zip_derived_cl1301])).
% 4.18/2.31 thf(zip_derived_cl1497, plain,
% 4.18/2.31 (![X0 : $i]: ( (outputs @ X0 @ bad) | ~ (zip_tseitin_13 @ X0))),
% 4.18/2.31 inference('condensation', [status(thm)], [zip_derived_cl1462])).
% 4.18/2.31 thf(zip_derived_cl37, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_17 @ X0 @ X1)
% 4.18/2.31 | ~ (halts2 @ X1 @ X0)
% 4.18/2.31 | ~ (outputs @ X1 @ bad))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_30])).
% 4.18/2.31 thf(zip_derived_cl1499, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | ~ (halts2 @ X0 @ X1)
% 4.18/2.31 | (zip_tseitin_17 @ X1 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1497, zip_derived_cl37])).
% 4.18/2.31 thf(zip_derived_cl1510, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_16 @ X0)
% 4.18/2.31 | (zip_tseitin_17 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1123, zip_derived_cl1499])).
% 4.18/2.31 thf(zip_derived_cl1523, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_17 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_16 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_13 @ X1))),
% 4.18/2.31 inference('simplify', [status(thm)], [zip_derived_cl1510])).
% 4.18/2.31 thf(zip_derived_cl38, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_17 @ X0 @ X1) | (zip_tseitin_16 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_30])).
% 4.18/2.31 thf(zip_derived_cl1551, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X1) | (zip_tseitin_17 @ X0 @ X1))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl1523, zip_derived_cl38])).
% 4.18/2.31 thf(zip_derived_cl1005, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 (~ (program @ X0)
% 4.18/2.31 | ~ (zip_tseitin_17 @ (sk__8 @ X0) @ X0)
% 4.18/2.31 | ~ (zip_tseitin_15 @ (sk__8 @ X0) @ X0))),
% 4.18/2.31 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl1004])).
% 4.18/2.31 thf(zip_derived_cl1552, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_15 @ (sk__8 @ X0) @ X0)
% 4.18/2.31 | ~ (program @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1551, zip_derived_cl1005])).
% 4.18/2.31 thf(zip_derived_cl1297, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_13 @ X1) | (zip_tseitin_15 @ X0 @ X1))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl1226, zip_derived_cl34])).
% 4.18/2.31 thf(zip_derived_cl1585, plain,
% 4.18/2.31 (![X0 : $i]: (~ (program @ X0) | ~ (zip_tseitin_13 @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl1552, zip_derived_cl1297])).
% 4.18/2.31 thf(zip_derived_cl29, plain,
% 4.18/2.31 (![X0 : $i]: ( (program @ X0) | ~ (zip_tseitin_13 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_15])).
% 4.18/2.31 thf(zip_derived_cl1586, plain, (![X0 : $i]: ~ (zip_tseitin_13 @ X0)),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl1585, zip_derived_cl29])).
% 4.18/2.31 thf(zip_derived_cl1847, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X0) | ~ (zip_tseitin_7 @ (sk__6 @ X0) @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl1846, zip_derived_cl1586])).
% 4.18/2.31 thf(zip_derived_cl1848, plain,
% 4.18/2.31 (![X0 : $i]: ( (zip_tseitin_6 @ (sk__6 @ X0)) | ~ (zip_tseitin_1 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl1847])).
% 4.18/2.31 thf(zip_derived_cl1881, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (outputs @ X1 @ good)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X0))),
% 4.18/2.31 inference('sup+', [status(thm)], [zip_derived_cl1878, zip_derived_cl1848])).
% 4.18/2.31 thf(zip_derived_cl1894, plain,
% 4.18/2.31 (![X0 : $i]: ( (outputs @ X0 @ good) | ~ (zip_tseitin_1 @ X0))),
% 4.18/2.31 inference('condensation', [status(thm)], [zip_derived_cl1881])).
% 4.18/2.31 thf(zip_derived_cl16, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_7 @ X0 @ X1)
% 4.18/2.31 | ~ (halts3 @ X1 @ X0 @ X0)
% 4.18/2.31 | ~ (outputs @ X1 @ good))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_11])).
% 4.18/2.31 thf(zip_derived_cl1895, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X0)
% 4.18/2.31 | ~ (halts3 @ X0 @ X1 @ X1)
% 4.18/2.31 | (zip_tseitin_7 @ X1 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1894, zip_derived_cl16])).
% 4.18/2.31 thf(zip_derived_cl1935, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_6 @ X0)
% 4.18/2.31 | (zip_tseitin_7 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1877, zip_derived_cl1895])).
% 4.18/2.31 thf(zip_derived_cl1945, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_7 @ X0 @ X1)
% 4.18/2.31 | ~ (zip_tseitin_6 @ X0)
% 4.18/2.31 | ~ (zip_tseitin_1 @ X1))),
% 4.18/2.31 inference('simplify', [status(thm)], [zip_derived_cl1935])).
% 4.18/2.31 thf(zip_derived_cl17, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_7 @ X0 @ X1) | (zip_tseitin_6 @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_11])).
% 4.18/2.31 thf(zip_derived_cl1946, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X1) | (zip_tseitin_7 @ X0 @ X1))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl1945, zip_derived_cl17])).
% 4.18/2.31 thf(zip_derived_cl1847, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 (~ (zip_tseitin_1 @ X0) | ~ (zip_tseitin_7 @ (sk__6 @ X0) @ X0))),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl1846, zip_derived_cl1586])).
% 4.18/2.31 thf(zip_derived_cl1948, plain,
% 4.18/2.31 (![X0 : $i]: (~ (zip_tseitin_1 @ X0) | ~ (zip_tseitin_1 @ X0))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl1946, zip_derived_cl1847])).
% 4.18/2.31 thf(zip_derived_cl1949, plain, (![X0 : $i]: ~ (zip_tseitin_1 @ X0)),
% 4.18/2.31 inference('simplify', [status(thm)], [zip_derived_cl1948])).
% 4.18/2.31 thf(prove_this, conjecture,
% 4.18/2.31 (~( ?[X1:$i]:
% 4.18/2.31 ( ( ![Y1:$i]:
% 4.18/2.31 ( ( program @ Y1 ) => ( ![Z1:$i]: ( decides @ X1 @ Y1 @ Z1 ) ) ) ) &
% 4.18/2.31 ( algorithm @ X1 ) ) ))).
% 4.18/2.31 thf(zf_stmt_42, negated_conjecture,
% 4.18/2.31 (?[X1:$i]:
% 4.18/2.31 ( ( ![Y1:$i]:
% 4.18/2.31 ( ( program @ Y1 ) => ( ![Z1:$i]: ( decides @ X1 @ Y1 @ Z1 ) ) ) ) &
% 4.18/2.31 ( algorithm @ X1 ) )),
% 4.18/2.31 inference('cnf.neg', [status(esa)], [prove_this])).
% 4.18/2.31 thf(zip_derived_cl47, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]: ( (decides @ sk__9 @ X0 @ X1) | ~ (program @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_42])).
% 4.18/2.31 thf(zf_stmt_43, axiom,
% 4.18/2.31 (![Y:$i,X:$i]:
% 4.18/2.31 ( ( ( program @ Y ) => ( ![Z:$i]: ( decides @ X @ Y @ Z ) ) ) =>
% 4.18/2.31 ( zip_tseitin_0 @ Y @ X ) ))).
% 4.18/2.31 thf(zip_derived_cl0, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]:
% 4.18/2.31 ( (zip_tseitin_0 @ X0 @ X1) | ~ (decides @ X1 @ X0 @ (sk_ @ X1 @ X0)))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_43])).
% 4.18/2.31 thf(zip_derived_cl52, plain,
% 4.18/2.31 (![X0 : $i]: (~ (program @ X0) | (zip_tseitin_0 @ X0 @ sk__9))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl0])).
% 4.18/2.31 thf(zip_derived_cl1, plain,
% 4.18/2.31 (![X0 : $i, X1 : $i]: ( (zip_tseitin_0 @ X0 @ X1) | (program @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_43])).
% 4.18/2.31 thf(zip_derived_cl53, plain, (![X0 : $i]: (zip_tseitin_0 @ X0 @ sk__9)),
% 4.18/2.31 inference('clc', [status(thm)], [zip_derived_cl52, zip_derived_cl1])).
% 4.18/2.31 thf(zf_stmt_44, type, zip_tseitin_1 : $i > $o).
% 4.18/2.31 thf(zf_stmt_45, type, zip_tseitin_0 : $i > $i > $o).
% 4.18/2.31 thf(zf_stmt_46, axiom,
% 4.18/2.31 (( ?[X:$i]: ( ( ![Y:$i]: ( zip_tseitin_0 @ Y @ X ) ) & ( algorithm @ X ) ) ) =>
% 4.18/2.31 ( ?[W:$i]: ( zip_tseitin_1 @ W ) ))).
% 4.18/2.31 thf(zip_derived_cl4, plain,
% 4.18/2.31 (![X0 : $i]:
% 4.18/2.31 ( (zip_tseitin_1 @ sk__1)
% 4.18/2.31 | ~ (algorithm @ X0)
% 4.18/2.31 | ~ (zip_tseitin_0 @ (sk__2 @ X0) @ X0))),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_46])).
% 4.18/2.31 thf(zip_derived_cl77, plain,
% 4.18/2.31 ((~ (algorithm @ sk__9) | (zip_tseitin_1 @ sk__1))),
% 4.18/2.31 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl4])).
% 4.18/2.31 thf(zip_derived_cl46, plain, ( (algorithm @ sk__9)),
% 4.18/2.31 inference('cnf', [status(esa)], [zf_stmt_42])).
% 4.18/2.31 thf(zip_derived_cl78, plain, ( (zip_tseitin_1 @ sk__1)),
% 4.18/2.31 inference('demod', [status(thm)], [zip_derived_cl77, zip_derived_cl46])).
% 4.18/2.31 thf(zip_derived_cl1950, plain, ($false),
% 4.18/2.31 inference('sup+', [status(thm)], [zip_derived_cl1949, zip_derived_cl78])).
% 4.18/2.31
% 4.18/2.31 % SZS output end Refutation
% 4.18/2.31
% 4.18/2.31
% 4.18/2.31 % Terminating...
% 4.18/2.46 % Runner terminated.
% 4.18/2.48 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------