TSTP Solution File: SEU262+1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU262+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.qhFFiud8Y5 true
% Computer : n007.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 Aug 31 19:11:41 EDT 2023
% Result : Theorem 105.11s 15.81s
% Output : Refutation 105.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU262+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.qhFFiud8Y5 true
% 0.13/0.35 % Computer : n007.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 : Thu Aug 24 01:16:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.21/0.66 % Total configuration time : 435
% 0.21/0.66 % Estimated wc time : 1092
% 0.21/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.78 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.58/0.83 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 105.11/15.81 % Solved by fo/fo1_lcnf.sh.
% 105.11/15.81 % done 15549 iterations in 14.935s
% 105.11/15.81 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 105.11/15.81 % SZS output start Refutation
% 105.11/15.81 thf('#sk17_type', type, '#sk17': $i > $i > $i).
% 105.11/15.81 thf(relation_of2_type, type, relation_of2: $i > $i > $i > $o).
% 105.11/15.81 thf(cartesian_product2_type, type, cartesian_product2: $i > $i > $i).
% 105.11/15.81 thf('#sk6_type', type, '#sk6': $i).
% 105.11/15.81 thf(in_type, type, in: $i > $i > $o).
% 105.11/15.81 thf('#sk7_type', type, '#sk7': $i).
% 105.11/15.81 thf(ordered_pair_type, type, ordered_pair: $i > $i > $i).
% 105.11/15.81 thf('#sk18_type', type, '#sk18': $i > $i > $i).
% 105.11/15.81 thf(relation_of2_as_subset_type, type, relation_of2_as_subset: $i > $i > $i > $o).
% 105.11/15.81 thf(relation_rng_type, type, relation_rng: $i > $i).
% 105.11/15.81 thf(subset_type, type, subset: $i > $i > $o).
% 105.11/15.81 thf('#sk8_type', type, '#sk8': $i).
% 105.11/15.81 thf(powerset_type, type, powerset: $i > $i).
% 105.11/15.81 thf(empty_type, type, empty: $i > $o).
% 105.11/15.81 thf('#sk9_type', type, '#sk9': $i > $i > $i).
% 105.11/15.81 thf(relation_type, type, relation: $i > $o).
% 105.11/15.81 thf(element_type, type, element: $i > $i > $o).
% 105.11/15.81 thf(relation_dom_type, type, relation_dom: $i > $i).
% 105.11/15.81 thf(t12_relset_1, conjecture,
% 105.11/15.81 (![A:$i,B:$i,C:$i]:
% 105.11/15.81 ( ( relation_of2_as_subset @ C @ A @ B ) =>
% 105.11/15.81 ( ( subset @ ( relation_rng @ C ) @ B ) &
% 105.11/15.81 ( subset @ ( relation_dom @ C ) @ A ) ) ))).
% 105.11/15.81 thf(zf_stmt_0, negated_conjecture,
% 105.11/15.81 (~( ![A:$i,B:$i,C:$i]:
% 105.11/15.81 ( ( relation_of2_as_subset @ C @ A @ B ) =>
% 105.11/15.81 ( ( subset @ ( relation_rng @ C ) @ B ) &
% 105.11/15.81 ( subset @ ( relation_dom @ C ) @ A ) ) ) )),
% 105.11/15.81 inference('cnf.neg', [status(esa)], [t12_relset_1])).
% 105.11/15.81 thf(zip_derived_cl28, plain,
% 105.11/15.81 (~ (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((!!) @ (^[Y2 : $i]:
% 105.11/15.81 (((relation_of2_as_subset @ Y2 @
% 105.11/15.81 Y0 @ Y1) =>
% 105.11/15.81 (((subset @
% 105.11/15.81 (relation_rng @ Y2) @ Y1) &
% 105.11/15.81 (subset @
% 105.11/15.81 (relation_dom @ Y2) @ Y0))))))))))))))),
% 105.11/15.81 inference('cnf', [status(esa)], [zf_stmt_0])).
% 105.11/15.81 thf(zip_derived_cl71, plain,
% 105.11/15.81 (~ (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((relation_of2_as_subset @ Y1 @ '#sk6' @
% 105.11/15.81 Y0) =>
% 105.11/15.81 (((subset @ (relation_rng @ Y1) @ Y0) &
% 105.11/15.81 (subset @ (relation_dom @ Y1) @ '#sk6')))))))))))),
% 105.11/15.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])).
% 105.11/15.81 thf(zip_derived_cl72, plain,
% 105.11/15.81 (~ (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((relation_of2_as_subset @ Y0 @ '#sk6' @ '#sk7') =>
% 105.11/15.81 (((subset @ (relation_rng @ Y0) @ '#sk7') & (subset @
% 105.11/15.81 (relation_dom @ Y0) @ '#sk6'))))))))),
% 105.11/15.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl71])).
% 105.11/15.81 thf(zip_derived_cl73, plain,
% 105.11/15.81 (~ (((relation_of2_as_subset @ '#sk8' @ '#sk6' @ '#sk7') =>
% 105.11/15.81 (((subset @ (relation_rng @ '#sk8') @ '#sk7') & (subset @
% 105.11/15.81 (relation_dom @ '#sk8') @ '#sk6')))))),
% 105.11/15.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl72])).
% 105.11/15.81 thf(zip_derived_cl75, plain,
% 105.11/15.81 (~ (((subset @ (relation_rng @ '#sk8') @ '#sk7') & (subset @
% 105.11/15.81 (relation_dom @ '#sk8') @ '#sk6')))),
% 105.11/15.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])).
% 105.11/15.81 thf(zip_derived_cl76, plain,
% 105.11/15.81 ((~ (subset @ (relation_rng @ '#sk8') @ '#sk7')
% 105.11/15.81 | ~ (subset @ (relation_dom @ '#sk8') @ '#sk6'))),
% 105.11/15.81 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl75])).
% 105.11/15.81 thf(d4_relat_1, axiom,
% 105.11/15.81 (![A:$i]:
% 105.11/15.81 ( ( relation @ A ) =>
% 105.11/15.81 ( ![B:$i]:
% 105.11/15.81 ( ( ( B ) = ( relation_dom @ A ) ) <=>
% 105.11/15.81 ( ![C:$i]:
% 105.11/15.81 ( ( in @ C @ B ) <=>
% 105.11/15.81 ( ?[D:$i]: ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) ) ) ))).
% 105.11/15.81 thf(zip_derived_cl4, plain,
% 105.11/15.81 ( (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((relation @ Y0) =>
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((((Y1) = (relation_dom @ Y0))) <=>
% 105.11/15.81 (((!!) @ (^[Y2 : $i]:
% 105.11/15.81 (((in @ Y2 @ Y1) <=>
% 105.11/15.81 (((??) @ (^[Y3 : $i]:
% 105.11/15.81 (in @
% 105.11/15.81 (ordered_pair @
% 105.11/15.81 Y2 @ Y3) @
% 105.11/15.81 Y0)))))))))))))))))))),
% 105.11/15.81 inference('cnf', [status(esa)], [d4_relat_1])).
% 105.11/15.81 thf(zip_derived_cl116, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (((relation @ X2) =>
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((((Y0) = (relation_dom @ X2))) <=>
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((in @ Y1 @ Y0) <=>
% 105.11/15.81 (((??) @ (^[Y2 : $i]:
% 105.11/15.81 (in @
% 105.11/15.81 (ordered_pair @ Y1 @ Y2) @
% 105.11/15.81 X2))))))))))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])).
% 105.11/15.81 thf(zip_derived_cl117, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (~ (relation @ X2)
% 105.11/15.81 | (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((((Y0) = (relation_dom @ X2))) <=>
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((in @ Y1 @ Y0) <=>
% 105.11/15.81 (((??) @ (^[Y2 : $i]:
% 105.11/15.81 (in @
% 105.11/15.81 (ordered_pair @ Y1 @ Y2) @
% 105.11/15.81 X2)))))))))))))))),
% 105.11/15.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl116])).
% 105.11/15.81 thf(zip_derived_cl118, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ( (((((X4) = (relation_dom @ X2))) <=>
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((in @ Y0 @ X4) <=>
% 105.11/15.81 (((??) @ (^[Y1 : $i]:
% 105.11/15.81 (in @ (ordered_pair @ Y0 @ Y1) @ X2)))))))))))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl117])).
% 105.11/15.81 thf(zip_derived_cl119, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (((((X4) = (relation_dom @ X2)))
% 105.11/15.81 = (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((in @ Y0 @ X4) <=>
% 105.11/15.81 (((??) @ (^[Y1 : $i]:
% 105.11/15.81 (in @ (ordered_pair @ Y0 @ Y1) @ X2))))))))))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl118])).
% 105.11/15.81 thf(zip_derived_cl120, plain,
% 105.11/15.81 (![X-72 : $i, X2 : $i, X4 : $i]:
% 105.11/15.81 ( ((^[Y0 : $i]:
% 105.11/15.81 (((in @ Y0 @ X4) <=>
% 105.11/15.81 (((??) @ (^[Y1 : $i]: (in @ (ordered_pair @ Y0 @ Y1) @ X2))))))) @
% 105.11/15.81 X-72)
% 105.11/15.81 | ~ (((X4) = (relation_dom @ X2)))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('forall_hoist', [status(thm)], [zip_derived_cl119])).
% 105.11/15.81 thf(zip_derived_cl123, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X5 : $i]:
% 105.11/15.81 ( ((^[Y0 : $i]:
% 105.11/15.81 (((in @ Y0 @ X4) <=>
% 105.11/15.81 (((??) @ (^[Y1 : $i]: (in @ (ordered_pair @ Y0 @ Y1) @ X2))))))) @
% 105.11/15.81 X5)
% 105.11/15.81 | ~ (((X4) = (relation_dom @ X2)))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('cannonize vars', [status(thm)], [zip_derived_cl120])).
% 105.11/15.81 thf(zip_derived_cl124, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X5 : $i]:
% 105.11/15.81 ( ((^[Y0 : $i]:
% 105.11/15.81 (((in @ Y0 @ X4) <=>
% 105.11/15.81 (((??) @ (^[Y1 : $i]: (in @ (ordered_pair @ Y0 @ Y1) @ X2))))))) @
% 105.11/15.81 X5)
% 105.11/15.81 | ((X4) != (relation_dom @ X2))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl123])).
% 105.11/15.81 thf(zip_derived_cl125, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X5 : $i]:
% 105.11/15.81 ( (((in @ X5 @ X4) <=>
% 105.11/15.81 (((??) @ (^[Y0 : $i]: (in @ (ordered_pair @ X5 @ Y0) @ X2))))))
% 105.11/15.81 | ((X4) != (relation_dom @ X2))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('rw', [status(thm)], [zip_derived_cl124])).
% 105.11/15.81 thf(zip_derived_cl126, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X5 : $i]:
% 105.11/15.81 (((in @ X5 @ X4)
% 105.11/15.81 = (((??) @ (^[Y0 : $i]: (in @ (ordered_pair @ X5 @ Y0) @ X2)))))
% 105.11/15.81 | ((X4) != (relation_dom @ X2))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl125])).
% 105.11/15.81 thf(zip_derived_cl555, plain,
% 105.11/15.81 (![X0 : $i, X1 : $i]:
% 105.11/15.81 (~ (relation @ X0)
% 105.11/15.81 | ((in @ X1 @ (relation_dom @ X0))
% 105.11/15.81 = (((??) @ (^[Y0 : $i]: (in @ (ordered_pair @ X1 @ Y0) @ X0))))))),
% 105.11/15.81 inference('eq_res', [status(thm)], [zip_derived_cl126])).
% 105.11/15.81 thf(zip_derived_cl4627, plain,
% 105.11/15.81 (![X0 : $i, X1 : $i]:
% 105.11/15.81 (~ (relation @ X0)
% 105.11/15.81 | ((in @ X1 @ (relation_dom @ X0))
% 105.11/15.81 = ((^[Y0 : $i]: (in @ (ordered_pair @ X1 @ Y0) @ X0)) @
% 105.11/15.81 ('#sk17' @ X0 @ X1))))),
% 105.11/15.81 inference('quantifier_rw', [status(thm)], [zip_derived_cl555])).
% 105.11/15.81 thf(zip_derived_cl4628, plain,
% 105.11/15.81 (![X0 : $i, X1 : $i]:
% 105.11/15.81 (~ (relation @ X0)
% 105.11/15.81 | ((in @ X1 @ (relation_dom @ X0))
% 105.11/15.81 = (in @ (ordered_pair @ X1 @ ('#sk17' @ X0 @ X1)) @ X0)))),
% 105.11/15.81 inference('rw', [status(thm)], [zip_derived_cl4627])).
% 105.11/15.81 thf(redefinition_m2_relset_1, axiom,
% 105.11/15.81 (![A:$i,B:$i,C:$i]:
% 105.11/15.81 ( ( relation_of2_as_subset @ C @ A @ B ) <=> ( relation_of2 @ C @ A @ B ) ))).
% 105.11/15.81 thf(zip_derived_cl25, plain,
% 105.11/15.81 ( (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((!!) @ (^[Y2 : $i]:
% 105.11/15.81 (((relation_of2_as_subset @ Y2 @
% 105.11/15.81 Y0 @ Y1) <=> (relation_of2 @
% 105.11/15.81 Y2 @ Y0 @ Y1))))))))))))),
% 105.11/15.81 inference('cnf', [status(esa)], [redefinition_m2_relset_1])).
% 105.11/15.81 thf(zip_derived_cl148, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((relation_of2_as_subset @ Y1 @ X2 @ Y0) <=>
% 105.11/15.81 (relation_of2 @ Y1 @ X2 @ Y0)))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])).
% 105.11/15.81 thf(zip_derived_cl149, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((relation_of2_as_subset @ Y0 @ X2 @ X4) <=>
% 105.11/15.81 (relation_of2 @ Y0 @ X2 @ X4))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl148])).
% 105.11/15.81 thf(zip_derived_cl150, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (((relation_of2_as_subset @ X6 @ X2 @ X4) <=> (relation_of2 @ X6 @
% 105.11/15.81 X2 @ X4)))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl149])).
% 105.11/15.81 thf(zip_derived_cl151, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 ((relation_of2_as_subset @ X6 @ X2 @ X4)
% 105.11/15.81 = (relation_of2 @ X6 @ X2 @ X4))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl150])).
% 105.11/15.81 thf(zip_derived_cl74, plain,
% 105.11/15.81 ( (relation_of2_as_subset @ '#sk8' @ '#sk6' @ '#sk7')),
% 105.11/15.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])).
% 105.11/15.81 thf(zip_derived_cl153, plain, ( (relation_of2 @ '#sk8' @ '#sk6' @ '#sk7')),
% 105.11/15.81 inference('s_sup+', [status(thm)], [zip_derived_cl151, zip_derived_cl74])).
% 105.11/15.81 thf(dt_m2_relset_1, axiom,
% 105.11/15.81 (![A:$i,B:$i,C:$i]:
% 105.11/15.81 ( ( relation_of2_as_subset @ C @ A @ B ) =>
% 105.11/15.81 ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ))).
% 105.11/15.81 thf(zip_derived_cl17, plain,
% 105.11/15.81 ( (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((!!) @ (^[Y2 : $i]:
% 105.11/15.81 (((relation_of2_as_subset @ Y2 @
% 105.11/15.81 Y0 @ Y1) => (element @ Y2 @
% 105.11/15.81 (powerset @
% 105.11/15.81 (cartesian_product2 @ Y0 @ Y1))))))))))))))),
% 105.11/15.81 inference('cnf', [status(esa)], [dt_m2_relset_1])).
% 105.11/15.81 thf(zip_derived_cl228, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((relation_of2_as_subset @ Y1 @ X2 @ Y0) =>
% 105.11/15.81 (element @ Y1 @
% 105.11/15.81 (powerset @ (cartesian_product2 @ X2 @ Y0)))))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])).
% 105.11/15.81 thf(zip_derived_cl229, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((relation_of2_as_subset @ Y0 @ X2 @ X4) => (element @
% 105.11/15.81 Y0 @ (powerset @ (cartesian_product2 @ X2 @ X4))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl228])).
% 105.11/15.81 thf(zip_derived_cl230, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (((relation_of2_as_subset @ X6 @ X2 @ X4) => (element @ X6 @
% 105.11/15.81 (powerset @ (cartesian_product2 @ X2 @ X4)))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl229])).
% 105.11/15.81 thf(zip_derived_cl151, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 ((relation_of2_as_subset @ X6 @ X2 @ X4)
% 105.11/15.81 = (relation_of2 @ X6 @ X2 @ X4))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl150])).
% 105.11/15.81 thf(t3_subset, axiom,
% 105.11/15.81 (![A:$i,B:$i]:
% 105.11/15.81 ( ( element @ A @ ( powerset @ B ) ) <=> ( subset @ A @ B ) ))).
% 105.11/15.81 thf(zip_derived_cl31, plain,
% 105.11/15.81 ( (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((element @ Y0 @ (powerset @ Y1)) <=>
% 105.11/15.81 (subset @ Y0 @ Y1)))))))))),
% 105.11/15.81 inference('cnf', [status(esa)], [t3_subset])).
% 105.11/15.81 thf(zip_derived_cl108, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((element @ X2 @ (powerset @ Y0)) <=> (subset @ X2 @ Y0))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])).
% 105.11/15.81 thf(zip_derived_cl109, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (((element @ X2 @ (powerset @ X4)) <=> (subset @ X2 @ X4)))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl108])).
% 105.11/15.81 thf(zip_derived_cl110, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ((element @ X2 @ (powerset @ X4)) = (subset @ X2 @ X4))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl109])).
% 105.11/15.81 thf(zip_derived_cl231, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (((relation_of2 @ X6 @ X2 @ X4) => (subset @ X6 @
% 105.11/15.81 (cartesian_product2 @ X2 @ X4))))),
% 105.11/15.81 inference('demod', [status(thm)],
% 105.11/15.81 [zip_derived_cl230, zip_derived_cl151, zip_derived_cl110])).
% 105.11/15.81 thf(zip_derived_cl232, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (~ (relation_of2 @ X6 @ X2 @ X4)
% 105.11/15.81 | (subset @ X6 @ (cartesian_product2 @ X2 @ X4)))),
% 105.11/15.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl231])).
% 105.11/15.81 thf(t4_subset, axiom,
% 105.11/15.81 (![A:$i,B:$i,C:$i]:
% 105.11/15.81 ( ( ( element @ B @ ( powerset @ C ) ) & ( in @ A @ B ) ) =>
% 105.11/15.81 ( element @ A @ C ) ))).
% 105.11/15.81 thf(zip_derived_cl32, plain,
% 105.11/15.81 ( (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((!!) @ (^[Y2 : $i]:
% 105.11/15.81 (((((element @ Y1 @
% 105.11/15.81 (powerset @ Y2)) & (in @ Y0 @
% 105.11/15.81 Y1))) =>
% 105.11/15.81 (element @ Y0 @ Y2))))))))))))),
% 105.11/15.81 inference('cnf', [status(esa)], [t4_subset])).
% 105.11/15.81 thf(zip_derived_cl351, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((((element @ Y0 @ (powerset @ Y1)) & (in @
% 105.11/15.81 X2 @ Y0))) =>
% 105.11/15.81 (element @ X2 @ Y1)))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])).
% 105.11/15.81 thf(zip_derived_cl352, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((((element @ X4 @ (powerset @ Y0)) & (in @ X2 @ X4))) =>
% 105.11/15.81 (element @ X2 @ Y0))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl351])).
% 105.11/15.81 thf(zip_derived_cl353, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (((((element @ X4 @ (powerset @ X6)) & (in @ X2 @ X4))) =>
% 105.11/15.81 (element @ X2 @ X6)))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl352])).
% 105.11/15.81 thf(zip_derived_cl110, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ((element @ X2 @ (powerset @ X4)) = (subset @ X2 @ X4))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl109])).
% 105.11/15.81 thf(zip_derived_cl354, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (((((subset @ X4 @ X6) & (in @ X2 @ X4))) => (element @ X2 @ X6)))),
% 105.11/15.81 inference('demod', [status(thm)], [zip_derived_cl353, zip_derived_cl110])).
% 105.11/15.81 thf(zip_derived_cl355, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (~ (((subset @ X4 @ X6) & (in @ X2 @ X4))) | (element @ X2 @ X6))),
% 105.11/15.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl354])).
% 105.11/15.81 thf(zip_derived_cl356, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (~ (subset @ X4 @ X6) | ~ (in @ X2 @ X4) | (element @ X2 @ X6))),
% 105.11/15.81 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl355])).
% 105.11/15.81 thf(zip_derived_cl359, plain,
% 105.11/15.81 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 105.11/15.81 (~ (relation_of2 @ X2 @ X1 @ X0)
% 105.11/15.81 | ~ (in @ X3 @ X2)
% 105.11/15.81 | (element @ X3 @ (cartesian_product2 @ X1 @ X0)))),
% 105.11/15.81 inference('s_sup-', [status(thm)], [zip_derived_cl232, zip_derived_cl356])).
% 105.11/15.81 thf(zip_derived_cl2666, plain,
% 105.11/15.81 (![X0 : $i]:
% 105.11/15.81 (~ (in @ X0 @ '#sk8')
% 105.11/15.81 | (element @ X0 @ (cartesian_product2 @ '#sk6' @ '#sk7')))),
% 105.11/15.81 inference('s_sup-', [status(thm)], [zip_derived_cl153, zip_derived_cl359])).
% 105.11/15.81 thf(t2_subset, axiom,
% 105.11/15.81 (![A:$i,B:$i]:
% 105.11/15.81 ( ( element @ A @ B ) => ( ( in @ A @ B ) | ( empty @ B ) ) ))).
% 105.11/15.81 thf(zip_derived_cl30, plain,
% 105.11/15.81 ( (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((element @ Y0 @ Y1) =>
% 105.11/15.81 (((in @ Y0 @ Y1) | (empty @ Y1)))))))))))),
% 105.11/15.81 inference('cnf', [status(esa)], [t2_subset])).
% 105.11/15.81 thf(zip_derived_cl205, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((element @ X2 @ Y0) =>
% 105.11/15.81 (((in @ X2 @ Y0) | (empty @ Y0))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl30])).
% 105.11/15.81 thf(zip_derived_cl206, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (((element @ X2 @ X4) => (((in @ X2 @ X4) | (empty @ X4)))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl205])).
% 105.11/15.81 thf(zip_derived_cl207, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (~ (element @ X2 @ X4) | (((in @ X2 @ X4) | (empty @ X4))))),
% 105.11/15.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 105.11/15.81 thf(zip_derived_cl208, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ( (in @ X2 @ X4) | (empty @ X4) | ~ (element @ X2 @ X4))),
% 105.11/15.81 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl207])).
% 105.11/15.81 thf(zip_derived_cl2667, plain,
% 105.11/15.81 (![X0 : $i]:
% 105.11/15.81 (~ (in @ X0 @ '#sk8')
% 105.11/15.81 | (in @ X0 @ (cartesian_product2 @ '#sk6' @ '#sk7'))
% 105.11/15.81 | (empty @ (cartesian_product2 @ '#sk6' @ '#sk7')))),
% 105.11/15.81 inference('s_sup-', [status(thm)],
% 105.11/15.81 [zip_derived_cl2666, zip_derived_cl208])).
% 105.11/15.81 thf(zip_derived_cl153, plain, ( (relation_of2 @ '#sk8' @ '#sk6' @ '#sk7')),
% 105.11/15.81 inference('s_sup+', [status(thm)], [zip_derived_cl151, zip_derived_cl74])).
% 105.11/15.81 thf(zip_derived_cl232, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (~ (relation_of2 @ X6 @ X2 @ X4)
% 105.11/15.81 | (subset @ X6 @ (cartesian_product2 @ X2 @ X4)))),
% 105.11/15.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl231])).
% 105.11/15.81 thf(t5_subset, axiom,
% 105.11/15.81 (![A:$i,B:$i,C:$i]:
% 105.11/15.81 ( ~( ( empty @ C ) & ( element @ B @ ( powerset @ C ) ) & ( in @ A @ B ) ) ))).
% 105.11/15.81 thf(zip_derived_cl33, plain,
% 105.11/15.81 ( (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((!!) @ (^[Y2 : $i]:
% 105.11/15.81 (((~) @ (((empty @ Y2) &
% 105.11/15.81 (element @ Y1 @
% 105.11/15.81 (powerset @ Y2)) &
% 105.11/15.81 (in @ Y0 @ Y1))))))))))))))),
% 105.11/15.81 inference('cnf', [status(esa)], [t5_subset])).
% 105.11/15.81 thf(zip_derived_cl238, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((~) @ (((empty @ Y1) &
% 105.11/15.81 (element @ Y0 @ (powerset @ Y1)) &
% 105.11/15.81 (in @ X2 @ Y0)))))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])).
% 105.11/15.81 thf(zip_derived_cl239, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((~) @ (((empty @ Y0) &
% 105.11/15.81 (element @ X4 @ (powerset @ Y0)) &
% 105.11/15.81 (in @ X2 @ X4))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl238])).
% 105.11/15.81 thf(zip_derived_cl240, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 ~ (((empty @ X6) & (element @ X4 @ (powerset @ X6)) & (in @ X2 @ X4)))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl239])).
% 105.11/15.81 thf(zip_derived_cl110, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ((element @ X2 @ (powerset @ X4)) = (subset @ X2 @ X4))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl109])).
% 105.11/15.81 thf(zip_derived_cl241, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 ~ (((empty @ X6) & (subset @ X4 @ X6) & (in @ X2 @ X4)))),
% 105.11/15.81 inference('demod', [status(thm)], [zip_derived_cl240, zip_derived_cl110])).
% 105.11/15.81 thf(zip_derived_cl242, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (~ (empty @ X6) | ~ (subset @ X4 @ X6) | ~ (in @ X2 @ X4))),
% 105.11/15.81 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl241])).
% 105.11/15.81 thf(zip_derived_cl245, plain,
% 105.11/15.81 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 105.11/15.81 (~ (relation_of2 @ X2 @ X1 @ X0)
% 105.11/15.81 | ~ (empty @ (cartesian_product2 @ X1 @ X0))
% 105.11/15.81 | ~ (in @ X3 @ X2))),
% 105.11/15.81 inference('s_sup-', [status(thm)], [zip_derived_cl232, zip_derived_cl242])).
% 105.11/15.81 thf(zip_derived_cl1419, plain,
% 105.11/15.81 (![X0 : $i]:
% 105.11/15.81 (~ (empty @ (cartesian_product2 @ '#sk6' @ '#sk7'))
% 105.11/15.81 | ~ (in @ X0 @ '#sk8'))),
% 105.11/15.81 inference('s_sup-', [status(thm)], [zip_derived_cl153, zip_derived_cl245])).
% 105.11/15.81 thf(zip_derived_cl3691, plain,
% 105.11/15.81 (![X0 : $i]:
% 105.11/15.81 ( (in @ X0 @ (cartesian_product2 @ '#sk6' @ '#sk7'))
% 105.11/15.81 | ~ (in @ X0 @ '#sk8'))),
% 105.11/15.81 inference('clc', [status(thm)], [zip_derived_cl2667, zip_derived_cl1419])).
% 105.11/15.81 thf(t106_zfmisc_1, axiom,
% 105.11/15.81 (![A:$i,B:$i,C:$i,D:$i]:
% 105.11/15.81 ( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) <=>
% 105.11/15.81 ( ( in @ B @ D ) & ( in @ A @ C ) ) ))).
% 105.11/15.81 thf(zip_derived_cl27, plain,
% 105.11/15.81 ( (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((!!) @ (^[Y2 : $i]:
% 105.11/15.81 (((!!) @ (^[Y3 : $i]:
% 105.11/15.81 (((in @
% 105.11/15.81 (ordered_pair @ Y0 @
% 105.11/15.81 Y1) @
% 105.11/15.81 (cartesian_product2 @
% 105.11/15.81 Y2 @ Y3)) <=>
% 105.11/15.81 (((in @ Y1 @ Y3) &
% 105.11/15.81 (in @ Y0 @ Y2)))))))))))))))))),
% 105.11/15.81 inference('cnf', [status(esa)], [t106_zfmisc_1])).
% 105.11/15.81 thf(zip_derived_cl277, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((!!) @ (^[Y2 : $i]:
% 105.11/15.81 (((in @
% 105.11/15.81 (ordered_pair @ X2 @ Y0) @
% 105.11/15.81 (cartesian_product2 @ Y1 @ Y2)) <=>
% 105.11/15.81 (((in @ Y0 @ Y2) & (in @ X2 @
% 105.11/15.81 Y1))))))))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl27])).
% 105.11/15.81 thf(zip_derived_cl278, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((in @ (ordered_pair @ X2 @ X4) @
% 105.11/15.81 (cartesian_product2 @ Y0 @ Y1)) <=>
% 105.11/15.81 (((in @ X4 @ Y1) & (in @ X2 @ Y0)))))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl277])).
% 105.11/15.81 thf(zip_derived_cl279, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((in @ (ordered_pair @ X2 @ X4) @
% 105.11/15.81 (cartesian_product2 @ X6 @ Y0)) <=>
% 105.11/15.81 (((in @ X4 @ Y0) & (in @ X2 @ X6))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl278])).
% 105.11/15.81 thf(zip_derived_cl280, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 105.11/15.81 (((in @ (ordered_pair @ X2 @ X4) @
% 105.11/15.81 (cartesian_product2 @ X6 @ X8)) <=>
% 105.11/15.81 (((in @ X4 @ X8) & (in @ X2 @ X6)))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl279])).
% 105.11/15.81 thf(zip_derived_cl281, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 105.11/15.81 ((in @ (ordered_pair @ X2 @ X4) @ (cartesian_product2 @ X6 @ X8))
% 105.11/15.81 = (((in @ X4 @ X8) & (in @ X2 @ X6))))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl280])).
% 105.11/15.81 thf(zip_derived_cl291, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 105.11/15.81 (~ (in @ (ordered_pair @ X2 @ X4) @ (cartesian_product2 @ X6 @ X8))
% 105.11/15.81 | (((in @ X4 @ X8) & (in @ X2 @ X6))))),
% 105.11/15.81 inference('eq_elim', [status(thm)], [zip_derived_cl281])).
% 105.11/15.81 thf(zip_derived_cl299, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 105.11/15.81 ( (in @ X2 @ X6)
% 105.11/15.81 | ~ (in @ (ordered_pair @ X2 @ X4) @ (cartesian_product2 @ X6 @ X8)))),
% 105.11/15.81 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl291])).
% 105.11/15.81 thf(zip_derived_cl3724, plain,
% 105.11/15.81 (![X0 : $i, X1 : $i]:
% 105.11/15.81 (~ (in @ (ordered_pair @ X1 @ X0) @ '#sk8') | (in @ X1 @ '#sk6'))),
% 105.11/15.81 inference('s_sup-', [status(thm)],
% 105.11/15.81 [zip_derived_cl3691, zip_derived_cl299])).
% 105.11/15.81 thf(zip_derived_cl4659, plain,
% 105.11/15.81 (![X0 : $i]:
% 105.11/15.81 (~ (relation @ '#sk8')
% 105.11/15.81 | ~ (in @ X0 @ (relation_dom @ '#sk8'))
% 105.11/15.81 | (in @ X0 @ '#sk6'))),
% 105.11/15.81 inference('s_sup-', [status(thm)],
% 105.11/15.81 [zip_derived_cl4628, zip_derived_cl3724])).
% 105.11/15.81 thf(zip_derived_cl232, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (~ (relation_of2 @ X6 @ X2 @ X4)
% 105.11/15.81 | (subset @ X6 @ (cartesian_product2 @ X2 @ X4)))),
% 105.11/15.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl231])).
% 105.11/15.81 thf(zip_derived_cl110, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ((element @ X2 @ (powerset @ X4)) = (subset @ X2 @ X4))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl109])).
% 105.11/15.81 thf(cc1_relset_1, axiom,
% 105.11/15.81 (![A:$i,B:$i,C:$i]:
% 105.11/15.81 ( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) =>
% 105.11/15.81 ( relation @ C ) ))).
% 105.11/15.81 thf(zip_derived_cl1, plain,
% 105.11/15.81 ( (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((!!) @ (^[Y2 : $i]:
% 105.11/15.81 (((element @ Y2 @
% 105.11/15.81 (powerset @
% 105.11/15.81 (cartesian_product2 @ Y0 @ Y1))) =>
% 105.11/15.81 (relation @ Y2))))))))))))),
% 105.11/15.81 inference('cnf', [status(esa)], [cc1_relset_1])).
% 105.11/15.81 thf(zip_derived_cl45, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((element @ Y1 @
% 105.11/15.81 (powerset @ (cartesian_product2 @ X2 @ Y0))) =>
% 105.11/15.81 (relation @ Y1)))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])).
% 105.11/15.81 thf(zip_derived_cl46, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((element @ Y0 @
% 105.11/15.81 (powerset @ (cartesian_product2 @ X2 @ X4))) =>
% 105.11/15.81 (relation @ Y0))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl45])).
% 105.11/15.81 thf(zip_derived_cl47, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (((element @ X6 @ (powerset @ (cartesian_product2 @ X2 @ X4))) =>
% 105.11/15.81 (relation @ X6)))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl46])).
% 105.11/15.81 thf(zip_derived_cl48, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i]:
% 105.11/15.81 (~ (element @ X6 @ (powerset @ (cartesian_product2 @ X2 @ X4)))
% 105.11/15.81 | (relation @ X6))),
% 105.11/15.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])).
% 105.11/15.81 thf(zip_derived_cl111, plain,
% 105.11/15.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 105.11/15.81 (~ (subset @ X2 @ (cartesian_product2 @ X1 @ X0)) | (relation @ X2))),
% 105.11/15.81 inference('s_sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl48])).
% 105.11/15.81 thf(zip_derived_cl233, plain,
% 105.11/15.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 105.11/15.81 (~ (relation_of2 @ X2 @ X1 @ X0) | (relation @ X2))),
% 105.11/15.81 inference('s_sup-', [status(thm)], [zip_derived_cl232, zip_derived_cl111])).
% 105.11/15.81 thf(zip_derived_cl153, plain, ( (relation_of2 @ '#sk8' @ '#sk6' @ '#sk7')),
% 105.11/15.81 inference('s_sup+', [status(thm)], [zip_derived_cl151, zip_derived_cl74])).
% 105.11/15.81 thf(zip_derived_cl273, plain, ( (relation @ '#sk8')),
% 105.11/15.81 inference('s_sup+', [status(thm)], [zip_derived_cl233, zip_derived_cl153])).
% 105.11/15.81 thf(zip_derived_cl4676, plain,
% 105.11/15.81 (![X0 : $i]:
% 105.11/15.81 (~ (in @ X0 @ (relation_dom @ '#sk8')) | (in @ X0 @ '#sk6'))),
% 105.11/15.81 inference('demod', [status(thm)], [zip_derived_cl4659, zip_derived_cl273])).
% 105.11/15.81 thf(d3_tarski, axiom,
% 105.11/15.81 (![A:$i,B:$i]:
% 105.11/15.81 ( ( subset @ A @ B ) <=> ( ![C:$i]: ( ( in @ C @ A ) => ( in @ C @ B ) ) ) ))).
% 105.11/15.81 thf(zip_derived_cl3, plain,
% 105.11/15.81 ( (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((subset @ Y0 @ Y1) <=>
% 105.11/15.81 (((!!) @ (^[Y2 : $i]:
% 105.11/15.81 (((in @ Y2 @ Y0) => (in @ Y2 @
% 105.11/15.81 Y1))))))))))))))),
% 105.11/15.81 inference('cnf', [status(esa)], [d3_tarski])).
% 105.11/15.81 thf(zip_derived_cl77, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((subset @ X2 @ Y0) <=>
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((in @ Y1 @ X2) => (in @ Y1 @ Y0)))))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])).
% 105.11/15.81 thf(zip_derived_cl78, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (((subset @ X2 @ X4) <=>
% 105.11/15.81 (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (in @ Y0 @ X4))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl77])).
% 105.11/15.81 thf(zip_derived_cl79, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ((subset @ X2 @ X4)
% 105.11/15.81 = (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (in @ Y0 @ X4)))))))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)], [zip_derived_cl78])).
% 105.11/15.81 thf(zip_derived_cl81, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ((subset @ X2 @ X4)
% 105.11/15.81 = ((^[Y0 : $i]: (((in @ Y0 @ X2) => (in @ Y0 @ X4)))) @
% 105.11/15.81 ('#sk9' @ X2 @ X4)))),
% 105.11/15.81 inference('quantifier_rw', [status(thm)], [zip_derived_cl79])).
% 105.11/15.81 thf(zip_derived_cl82, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ((subset @ X2 @ X4)
% 105.11/15.81 = (((in @ ('#sk9' @ X2 @ X4) @ X2) => (in @ ('#sk9' @ X2 @ X4) @ X4))))),
% 105.11/15.81 inference('rw', [status(thm)], [zip_derived_cl81])).
% 105.11/15.81 thf(zip_derived_cl88, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ( (in @ ('#sk9' @ X2 @ X4) @ X2)
% 105.11/15.81 | ((subset @ X2 @ X4)
% 105.11/15.81 = ((($false) => (in @ ('#sk9' @ X2 @ X4) @ X4)))))),
% 105.11/15.81 inference('bool_hoist', [status(thm)], [zip_derived_cl82])).
% 105.11/15.81 thf(zip_derived_cl89, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ( (in @ ('#sk9' @ X2 @ X4) @ X2) | (subset @ X2 @ X4))),
% 105.11/15.81 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl88])).
% 105.11/15.81 thf(zip_derived_cl4700, plain,
% 105.11/15.81 (![X0 : $i]:
% 105.11/15.81 ( (in @ ('#sk9' @ (relation_dom @ '#sk8') @ X0) @ '#sk6')
% 105.11/15.81 | (subset @ (relation_dom @ '#sk8') @ X0))),
% 105.11/15.81 inference('s_sup+', [status(thm)], [zip_derived_cl4676, zip_derived_cl89])).
% 105.11/15.81 thf(zip_derived_cl82, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ((subset @ X2 @ X4)
% 105.11/15.81 = (((in @ ('#sk9' @ X2 @ X4) @ X2) => (in @ ('#sk9' @ X2 @ X4) @ X4))))),
% 105.11/15.81 inference('rw', [status(thm)], [zip_derived_cl81])).
% 105.11/15.81 thf(zip_derived_cl86, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ( (subset @ X2 @ X4)
% 105.11/15.81 | ~ (((in @ ('#sk9' @ X2 @ X4) @ X2) => (in @ ('#sk9' @ X2 @ X4) @
% 105.11/15.81 X4))))),
% 105.11/15.81 inference('eq_elim', [status(thm)], [zip_derived_cl82])).
% 105.11/15.81 thf(zip_derived_cl103, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (~ (in @ ('#sk9' @ X2 @ X4) @ X4) | (subset @ X2 @ X4))),
% 105.11/15.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl86])).
% 105.11/15.81 thf(zip_derived_cl80258, plain,
% 105.11/15.81 (( (subset @ (relation_dom @ '#sk8') @ '#sk6')
% 105.11/15.81 | (subset @ (relation_dom @ '#sk8') @ '#sk6'))),
% 105.11/15.81 inference('s_sup-', [status(thm)],
% 105.11/15.81 [zip_derived_cl4700, zip_derived_cl103])).
% 105.11/15.81 thf(zip_derived_cl80298, plain,
% 105.11/15.81 ( (subset @ (relation_dom @ '#sk8') @ '#sk6')),
% 105.11/15.81 inference('simplify', [status(thm)], [zip_derived_cl80258])).
% 105.11/15.81 thf(zip_derived_cl80303, plain,
% 105.11/15.81 (~ (subset @ (relation_rng @ '#sk8') @ '#sk7')),
% 105.11/15.81 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl80298])).
% 105.11/15.81 thf(d5_relat_1, axiom,
% 105.11/15.81 (![A:$i]:
% 105.11/15.81 ( ( relation @ A ) =>
% 105.11/15.81 ( ![B:$i]:
% 105.11/15.81 ( ( ( B ) = ( relation_rng @ A ) ) <=>
% 105.11/15.81 ( ![C:$i]:
% 105.11/15.81 ( ( in @ C @ B ) <=>
% 105.11/15.81 ( ?[D:$i]: ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) ) ))).
% 105.11/15.81 thf(zip_derived_cl5, plain,
% 105.11/15.81 ( (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((relation @ Y0) =>
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((((Y1) = (relation_rng @ Y0))) <=>
% 105.11/15.81 (((!!) @ (^[Y2 : $i]:
% 105.11/15.81 (((in @ Y2 @ Y1) <=>
% 105.11/15.81 (((??) @ (^[Y3 : $i]:
% 105.11/15.81 (in @
% 105.11/15.81 (ordered_pair @
% 105.11/15.81 Y3 @ Y2) @
% 105.11/15.81 Y0)))))))))))))))))))),
% 105.11/15.81 inference('cnf', [status(esa)], [d5_relat_1])).
% 105.11/15.81 thf(zip_derived_cl161, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (((relation @ X2) =>
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((((Y0) = (relation_rng @ X2))) <=>
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((in @ Y1 @ Y0) <=>
% 105.11/15.81 (((??) @ (^[Y2 : $i]:
% 105.11/15.81 (in @
% 105.11/15.81 (ordered_pair @ Y2 @ Y1) @
% 105.11/15.81 X2))))))))))))))))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])).
% 105.11/15.81 thf(zip_derived_cl162, plain,
% 105.11/15.81 (![X2 : $i]:
% 105.11/15.81 (~ (relation @ X2)
% 105.11/15.81 | (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((((Y0) = (relation_rng @ X2))) <=>
% 105.11/15.81 (((!!) @ (^[Y1 : $i]:
% 105.11/15.81 (((in @ Y1 @ Y0) <=>
% 105.11/15.81 (((??) @ (^[Y2 : $i]:
% 105.11/15.81 (in @
% 105.11/15.81 (ordered_pair @ Y2 @ Y1) @
% 105.11/15.81 X2)))))))))))))))),
% 105.11/15.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl161])).
% 105.11/15.81 thf(zip_derived_cl163, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ( (((((X4) = (relation_rng @ X2))) <=>
% 105.11/15.81 (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((in @ Y0 @ X4) <=>
% 105.11/15.81 (((??) @ (^[Y1 : $i]:
% 105.11/15.81 (in @ (ordered_pair @ Y1 @ Y0) @ X2)))))))))))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl162])).
% 105.11/15.81 thf(zip_derived_cl164, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (((((X4) = (relation_rng @ X2)))
% 105.11/15.81 = (((!!) @ (^[Y0 : $i]:
% 105.11/15.81 (((in @ Y0 @ X4) <=>
% 105.11/15.81 (((??) @ (^[Y1 : $i]:
% 105.11/15.81 (in @ (ordered_pair @ Y1 @ Y0) @ X2))))))))))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl163])).
% 105.11/15.81 thf(zip_derived_cl165, plain,
% 105.11/15.81 (![X-73 : $i, X2 : $i, X4 : $i]:
% 105.11/15.81 ( ((^[Y0 : $i]:
% 105.11/15.81 (((in @ Y0 @ X4) <=>
% 105.11/15.81 (((??) @ (^[Y1 : $i]: (in @ (ordered_pair @ Y1 @ Y0) @ X2))))))) @
% 105.11/15.81 X-73)
% 105.11/15.81 | ~ (((X4) = (relation_rng @ X2)))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('forall_hoist', [status(thm)], [zip_derived_cl164])).
% 105.11/15.81 thf(zip_derived_cl168, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X5 : $i]:
% 105.11/15.81 ( ((^[Y0 : $i]:
% 105.11/15.81 (((in @ Y0 @ X4) <=>
% 105.11/15.81 (((??) @ (^[Y1 : $i]: (in @ (ordered_pair @ Y1 @ Y0) @ X2))))))) @
% 105.11/15.81 X5)
% 105.11/15.81 | ~ (((X4) = (relation_rng @ X2)))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('cannonize vars', [status(thm)], [zip_derived_cl165])).
% 105.11/15.81 thf(zip_derived_cl169, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X5 : $i]:
% 105.11/15.81 ( ((^[Y0 : $i]:
% 105.11/15.81 (((in @ Y0 @ X4) <=>
% 105.11/15.81 (((??) @ (^[Y1 : $i]: (in @ (ordered_pair @ Y1 @ Y0) @ X2))))))) @
% 105.11/15.81 X5)
% 105.11/15.81 | ((X4) != (relation_rng @ X2))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl168])).
% 105.11/15.81 thf(zip_derived_cl170, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X5 : $i]:
% 105.11/15.81 ( (((in @ X5 @ X4) <=>
% 105.11/15.81 (((??) @ (^[Y0 : $i]: (in @ (ordered_pair @ Y0 @ X5) @ X2))))))
% 105.11/15.81 | ((X4) != (relation_rng @ X2))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('rw', [status(thm)], [zip_derived_cl169])).
% 105.11/15.81 thf(zip_derived_cl171, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X5 : $i]:
% 105.11/15.81 (((in @ X5 @ X4)
% 105.11/15.81 = (((??) @ (^[Y0 : $i]: (in @ (ordered_pair @ Y0 @ X5) @ X2)))))
% 105.11/15.81 | ((X4) != (relation_rng @ X2))
% 105.11/15.81 | ~ (relation @ X2))),
% 105.11/15.81 inference('simplify nested equalities', [status(thm)],
% 105.11/15.81 [zip_derived_cl170])).
% 105.11/15.81 thf(zip_derived_cl618, plain,
% 105.11/15.81 (![X0 : $i, X1 : $i]:
% 105.11/15.81 (~ (relation @ X0)
% 105.11/15.81 | ((in @ X1 @ (relation_rng @ X0))
% 105.11/15.81 = (((??) @ (^[Y0 : $i]: (in @ (ordered_pair @ Y0 @ X1) @ X0))))))),
% 105.11/15.81 inference('eq_res', [status(thm)], [zip_derived_cl171])).
% 105.11/15.81 thf(zip_derived_cl5498, plain,
% 105.11/15.81 (![X0 : $i, X1 : $i]:
% 105.11/15.81 (~ (relation @ X0)
% 105.11/15.81 | ((in @ X1 @ (relation_rng @ X0))
% 105.11/15.81 = ((^[Y0 : $i]: (in @ (ordered_pair @ Y0 @ X1) @ X0)) @
% 105.11/15.81 ('#sk18' @ X0 @ X1))))),
% 105.11/15.81 inference('quantifier_rw', [status(thm)], [zip_derived_cl618])).
% 105.11/15.81 thf(zip_derived_cl5499, plain,
% 105.11/15.81 (![X0 : $i, X1 : $i]:
% 105.11/15.81 (~ (relation @ X0)
% 105.11/15.81 | ((in @ X1 @ (relation_rng @ X0))
% 105.11/15.81 = (in @ (ordered_pair @ ('#sk18' @ X0 @ X1) @ X1) @ X0)))),
% 105.11/15.81 inference('rw', [status(thm)], [zip_derived_cl5498])).
% 105.11/15.81 thf(zip_derived_cl3691, plain,
% 105.11/15.81 (![X0 : $i]:
% 105.11/15.81 ( (in @ X0 @ (cartesian_product2 @ '#sk6' @ '#sk7'))
% 105.11/15.81 | ~ (in @ X0 @ '#sk8'))),
% 105.11/15.81 inference('clc', [status(thm)], [zip_derived_cl2667, zip_derived_cl1419])).
% 105.11/15.81 thf(zip_derived_cl298, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 105.11/15.81 ( (in @ X4 @ X8)
% 105.11/15.81 | ~ (in @ (ordered_pair @ X2 @ X4) @ (cartesian_product2 @ X6 @ X8)))),
% 105.11/15.81 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl291])).
% 105.11/15.81 thf(zip_derived_cl3723, plain,
% 105.11/15.81 (![X0 : $i, X1 : $i]:
% 105.11/15.81 (~ (in @ (ordered_pair @ X1 @ X0) @ '#sk8') | (in @ X0 @ '#sk7'))),
% 105.11/15.81 inference('s_sup-', [status(thm)],
% 105.11/15.81 [zip_derived_cl3691, zip_derived_cl298])).
% 105.11/15.81 thf(zip_derived_cl5535, plain,
% 105.11/15.81 (![X0 : $i]:
% 105.11/15.81 (~ (relation @ '#sk8')
% 105.11/15.81 | ~ (in @ X0 @ (relation_rng @ '#sk8'))
% 105.11/15.81 | (in @ X0 @ '#sk7'))),
% 105.11/15.81 inference('s_sup-', [status(thm)],
% 105.11/15.81 [zip_derived_cl5499, zip_derived_cl3723])).
% 105.11/15.81 thf(zip_derived_cl273, plain, ( (relation @ '#sk8')),
% 105.11/15.81 inference('s_sup+', [status(thm)], [zip_derived_cl233, zip_derived_cl153])).
% 105.11/15.81 thf(zip_derived_cl5551, plain,
% 105.11/15.81 (![X0 : $i]:
% 105.11/15.81 (~ (in @ X0 @ (relation_rng @ '#sk8')) | (in @ X0 @ '#sk7'))),
% 105.11/15.81 inference('demod', [status(thm)], [zip_derived_cl5535, zip_derived_cl273])).
% 105.11/15.81 thf(zip_derived_cl89, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 ( (in @ ('#sk9' @ X2 @ X4) @ X2) | (subset @ X2 @ X4))),
% 105.11/15.81 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl88])).
% 105.11/15.81 thf(zip_derived_cl5565, plain,
% 105.11/15.81 (![X0 : $i]:
% 105.11/15.81 ( (in @ ('#sk9' @ (relation_rng @ '#sk8') @ X0) @ '#sk7')
% 105.11/15.81 | (subset @ (relation_rng @ '#sk8') @ X0))),
% 105.11/15.81 inference('s_sup+', [status(thm)], [zip_derived_cl5551, zip_derived_cl89])).
% 105.11/15.81 thf(zip_derived_cl103, plain,
% 105.11/15.81 (![X2 : $i, X4 : $i]:
% 105.11/15.81 (~ (in @ ('#sk9' @ X2 @ X4) @ X4) | (subset @ X2 @ X4))),
% 105.11/15.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl86])).
% 105.11/15.81 thf(zip_derived_cl106222, plain,
% 105.11/15.81 (( (subset @ (relation_rng @ '#sk8') @ '#sk7')
% 105.11/15.81 | (subset @ (relation_rng @ '#sk8') @ '#sk7'))),
% 105.11/15.81 inference('s_sup-', [status(thm)],
% 105.11/15.81 [zip_derived_cl5565, zip_derived_cl103])).
% 105.11/15.81 thf(zip_derived_cl106239, plain,
% 105.11/15.81 ( (subset @ (relation_rng @ '#sk8') @ '#sk7')),
% 105.11/15.81 inference('simplify', [status(thm)], [zip_derived_cl106222])).
% 105.11/15.81 thf(zip_derived_cl106243, plain, ($false),
% 105.11/15.81 inference('demod', [status(thm)],
% 105.11/15.81 [zip_derived_cl80303, zip_derived_cl106239])).
% 105.11/15.81
% 105.11/15.81 % SZS output end Refutation
% 105.11/15.81
% 105.11/15.81
% 105.11/15.81 % Terminating...
% 105.42/15.91 % Runner terminated.
% 105.42/15.91 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------