%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU329+1 : TPTP v9.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bHmRBwDLXf 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 04:54:16 PM UTC 2025
% Result : Theorem 194.02s 28.54s
% Output : Refutation 194.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU329+1 : TPTP v9.2.0. Released v3.3.0.
% 0.08/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bHmRBwDLXf true
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 1 16:05:38 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.57/0.67 % Total configuration time : 435
% 0.57/0.67 % Estimated wc time : 1092
% 0.57/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.59/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.59/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 194.02/28.54 % Solved by fo/fo7.sh.
% 194.02/28.54 % done 6312 iterations in 27.716s
% 194.02/28.54 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 194.02/28.54 % SZS output start Refutation
% 194.02/28.54 thf(powerset_type, type, powerset: $i > $i).
% 194.02/28.54 thf(sk__type, type, sk_: $i).
% 194.02/28.54 thf(zip_tseitin_5_type, type, zip_tseitin_5: $i > $i > $i > $i > $o).
% 194.02/28.54 thf(subset_complement_type, type, subset_complement: $i > $i > $i).
% 194.02/28.54 thf(sk__6_type, type, sk__6: $i > $i).
% 194.02/28.54 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(zip_tseitin_7_type, type, zip_tseitin_7: $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(the_carrier_type, type, the_carrier: $i > $i).
% 194.02/28.54 thf(sk__21_type, type, sk__21: $i > $i > $i).
% 194.02/28.54 thf(sk__2_type, type, sk__2: $i).
% 194.02/28.54 thf(one_sorted_str_type, type, one_sorted_str: $i > $o).
% 194.02/28.54 thf(zip_tseitin_8_type, type, zip_tseitin_8: $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(sk__18_type, type, sk__18: $i > $i > $i > $i).
% 194.02/28.54 thf(sk__20_type, type, sk__20: $i > $i > $i).
% 194.02/28.54 thf(sk__5_type, type, sk__5: $i > $i).
% 194.02/28.54 thf(sk__1_type, type, sk__1: $i).
% 194.02/28.54 thf(cartesian_product2_type, type, cartesian_product2: $i > $i > $i).
% 194.02/28.54 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(sk__4_type, type, sk__4: $i > $i > $i).
% 194.02/28.54 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(sk__16_type, type, sk__16: $i > $i > $i > $i).
% 194.02/28.54 thf(sk__19_type, type, sk__19: $i > $i > $i).
% 194.02/28.54 thf(sk__14_type, type, sk__14: $i > $i > $i > $i).
% 194.02/28.54 thf(element_type, type, element: $i > $i > $o).
% 194.02/28.54 thf(in_type, type, in: $i > $i > $o).
% 194.02/28.54 thf(zip_tseitin_4_type, type, zip_tseitin_4: $i > $i > $i > $i > $o).
% 194.02/28.54 thf(complements_of_subsets_type, type, complements_of_subsets: $i > $i > $i).
% 194.02/28.54 thf(sk__3_type, type, sk__3: $i > $i).
% 194.02/28.54 thf(sk__15_type, type, sk__15: $i > $i > $i > $i).
% 194.02/28.54 thf(zip_tseitin_6_type, type, zip_tseitin_6: $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(sk__17_type, type, sk__17: $i > $i > $i > $i > $i).
% 194.02/28.54 thf(ordered_pair_type, type, ordered_pair: $i > $i > $i).
% 194.02/28.54 thf(s1_tarski__e4_7_1__tops_2__2, axiom,
% 194.02/28.54 (![A:$i,B:$i]:
% 194.02/28.54 ( ( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) &
% 194.02/28.54 ( one_sorted_str @ A ) ) =>
% 194.02/28.54 ( ![C:$i]:
% 194.02/28.54 ( ( ![D:$i,E:$i,F:$i]:
% 194.02/28.54 ( ( ( ?[J:$i,K:$i]:
% 194.02/28.54 ( ( ( ordered_pair @ J @ K ) = ( F ) ) &
% 194.02/28.54 ( in @
% 194.02/28.54 J @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) ) &
% 194.02/28.54 ( ![L:$i]:
% 194.02/28.54 ( ( element @ L @ ( powerset @ ( the_carrier @ A ) ) ) =>
% 194.02/28.54 ( ( ( L ) = ( J ) ) =>
% 194.02/28.54 ( ( K ) =
% 194.02/28.54 ( subset_complement @ ( the_carrier @ A ) @ L ) ) ) ) ) ) ) &
% 194.02/28.54 ( ( D ) = ( F ) ) &
% 194.02/28.54 ( ?[G:$i,H:$i]:
% 194.02/28.54 ( ( ( ordered_pair @ G @ H ) = ( E ) ) &
% 194.02/28.54 ( in @
% 194.02/28.54 G @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) ) &
% 194.02/28.54 ( ![I:$i]:
% 194.02/28.54 ( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) ) =>
% 194.02/28.54 ( ( ( I ) = ( G ) ) =>
% 194.02/28.54 ( ( H ) =
% 194.02/28.54 ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) ) ) &
% 194.02/28.54 ( ( D ) = ( E ) ) ) =>
% 194.02/28.54 ( ( E ) = ( F ) ) ) ) =>
% 194.02/28.54 ( ?[D:$i]:
% 194.02/28.54 ( ![E:$i]:
% 194.02/28.54 ( ( in @ E @ D ) <=>
% 194.02/28.54 ( ?[F:$i]:
% 194.02/28.54 ( ( in @
% 194.02/28.54 F @
% 194.02/28.54 ( cartesian_product2 @
% 194.02/28.54 ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @
% 194.02/28.54 C ) ) &
% 194.02/28.54 ( ( F ) = ( E ) ) &
% 194.02/28.54 ( ?[M:$i,N:$i]:
% 194.02/28.54 ( ( ( ordered_pair @ M @ N ) = ( E ) ) &
% 194.02/28.54 ( in @
% 194.02/28.54 M @
% 194.02/28.54 ( complements_of_subsets @ ( the_carrier @ A ) @ B ) ) &
% 194.02/28.54 ( ![O:$i]:
% 194.02/28.54 ( ( element @ O @ ( powerset @ ( the_carrier @ A ) ) ) =>
% 194.02/28.54 ( ( ( O ) = ( M ) ) =>
% 194.02/28.54 ( ( N ) =
% 194.02/28.54 ( subset_complement @ ( the_carrier @ A ) @ O ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 194.02/28.54 thf(zf_stmt_0, axiom,
% 194.02/28.54 (![F:$i,E:$i,D:$i,B:$i,A:$i]:
% 194.02/28.54 ( ( ( zip_tseitin_2 @ F @ E @ D @ B @ A ) => ( ( E ) = ( F ) ) ) =>
% 194.02/28.54 ( zip_tseitin_3 @ F @ E @ D @ B @ A ) ))).
% 194.02/28.54 thf(zip_derived_cl83, plain,
% 194.02/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.02/28.54 ( (zip_tseitin_3 @ X0 @ X1 @ X2 @ X3 @ X4)
% 194.02/28.54 | (zip_tseitin_2 @ X0 @ X1 @ X2 @ X3 @ X4))),
% 194.02/28.54 inference('cnf', [status(esa)], [zf_stmt_0])).
% 194.02/28.54 thf(s1_xboole_0__e4_7_1__tops_2__1, conjecture,
% 194.02/28.54 (![A:$i,B:$i]:
% 194.02/28.54 ( ( ( one_sorted_str @ A ) &
% 194.02/28.54 ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ) =>
% 194.02/28.54 ( ![C:$i]:
% 194.02/28.54 ( ?[D:$i]:
% 194.02/28.54 ( ![E:$i]:
% 194.02/28.54 ( ( in @ E @ D ) <=>
% 194.02/28.54 ( ( in @
% 194.02/28.54 E @
% 194.02/28.54 ( cartesian_product2 @
% 194.02/28.54 ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ C ) ) &
% 194.02/28.54 ( ?[F:$i,G:$i]:
% 194.02/28.54 ( ( ![H:$i]:
% 194.02/28.54 ( ( element @ H @ ( powerset @ ( the_carrier @ A ) ) ) =>
% 194.02/28.54 ( ( ( H ) = ( F ) ) =>
% 194.02/28.54 ( ( G ) =
% 194.02/28.54 ( subset_complement @ ( the_carrier @ A ) @ H ) ) ) ) ) &
% 194.02/28.54 ( in @
% 194.02/28.54 F @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) ) &
% 194.02/28.54 ( ( ordered_pair @ F @ G ) = ( E ) ) ) ) ) ) ) ) ) ))).
% 194.02/28.54 thf(zf_stmt_1, negated_conjecture,
% 194.02/28.54 (~( ![A:$i,B:$i]:
% 194.02/28.54 ( ( ( one_sorted_str @ A ) &
% 194.02/28.54 ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ) =>
% 194.02/28.54 ( ![C:$i]:
% 194.02/28.54 ( ?[D:$i]:
% 194.02/28.54 ( ![E:$i]:
% 194.02/28.54 ( ( in @ E @ D ) <=>
% 194.02/28.54 ( ( in @
% 194.02/28.54 E @
% 194.02/28.54 ( cartesian_product2 @
% 194.02/28.54 ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @
% 194.02/28.54 C ) ) &
% 194.02/28.54 ( ?[F:$i,G:$i]:
% 194.02/28.54 ( ( ![H:$i]:
% 194.02/28.54 ( ( element @ H @ ( powerset @ ( the_carrier @ A ) ) ) =>
% 194.02/28.54 ( ( ( H ) = ( F ) ) =>
% 194.02/28.54 ( ( G ) =
% 194.02/28.54 ( subset_complement @ ( the_carrier @ A ) @ H ) ) ) ) ) &
% 194.02/28.54 ( in @
% 194.02/28.54 F @
% 194.02/28.54 ( complements_of_subsets @ ( the_carrier @ A ) @ B ) ) &
% 194.02/28.54 ( ( ordered_pair @ F @ G ) = ( E ) ) ) ) ) ) ) ) ) ) )),
% 194.02/28.54 inference('cnf.neg', [status(esa)], [s1_xboole_0__e4_7_1__tops_2__1])).
% 194.02/28.54 thf(zip_derived_cl7, plain,
% 194.02/28.54 ( (element @ sk__1 @ (powerset @ (powerset @ (the_carrier @ sk_))))),
% 194.02/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.02/28.54 thf(zf_stmt_2, type, zip_tseitin_8 : $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(zf_stmt_3, axiom,
% 194.02/28.54 (![E:$i,D:$i,C:$i,B:$i,A:$i]:
% 194.02/28.54 ( ( zip_tseitin_8 @ E @ D @ C @ B @ A ) =>
% 194.02/28.54 ( ( in @ E @ D ) <=> ( ?[F:$i]: ( zip_tseitin_7 @ F @ E @ C @ B @ A ) ) ) ))).
% 194.02/28.54 thf(zf_stmt_4, type, zip_tseitin_7 : $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(zf_stmt_5, axiom,
% 194.02/28.54 (![F:$i,E:$i,C:$i,B:$i,A:$i]:
% 194.02/28.54 ( ( zip_tseitin_7 @ F @ E @ C @ B @ A ) <=>
% 194.02/28.54 ( ( ?[M:$i,N:$i]: ( zip_tseitin_6 @ N @ M @ E @ B @ A ) ) &
% 194.02/28.54 ( ( F ) = ( E ) ) &
% 194.02/28.54 ( in @
% 194.02/28.54 F @
% 194.02/28.54 ( cartesian_product2 @
% 194.02/28.54 ( complements_of_subsets @ ( the_carrier @ A ) @ B ) @ C ) ) ) ))).
% 194.02/28.54 thf(zf_stmt_6, type, zip_tseitin_6 : $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(zf_stmt_7, axiom,
% 194.02/28.54 (![N:$i,M:$i,E:$i,B:$i,A:$i]:
% 194.02/28.54 ( ( zip_tseitin_6 @ N @ M @ E @ B @ A ) <=>
% 194.02/28.54 ( ( ![O:$i]: ( zip_tseitin_5 @ O @ N @ M @ A ) ) &
% 194.02/28.54 ( in @ M @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) ) &
% 194.02/28.54 ( ( ordered_pair @ M @ N ) = ( E ) ) ) ))).
% 194.02/28.54 thf(zf_stmt_8, type, zip_tseitin_5 : $i > $i > $i > $i > $o).
% 194.02/28.54 thf(zf_stmt_9, axiom,
% 194.02/28.54 (![O:$i,N:$i,M:$i,A:$i]:
% 194.02/28.54 ( ( zip_tseitin_5 @ O @ N @ M @ A ) <=>
% 194.02/28.54 ( ( element @ O @ ( powerset @ ( the_carrier @ A ) ) ) =>
% 194.02/28.54 ( zip_tseitin_4 @ O @ N @ M @ A ) ) ))).
% 194.02/28.54 thf(zf_stmt_10, type, zip_tseitin_4 : $i > $i > $i > $i > $o).
% 194.02/28.54 thf(zf_stmt_11, axiom,
% 194.02/28.54 (![O:$i,N:$i,M:$i,A:$i]:
% 194.02/28.54 ( ( zip_tseitin_4 @ O @ N @ M @ A ) <=>
% 194.02/28.54 ( ( ( O ) = ( M ) ) =>
% 194.02/28.54 ( ( N ) = ( subset_complement @ ( the_carrier @ A ) @ O ) ) ) ))).
% 194.02/28.54 thf(zf_stmt_12, type, zip_tseitin_3 : $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(zf_stmt_13, type, zip_tseitin_2 : $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(zf_stmt_14, axiom,
% 194.02/28.54 (![F:$i,E:$i,D:$i,B:$i,A:$i]:
% 194.02/28.54 ( ( zip_tseitin_2 @ F @ E @ D @ B @ A ) =>
% 194.02/28.54 ( ( ( D ) = ( E ) ) &
% 194.02/28.54 ( ?[G:$i,H:$i]: ( zip_tseitin_1 @ H @ G @ E @ B @ A ) ) &
% 194.02/28.54 ( ( D ) = ( F ) ) &
% 194.02/28.54 ( ?[J:$i,K:$i]: ( zip_tseitin_0 @ K @ J @ F @ B @ A ) ) ) ))).
% 194.02/28.54 thf(zf_stmt_15, type, zip_tseitin_1 : $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(zf_stmt_16, axiom,
% 194.02/28.54 (![H:$i,G:$i,E:$i,B:$i,A:$i]:
% 194.02/28.54 ( ( zip_tseitin_1 @ H @ G @ E @ B @ A ) =>
% 194.02/28.54 ( ( ![I:$i]:
% 194.02/28.54 ( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) ) =>
% 194.02/28.54 ( ( ( I ) = ( G ) ) =>
% 194.02/28.54 ( ( H ) = ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) &
% 194.02/28.54 ( in @ G @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) ) &
% 194.02/28.54 ( ( ordered_pair @ G @ H ) = ( E ) ) ) ))).
% 194.02/28.54 thf(zf_stmt_17, type, zip_tseitin_0 : $i > $i > $i > $i > $i > $o).
% 194.02/28.54 thf(zf_stmt_18, axiom,
% 194.02/28.54 (![K:$i,J:$i,F:$i,B:$i,A:$i]:
% 194.02/28.54 ( ( zip_tseitin_0 @ K @ J @ F @ B @ A ) =>
% 194.02/28.54 ( ( ![L:$i]:
% 194.02/28.54 ( ( element @ L @ ( powerset @ ( the_carrier @ A ) ) ) =>
% 194.02/28.54 ( ( ( L ) = ( J ) ) =>
% 194.02/28.54 ( ( K ) = ( subset_complement @ ( the_carrier @ A ) @ L ) ) ) ) ) &
% 194.02/28.54 ( in @ J @ ( complements_of_subsets @ ( the_carrier @ A ) @ B ) ) &
% 194.02/28.54 ( ( ordered_pair @ J @ K ) = ( F ) ) ) ))).
% 194.02/28.54 thf(zf_stmt_19, axiom,
% 194.02/28.54 (![A:$i,B:$i]:
% 194.02/28.54 ( ( ( one_sorted_str @ A ) &
% 194.02/28.54 ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ) =>
% 194.02/28.54 ( ![C:$i]:
% 194.02/28.54 ( ( ![D:$i,E:$i,F:$i]: ( zip_tseitin_3 @ F @ E @ D @ B @ A ) ) =>
% 194.02/28.54 ( ?[D:$i]: ( ![E:$i]: ( zip_tseitin_8 @ E @ D @ C @ B @ A ) ) ) ) ) ))).
% 194.02/28.54 thf(zip_derived_cl100, plain,
% 194.02/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.02/28.54 (~ (one_sorted_str @ X0)
% 194.02/28.54 | ~ (element @ X1 @ (powerset @ (powerset @ (the_carrier @ X0))))
% 194.02/28.54 | ~ (zip_tseitin_3 @ (sk__21 @ X1 @ X0) @ (sk__20 @ X1 @ X0) @
% 194.24/28.54 (sk__19 @ X1 @ X0) @ X1 @ X0)
% 194.24/28.54 | (zip_tseitin_8 @ X2 @ (sk__18 @ X3 @ X1 @ X0) @ X3 @ X1 @ X0))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_19])).
% 194.24/28.54 thf(zip_derived_cl2438, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @ sk_)
% 194.24/28.54 | ~ (zip_tseitin_3 @ (sk__21 @ sk__1 @ sk_) @
% 194.24/28.54 (sk__20 @ sk__1 @ sk_) @ (sk__19 @ sk__1 @ sk_) @ sk__1 @ sk_)
% 194.24/28.54 | ~ (one_sorted_str @ sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl100])).
% 194.24/28.54 thf(zip_derived_cl8, plain, ( (one_sorted_str @ sk_)),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.24/28.54 thf(zip_derived_cl2447, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @ sk_)
% 194.24/28.54 | ~ (zip_tseitin_3 @ (sk__21 @ sk__1 @ sk_) @
% 194.24/28.54 (sk__20 @ sk__1 @ sk_) @ (sk__19 @ sk__1 @ sk_) @ sk__1 @ sk_))),
% 194.24/28.54 inference('demod', [status(thm)], [zip_derived_cl2438, zip_derived_cl8])).
% 194.24/28.54 thf(zip_derived_cl2483, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (zip_tseitin_2 @ (sk__21 @ sk__1 @ sk_) @ (sk__20 @ sk__1 @ sk_) @
% 194.24/28.54 (sk__19 @ sk__1 @ sk_) @ sk__1 @ sk_)
% 194.24/28.54 | (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @
% 194.24/28.54 sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl83, zip_derived_cl2447])).
% 194.24/28.54 thf(zip_derived_cl80, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.24/28.54 (((X1) = (X0)) | ~ (zip_tseitin_2 @ X0 @ X2 @ X1 @ X3 @ X4))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_14])).
% 194.24/28.54 thf(zip_derived_cl2543, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @ sk_)
% 194.24/28.54 | ((sk__19 @ sk__1 @ sk_) = (sk__21 @ sk__1 @ sk_)))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl2483, zip_derived_cl80])).
% 194.24/28.54 thf(zip_derived_cl2483, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (zip_tseitin_2 @ (sk__21 @ sk__1 @ sk_) @ (sk__20 @ sk__1 @ sk_) @
% 194.24/28.54 (sk__19 @ sk__1 @ sk_) @ sk__1 @ sk_)
% 194.24/28.54 | (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @
% 194.24/28.54 sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl83, zip_derived_cl2447])).
% 194.24/28.54 thf(zip_derived_cl78, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.24/28.54 (((X1) = (X0)) | ~ (zip_tseitin_2 @ X2 @ X0 @ X1 @ X3 @ X4))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_14])).
% 194.24/28.54 thf(zip_derived_cl2541, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @ sk_)
% 194.24/28.54 | ((sk__19 @ sk__1 @ sk_) = (sk__20 @ sk__1 @ sk_)))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl2483, zip_derived_cl78])).
% 194.24/28.54 thf(zip_derived_cl2447, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @ sk_)
% 194.24/28.54 | ~ (zip_tseitin_3 @ (sk__21 @ sk__1 @ sk_) @
% 194.24/28.54 (sk__20 @ sk__1 @ sk_) @ (sk__19 @ sk__1 @ sk_) @ sk__1 @ sk_))),
% 194.24/28.54 inference('demod', [status(thm)], [zip_derived_cl2438, zip_derived_cl8])).
% 194.24/28.54 thf(zip_derived_cl2579, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (~ (zip_tseitin_3 @ (sk__21 @ sk__1 @ sk_) @ (sk__19 @ sk__1 @ sk_) @
% 194.24/28.54 (sk__19 @ sk__1 @ sk_) @ sk__1 @ sk_)
% 194.24/28.54 | (zip_tseitin_8 @ X3 @ (sk__18 @ X2 @ sk__1 @ sk_) @ X2 @ sk__1 @
% 194.24/28.54 sk_)
% 194.24/28.54 | (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @
% 194.24/28.54 sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl2541, zip_derived_cl2447])).
% 194.24/28.54 thf(zip_derived_cl32862, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (zip_tseitin_3 @ (sk__21 @ sk__1 @ sk_) @ (sk__19 @ sk__1 @ sk_) @
% 194.24/28.54 (sk__19 @ sk__1 @ sk_) @ sk__1 @ sk_)
% 194.24/28.54 | (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @
% 194.24/28.54 sk_))),
% 194.24/28.54 inference('condensation', [status(thm)], [zip_derived_cl2579])).
% 194.24/28.54 thf(zip_derived_cl32882, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (~ (zip_tseitin_3 @ (sk__19 @ sk__1 @ sk_) @ (sk__19 @ sk__1 @ sk_) @
% 194.24/28.54 (sk__19 @ sk__1 @ sk_) @ sk__1 @ sk_)
% 194.24/28.54 | (zip_tseitin_8 @ X3 @ (sk__18 @ X2 @ sk__1 @ sk_) @ X2 @ sk__1 @
% 194.24/28.54 sk_)
% 194.24/28.54 | (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @
% 194.24/28.54 sk_))),
% 194.24/28.54 inference('sup-', [status(thm)],
% 194.24/28.54 [zip_derived_cl2543, zip_derived_cl32862])).
% 194.24/28.54 thf(zip_derived_cl82, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.24/28.54 ( (zip_tseitin_3 @ X0 @ X1 @ X2 @ X3 @ X4) | ((X1) != (X0)))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_0])).
% 194.24/28.54 thf(zip_derived_cl205, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (zip_tseitin_3 @ X3 @ X3 @ X2 @ X1 @ X0)),
% 194.24/28.54 inference('eq_res', [status(thm)], [zip_derived_cl82])).
% 194.24/28.54 thf(zip_derived_cl32887, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (zip_tseitin_8 @ X3 @ (sk__18 @ X2 @ sk__1 @ sk_) @ X2 @ sk__1 @ sk_)
% 194.24/28.54 | (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @
% 194.24/28.54 sk_))),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl32882, zip_derived_cl205])).
% 194.24/28.54 thf(zip_derived_cl32964, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @ sk_)),
% 194.24/28.54 inference('condensation', [status(thm)], [zip_derived_cl32887])).
% 194.24/28.54 thf(involutiveness_k7_setfam_1, axiom,
% 194.24/28.54 (![A:$i,B:$i]:
% 194.24/28.54 ( ( element @ B @ ( powerset @ ( powerset @ A ) ) ) =>
% 194.24/28.54 ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) ) =
% 194.24/28.54 ( B ) ) ))).
% 194.24/28.54 thf(zip_derived_cl60, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (((complements_of_subsets @ X1 @ (complements_of_subsets @ X1 @ X0))
% 194.24/28.54 = (X0))
% 194.24/28.54 | ~ (element @ X0 @ (powerset @ (powerset @ X1))))),
% 194.24/28.54 inference('cnf', [status(esa)], [involutiveness_k7_setfam_1])).
% 194.24/28.54 thf(zip_derived_cl85, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (zip_tseitin_4 @ X0 @ X1 @ X2 @ X3)
% 194.24/28.54 | ((X1) != (subset_complement @ (the_carrier @ X3) @ X0)))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_11])).
% 194.24/28.54 thf(zip_derived_cl291, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 (zip_tseitin_4 @ X2 @
% 194.24/28.54 (subset_complement @ (the_carrier @ X0) @ X2) @ X1 @ X0)),
% 194.24/28.54 inference('eq_res', [status(thm)], [zip_derived_cl85])).
% 194.24/28.54 thf(zip_derived_cl86, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (zip_tseitin_4 @ X0 @ X1 @ X2 @ X3) | ((X0) = (X2)))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_11])).
% 194.24/28.54 thf(zip_derived_cl88, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ X0 @ X1 @ X2 @ X3)
% 194.24/28.54 | ~ (zip_tseitin_4 @ X0 @ X1 @ X2 @ X3))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_9])).
% 194.24/28.54 thf(zip_derived_cl3, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ( (in @ (sk__5 @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.24/28.54 thf(zip_derived_cl93, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.24/28.54 ( (zip_tseitin_6 @ X0 @ X1 @ X2 @ X3 @ X4)
% 194.24/28.54 | ((ordered_pair @ X1 @ X0) != (X2))
% 194.24/28.54 | ~ (in @ X1 @ (complements_of_subsets @ (the_carrier @ X4) @ X3))
% 194.24/28.54 | ~ (zip_tseitin_5 @ (sk__14 @ X4 @ X1 @ X0) @ X0 @ X1 @ X4))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_7])).
% 194.24/28.54 thf(zip_derived_cl669, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (~ (zip_tseitin_5 @ (sk__14 @ X0 @ X1 @ X2) @ X2 @ X1 @ X0)
% 194.24/28.54 | ~ (in @ X1 @ (complements_of_subsets @ (the_carrier @ X0) @ X3))
% 194.24/28.54 | (zip_tseitin_6 @ X2 @ X1 @ (ordered_pair @ X1 @ X2) @ X3 @ X0))),
% 194.24/28.54 inference('eq_res', [status(thm)], [zip_derived_cl93])).
% 194.24/28.54 thf(zip_derived_cl719, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_6 @ X1 @ (sk__5 @ X0) @
% 194.24/28.54 (ordered_pair @ (sk__5 @ X0) @ X1) @ sk__1 @ sk_)
% 194.24/28.54 | ~ (zip_tseitin_5 @ (sk__14 @ sk_ @ (sk__5 @ X0) @ X1) @ X1 @
% 194.24/28.54 (sk__5 @ X0) @ sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl669])).
% 194.24/28.54 thf(zip_derived_cl90, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ X0 @ X1 @ X2 @ X3)
% 194.24/28.54 | ~ (zip_tseitin_6 @ X1 @ X2 @ X4 @ X5 @ X3))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_7])).
% 194.24/28.54 thf(zip_derived_cl4343, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 (~ (zip_tseitin_5 @ (sk__14 @ sk_ @ (sk__5 @ X1) @ X0) @ X0 @
% 194.24/28.54 (sk__5 @ X1) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X1) @ X1)
% 194.24/28.54 | (zip_tseitin_5 @ X2 @ X0 @ (sk__5 @ X1) @ sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl719, zip_derived_cl90])).
% 194.24/28.54 thf(zip_derived_cl4362, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 (~ (zip_tseitin_4 @ (sk__14 @ sk_ @ (sk__5 @ X0) @ X1) @ X1 @
% 194.24/28.54 (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (zip_tseitin_5 @ X2 @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl4343])).
% 194.24/28.54 thf(zip_derived_cl4377, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 (((sk__14 @ sk_ @ (sk__5 @ X0) @ X1) = (sk__5 @ X0))
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_5 @ X2 @ X1 @ (sk__5 @ X0) @ sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl86, zip_derived_cl4362])).
% 194.24/28.54 thf(zip_derived_cl4362, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 (~ (zip_tseitin_4 @ (sk__14 @ sk_ @ (sk__5 @ X0) @ X1) @ X1 @
% 194.24/28.54 (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (zip_tseitin_5 @ X2 @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl4343])).
% 194.24/28.54 thf(zip_derived_cl4391, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (~ (zip_tseitin_4 @ (sk__5 @ X0) @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (zip_tseitin_5 @ X3 @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_5 @ X2 @ X1 @ (sk__5 @ X0) @ sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl4377, zip_derived_cl4362])).
% 194.24/28.54 thf(zip_derived_cl4431, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ X2 @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_5 @ X3 @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | ~ (zip_tseitin_4 @ (sk__5 @ X0) @ X1 @ (sk__5 @ X0) @ sk_))),
% 194.24/28.54 inference('simplify', [status(thm)], [zip_derived_cl4391])).
% 194.24/28.54 thf(zip_derived_cl12471, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 (~ (zip_tseitin_4 @ (sk__5 @ X0) @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_5 @ X2 @ X1 @ (sk__5 @ X0) @ sk_))),
% 194.24/28.54 inference('condensation', [status(thm)], [zip_derived_cl4431])).
% 194.24/28.54 thf(zip_derived_cl12473, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ X1 @
% 194.24/28.54 (subset_complement @ (the_carrier @ sk_) @ (sk__5 @ X0)) @
% 194.24/28.54 (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl291, zip_derived_cl12471])).
% 194.24/28.54 thf(zip_derived_cl3, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ( (in @ (sk__5 @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.24/28.54 thf(zip_derived_cl7, plain,
% 194.24/28.54 ( (element @ sk__1 @ (powerset @ (powerset @ (the_carrier @ sk_))))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.24/28.54 thf(dt_k7_setfam_1, axiom,
% 194.24/28.54 (![A:$i,B:$i]:
% 194.24/28.54 ( ( element @ B @ ( powerset @ ( powerset @ A ) ) ) =>
% 194.24/28.54 ( element @
% 194.24/28.54 ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 194.24/28.54 thf(zip_derived_cl66, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (element @ (complements_of_subsets @ X0 @ X1) @
% 194.24/28.54 (powerset @ (powerset @ X0)))
% 194.24/28.54 | ~ (element @ X1 @ (powerset @ (powerset @ X0))))),
% 194.24/28.54 inference('cnf', [status(esa)], [dt_k7_setfam_1])).
% 194.24/28.54 thf(zip_derived_cl60, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (((complements_of_subsets @ X1 @ (complements_of_subsets @ X1 @ X0))
% 194.24/28.54 = (X0))
% 194.24/28.54 | ~ (element @ X0 @ (powerset @ (powerset @ X1))))),
% 194.24/28.54 inference('cnf', [status(esa)], [involutiveness_k7_setfam_1])).
% 194.24/28.54 thf(zip_derived_cl669, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (~ (zip_tseitin_5 @ (sk__14 @ X0 @ X1 @ X2) @ X2 @ X1 @ X0)
% 194.24/28.54 | ~ (in @ X1 @ (complements_of_subsets @ (the_carrier @ X0) @ X3))
% 194.24/28.54 | (zip_tseitin_6 @ X2 @ X1 @ (ordered_pair @ X1 @ X2) @ X3 @ X0))),
% 194.24/28.54 inference('eq_res', [status(thm)], [zip_derived_cl93])).
% 194.24/28.54 thf(zip_derived_cl720, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (~ (in @ X2 @ X0)
% 194.24/28.54 | ~ (element @ X0 @ (powerset @ (powerset @ (the_carrier @ X1))))
% 194.24/28.54 | (zip_tseitin_6 @ X3 @ X2 @ (ordered_pair @ X2 @ X3) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ X1) @ X0) @ X1)
% 194.24/28.54 | ~ (zip_tseitin_5 @ (sk__14 @ X1 @ X2 @ X3) @ X3 @ X2 @ X1))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl669])).
% 194.24/28.54 thf(zip_derived_cl2677, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (~ (element @ X1 @ (powerset @ (powerset @ (the_carrier @ X0))))
% 194.24/28.54 | ~ (zip_tseitin_5 @ (sk__14 @ X0 @ X2 @ X3) @ X3 @ X2 @ X0)
% 194.24/28.54 | (zip_tseitin_6 @ X3 @ X2 @ (ordered_pair @ X2 @ X3) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ X0) @ X1)) @
% 194.24/28.54 X0)
% 194.24/28.54 | ~ (in @ X2 @ (complements_of_subsets @ (the_carrier @ X0) @ X1)))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl720])).
% 194.24/28.54 thf(zip_derived_cl3026, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (in @ X0 @ (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | (zip_tseitin_6 @ X1 @ X0 @ (ordered_pair @ X0 @ X1) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 sk_)
% 194.24/28.54 | ~ (zip_tseitin_5 @ (sk__14 @ sk_ @ X0 @ X1) @ X1 @ X0 @ sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2677])).
% 194.24/28.54 thf(zip_derived_cl91, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.24/28.54 ( (in @ X0 @ (complements_of_subsets @ (the_carrier @ X1) @ X2))
% 194.24/28.54 | ~ (zip_tseitin_6 @ X3 @ X0 @ X4 @ X2 @ X1))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_7])).
% 194.24/28.54 thf(zip_derived_cl20894, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (zip_tseitin_5 @ (sk__14 @ sk_ @ X1 @ X0) @ X0 @ X1 @ sk_)
% 194.24/28.54 | ~ (in @ X1 @ (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | (in @ X1 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)))))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl3026, zip_derived_cl91])).
% 194.24/28.54 thf(zip_derived_cl21064, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (in @ (sk__5 @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))))
% 194.24/28.54 | ~ (zip_tseitin_5 @ (sk__14 @ sk_ @ (sk__5 @ X0) @ X1) @ X1 @
% 194.24/28.54 (sk__5 @ X0) @ sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl20894])).
% 194.24/28.54 thf(zip_derived_cl21131, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (in @ (sk__5 @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))))
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('sup-', [status(thm)],
% 194.24/28.54 [zip_derived_cl12473, zip_derived_cl21064])).
% 194.24/28.54 thf(zip_derived_cl21168, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ( (in @ (sk__5 @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))))
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('simplify', [status(thm)], [zip_derived_cl21131])).
% 194.24/28.54 thf(zip_derived_cl2, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 (((ordered_pair @ (sk__5 @ X0) @ (sk__6 @ X0)) = (sk__3 @ X0))
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.24/28.54 thf(zip_derived_cl93, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.24/28.54 ( (zip_tseitin_6 @ X0 @ X1 @ X2 @ X3 @ X4)
% 194.24/28.54 | ((ordered_pair @ X1 @ X0) != (X2))
% 194.24/28.54 | ~ (in @ X1 @ (complements_of_subsets @ (the_carrier @ X4) @ X3))
% 194.24/28.54 | ~ (zip_tseitin_5 @ (sk__14 @ X4 @ X1 @ X0) @ X0 @ X1 @ X4))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_7])).
% 194.24/28.54 thf(zip_derived_cl668, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (((sk__3 @ X0) != (X1))
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | ~ (zip_tseitin_5 @ (sk__14 @ X2 @ (sk__5 @ X0) @ (sk__6 @ X0)) @
% 194.24/28.54 (sk__6 @ X0) @ (sk__5 @ X0) @ X2)
% 194.24/28.54 | ~ (in @ (sk__5 @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ X2) @ X3))
% 194.24/28.54 | (zip_tseitin_6 @ (sk__6 @ X0) @ (sk__5 @ X0) @ X1 @ X3 @ X2))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl93])).
% 194.24/28.54 thf(zip_derived_cl2726, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 ( (zip_tseitin_6 @ (sk__6 @ X2) @ (sk__5 @ X2) @ (sk__3 @ X2) @ X1 @
% 194.24/28.54 X0)
% 194.24/28.54 | ~ (in @ (sk__5 @ X2) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ X0) @ X1))
% 194.24/28.54 | ~ (zip_tseitin_5 @ (sk__14 @ X0 @ (sk__5 @ X2) @ (sk__6 @ X2)) @
% 194.24/28.54 (sk__6 @ X2) @ (sk__5 @ X2) @ X0)
% 194.24/28.54 | (in @ (sk__3 @ X2) @ X2))),
% 194.24/28.54 inference('eq_res', [status(thm)], [zip_derived_cl668])).
% 194.24/28.54 thf(zip_derived_cl21176, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | ~ (zip_tseitin_5 @ (sk__14 @ sk_ @ (sk__5 @ X0) @ (sk__6 @ X0)) @
% 194.24/28.54 (sk__6 @ X0) @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (zip_tseitin_6 @ (sk__6 @ X0) @ (sk__5 @ X0) @ (sk__3 @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 sk_))),
% 194.24/28.54 inference('sup-', [status(thm)],
% 194.24/28.54 [zip_derived_cl21168, zip_derived_cl2726])).
% 194.24/28.54 thf(zip_derived_cl21224, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ( (zip_tseitin_6 @ (sk__6 @ X0) @ (sk__5 @ X0) @ (sk__3 @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 sk_)
% 194.24/28.54 | ~ (zip_tseitin_5 @ (sk__14 @ sk_ @ (sk__5 @ X0) @ (sk__6 @ X0)) @
% 194.24/28.54 (sk__6 @ X0) @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('simplify', [status(thm)], [zip_derived_cl21176])).
% 194.24/28.54 thf(zip_derived_cl89, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ X0 @ X1 @ X2 @ X3)
% 194.24/28.54 | (element @ X0 @ (powerset @ (the_carrier @ X3))))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_9])).
% 194.24/28.54 thf(zip_derived_cl1, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (element @ X1 @ (powerset @ (the_carrier @ sk_)))
% 194.24/28.54 | ((sk__6 @ X0) = (subset_complement @ (the_carrier @ sk_) @ X1))
% 194.24/28.54 | ((X1) != (sk__5 @ X0))
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.24/28.54 thf(zip_derived_cl518, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | ((sk__6 @ X0)
% 194.24/28.54 = (subset_complement @ (the_carrier @ sk_) @ (sk__5 @ X0)))
% 194.24/28.54 | ~ (element @ (sk__5 @ X0) @ (powerset @ (the_carrier @ sk_))))),
% 194.24/28.54 inference('eq_res', [status(thm)], [zip_derived_cl1])).
% 194.24/28.54 thf(zip_derived_cl12473, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ X1 @
% 194.24/28.54 (subset_complement @ (the_carrier @ sk_) @ (sk__5 @ X0)) @
% 194.24/28.54 (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl291, zip_derived_cl12471])).
% 194.24/28.54 thf(zip_derived_cl12540, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ X1 @ (sk__6 @ X0) @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | ~ (element @ (sk__5 @ X0) @ (powerset @ (the_carrier @ sk_)))
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('sup+', [status(thm)], [zip_derived_cl518, zip_derived_cl12473])).
% 194.24/28.54 thf(zip_derived_cl12554, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | ~ (element @ (sk__5 @ X0) @ (powerset @ (the_carrier @ sk_)))
% 194.24/28.54 | (zip_tseitin_5 @ X1 @ (sk__6 @ X0) @ (sk__5 @ X0) @ sk_))),
% 194.24/28.54 inference('simplify', [status(thm)], [zip_derived_cl12540])).
% 194.24/28.54 thf(zip_derived_cl12558, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ (sk__5 @ X0) @ X3 @ X2 @ sk_)
% 194.24/28.54 | (zip_tseitin_5 @ X1 @ (sk__6 @ X0) @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl89, zip_derived_cl12554])).
% 194.24/28.54 thf(zip_derived_cl4377, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 (((sk__14 @ sk_ @ (sk__5 @ X0) @ X1) = (sk__5 @ X0))
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_5 @ X2 @ X1 @ (sk__5 @ X0) @ sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl86, zip_derived_cl4362])).
% 194.24/28.54 thf(zip_derived_cl4343, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 (~ (zip_tseitin_5 @ (sk__14 @ sk_ @ (sk__5 @ X1) @ X0) @ X0 @
% 194.24/28.54 (sk__5 @ X1) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X1) @ X1)
% 194.24/28.54 | (zip_tseitin_5 @ X2 @ X0 @ (sk__5 @ X1) @ sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl719, zip_derived_cl90])).
% 194.24/28.54 thf(zip_derived_cl4392, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (~ (zip_tseitin_5 @ (sk__5 @ X0) @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (zip_tseitin_5 @ X3 @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_5 @ X2 @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl4377, zip_derived_cl4343])).
% 194.24/28.54 thf(zip_derived_cl4432, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ X2 @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_5 @ X3 @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | ~ (zip_tseitin_5 @ (sk__5 @ X0) @ X1 @ (sk__5 @ X0) @ sk_))),
% 194.24/28.54 inference('simplify', [status(thm)], [zip_derived_cl4392])).
% 194.24/28.54 thf(zip_derived_cl12487, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 (~ (zip_tseitin_5 @ (sk__5 @ X0) @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_5 @ X2 @ X1 @ (sk__5 @ X0) @ sk_))),
% 194.24/28.54 inference('condensation', [status(thm)], [zip_derived_cl4432])).
% 194.24/28.54 thf(zip_derived_cl13908, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_5 @ X3 @ (sk__6 @ X0) @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (zip_tseitin_5 @ X2 @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('sup-', [status(thm)],
% 194.24/28.54 [zip_derived_cl12558, zip_derived_cl12487])).
% 194.24/28.54 thf(zip_derived_cl13953, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ X2 @ X1 @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (zip_tseitin_5 @ X3 @ (sk__6 @ X0) @ (sk__5 @ X0) @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('simplify', [status(thm)], [zip_derived_cl13908])).
% 194.24/28.54 thf(zip_derived_cl14404, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_5 @ X1 @ (sk__6 @ X0) @ (sk__5 @ X0) @ sk_))),
% 194.24/28.54 inference('condensation', [status(thm)], [zip_derived_cl13953])).
% 194.24/28.54 thf(zip_derived_cl50220, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_6 @ (sk__6 @ X0) @ (sk__5 @ X0) @ (sk__3 @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 sk_))),
% 194.24/28.54 inference('clc', [status(thm)],
% 194.24/28.54 [zip_derived_cl21224, zip_derived_cl14404])).
% 194.24/28.54 thf(zip_derived_cl66, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (element @ (complements_of_subsets @ X0 @ X1) @
% 194.24/28.54 (powerset @ (powerset @ X0)))
% 194.24/28.54 | ~ (element @ X1 @ (powerset @ (powerset @ X0))))),
% 194.24/28.54 inference('cnf', [status(esa)], [dt_k7_setfam_1])).
% 194.24/28.54 thf(zip_derived_cl0, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1) @ sk__2))
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.24/28.54 thf(zip_derived_cl60, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (((complements_of_subsets @ X1 @ (complements_of_subsets @ X1 @ X0))
% 194.24/28.54 = (X0))
% 194.24/28.54 | ~ (element @ X0 @ (powerset @ (powerset @ X1))))),
% 194.24/28.54 inference('cnf', [status(esa)], [involutiveness_k7_setfam_1])).
% 194.24/28.54 thf(zip_derived_cl97, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 194.24/28.54 ( (zip_tseitin_7 @ X0 @ X1 @ X2 @ X3 @ X4)
% 194.24/28.54 | ~ (in @ X0 @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ X4) @ X3) @ X2))
% 194.24/28.54 | ((X0) != (X1))
% 194.24/28.54 | ~ (zip_tseitin_6 @ X5 @ X6 @ X1 @ X3 @ X4))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_5])).
% 194.24/28.54 thf(zip_derived_cl654, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 194.24/28.54 (~ (zip_tseitin_6 @ X4 @ X3 @ X2 @ X1 @ X0)
% 194.24/28.54 | ~ (in @ X2 @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ X0) @ X1) @ X5))
% 194.24/28.54 | (zip_tseitin_7 @ X2 @ X2 @ X5 @ X1 @ X0))),
% 194.24/28.54 inference('eq_res', [status(thm)], [zip_derived_cl97])).
% 194.24/28.54 thf(zip_derived_cl667, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 194.24/28.54 (~ (in @ X3 @ (cartesian_product2 @ X0 @ X1))
% 194.24/28.54 | ~ (element @ X0 @ (powerset @ (powerset @ (the_carrier @ X2))))
% 194.24/28.54 | (zip_tseitin_7 @ X3 @ X3 @ X1 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ X2) @ X0) @ X2)
% 194.24/28.54 | ~ (zip_tseitin_6 @ X5 @ X4 @ X3 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ X2) @ X0) @ X2))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl654])).
% 194.24/28.54 thf(zip_derived_cl2453, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | ~ (zip_tseitin_6 @ X3 @ X2 @ (sk__3 @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ X1) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 X1)
% 194.24/28.54 | (zip_tseitin_7 @ (sk__3 @ X0) @ (sk__3 @ X0) @ sk__2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ X1) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 X1)
% 194.24/28.54 | ~ (element @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1) @
% 194.24/28.54 (powerset @ (powerset @ (the_carrier @ X1)))))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl667])).
% 194.24/28.54 thf(zip_derived_cl52802, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 (~ (element @ sk__1 @ (powerset @ (powerset @ (the_carrier @ sk_))))
% 194.24/28.54 | (zip_tseitin_7 @ (sk__3 @ X0) @ (sk__3 @ X0) @ sk__2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 sk_)
% 194.24/28.54 | ~ (zip_tseitin_6 @ X2 @ X1 @ (sk__3 @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl2453])).
% 194.24/28.54 thf(zip_derived_cl7, plain,
% 194.24/28.54 ( (element @ sk__1 @ (powerset @ (powerset @ (the_carrier @ sk_))))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.24/28.54 thf(zip_derived_cl52817, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 ( (zip_tseitin_7 @ (sk__3 @ X0) @ (sk__3 @ X0) @ sk__2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 sk_)
% 194.24/28.54 | ~ (zip_tseitin_6 @ X2 @ X1 @ (sk__3 @ X0) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('demod', [status(thm)], [zip_derived_cl52802, zip_derived_cl7])).
% 194.24/28.54 thf(zip_derived_cl52818, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (zip_tseitin_7 @ (sk__3 @ X0) @ (sk__3 @ X0) @ sk__2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 sk_))),
% 194.24/28.54 inference('sup-', [status(thm)],
% 194.24/28.54 [zip_derived_cl50220, zip_derived_cl52817])).
% 194.24/28.54 thf(zip_derived_cl52838, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ( (zip_tseitin_7 @ (sk__3 @ X0) @ (sk__3 @ X0) @ sk__2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('simplify', [status(thm)], [zip_derived_cl52818])).
% 194.24/28.54 thf(zip_derived_cl98, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 194.24/28.54 (~ (zip_tseitin_7 @ X0 @ X1 @ X2 @ X3 @ X4)
% 194.24/28.54 | (in @ X1 @ X5)
% 194.24/28.54 | ~ (zip_tseitin_8 @ X1 @ X5 @ X2 @ X3 @ X4))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_3])).
% 194.24/28.54 thf(zip_derived_cl52849, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | ~ (zip_tseitin_8 @ (sk__3 @ X0) @ X1 @ sk__2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)) @
% 194.24/28.54 sk_)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ X1))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl52838, zip_derived_cl98])).
% 194.24/28.54 thf(zip_derived_cl52920, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (zip_tseitin_8 @ (sk__3 @ X1) @ X0 @ sk__2 @ sk__1 @ sk_)
% 194.24/28.54 | ~ (element @ sk__1 @ (powerset @ (powerset @ (the_carrier @ sk_))))
% 194.24/28.54 | (in @ (sk__3 @ X1) @ X0)
% 194.24/28.54 | (in @ (sk__3 @ X1) @ X1))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl52849])).
% 194.24/28.54 thf(zip_derived_cl7, plain,
% 194.24/28.54 ( (element @ sk__1 @ (powerset @ (powerset @ (the_carrier @ sk_))))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.24/28.54 thf(zip_derived_cl52937, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (zip_tseitin_8 @ (sk__3 @ X1) @ X0 @ sk__2 @ sk__1 @ sk_)
% 194.24/28.54 | (in @ (sk__3 @ X1) @ X0)
% 194.24/28.54 | (in @ (sk__3 @ X1) @ X1))),
% 194.24/28.54 inference('demod', [status(thm)], [zip_derived_cl52920, zip_derived_cl7])).
% 194.24/28.54 thf(zip_derived_cl52938, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ( (in @ (sk__3 @ X0) @ X0)
% 194.24/28.54 | (in @ (sk__3 @ X0) @ (sk__18 @ sk__2 @ sk__1 @ sk_)))),
% 194.24/28.54 inference('sup-', [status(thm)],
% 194.24/28.54 [zip_derived_cl32964, zip_derived_cl52937])).
% 194.24/28.54 thf(zip_derived_cl52981, plain,
% 194.24/28.54 ( (in @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @
% 194.24/28.54 (sk__18 @ sk__2 @ sk__1 @ sk_))),
% 194.24/28.54 inference('eq_fact', [status(thm)], [zip_derived_cl52938])).
% 194.24/28.54 thf(zip_derived_cl32964, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (zip_tseitin_8 @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_) @ X0 @ sk__1 @ sk_)),
% 194.24/28.54 inference('condensation', [status(thm)], [zip_derived_cl32887])).
% 194.24/28.54 thf(zip_derived_cl99, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.24/28.54 (~ (in @ X0 @ X1)
% 194.24/28.54 | (zip_tseitin_7 @ (sk__17 @ X2 @ X3 @ X4 @ X0) @ X0 @ X4 @ X3 @ X2)
% 194.24/28.54 | ~ (zip_tseitin_8 @ X0 @ X1 @ X4 @ X3 @ X2))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_3])).
% 194.24/28.54 thf(zip_derived_cl32965, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (zip_tseitin_7 @ (sk__17 @ sk_ @ sk__1 @ X0 @ X1) @ X1 @ X0 @
% 194.24/28.54 sk__1 @ sk_)
% 194.24/28.54 | ~ (in @ X1 @ (sk__18 @ X0 @ sk__1 @ sk_)))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl32964, zip_derived_cl99])).
% 194.24/28.54 thf(zip_derived_cl52984, plain,
% 194.24/28.54 ( (zip_tseitin_7 @
% 194.24/28.54 (sk__17 @ sk_ @ sk__1 @ sk__2 @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @ sk__2 @ sk__1 @ sk_)),
% 194.24/28.54 inference('sup-', [status(thm)],
% 194.24/28.54 [zip_derived_cl52981, zip_derived_cl32965])).
% 194.24/28.54 thf(zip_derived_cl52984, plain,
% 194.24/28.54 ( (zip_tseitin_7 @
% 194.24/28.54 (sk__17 @ sk_ @ sk__1 @ sk__2 @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @ sk__2 @ sk__1 @ sk_)),
% 194.24/28.54 inference('sup-', [status(thm)],
% 194.24/28.54 [zip_derived_cl52981, zip_derived_cl32965])).
% 194.24/28.54 thf(zip_derived_cl95, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.24/28.54 (((X1) = (X0)) | ~ (zip_tseitin_7 @ X1 @ X0 @ X2 @ X3 @ X4))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_5])).
% 194.24/28.54 thf(zip_derived_cl53300, plain,
% 194.24/28.54 (((sk__17 @ sk_ @ sk__1 @ sk__2 @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 = (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl52984, zip_derived_cl95])).
% 194.24/28.54 thf(zip_derived_cl53337, plain,
% 194.24/28.54 ( (zip_tseitin_7 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @ sk__2 @ sk__1 @ sk_)),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl52984, zip_derived_cl53300])).
% 194.24/28.54 thf(zip_derived_cl94, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.24/28.54 ( (zip_tseitin_6 @ (sk__16 @ X0 @ X1 @ X2) @
% 194.24/28.54 (sk__15 @ X0 @ X1 @ X2) @ X2 @ X1 @ X0)
% 194.24/28.54 | ~ (zip_tseitin_7 @ X3 @ X2 @ X4 @ X1 @ X0))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_5])).
% 194.24/28.54 thf(zip_derived_cl53354, plain,
% 194.24/28.54 ( (zip_tseitin_6 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @ sk__1 @ sk_)),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53337, zip_derived_cl94])).
% 194.24/28.54 thf(zip_derived_cl92, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.24/28.54 (((ordered_pair @ X1 @ X2) = (X0))
% 194.24/28.54 | ~ (zip_tseitin_6 @ X2 @ X1 @ X0 @ X3 @ X4))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_7])).
% 194.24/28.54 thf(zip_derived_cl54590, plain,
% 194.24/28.54 (((ordered_pair @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))
% 194.24/28.54 = (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53354, zip_derived_cl92])).
% 194.24/28.54 thf(zip_derived_cl52981, plain,
% 194.24/28.54 ( (in @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @
% 194.24/28.54 (sk__18 @ sk__2 @ sk__1 @ sk_))),
% 194.24/28.54 inference('eq_fact', [status(thm)], [zip_derived_cl52938])).
% 194.24/28.54 thf(zip_derived_cl6, plain,
% 194.24/28.54 (![X0 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (element @ (sk__4 @ X3 @ X2) @ (powerset @ (the_carrier @ sk_)))
% 194.24/28.54 | ((ordered_pair @ X2 @ X3) != (sk__3 @ X0))
% 194.24/28.54 | ~ (in @ X2 @ (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | ~ (in @ (sk__3 @ X0) @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1) @ sk__2))
% 194.24/28.54 | ~ (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.24/28.54 thf(zip_derived_cl52987, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (in @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1) @ sk__2))
% 194.24/28.54 | ~ (in @ X0 @ (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | ((ordered_pair @ X0 @ X1)
% 194.24/28.54 != (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 | (element @ (sk__4 @ X1 @ X0) @ (powerset @ (the_carrier @ sk_))))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl52981, zip_derived_cl6])).
% 194.24/28.54 thf(zip_derived_cl53337, plain,
% 194.24/28.54 ( (zip_tseitin_7 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @ sk__2 @ sk__1 @ sk_)),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl52984, zip_derived_cl53300])).
% 194.24/28.54 thf(zip_derived_cl96, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.24/28.54 ( (in @ X0 @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ X1) @ X2) @ X3))
% 194.24/28.54 | ~ (zip_tseitin_7 @ X0 @ X4 @ X3 @ X2 @ X1))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_5])).
% 194.24/28.54 thf(zip_derived_cl53356, plain,
% 194.24/28.54 ( (in @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1) @ sk__2))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53337, zip_derived_cl96])).
% 194.24/28.54 thf(zip_derived_cl53386, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (in @ X0 @ (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | ((ordered_pair @ X0 @ X1)
% 194.24/28.54 != (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 | (element @ (sk__4 @ X1 @ X0) @ (powerset @ (the_carrier @ sk_))))),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl52987, zip_derived_cl53356])).
% 194.24/28.54 thf(zip_derived_cl54845, plain,
% 194.24/28.54 ((((sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))
% 194.24/28.54 != (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 | (element @
% 194.24/28.54 (sk__4 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))) @
% 194.24/28.54 (powerset @ (the_carrier @ sk_)))
% 194.24/28.54 | ~ (in @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)))),
% 194.24/28.54 inference('sup-', [status(thm)],
% 194.24/28.54 [zip_derived_cl54590, zip_derived_cl53386])).
% 194.24/28.54 thf(zip_derived_cl53354, plain,
% 194.24/28.54 ( (zip_tseitin_6 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @ sk__1 @ sk_)),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53337, zip_derived_cl94])).
% 194.24/28.54 thf(zip_derived_cl91, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 194.24/28.54 ( (in @ X0 @ (complements_of_subsets @ (the_carrier @ X1) @ X2))
% 194.24/28.54 | ~ (zip_tseitin_6 @ X3 @ X0 @ X4 @ X2 @ X1))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_7])).
% 194.24/28.54 thf(zip_derived_cl54589, plain,
% 194.24/28.54 ( (in @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53354, zip_derived_cl91])).
% 194.24/28.54 thf(zip_derived_cl54977, plain,
% 194.24/28.54 ((((sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))
% 194.24/28.54 != (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 | (element @
% 194.24/28.54 (sk__4 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))) @
% 194.24/28.54 (powerset @ (the_carrier @ sk_))))),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl54845, zip_derived_cl54589])).
% 194.24/28.54 thf(zip_derived_cl54978, plain,
% 194.24/28.54 ( (element @
% 194.24/28.54 (sk__4 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))) @
% 194.24/28.54 (powerset @ (the_carrier @ sk_)))),
% 194.24/28.54 inference('simplify', [status(thm)], [zip_derived_cl54977])).
% 194.24/28.54 thf(zip_derived_cl54590, plain,
% 194.24/28.54 (((ordered_pair @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))
% 194.24/28.54 = (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53354, zip_derived_cl92])).
% 194.24/28.54 thf(zip_derived_cl52981, plain,
% 194.24/28.54 ( (in @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @
% 194.24/28.54 (sk__18 @ sk__2 @ sk__1 @ sk_))),
% 194.24/28.54 inference('eq_fact', [status(thm)], [zip_derived_cl52938])).
% 194.24/28.54 thf(zip_derived_cl4, plain,
% 194.24/28.54 (![X0 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (((sk__4 @ X3 @ X2) = (X2))
% 194.24/28.54 | ((ordered_pair @ X2 @ X3) != (sk__3 @ X0))
% 194.24/28.54 | ~ (in @ X2 @ (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | ~ (in @ (sk__3 @ X0) @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1) @ sk__2))
% 194.24/28.54 | ~ (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.24/28.54 thf(zip_derived_cl52985, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (in @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1) @ sk__2))
% 194.24/28.54 | ~ (in @ X0 @ (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | ((ordered_pair @ X0 @ X1)
% 194.24/28.54 != (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 | ((sk__4 @ X1 @ X0) = (X0)))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl52981, zip_derived_cl4])).
% 194.24/28.54 thf(zip_derived_cl53356, plain,
% 194.24/28.54 ( (in @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1) @ sk__2))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53337, zip_derived_cl96])).
% 194.24/28.54 thf(zip_derived_cl53384, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (in @ X0 @ (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | ((ordered_pair @ X0 @ X1)
% 194.24/28.54 != (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 | ((sk__4 @ X1 @ X0) = (X0)))),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl52985, zip_derived_cl53356])).
% 194.24/28.54 thf(zip_derived_cl54843, plain,
% 194.24/28.54 ((((sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))
% 194.24/28.54 != (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 | ((sk__4 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))
% 194.24/28.54 = (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))
% 194.24/28.54 | ~ (in @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)))),
% 194.24/28.54 inference('sup-', [status(thm)],
% 194.24/28.54 [zip_derived_cl54590, zip_derived_cl53384])).
% 194.24/28.54 thf(zip_derived_cl54589, plain,
% 194.24/28.54 ( (in @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53354, zip_derived_cl91])).
% 194.24/28.54 thf(zip_derived_cl54973, plain,
% 194.24/28.54 ((((sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))
% 194.24/28.54 != (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 | ((sk__4 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))
% 194.24/28.54 = (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))))),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl54843, zip_derived_cl54589])).
% 194.24/28.54 thf(zip_derived_cl54974, plain,
% 194.24/28.54 (((sk__4 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))
% 194.24/28.54 = (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))),
% 194.24/28.54 inference('simplify', [status(thm)], [zip_derived_cl54973])).
% 194.24/28.54 thf(zip_derived_cl55200, plain,
% 194.24/28.54 ( (element @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (powerset @ (the_carrier @ sk_)))),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl54978, zip_derived_cl54974])).
% 194.24/28.54 thf(zip_derived_cl87, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (~ (element @ X0 @ (powerset @ (the_carrier @ X1)))
% 194.24/28.54 | (zip_tseitin_4 @ X0 @ X2 @ X3 @ X1)
% 194.24/28.54 | ~ (zip_tseitin_5 @ X0 @ X2 @ X3 @ X1))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_9])).
% 194.24/28.54 thf(zip_derived_cl55231, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (zip_tseitin_5 @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 X1 @ X0 @ sk_)
% 194.24/28.54 | (zip_tseitin_4 @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 X1 @ X0 @ sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl55200, zip_derived_cl87])).
% 194.24/28.54 thf(zip_derived_cl53354, plain,
% 194.24/28.54 ( (zip_tseitin_6 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @ sk__1 @ sk_)),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53337, zip_derived_cl94])).
% 194.24/28.54 thf(zip_derived_cl90, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ X0 @ X1 @ X2 @ X3)
% 194.24/28.54 | ~ (zip_tseitin_6 @ X1 @ X2 @ X4 @ X5 @ X3))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_7])).
% 194.24/28.54 thf(zip_derived_cl54588, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 (zip_tseitin_5 @ X0 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 sk_)),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53354, zip_derived_cl90])).
% 194.24/28.54 thf(zip_derived_cl89, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ X0 @ X1 @ X2 @ X3)
% 194.24/28.54 | (element @ X0 @ (powerset @ (the_carrier @ X3))))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_9])).
% 194.24/28.54 thf(zip_derived_cl87, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (~ (element @ X0 @ (powerset @ (the_carrier @ X1)))
% 194.24/28.54 | (zip_tseitin_4 @ X0 @ X2 @ X3 @ X1)
% 194.24/28.54 | ~ (zip_tseitin_5 @ X0 @ X2 @ X3 @ X1))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_9])).
% 194.24/28.54 thf(zip_derived_cl482, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @ X1 @ X5 @ X4 @ X0)
% 194.24/28.54 | ~ (zip_tseitin_5 @ X1 @ X3 @ X2 @ X0)
% 194.24/28.54 | (zip_tseitin_4 @ X1 @ X3 @ X2 @ X0))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl89, zip_derived_cl87])).
% 194.24/28.54 thf(zip_derived_cl54689, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 ( (zip_tseitin_4 @ X0 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 sk_)
% 194.24/28.54 | (zip_tseitin_5 @ X0 @ X2 @ X1 @ sk_))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl54588, zip_derived_cl482])).
% 194.24/28.54 thf(zip_derived_cl84, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (((X1) != (X0))
% 194.24/28.54 | ((X3) = (subset_complement @ (the_carrier @ X2) @ X1))
% 194.24/28.54 | ~ (zip_tseitin_4 @ X1 @ X3 @ X0 @ X2))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_11])).
% 194.24/28.54 thf(zip_derived_cl296, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 (~ (zip_tseitin_4 @ X1 @ X2 @ X1 @ X0)
% 194.24/28.54 | ((X2) = (subset_complement @ (the_carrier @ X0) @ X1)))),
% 194.24/28.54 inference('eq_res', [status(thm)], [zip_derived_cl84])).
% 194.24/28.54 thf(zip_derived_cl61078, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 ( (zip_tseitin_5 @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 X1 @ X0 @ sk_)
% 194.24/28.54 | ((sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 = (subset_complement @ (the_carrier @ sk_) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl54689, zip_derived_cl296])).
% 194.24/28.54 thf(zip_derived_cl54590, plain,
% 194.24/28.54 (((ordered_pair @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))
% 194.24/28.54 = (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53354, zip_derived_cl92])).
% 194.24/28.54 thf(zip_derived_cl52981, plain,
% 194.24/28.54 ( (in @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @
% 194.24/28.54 (sk__18 @ sk__2 @ sk__1 @ sk_))),
% 194.24/28.54 inference('eq_fact', [status(thm)], [zip_derived_cl52938])).
% 194.24/28.54 thf(zip_derived_cl5, plain,
% 194.24/28.54 (![X0 : $i, X2 : $i, X3 : $i]:
% 194.24/28.54 (((X3)
% 194.24/28.54 != (subset_complement @ (the_carrier @ sk_) @ (sk__4 @ X3 @ X2)))
% 194.24/28.54 | ((ordered_pair @ X2 @ X3) != (sk__3 @ X0))
% 194.24/28.54 | ~ (in @ X2 @ (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | ~ (in @ (sk__3 @ X0) @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1) @ sk__2))
% 194.24/28.54 | ~ (in @ (sk__3 @ X0) @ X0))),
% 194.24/28.54 inference('cnf', [status(esa)], [zf_stmt_1])).
% 194.24/28.54 thf(zip_derived_cl52986, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (in @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1) @ sk__2))
% 194.24/28.54 | ~ (in @ X0 @ (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | ((ordered_pair @ X0 @ X1)
% 194.24/28.54 != (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 | ((X1)
% 194.24/28.54 != (subset_complement @ (the_carrier @ sk_) @ (sk__4 @ X1 @ X0))))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl52981, zip_derived_cl5])).
% 194.24/28.54 thf(zip_derived_cl53356, plain,
% 194.24/28.54 ( (in @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)) @
% 194.24/28.54 (cartesian_product2 @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1) @ sk__2))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53337, zip_derived_cl96])).
% 194.24/28.54 thf(zip_derived_cl53385, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (~ (in @ X0 @ (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))
% 194.24/28.54 | ((ordered_pair @ X0 @ X1)
% 194.24/28.54 != (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 | ((X1)
% 194.24/28.54 != (subset_complement @ (the_carrier @ sk_) @ (sk__4 @ X1 @ X0))))),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl52986, zip_derived_cl53356])).
% 194.24/28.54 thf(zip_derived_cl54844, plain,
% 194.24/28.54 ((((sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))
% 194.24/28.54 != (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 | ((sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 != (subset_complement @ (the_carrier @ sk_) @
% 194.24/28.54 (sk__4 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))))
% 194.24/28.54 | ~ (in @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1)))),
% 194.24/28.54 inference('sup-', [status(thm)],
% 194.24/28.54 [zip_derived_cl54590, zip_derived_cl53385])).
% 194.24/28.54 thf(zip_derived_cl54589, plain,
% 194.24/28.54 ( (in @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (complements_of_subsets @ (the_carrier @ sk_) @ sk__1))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl53354, zip_derived_cl91])).
% 194.24/28.54 thf(zip_derived_cl54975, plain,
% 194.24/28.54 ((((sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))
% 194.24/28.54 != (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 | ((sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 != (subset_complement @ (the_carrier @ sk_) @
% 194.24/28.54 (sk__4 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @
% 194.24/28.54 (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))))))),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl54844, zip_derived_cl54589])).
% 194.24/28.54 thf(zip_derived_cl54976, plain,
% 194.24/28.54 (((sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 != (subset_complement @ (the_carrier @ sk_) @
% 194.24/28.54 (sk__4 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))))),
% 194.24/28.54 inference('simplify', [status(thm)], [zip_derived_cl54975])).
% 194.24/28.54 thf(zip_derived_cl54974, plain,
% 194.24/28.54 (((sk__4 @
% 194.24/28.54 (sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))
% 194.24/28.54 = (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))))),
% 194.24/28.54 inference('simplify', [status(thm)], [zip_derived_cl54973])).
% 194.24/28.54 thf(zip_derived_cl55102, plain,
% 194.24/28.54 (((sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 != (subset_complement @ (the_carrier @ sk_) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))))),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl54976, zip_derived_cl54974])).
% 194.24/28.54 thf(zip_derived_cl61172, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (zip_tseitin_5 @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 X1 @ X0 @ sk_)),
% 194.24/28.54 inference('simplify_reflect-', [status(thm)],
% 194.24/28.54 [zip_derived_cl61078, zip_derived_cl55102])).
% 194.24/28.54 thf(zip_derived_cl61173, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i]:
% 194.24/28.54 (zip_tseitin_4 @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_))) @
% 194.24/28.54 X1 @ X0 @ sk_)),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl55231, zip_derived_cl61172])).
% 194.24/28.54 thf(zip_derived_cl296, plain,
% 194.24/28.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 194.24/28.54 (~ (zip_tseitin_4 @ X1 @ X2 @ X1 @ X0)
% 194.24/28.54 | ((X2) = (subset_complement @ (the_carrier @ X0) @ X1)))),
% 194.24/28.54 inference('eq_res', [status(thm)], [zip_derived_cl84])).
% 194.24/28.54 thf(zip_derived_cl61194, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ((X0)
% 194.24/28.54 = (subset_complement @ (the_carrier @ sk_) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl61173, zip_derived_cl296])).
% 194.24/28.54 thf(zip_derived_cl55102, plain,
% 194.24/28.54 (((sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 != (subset_complement @ (the_carrier @ sk_) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))))),
% 194.24/28.54 inference('demod', [status(thm)],
% 194.24/28.54 [zip_derived_cl54976, zip_derived_cl54974])).
% 194.24/28.54 thf(zip_derived_cl62850, plain,
% 194.24/28.54 (((sk__16 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))
% 194.24/28.54 != (subset_complement @ (the_carrier @ sk_) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))))),
% 194.24/28.54 inference('sup-', [status(thm)],
% 194.24/28.54 [zip_derived_cl61194, zip_derived_cl55102])).
% 194.24/28.54 thf(zip_derived_cl61194, plain,
% 194.24/28.54 (![X0 : $i]:
% 194.24/28.54 ((X0)
% 194.24/28.54 = (subset_complement @ (the_carrier @ sk_) @
% 194.24/28.54 (sk__15 @ sk_ @ sk__1 @ (sk__3 @ (sk__18 @ sk__2 @ sk__1 @ sk_)))))),
% 194.24/28.54 inference('sup-', [status(thm)], [zip_derived_cl61173, zip_derived_cl296])).
% 194.24/28.54 thf(zip_derived_cl64297, plain, ($false),
% 194.24/28.54 inference('simplify_reflect+', [status(thm)],
% 194.24/28.54 [zip_derived_cl62850, zip_derived_cl61194])).
% 194.24/28.54
% 194.24/28.54 % SZS output end Refutation
% 194.24/28.54
% 194.24/28.54
% 194.24/28.54 % Terminating...
% 194.24/28.64 % Runner terminated.
% 194.24/28.67 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------