%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET894+1 : TPTP v9.2.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.aiyL5S3cVu true
% Computer : n024.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 04:53:06 PM UTC 2025
% Result : Theorem 86.17s 12.94s
% Output : Refutation 86.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET894+1 : TPTP v9.2.0. Bugfixed v4.0.0.
% 0.03/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.aiyL5S3cVu true
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 13:15:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.43/0.62 % Total configuration time : 435
% 0.43/0.62 % Estimated wc time : 1092
% 0.43/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.52/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.52/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.52/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.52/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.52/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 86.17/12.94 % Solved by fo/fo6_bce.sh.
% 86.17/12.94 % BCE start: 24
% 86.17/12.94 % BCE eliminated: 0
% 86.17/12.94 % PE start: 24
% 86.17/12.94 logic: eq
% 86.17/12.94 % PE eliminated: 1
% 86.17/12.94 % done 1562 iterations in 12.233s
% 86.17/12.94 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 86.17/12.94 % SZS output start Refutation
% 86.17/12.94 thf(sk__5_type, type, sk__5: $i > $i > $i > $i).
% 86.17/12.94 thf(sk__9_type, type, sk__9: $i).
% 86.17/12.94 thf(sk__4_type, type, sk__4: $i > $i > $i > $i).
% 86.17/12.94 thf(in_type, type, in: $i > $i > $o).
% 86.17/12.94 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $i > $i > $o).
% 86.17/12.94 thf(sk__type, type, sk_: $i > $i > $i).
% 86.17/12.94 thf(singleton_type, type, singleton: $i > $i).
% 86.17/12.94 thf(ordered_pair_type, type, ordered_pair: $i > $i > $i).
% 86.17/12.94 thf(cartesian_product2_type, type, cartesian_product2: $i > $i > $i).
% 86.17/12.94 thf(sk__10_type, type, sk__10: $i).
% 86.17/12.94 thf(t35_zfmisc_1, conjecture,
% 86.17/12.94 (![A:$i,B:$i]:
% 86.17/12.94 ( ( cartesian_product2 @ ( singleton @ A ) @ ( singleton @ B ) ) =
% 86.17/12.94 ( singleton @ ( ordered_pair @ A @ B ) ) ))).
% 86.17/12.94 thf(zf_stmt_0, negated_conjecture,
% 86.17/12.94 (~( ![A:$i,B:$i]:
% 86.17/12.94 ( ( cartesian_product2 @ ( singleton @ A ) @ ( singleton @ B ) ) =
% 86.17/12.94 ( singleton @ ( ordered_pair @ A @ B ) ) ) )),
% 86.17/12.94 inference('cnf.neg', [status(esa)], [t35_zfmisc_1])).
% 86.17/12.94 thf(zip_derived_cl23, plain,
% 86.17/12.94 (((cartesian_product2 @ (singleton @ sk__9) @ (singleton @ sk__10))
% 86.17/12.94 != (singleton @ (ordered_pair @ sk__9 @ sk__10)))),
% 86.17/12.94 inference('cnf', [status(esa)], [zf_stmt_0])).
% 86.17/12.94 thf(d1_tarski, axiom,
% 86.17/12.94 (![A:$i,B:$i]:
% 86.17/12.94 ( ( ( B ) = ( singleton @ A ) ) <=>
% 86.17/12.94 ( ![C:$i]: ( ( in @ C @ B ) <=> ( ( C ) = ( A ) ) ) ) ))).
% 86.17/12.94 thf(zip_derived_cl5, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i]:
% 86.17/12.94 (((X1) = (singleton @ X0))
% 86.17/12.94 | ((sk_ @ X1 @ X0) = (X0))
% 86.17/12.94 | (in @ (sk_ @ X1 @ X0) @ X1))),
% 86.17/12.94 inference('cnf', [status(esa)], [d1_tarski])).
% 86.17/12.94 thf(d2_zfmisc_1, axiom,
% 86.17/12.94 (![A:$i,B:$i,C:$i]:
% 86.17/12.94 ( ( ( C ) = ( cartesian_product2 @ A @ B ) ) <=>
% 86.17/12.94 ( ![D:$i]:
% 86.17/12.94 ( ( in @ D @ C ) <=>
% 86.17/12.94 ( ?[E:$i,F:$i]:
% 86.17/12.94 ( ( in @ E @ A ) & ( in @ F @ B ) &
% 86.17/12.94 ( ( D ) = ( ordered_pair @ E @ F ) ) ) ) ) ) ))).
% 86.17/12.94 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $i > $i > $o).
% 86.17/12.94 thf(zf_stmt_2, axiom,
% 86.17/12.94 (![F:$i,E:$i,D:$i,B:$i,A:$i]:
% 86.17/12.94 ( ( zip_tseitin_0 @ F @ E @ D @ B @ A ) <=>
% 86.17/12.94 ( ( ( D ) = ( ordered_pair @ E @ F ) ) & ( in @ F @ B ) & ( in @ E @ A ) ) ))).
% 86.17/12.94 thf(zf_stmt_3, axiom,
% 86.17/12.94 (![A:$i,B:$i,C:$i]:
% 86.17/12.94 ( ( ( C ) = ( cartesian_product2 @ A @ B ) ) <=>
% 86.17/12.94 ( ![D:$i]:
% 86.17/12.94 ( ( in @ D @ C ) <=>
% 86.17/12.94 ( ?[E:$i,F:$i]: ( zip_tseitin_0 @ F @ E @ D @ B @ A ) ) ) ) ))).
% 86.17/12.94 thf(zip_derived_cl11, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 86.17/12.94 (~ (in @ X0 @ X1)
% 86.17/12.94 | (zip_tseitin_0 @ (sk__5 @ X0 @ X2 @ X3) @
% 86.17/12.94 (sk__4 @ X0 @ X2 @ X3) @ X0 @ X2 @ X3)
% 86.17/12.94 | ((X1) != (cartesian_product2 @ X3 @ X2)))),
% 86.17/12.94 inference('cnf', [status(esa)], [zf_stmt_3])).
% 86.17/12.94 thf(zip_derived_cl8, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 86.17/12.94 ( (in @ X0 @ X1) | ~ (zip_tseitin_0 @ X2 @ X0 @ X3 @ X4 @ X1))),
% 86.17/12.94 inference('cnf', [status(esa)], [zf_stmt_2])).
% 86.17/12.94 thf(zip_derived_cl113, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 86.17/12.94 (((X0) != (cartesian_product2 @ X2 @ X3))
% 86.17/12.94 | ~ (in @ X1 @ X0)
% 86.17/12.94 | (in @ (sk__4 @ X1 @ X3 @ X2) @ X2))),
% 86.17/12.94 inference('dp-resolution', [status(thm)],
% 86.17/12.94 [zip_derived_cl11, zip_derived_cl8])).
% 86.17/12.94 thf(zip_derived_cl177, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 ( (in @ (sk__4 @ X2 @ X1 @ X0) @ X0)
% 86.17/12.94 | ~ (in @ X2 @ (cartesian_product2 @ X0 @ X1)))),
% 86.17/12.94 inference('eq_res', [status(thm)], [zip_derived_cl113])).
% 86.17/12.94 thf(zip_derived_cl3, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (~ (in @ X0 @ X1) | ((X0) = (X2)) | ((X1) != (singleton @ X2)))),
% 86.17/12.94 inference('cnf', [status(esa)], [d1_tarski])).
% 86.17/12.94 thf(zip_derived_cl120, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i]: (((X0) = (X1)) | ~ (in @ X0 @ (singleton @ X1)))),
% 86.17/12.94 inference('eq_res', [status(thm)], [zip_derived_cl3])).
% 86.17/12.94 thf(zip_derived_cl215, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (~ (in @ X2 @ (cartesian_product2 @ (singleton @ X0) @ X1))
% 86.17/12.94 | ((sk__4 @ X2 @ X1 @ (singleton @ X0)) = (X0)))),
% 86.17/12.94 inference('s_sup-', [status(thm)], [zip_derived_cl177, zip_derived_cl120])).
% 86.17/12.94 thf(zip_derived_cl11, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 86.17/12.94 (~ (in @ X0 @ X1)
% 86.17/12.94 | (zip_tseitin_0 @ (sk__5 @ X0 @ X2 @ X3) @
% 86.17/12.94 (sk__4 @ X0 @ X2 @ X3) @ X0 @ X2 @ X3)
% 86.17/12.94 | ((X1) != (cartesian_product2 @ X3 @ X2)))),
% 86.17/12.94 inference('cnf', [status(esa)], [zf_stmt_3])).
% 86.17/12.94 thf(zip_derived_cl7, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 86.17/12.94 ( (in @ X0 @ X1) | ~ (zip_tseitin_0 @ X0 @ X2 @ X3 @ X1 @ X4))),
% 86.17/12.94 inference('cnf', [status(esa)], [zf_stmt_2])).
% 86.17/12.94 thf(zip_derived_cl112, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 86.17/12.94 (((X0) != (cartesian_product2 @ X2 @ X3))
% 86.17/12.94 | ~ (in @ X1 @ X0)
% 86.17/12.94 | (in @ (sk__5 @ X1 @ X3 @ X2) @ X3))),
% 86.17/12.94 inference('dp-resolution', [status(thm)],
% 86.17/12.94 [zip_derived_cl11, zip_derived_cl7])).
% 86.17/12.94 thf(zip_derived_cl174, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 ( (in @ (sk__5 @ X2 @ X0 @ X1) @ X0)
% 86.17/12.94 | ~ (in @ X2 @ (cartesian_product2 @ X1 @ X0)))),
% 86.17/12.94 inference('eq_res', [status(thm)], [zip_derived_cl112])).
% 86.17/12.94 thf(zip_derived_cl120, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i]: (((X0) = (X1)) | ~ (in @ X0 @ (singleton @ X1)))),
% 86.17/12.94 inference('eq_res', [status(thm)], [zip_derived_cl3])).
% 86.17/12.94 thf(zip_derived_cl176, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (~ (in @ X2 @ (cartesian_product2 @ X1 @ (singleton @ X0)))
% 86.17/12.94 | ((sk__5 @ X2 @ (singleton @ X0) @ X1) = (X0)))),
% 86.17/12.94 inference('s_sup-', [status(thm)], [zip_derived_cl174, zip_derived_cl120])).
% 86.17/12.94 thf(zip_derived_cl11, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 86.17/12.94 (~ (in @ X0 @ X1)
% 86.17/12.94 | (zip_tseitin_0 @ (sk__5 @ X0 @ X2 @ X3) @
% 86.17/12.94 (sk__4 @ X0 @ X2 @ X3) @ X0 @ X2 @ X3)
% 86.17/12.94 | ((X1) != (cartesian_product2 @ X3 @ X2)))),
% 86.17/12.94 inference('cnf', [status(esa)], [zf_stmt_3])).
% 86.17/12.94 thf(zip_derived_cl6, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 86.17/12.94 (((X2) = (ordered_pair @ X0 @ X1))
% 86.17/12.94 | ~ (zip_tseitin_0 @ X1 @ X0 @ X2 @ X3 @ X4))),
% 86.17/12.94 inference('cnf', [status(esa)], [zf_stmt_2])).
% 86.17/12.94 thf(zip_derived_cl111, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 86.17/12.94 (((X0) != (cartesian_product2 @ X2 @ X3))
% 86.17/12.94 | ~ (in @ X1 @ X0)
% 86.17/12.94 | ((X1)
% 86.17/12.94 = (ordered_pair @ (sk__4 @ X1 @ X3 @ X2) @ (sk__5 @ X1 @ X3 @ X2))))),
% 86.17/12.94 inference('dp-resolution', [status(thm)],
% 86.17/12.94 [zip_derived_cl11, zip_derived_cl6])).
% 86.17/12.94 thf(zip_derived_cl173, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (((X0)
% 86.17/12.94 = (ordered_pair @ (sk__4 @ X0 @ X2 @ X1) @ (sk__5 @ X0 @ X2 @ X1)))
% 86.17/12.94 | ~ (in @ X0 @ (cartesian_product2 @ X1 @ X2)))),
% 86.17/12.94 inference('eq_res', [status(thm)], [zip_derived_cl111])).
% 86.17/12.94 thf(zip_derived_cl662, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (~ (in @ X2 @ (cartesian_product2 @ X1 @ (singleton @ X0)))
% 86.17/12.94 | ((X2) = (ordered_pair @ (sk__4 @ X2 @ (singleton @ X0) @ X1) @ X0))
% 86.17/12.94 | ~ (in @ X2 @ (cartesian_product2 @ X1 @ (singleton @ X0))))),
% 86.17/12.94 inference('s_sup+', [status(thm)], [zip_derived_cl176, zip_derived_cl173])).
% 86.17/12.94 thf(zip_derived_cl664, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (((X2) = (ordered_pair @ (sk__4 @ X2 @ (singleton @ X0) @ X1) @ X0))
% 86.17/12.94 | ~ (in @ X2 @ (cartesian_product2 @ X1 @ (singleton @ X0))))),
% 86.17/12.94 inference('simplify', [status(thm)], [zip_derived_cl662])).
% 86.17/12.94 thf(zip_derived_cl689, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (~ (in @ X2 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X0) @ (singleton @ X1)))
% 86.17/12.94 | ((X2) = (ordered_pair @ X0 @ X1))
% 86.17/12.94 | ~ (in @ X2 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X0) @ (singleton @ X1))))),
% 86.17/12.94 inference('s_sup+', [status(thm)], [zip_derived_cl215, zip_derived_cl664])).
% 86.17/12.94 thf(zip_derived_cl690, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (((X2) = (ordered_pair @ X0 @ X1))
% 86.17/12.94 | ~ (in @ X2 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X0) @ (singleton @ X1))))),
% 86.17/12.94 inference('simplify', [status(thm)], [zip_derived_cl689])).
% 86.17/12.94 thf(zip_derived_cl726, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (((sk_ @ (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0)) @
% 86.17/12.94 X2) = (X2))
% 86.17/12.94 | ((cartesian_product2 @ (singleton @ X1) @ (singleton @ X0))
% 86.17/12.94 = (singleton @ X2))
% 86.17/12.94 | ((sk_ @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0)) @ X2)
% 86.17/12.94 = (ordered_pair @ X1 @ X0)))),
% 86.17/12.94 inference('s_sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl690])).
% 86.17/12.94 thf(zip_derived_cl19620, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (((ordered_pair @ X1 @ X0) != (X2))
% 86.17/12.94 | ((cartesian_product2 @ (singleton @ X1) @ (singleton @ X0))
% 86.17/12.94 = (singleton @ X2))
% 86.17/12.94 | ((sk_ @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0)) @ X2)
% 86.17/12.94 = (X2)))),
% 86.17/12.94 inference('eq_fact', [status(thm)], [zip_derived_cl726])).
% 86.17/12.94 thf(zip_derived_cl4, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i]:
% 86.17/12.94 (((X1) = (singleton @ X0))
% 86.17/12.94 | ((sk_ @ X1 @ X0) != (X0))
% 86.17/12.94 | ~ (in @ (sk_ @ X1 @ X0) @ X1))),
% 86.17/12.94 inference('cnf', [status(esa)], [d1_tarski])).
% 86.17/12.94 thf(zip_derived_cl19982, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (((cartesian_product2 @ (singleton @ X2) @ (singleton @ X1))
% 86.17/12.94 = (singleton @ X0))
% 86.17/12.94 | ((ordered_pair @ X2 @ X1) != (X0))
% 86.17/12.94 | ((cartesian_product2 @ (singleton @ X2) @ (singleton @ X1))
% 86.17/12.94 = (singleton @ X0))
% 86.17/12.94 | ((X0) != (X0))
% 86.17/12.94 | ~ (in @ X0 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X2) @ (singleton @ X1))))),
% 86.17/12.94 inference('s_sup-', [status(thm)], [zip_derived_cl19620, zip_derived_cl4])).
% 86.17/12.94 thf(zip_derived_cl19994, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (~ (in @ X0 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X2) @ (singleton @ X1)))
% 86.17/12.94 | ((ordered_pair @ X2 @ X1) != (X0))
% 86.17/12.94 | ((cartesian_product2 @ (singleton @ X2) @ (singleton @ X1))
% 86.17/12.94 = (singleton @ X0)))),
% 86.17/12.94 inference('simplify', [status(thm)], [zip_derived_cl19982])).
% 86.17/12.94 thf(zip_derived_cl20307, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i]:
% 86.17/12.94 (((cartesian_product2 @ (singleton @ X1) @ (singleton @ X0))
% 86.17/12.94 = (singleton @ (ordered_pair @ X1 @ X0)))
% 86.17/12.94 | ~ (in @ (ordered_pair @ X1 @ X0) @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0))))),
% 86.17/12.94 inference('eq_res', [status(thm)], [zip_derived_cl19994])).
% 86.17/12.94 thf(zip_derived_cl2, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (((X1) != (X0)) | (in @ X1 @ X2) | ((X2) != (singleton @ X0)))),
% 86.17/12.94 inference('cnf', [status(esa)], [d1_tarski])).
% 86.17/12.94 thf(zip_derived_cl121, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i]: (((X0) != (singleton @ X1)) | (in @ X1 @ X0))),
% 86.17/12.94 inference('eq_res', [status(thm)], [zip_derived_cl2])).
% 86.17/12.94 thf(zip_derived_cl123, plain, (![X0 : $i]: (in @ X0 @ (singleton @ X0))),
% 86.17/12.94 inference('eq_res', [status(thm)], [zip_derived_cl121])).
% 86.17/12.94 thf(zip_derived_cl123, plain, (![X0 : $i]: (in @ X0 @ (singleton @ X0))),
% 86.17/12.94 inference('eq_res', [status(thm)], [zip_derived_cl121])).
% 86.17/12.94 thf(l55_zfmisc_1, axiom,
% 86.17/12.94 (![A:$i,B:$i,C:$i,D:$i]:
% 86.17/12.94 ( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) <=>
% 86.17/12.94 ( ( in @ A @ C ) & ( in @ B @ D ) ) ))).
% 86.17/12.94 thf(zip_derived_cl18, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 86.17/12.94 ( (in @ (ordered_pair @ X0 @ X1) @ (cartesian_product2 @ X2 @ X3))
% 86.17/12.94 | ~ (in @ X1 @ X3)
% 86.17/12.94 | ~ (in @ X0 @ X2))),
% 86.17/12.94 inference('cnf', [status(esa)], [l55_zfmisc_1])).
% 86.17/12.94 thf(zip_derived_cl18, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 86.17/12.94 ( (in @ (ordered_pair @ X0 @ X1) @ (cartesian_product2 @ X2 @ X3))
% 86.17/12.94 | ~ (in @ X1 @ X3)
% 86.17/12.94 | ~ (in @ X0 @ X2))),
% 86.17/12.94 inference('cnf', [status(esa)], [l55_zfmisc_1])).
% 86.17/12.94 thf(zip_derived_cl177, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 ( (in @ (sk__4 @ X2 @ X1 @ X0) @ X0)
% 86.17/12.94 | ~ (in @ X2 @ (cartesian_product2 @ X0 @ X1)))),
% 86.17/12.94 inference('eq_res', [status(thm)], [zip_derived_cl113])).
% 86.17/12.94 thf(zip_derived_cl690, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (((X2) = (ordered_pair @ X0 @ X1))
% 86.17/12.94 | ~ (in @ X2 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X0) @ (singleton @ X1))))),
% 86.17/12.94 inference('simplify', [status(thm)], [zip_derived_cl689])).
% 86.17/12.94 thf(zip_derived_cl731, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 86.17/12.94 (~ (in @ X3 @
% 86.17/12.94 (cartesian_product2 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0)) @ X2))
% 86.17/12.94 | ((sk__4 @ X3 @ X2 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0)))
% 86.17/12.94 = (ordered_pair @ X1 @ X0)))),
% 86.17/12.94 inference('s_sup-', [status(thm)], [zip_derived_cl177, zip_derived_cl690])).
% 86.17/12.94 thf(zip_derived_cl177, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 ( (in @ (sk__4 @ X2 @ X1 @ X0) @ X0)
% 86.17/12.94 | ~ (in @ X2 @ (cartesian_product2 @ X0 @ X1)))),
% 86.17/12.94 inference('eq_res', [status(thm)], [zip_derived_cl113])).
% 86.17/12.94 thf(zip_derived_cl1701, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 86.17/12.94 (~ (in @ X3 @
% 86.17/12.94 (cartesian_product2 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0)) @ X2))
% 86.17/12.94 | (in @ (ordered_pair @ X1 @ X0) @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0)))
% 86.17/12.94 | ~ (in @ X3 @
% 86.17/12.94 (cartesian_product2 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0)) @ X2)))),
% 86.17/12.94 inference('s_sup+', [status(thm)], [zip_derived_cl731, zip_derived_cl177])).
% 86.17/12.94 thf(zip_derived_cl1705, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 86.17/12.94 ( (in @ (ordered_pair @ X1 @ X0) @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0)))
% 86.17/12.94 | ~ (in @ X3 @
% 86.17/12.94 (cartesian_product2 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0)) @ X2)))),
% 86.17/12.94 inference('simplify', [status(thm)], [zip_derived_cl1701])).
% 86.17/12.94 thf(zip_derived_cl1797, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 86.17/12.94 (~ (in @ X4 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X2) @ (singleton @ X1)))
% 86.17/12.94 | ~ (in @ X3 @ X0)
% 86.17/12.94 | (in @ (ordered_pair @ X2 @ X1) @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X2) @ (singleton @ X1))))),
% 86.17/12.94 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl1705])).
% 86.17/12.94 thf(zip_derived_cl1888, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (~ (in @ X2 @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0)))
% 86.17/12.94 | (in @ (ordered_pair @ X1 @ X0) @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0))))),
% 86.17/12.94 inference('condensation', [status(thm)], [zip_derived_cl1797])).
% 86.17/12.94 thf(zip_derived_cl1889, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 86.17/12.94 (~ (in @ X3 @ (singleton @ X1))
% 86.17/12.94 | ~ (in @ X2 @ (singleton @ X0))
% 86.17/12.94 | (in @ (ordered_pair @ X1 @ X0) @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0))))),
% 86.17/12.94 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl1888])).
% 86.17/12.94 thf(zip_derived_cl1924, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.17/12.94 (~ (in @ X2 @ (singleton @ X1))
% 86.17/12.94 | (in @ (ordered_pair @ X0 @ X1) @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X0) @ (singleton @ X1))))),
% 86.17/12.94 inference('s_sup-', [status(thm)],
% 86.17/12.94 [zip_derived_cl123, zip_derived_cl1889])).
% 86.17/12.94 thf(zip_derived_cl1945, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i]:
% 86.17/12.94 (in @ (ordered_pair @ X1 @ X0) @
% 86.17/12.94 (cartesian_product2 @ (singleton @ X1) @ (singleton @ X0)))),
% 86.17/12.94 inference('s_sup-', [status(thm)],
% 86.17/12.94 [zip_derived_cl123, zip_derived_cl1924])).
% 86.17/12.94 thf(zip_derived_cl20308, plain,
% 86.17/12.94 (![X0 : $i, X1 : $i]:
% 86.17/12.94 ((cartesian_product2 @ (singleton @ X1) @ (singleton @ X0))
% 86.17/12.94 = (singleton @ (ordered_pair @ X1 @ X0)))),
% 86.17/12.94 inference('demod', [status(thm)],
% 86.17/12.94 [zip_derived_cl20307, zip_derived_cl1945])).
% 86.17/12.94 thf(zip_derived_cl20309, plain,
% 86.17/12.94 (((singleton @ (ordered_pair @ sk__9 @ sk__10))
% 86.17/12.94 != (singleton @ (ordered_pair @ sk__9 @ sk__10)))),
% 86.17/12.94 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl20308])).
% 86.17/12.94 thf(zip_derived_cl20310, plain, ($false),
% 86.17/12.94 inference('simplify', [status(thm)], [zip_derived_cl20309])).
% 86.17/12.94
% 86.17/12.94 % SZS output end Refutation
% 86.17/12.94
% 86.17/12.94
% 86.17/12.94 % Terminating...
% 86.87/13.08 % Runner terminated.
% 86.87/13.09 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------