%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU166+1 : TPTP v9.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.tZ4Pp8d3uj true
% Computer : n004.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 04:53:41 PM UTC 2025
% Result : Theorem 32.27s 5.24s
% Output : Refutation 32.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU166+1 : TPTP v9.2.0. Released v3.3.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.tZ4Pp8d3uj true
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Wed Oct 1 16:14:08 EDT 2025
% 0.18/0.34 % CPUTime :
% 0.18/0.34 % Running portfolio for 300 s
% 0.18/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.34 % Number of cores: 8
% 0.18/0.34 % Python version: Python 3.6.8
% 0.18/0.34 % Running in FO mode
% 0.51/0.63 % Total configuration time : 435
% 0.51/0.63 % Estimated wc time : 1092
% 0.51/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 32.27/5.24 % Solved by fo/fo4.sh.
% 32.27/5.24 % done 1238 iterations in 4.443s
% 32.27/5.24 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 32.27/5.24 % SZS output start Refutation
% 32.27/5.24 thf(sk__5_type, type, sk__5: $i > $i > $i).
% 32.27/5.24 thf(sk__10_type, type, sk__10: $i).
% 32.27/5.24 thf(sk__4_type, type, sk__4: $i > $i > $i > $i).
% 32.27/5.24 thf(sk__3_type, type, sk__3: $i > $i > $i > $i).
% 32.27/5.24 thf(in_type, type, in: $i > $i > $o).
% 32.27/5.24 thf(subset_type, type, subset: $i > $i > $o).
% 32.27/5.24 thf(sk__9_type, type, sk__9: $i).
% 32.27/5.24 thf(sk__8_type, type, sk__8: $i).
% 32.27/5.24 thf(cartesian_product2_type, type, cartesian_product2: $i > $i > $i).
% 32.27/5.24 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $i > $i > $o).
% 32.27/5.24 thf(ordered_pair_type, type, ordered_pair: $i > $i > $i).
% 32.27/5.24 thf(t118_zfmisc_1, conjecture,
% 32.27/5.24 (![A:$i,B:$i,C:$i]:
% 32.27/5.24 ( ( subset @ A @ B ) =>
% 32.27/5.24 ( ( subset @
% 32.27/5.24 ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) &
% 32.27/5.24 ( subset @
% 32.27/5.24 ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ))).
% 32.27/5.24 thf(zf_stmt_0, negated_conjecture,
% 32.27/5.24 (~( ![A:$i,B:$i,C:$i]:
% 32.27/5.24 ( ( subset @ A @ B ) =>
% 32.27/5.24 ( ( subset @
% 32.27/5.24 ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) &
% 32.27/5.24 ( subset @
% 32.27/5.24 ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )),
% 32.27/5.24 inference('cnf.neg', [status(esa)], [t118_zfmisc_1])).
% 32.27/5.24 thf(zip_derived_cl22, plain,
% 32.27/5.24 ((~ (subset @ (cartesian_product2 @ sk__8 @ sk__10) @
% 32.27/5.24 (cartesian_product2 @ sk__9 @ sk__10))
% 32.27/5.24 | ~ (subset @ (cartesian_product2 @ sk__10 @ sk__8) @
% 32.27/5.24 (cartesian_product2 @ sk__10 @ sk__9)))),
% 32.27/5.24 inference('cnf', [status(esa)], [zf_stmt_0])).
% 32.27/5.24 thf(d3_tarski, axiom,
% 32.27/5.24 (![A:$i,B:$i]:
% 32.27/5.24 ( ( subset @ A @ B ) <=> ( ![C:$i]: ( ( in @ C @ A ) => ( in @ C @ B ) ) ) ))).
% 32.27/5.24 thf(zip_derived_cl11, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i]:
% 32.27/5.24 ( (subset @ X0 @ X1) | ~ (in @ (sk__5 @ X1 @ X0) @ X1))),
% 32.27/5.24 inference('cnf', [status(esa)], [d3_tarski])).
% 32.27/5.24 thf(zip_derived_cl23, plain, ( (subset @ sk__8 @ sk__9)),
% 32.27/5.24 inference('cnf', [status(esa)], [zf_stmt_0])).
% 32.27/5.24 thf(zip_derived_cl12, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i]:
% 32.27/5.24 ( (subset @ X0 @ X1) | (in @ (sk__5 @ X1 @ X0) @ X0))),
% 32.27/5.24 inference('cnf', [status(esa)], [d3_tarski])).
% 32.27/5.24 thf(d2_zfmisc_1, axiom,
% 32.27/5.24 (![A:$i,B:$i,C:$i]:
% 32.27/5.24 ( ( ( C ) = ( cartesian_product2 @ A @ B ) ) <=>
% 32.27/5.24 ( ![D:$i]:
% 32.27/5.24 ( ( in @ D @ C ) <=>
% 32.27/5.24 ( ?[E:$i,F:$i]:
% 32.27/5.24 ( ( in @ E @ A ) & ( in @ F @ B ) &
% 32.27/5.24 ( ( D ) = ( ordered_pair @ E @ F ) ) ) ) ) ) ))).
% 32.27/5.24 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $i > $i > $o).
% 32.27/5.24 thf(zf_stmt_2, axiom,
% 32.27/5.24 (![F:$i,E:$i,D:$i,B:$i,A:$i]:
% 32.27/5.24 ( ( zip_tseitin_0 @ F @ E @ D @ B @ A ) <=>
% 32.27/5.24 ( ( ( D ) = ( ordered_pair @ E @ F ) ) & ( in @ F @ B ) & ( in @ E @ A ) ) ))).
% 32.27/5.24 thf(zf_stmt_3, axiom,
% 32.27/5.24 (![A:$i,B:$i,C:$i]:
% 32.27/5.24 ( ( ( C ) = ( cartesian_product2 @ A @ B ) ) <=>
% 32.27/5.24 ( ![D:$i]:
% 32.27/5.24 ( ( in @ D @ C ) <=>
% 32.27/5.24 ( ?[E:$i,F:$i]: ( zip_tseitin_0 @ F @ E @ D @ B @ A ) ) ) ) ))).
% 32.27/5.24 thf(zip_derived_cl7, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 32.27/5.24 (~ (in @ X0 @ X1)
% 32.27/5.24 | (zip_tseitin_0 @ (sk__4 @ X0 @ X2 @ X3) @
% 32.27/5.24 (sk__3 @ X0 @ X2 @ X3) @ X0 @ X2 @ X3)
% 32.27/5.24 | ((X1) != (cartesian_product2 @ X3 @ X2)))),
% 32.27/5.24 inference('cnf', [status(esa)], [zf_stmt_3])).
% 32.27/5.24 thf(zip_derived_cl39, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 32.27/5.24 ( (subset @ X0 @ X1)
% 32.27/5.24 | ((X0) != (cartesian_product2 @ X3 @ X2))
% 32.27/5.24 | (zip_tseitin_0 @ (sk__4 @ (sk__5 @ X1 @ X0) @ X2 @ X3) @
% 32.27/5.24 (sk__3 @ (sk__5 @ X1 @ X0) @ X2 @ X3) @ (sk__5 @ X1 @ X0) @ X2 @
% 32.27/5.24 X3))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl7])).
% 32.27/5.24 thf(zip_derived_cl106, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 32.27/5.24 ( (zip_tseitin_0 @
% 32.27/5.24 (sk__4 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 (sk__3 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0)
% 32.27/5.24 | (subset @ (cartesian_product2 @ X0 @ X1) @ X2))),
% 32.27/5.24 inference('eq_res', [status(thm)], [zip_derived_cl39])).
% 32.27/5.24 thf(zip_derived_cl3, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 32.27/5.24 ( (in @ X0 @ X1) | ~ (zip_tseitin_0 @ X0 @ X2 @ X3 @ X1 @ X4))),
% 32.27/5.24 inference('cnf', [status(esa)], [zf_stmt_2])).
% 32.27/5.24 thf(zip_derived_cl1463, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ X0 @ X1) @ X2)
% 32.27/5.24 | (in @
% 32.27/5.24 (sk__4 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 X1))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl3])).
% 32.27/5.24 thf(zip_derived_cl10, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 32.27/5.24 (~ (in @ X0 @ X1) | (in @ X0 @ X2) | ~ (subset @ X1 @ X2))),
% 32.27/5.24 inference('cnf', [status(esa)], [d3_tarski])).
% 32.27/5.24 thf(zip_derived_cl1469, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ X1 @ X0) @ X2)
% 32.27/5.24 | ~ (subset @ X0 @ X3)
% 32.27/5.24 | (in @
% 32.27/5.24 (sk__4 @ (sk__5 @ X2 @ (cartesian_product2 @ X1 @ X0)) @ X0 @ X1) @
% 32.27/5.24 X3))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl1463, zip_derived_cl10])).
% 32.27/5.24 thf(zip_derived_cl1507, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i]:
% 32.27/5.24 ( (in @
% 32.27/5.24 (sk__4 @ (sk__5 @ X1 @ (cartesian_product2 @ X0 @ sk__8)) @
% 32.27/5.24 sk__8 @ X0) @
% 32.27/5.24 sk__9)
% 32.27/5.24 | (subset @ (cartesian_product2 @ X0 @ sk__8) @ X1))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl1469])).
% 32.27/5.24 thf(zip_derived_cl106, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 32.27/5.24 ( (zip_tseitin_0 @
% 32.27/5.24 (sk__4 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 (sk__3 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0)
% 32.27/5.24 | (subset @ (cartesian_product2 @ X0 @ X1) @ X2))),
% 32.27/5.24 inference('eq_res', [status(thm)], [zip_derived_cl39])).
% 32.27/5.24 thf(zip_derived_cl4, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 32.27/5.24 ( (in @ X0 @ X1) | ~ (zip_tseitin_0 @ X2 @ X0 @ X3 @ X4 @ X1))),
% 32.27/5.24 inference('cnf', [status(esa)], [zf_stmt_2])).
% 32.27/5.24 thf(zip_derived_cl1464, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ X0 @ X1) @ X2)
% 32.27/5.24 | (in @
% 32.27/5.24 (sk__3 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 X0))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl4])).
% 32.27/5.24 thf(zip_derived_cl106, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 32.27/5.24 ( (zip_tseitin_0 @
% 32.27/5.24 (sk__4 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 (sk__3 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0)
% 32.27/5.24 | (subset @ (cartesian_product2 @ X0 @ X1) @ X2))),
% 32.27/5.24 inference('eq_res', [status(thm)], [zip_derived_cl39])).
% 32.27/5.24 thf(zip_derived_cl2, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 32.27/5.24 (((X2) = (ordered_pair @ X0 @ X1))
% 32.27/5.24 | ~ (zip_tseitin_0 @ X1 @ X0 @ X2 @ X3 @ X4))),
% 32.27/5.24 inference('cnf', [status(esa)], [zf_stmt_2])).
% 32.27/5.24 thf(zip_derived_cl1462, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ X0 @ X1) @ X2)
% 32.27/5.24 | ((sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1))
% 32.27/5.24 = (ordered_pair @
% 32.27/5.24 (sk__3 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @
% 32.27/5.24 X0) @
% 32.27/5.24 (sk__4 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @
% 32.27/5.24 X0))))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl2])).
% 32.27/5.24 thf(zip_derived_cl5, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 32.27/5.24 ( (zip_tseitin_0 @ X0 @ X1 @ X2 @ X3 @ X4)
% 32.27/5.24 | ~ (in @ X1 @ X4)
% 32.27/5.24 | ~ (in @ X0 @ X3)
% 32.27/5.24 | ((X2) != (ordered_pair @ X1 @ X0)))),
% 32.27/5.24 inference('cnf', [status(esa)], [zf_stmt_2])).
% 32.27/5.24 thf(zip_derived_cl6, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 32.27/5.24 (~ (zip_tseitin_0 @ X0 @ X1 @ X2 @ X3 @ X4)
% 32.27/5.24 | (in @ X2 @ X5)
% 32.27/5.24 | ((X5) != (cartesian_product2 @ X4 @ X3)))),
% 32.27/5.24 inference('cnf', [status(esa)], [zf_stmt_3])).
% 32.27/5.24 thf(zip_derived_cl37, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 32.27/5.24 (((X2) != (ordered_pair @ X3 @ X4))
% 32.27/5.24 | ~ (in @ X4 @ X1)
% 32.27/5.24 | ~ (in @ X3 @ X0)
% 32.27/5.24 | ((X5) != (cartesian_product2 @ X0 @ X1))
% 32.27/5.24 | (in @ X2 @ X5))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl6])).
% 32.27/5.24 thf(zip_derived_cl76, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 32.27/5.24 ( (in @ (ordered_pair @ X2 @ X1) @ X0)
% 32.27/5.24 | ((X0) != (cartesian_product2 @ X4 @ X3))
% 32.27/5.24 | ~ (in @ X2 @ X4)
% 32.27/5.24 | ~ (in @ X1 @ X3))),
% 32.27/5.24 inference('eq_res', [status(thm)], [zip_derived_cl37])).
% 32.27/5.24 thf(zip_derived_cl77, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 32.27/5.24 (~ (in @ X1 @ X0)
% 32.27/5.24 | ~ (in @ X3 @ X2)
% 32.27/5.24 | (in @ (ordered_pair @ X3 @ X1) @ (cartesian_product2 @ X2 @ X0)))),
% 32.27/5.24 inference('eq_res', [status(thm)], [zip_derived_cl76])).
% 32.27/5.24 thf(zip_derived_cl15694, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 32.27/5.24 ( (in @ (sk__5 @ X2 @ (cartesian_product2 @ X1 @ X0)) @
% 32.27/5.24 (cartesian_product2 @ X4 @ X3))
% 32.27/5.24 | (subset @ (cartesian_product2 @ X1 @ X0) @ X2)
% 32.27/5.24 | ~ (in @
% 32.27/5.24 (sk__3 @ (sk__5 @ X2 @ (cartesian_product2 @ X1 @ X0)) @ X0 @ X1) @
% 32.27/5.24 X4)
% 32.27/5.24 | ~ (in @
% 32.27/5.24 (sk__4 @ (sk__5 @ X2 @ (cartesian_product2 @ X1 @ X0)) @ X0 @ X1) @
% 32.27/5.24 X3))),
% 32.27/5.24 inference('sup+', [status(thm)], [zip_derived_cl1462, zip_derived_cl77])).
% 32.27/5.24 thf(zip_derived_cl16167, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ X0 @ X1) @ X2)
% 32.27/5.24 | ~ (in @
% 32.27/5.24 (sk__4 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 X3)
% 32.27/5.24 | (subset @ (cartesian_product2 @ X0 @ X1) @ X2)
% 32.27/5.24 | (in @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @
% 32.27/5.24 (cartesian_product2 @ X0 @ X3)))),
% 32.27/5.24 inference('sup-', [status(thm)],
% 32.27/5.24 [zip_derived_cl1464, zip_derived_cl15694])).
% 32.27/5.24 thf(zip_derived_cl16169, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 32.27/5.24 ( (in @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @
% 32.27/5.24 (cartesian_product2 @ X0 @ X3))
% 32.27/5.24 | ~ (in @
% 32.27/5.24 (sk__4 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 X3)
% 32.27/5.24 | (subset @ (cartesian_product2 @ X0 @ X1) @ X2))),
% 32.27/5.24 inference('simplify', [status(thm)], [zip_derived_cl16167])).
% 32.27/5.24 thf(zip_derived_cl16172, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ X0 @ sk__8) @ X1)
% 32.27/5.24 | (subset @ (cartesian_product2 @ X0 @ sk__8) @ X1)
% 32.27/5.24 | (in @ (sk__5 @ X1 @ (cartesian_product2 @ X0 @ sk__8)) @
% 32.27/5.24 (cartesian_product2 @ X0 @ sk__9)))),
% 32.27/5.24 inference('sup-', [status(thm)],
% 32.27/5.24 [zip_derived_cl1507, zip_derived_cl16169])).
% 32.27/5.24 thf(zip_derived_cl16174, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i]:
% 32.27/5.24 ( (in @ (sk__5 @ X1 @ (cartesian_product2 @ X0 @ sk__8)) @
% 32.27/5.24 (cartesian_product2 @ X0 @ sk__9))
% 32.27/5.24 | (subset @ (cartesian_product2 @ X0 @ sk__8) @ X1))),
% 32.27/5.24 inference('simplify', [status(thm)], [zip_derived_cl16172])).
% 32.27/5.24 thf(zip_derived_cl16297, plain,
% 32.27/5.24 (![X0 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ X0 @ sk__8) @
% 32.27/5.24 (cartesian_product2 @ X0 @ sk__9))
% 32.27/5.24 | (subset @ (cartesian_product2 @ X0 @ sk__8) @
% 32.27/5.24 (cartesian_product2 @ X0 @ sk__9)))),
% 32.27/5.24 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl16174])).
% 32.27/5.24 thf(zip_derived_cl16298, plain,
% 32.27/5.24 (![X0 : $i]:
% 32.27/5.24 (subset @ (cartesian_product2 @ X0 @ sk__8) @
% 32.27/5.24 (cartesian_product2 @ X0 @ sk__9))),
% 32.27/5.24 inference('simplify', [status(thm)], [zip_derived_cl16297])).
% 32.27/5.24 thf(zip_derived_cl16317, plain,
% 32.27/5.24 (~ (subset @ (cartesian_product2 @ sk__8 @ sk__10) @
% 32.27/5.24 (cartesian_product2 @ sk__9 @ sk__10))),
% 32.27/5.24 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl16298])).
% 32.27/5.24 thf(zip_derived_cl11, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i]:
% 32.27/5.24 ( (subset @ X0 @ X1) | ~ (in @ (sk__5 @ X1 @ X0) @ X1))),
% 32.27/5.24 inference('cnf', [status(esa)], [d3_tarski])).
% 32.27/5.24 thf(zip_derived_cl1463, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ X0 @ X1) @ X2)
% 32.27/5.24 | (in @
% 32.27/5.24 (sk__4 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 X1))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl3])).
% 32.27/5.24 thf(zip_derived_cl23, plain, ( (subset @ sk__8 @ sk__9)),
% 32.27/5.24 inference('cnf', [status(esa)], [zf_stmt_0])).
% 32.27/5.24 thf(zip_derived_cl1464, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ X0 @ X1) @ X2)
% 32.27/5.24 | (in @
% 32.27/5.24 (sk__3 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 X0))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl4])).
% 32.27/5.24 thf(zip_derived_cl10, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 32.27/5.24 (~ (in @ X0 @ X1) | (in @ X0 @ X2) | ~ (subset @ X1 @ X2))),
% 32.27/5.24 inference('cnf', [status(esa)], [d3_tarski])).
% 32.27/5.24 thf(zip_derived_cl1510, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ X0 @ X1) @ X2)
% 32.27/5.24 | ~ (subset @ X0 @ X3)
% 32.27/5.24 | (in @
% 32.27/5.24 (sk__3 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @ X0) @
% 32.27/5.24 X3))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl1464, zip_derived_cl10])).
% 32.27/5.24 thf(zip_derived_cl1548, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i]:
% 32.27/5.24 ( (in @
% 32.27/5.24 (sk__3 @ (sk__5 @ X1 @ (cartesian_product2 @ sk__8 @ X0)) @ X0 @
% 32.27/5.24 sk__8) @
% 32.27/5.24 sk__9)
% 32.27/5.24 | (subset @ (cartesian_product2 @ sk__8 @ X0) @ X1))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl1510])).
% 32.27/5.24 thf(zip_derived_cl1462, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ X0 @ X1) @ X2)
% 32.27/5.24 | ((sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1))
% 32.27/5.24 = (ordered_pair @
% 32.27/5.24 (sk__3 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @
% 32.27/5.24 X0) @
% 32.27/5.24 (sk__4 @ (sk__5 @ X2 @ (cartesian_product2 @ X0 @ X1)) @ X1 @
% 32.27/5.24 X0))))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl2])).
% 32.27/5.24 thf(zip_derived_cl37, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 32.27/5.24 (((X2) != (ordered_pair @ X3 @ X4))
% 32.27/5.24 | ~ (in @ X4 @ X1)
% 32.27/5.24 | ~ (in @ X3 @ X0)
% 32.27/5.24 | ((X5) != (cartesian_product2 @ X0 @ X1))
% 32.27/5.24 | (in @ X2 @ X5))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl6])).
% 32.27/5.24 thf(zip_derived_cl15693, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 32.27/5.24 (((X3) != (sk__5 @ X2 @ (cartesian_product2 @ X1 @ X0)))
% 32.27/5.24 | (subset @ (cartesian_product2 @ X1 @ X0) @ X2)
% 32.27/5.24 | (in @ X3 @ X4)
% 32.27/5.24 | ((X4) != (cartesian_product2 @ X6 @ X5))
% 32.27/5.24 | ~ (in @
% 32.27/5.24 (sk__3 @ (sk__5 @ X2 @ (cartesian_product2 @ X1 @ X0)) @ X0 @ X1) @
% 32.27/5.24 X6)
% 32.27/5.24 | ~ (in @
% 32.27/5.24 (sk__4 @ (sk__5 @ X2 @ (cartesian_product2 @ X1 @ X0)) @ X0 @ X1) @
% 32.27/5.24 X5))),
% 32.27/5.24 inference('sup-', [status(thm)], [zip_derived_cl1462, zip_derived_cl37])).
% 32.27/5.24 thf(zip_derived_cl16301, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ sk__8 @ X0) @ X1)
% 32.27/5.24 | ~ (in @
% 32.27/5.24 (sk__4 @ (sk__5 @ X1 @ (cartesian_product2 @ sk__8 @ X0)) @
% 32.27/5.24 X0 @ sk__8) @
% 32.27/5.24 X2)
% 32.27/5.24 | ((X3) != (cartesian_product2 @ sk__9 @ X2))
% 32.27/5.24 | (in @ X4 @ X3)
% 32.27/5.24 | (subset @ (cartesian_product2 @ sk__8 @ X0) @ X1)
% 32.27/5.24 | ((X4) != (sk__5 @ X1 @ (cartesian_product2 @ sk__8 @ X0))))),
% 32.27/5.24 inference('sup-', [status(thm)],
% 32.27/5.24 [zip_derived_cl1548, zip_derived_cl15693])).
% 32.27/5.24 thf(zip_derived_cl16304, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 32.27/5.24 (((X4) != (sk__5 @ X1 @ (cartesian_product2 @ sk__8 @ X0)))
% 32.27/5.24 | (in @ X4 @ X3)
% 32.27/5.24 | ((X3) != (cartesian_product2 @ sk__9 @ X2))
% 32.27/5.24 | ~ (in @
% 32.27/5.24 (sk__4 @ (sk__5 @ X1 @ (cartesian_product2 @ sk__8 @ X0)) @
% 32.27/5.24 X0 @ sk__8) @
% 32.27/5.24 X2)
% 32.27/5.24 | (subset @ (cartesian_product2 @ sk__8 @ X0) @ X1))),
% 32.27/5.24 inference('simplify', [status(thm)], [zip_derived_cl16301])).
% 32.27/5.24 thf(zip_derived_cl17024, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ sk__8 @ X0) @ X1)
% 32.27/5.24 | (subset @ (cartesian_product2 @ sk__8 @ X0) @ X1)
% 32.27/5.24 | ((X2) != (cartesian_product2 @ sk__9 @ X0))
% 32.27/5.24 | (in @ X3 @ X2)
% 32.27/5.24 | ((X3) != (sk__5 @ X1 @ (cartesian_product2 @ sk__8 @ X0))))),
% 32.27/5.24 inference('sup-', [status(thm)],
% 32.27/5.24 [zip_derived_cl1463, zip_derived_cl16304])).
% 32.27/5.24 thf(zip_derived_cl17027, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 32.27/5.24 (((X3) != (sk__5 @ X1 @ (cartesian_product2 @ sk__8 @ X0)))
% 32.27/5.24 | (in @ X3 @ X2)
% 32.27/5.24 | ((X2) != (cartesian_product2 @ sk__9 @ X0))
% 32.27/5.24 | (subset @ (cartesian_product2 @ sk__8 @ X0) @ X1))),
% 32.27/5.24 inference('simplify', [status(thm)], [zip_derived_cl17024])).
% 32.27/5.24 thf(zip_derived_cl17029, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i, X2 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ sk__8 @ X1) @ X0)
% 32.27/5.24 | ((X2) != (cartesian_product2 @ sk__9 @ X1))
% 32.27/5.24 | (in @ (sk__5 @ X0 @ (cartesian_product2 @ sk__8 @ X1)) @ X2))),
% 32.27/5.24 inference('eq_res', [status(thm)], [zip_derived_cl17027])).
% 32.27/5.24 thf(zip_derived_cl17031, plain,
% 32.27/5.24 (![X0 : $i, X1 : $i]:
% 32.27/5.24 ( (in @ (sk__5 @ X1 @ (cartesian_product2 @ sk__8 @ X0)) @
% 32.27/5.24 (cartesian_product2 @ sk__9 @ X0))
% 32.27/5.24 | (subset @ (cartesian_product2 @ sk__8 @ X0) @ X1))),
% 32.27/5.24 inference('eq_res', [status(thm)], [zip_derived_cl17029])).
% 32.27/5.24 thf(zip_derived_cl17754, plain,
% 32.27/5.24 (![X0 : $i]:
% 32.27/5.24 ( (subset @ (cartesian_product2 @ sk__8 @ X0) @
% 32.27/5.24 (cartesian_product2 @ sk__9 @ X0))
% 32.27/5.24 | (subset @ (cartesian_product2 @ sk__8 @ X0) @
% 32.27/5.24 (cartesian_product2 @ sk__9 @ X0)))),
% 32.27/5.24 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl17031])).
% 32.27/5.24 thf(zip_derived_cl17755, plain,
% 32.27/5.24 (![X0 : $i]:
% 32.27/5.24 (subset @ (cartesian_product2 @ sk__8 @ X0) @
% 32.27/5.24 (cartesian_product2 @ sk__9 @ X0))),
% 32.27/5.24 inference('simplify', [status(thm)], [zip_derived_cl17754])).
% 32.27/5.24 thf(zip_derived_cl17757, plain, ($false),
% 32.27/5.24 inference('demod', [status(thm)],
% 32.27/5.24 [zip_derived_cl16317, zip_derived_cl17755])).
% 32.27/5.24
% 32.27/5.24 % SZS output end Refutation
% 32.27/5.24
% 32.27/5.24
% 32.27/5.24 % Terminating...
% 32.27/5.26 % Runner terminated.
% 32.27/5.27 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------