0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.SMfzjN6rix true 0.13/0.35 % Computer : n006.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 : 1200 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Jul 13 13:21:26 EDT 2021 0.13/0.35 % CPUTime : 0.13/0.35 % Running portfolio for 120 s 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.35 % Number of cores: 8 0.13/0.36 % Python version: Python 3.6.8 0.13/0.36 % Running in HO mode 0.54/0.65 % Total configuration time : 828 0.54/0.65 % Estimated wc time : 983 0.54/0.65 % Estimated cpu time (8 cpus) : 122.875 0.55/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.55/0.79 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.55/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 7.36/1.67 % Solved by lams/40_b.comb.sh. 7.36/1.67 % done 145 iterations in 0.837s 7.36/1.67 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 7.36/1.67 % SZS output start Refutation 7.36/1.67 thf(demorgan1a_type, type, demorgan1a: $o). 7.36/1.67 thf(binintersect_type, type, binintersect: $i > $i > $i). 7.36/1.67 thf(powerset_type, type, powerset: $i > $i). 7.36/1.67 thf(binintersectT_lem_type, type, binintersectT_lem: $o). 7.36/1.67 thf(demorgan1b_type, type, demorgan1b: $o). 7.36/1.67 thf(setminus_type, type, setminus: $i > $i > $i). 7.36/1.67 thf(binunion_type, type, binunion: $i > $i > $i). 7.36/1.67 thf('#sk4_type', type, '#sk4': $i > $i > $i > $i). 7.36/1.67 thf(binunionT_lem_type, type, binunionT_lem: $o). 7.36/1.67 thf(in_type, type, in: $i > $i > $o). 7.36/1.67 thf('#sk1_type', type, '#sk1': $i). 7.36/1.67 thf('#sk2_type', type, '#sk2': $i). 7.36/1.67 thf(setextT_type, type, setextT: $o). 7.36/1.67 thf(complementT_lem_type, type, complementT_lem: $o). 7.36/1.67 thf('#sk3_type', type, '#sk3': $i). 7.36/1.67 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 7.36/1.67 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 7.36/1.67 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 7.36/1.67 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 7.36/1.67 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 7.36/1.67 thf(demorgan1, conjecture, 7.36/1.67 (( binintersectT_lem ) => 7.36/1.67 ( ( binunionT_lem ) => 7.36/1.67 ( ( complementT_lem ) => 7.36/1.67 ( ( setextT ) => 7.36/1.67 ( ( demorgan1a ) => 7.36/1.67 ( ( demorgan1b ) => 7.36/1.67 ( ![A:$i,X:$i]: 7.36/1.67 ( ( in @ X @ ( powerset @ A ) ) => 7.36/1.67 ( ![Y:$i]: 7.36/1.67 ( ( in @ Y @ ( powerset @ A ) ) => 7.36/1.67 ( ( setminus @ A @ ( binintersect @ X @ Y ) ) = 7.36/1.67 ( binunion @ 7.36/1.67 ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ))). 7.36/1.67 thf(zf_stmt_0, negated_conjecture, 7.36/1.67 (~( ( binintersectT_lem ) => 7.36/1.67 ( ( binunionT_lem ) => 7.36/1.67 ( ( complementT_lem ) => 7.36/1.67 ( ( setextT ) => 7.36/1.67 ( ( demorgan1a ) => 7.36/1.67 ( ( demorgan1b ) => 7.36/1.67 ( ![A:$i,X:$i]: 7.36/1.67 ( ( in @ X @ ( powerset @ A ) ) => 7.36/1.67 ( ![Y:$i]: 7.36/1.67 ( ( in @ Y @ ( powerset @ A ) ) => 7.36/1.67 ( ( setminus @ A @ ( binintersect @ X @ Y ) ) = 7.36/1.67 ( binunion @ 7.36/1.67 ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ) )), 7.36/1.67 inference('cnf.neg', [status(esa)], [demorgan1])). 7.36/1.67 thf(zip_derived_cl0, plain, 7.36/1.67 (~ (((binintersectT_lem) => 7.36/1.67 (((binunionT_lem) => 7.36/1.67 (((complementT_lem) => 7.36/1.67 (((setextT) => 7.36/1.67 (((demorgan1a) => 7.36/1.67 (((demorgan1b) => 7.36/1.67 (((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y2 : $i]: 7.36/1.67 (((in @ Y2 @ 7.36/1.67 (powerset @ Y0)) => 7.36/1.67 (((setminus @ 7.36/1.67 Y0 @ 7.36/1.67 (binintersect @ 7.36/1.67 Y1 @ Y2)) = 7.36/1.67 (binunion @ 7.36/1.67 (setminus @ 7.36/1.67 Y0 @ Y1) @ 7.36/1.67 (setminus @ 7.36/1.67 Y0 @ Y2)))))))))))))))))))))))))))))), 7.36/1.67 inference('cnf', [status(esa)], [zf_stmt_0])). 7.36/1.67 thf(zip_derived_cl1, plain, 7.36/1.67 (~ (((binintersectT_lem) => 7.36/1.67 (((binunionT_lem) => 7.36/1.67 (((complementT_lem) => 7.36/1.67 (((setextT) => 7.36/1.67 (((demorgan1a) => 7.36/1.67 (((demorgan1b) => 7.36/1.67 (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 powerset)))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 powerset)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ( 7.36/1.67 (('#B') @ (=))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ( 7.36/1.67 '#B') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 '#B') @ 7.36/1.67 setminus)))) @ 7.36/1.67 binintersect)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ ( 7.36/1.67 '#B'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ binunion)) @ 7.36/1.67 setminus)))))) @ 7.36/1.67 setminus))))))))))))))))))))))))))), 7.36/1.67 inference('lams2combs', [status(thm)], [zip_derived_cl0])). 7.36/1.67 thf(zip_derived_cl3, plain, 7.36/1.67 (~ (((binunionT_lem) => 7.36/1.67 (((complementT_lem) => 7.36/1.67 (((setextT) => 7.36/1.67 (((demorgan1a) => 7.36/1.67 (((demorgan1b) => 7.36/1.67 (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 powerset)))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 powerset)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ( 7.36/1.67 (('#B') @ (=))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ( 7.36/1.67 '#B') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 '#B') @ 7.36/1.67 setminus)))) @ 7.36/1.67 binintersect)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#B'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ binunion)) @ 7.36/1.67 setminus)))))) @ 7.36/1.67 setminus))))))))))))))))))))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 7.36/1.67 thf(zip_derived_cl6, plain, 7.36/1.67 (~ (((complementT_lem) => 7.36/1.67 (((setextT) => 7.36/1.67 (((demorgan1a) => 7.36/1.67 (((demorgan1b) => 7.36/1.67 (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 powerset)))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 powerset)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ( 7.36/1.67 (('#B') @ (=))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ( 7.36/1.67 '#B') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 '#B') @ 7.36/1.67 setminus)))) @ 7.36/1.67 binintersect)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#B'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ binunion)) @ 7.36/1.67 setminus)))))) @ 7.36/1.67 setminus))))))))))))))))))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])). 7.36/1.67 thf(zip_derived_cl11, plain, 7.36/1.67 (~ (((setextT) => 7.36/1.67 (((demorgan1a) => 7.36/1.67 (((demorgan1b) => 7.36/1.67 (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 powerset)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (( 7.36/1.67 ('#B') @ ( 7.36/1.67 =))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ( 7.36/1.67 '#B') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 '#B') @ 7.36/1.67 setminus)))) @ 7.36/1.67 binintersect)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#B'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ binunion)) @ 7.36/1.67 setminus)))))) @ 7.36/1.67 setminus))))))))))))))))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 7.36/1.67 thf(zip_derived_cl16, plain, ( (setextT)), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 7.36/1.67 thf(setextT, axiom, (setextT) => 7.36/1.67 ((((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y2 : $i]: 7.36/1.67 (((in @ Y2 @ (powerset @ Y0)) => 7.36/1.67 (((((!!) @ (^[Y3 : $i]: 7.36/1.67 (((in @ Y3 @ Y0) => 7.36/1.67 (((in @ Y3 @ 7.36/1.67 Y1) => (in @ 7.36/1.67 Y3 @ Y2)))))))) => 7.36/1.67 (((((!!) @ (^[Y3 : $i]: 7.36/1.67 (((in @ Y3 @ 7.36/1.67 Y0) => 7.36/1.67 (((in @ Y3 @ 7.36/1.67 Y2) => (in @ 7.36/1.67 Y3 @ Y1)))))))) => 7.36/1.67 (((Y1) = (Y2)))))))))))))))))))) 7.36/1.67 = ($true))). 7.36/1.67 thf('0', plain, 7.36/1.67 (( setextT ) <=> 7.36/1.67 ( ![X5:$i,X7:$i]: 7.36/1.67 ( ( in @ X7 @ ( powerset @ X5 ) ) => 7.36/1.67 ( ![X9:$i]: 7.36/1.67 ( ( in @ X9 @ ( powerset @ X5 ) ) => 7.36/1.67 ( ( ![X11:$i]: 7.36/1.67 ( ( in @ X11 @ X5 ) => 7.36/1.67 ( ( in @ X11 @ X7 ) => ( in @ X11 @ X9 ) ) ) ) => 7.36/1.67 ( ( ![X13:$i]: 7.36/1.67 ( ( in @ X13 @ X5 ) => 7.36/1.67 ( ( in @ X13 @ X9 ) => ( in @ X13 @ X7 ) ) ) ) => 7.36/1.67 ( ( X7 ) = ( X9 ) ) ) ) ) ) ) )), 7.36/1.67 inference('rw.lit', [status(esa)], [setextT])). 7.36/1.67 thf(zip_derived_cl22, plain, 7.36/1.67 ( (((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y2 : $i]: 7.36/1.67 (((in @ Y2 @ (powerset @ Y0)) => 7.36/1.67 (((((!!) @ (^[Y3 : $i]: 7.36/1.67 (((in @ Y3 @ 7.36/1.67 Y0) => 7.36/1.67 (((in @ Y3 @ 7.36/1.67 Y1) => (in @ 7.36/1.67 Y3 @ Y2)))))))) => 7.36/1.67 (((((!!) @ (^[Y3 : $i]: 7.36/1.67 (((in @ Y3 @ 7.36/1.67 Y0) => 7.36/1.67 (((in @ Y3 @ 7.36/1.67 Y2) => 7.36/1.67 (in @ Y3 @ 7.36/1.67 Y1)))))))) => 7.36/1.67 (((Y1) = (Y2))))))))))))))))))))), 7.36/1.67 inference('rw_clause', [status(thm)], [zip_derived_cl16, '0'])). 7.36/1.67 thf(zip_derived_cl28, plain, 7.36/1.67 ( (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 '#S') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 (('#B') @ (=>))) @ 7.36/1.67 ((('#C') @ in)))))))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 '#S') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 (('#B') @ (=>))) @ 7.36/1.67 ((('#C') @ in)))))))) @ 7.36/1.67 ((('#C') @ in)))))))))))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ ( 7.36/1.67 !!))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 '#B') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 '#S') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 (('#B') @ (=>))) @ 7.36/1.67 ((('#C') @ in)))))))))) @ 7.36/1.67 ((('#B') @ ((('#C') @ ( 7.36/1.67 (('#B') @ ( 7.36/1.67 '#S') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 (('#B') @ (=>))) @ 7.36/1.67 ((('#C') @ in)))))))) @ 7.36/1.67 ((('#C') @ in)))))))))))))) @ 7.36/1.67 (=)))))))))))))))), 7.36/1.67 inference('comb-normalize', [status(thm)], [zip_derived_cl22])). 7.36/1.67 thf(zip_derived_cl29, plain, 7.36/1.67 (![X2 : $i]: 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#S') @ ( 7.36/1.67 (('#B') @ ( 7.36/1.67 =>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 X2)))))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 (('#B') @ (=>))) @ 7.36/1.67 ((('#C') @ in)))))))) @ 7.36/1.67 ((('#C') @ in)))))))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#S') @ ( 7.36/1.67 (('#B') @ ( 7.36/1.67 =>) @ 7.36/1.67 (( 7.36/1.67 ('#C') @ in @ 7.36/1.67 X2)))))))) @ 7.36/1.67 ((('#B') @ ((('#C') @ ((('#B') @ ( 7.36/1.67 '#S') @ 7.36/1.67 ( 7.36/1.67 ( 7.36/1.67 ('#B') @ ( 7.36/1.67 ( 7.36/1.67 ('#B') @ ( 7.36/1.67 =>))) @ 7.36/1.67 ( 7.36/1.67 ( 7.36/1.67 ('#C') @ in)))))))) @ 7.36/1.67 ((('#C') @ in)))))))))))) @ 7.36/1.67 (=)))))))))))))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 7.36/1.67 thf(zip_derived_cl36, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (((in @ X4 @ (powerset @ X2)) => 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ ( 7.36/1.67 =>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 X2)))))) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ ( 7.36/1.67 =>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 X4)))))) @ 7.36/1.67 ((('#C') @ in)))))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ ( 7.36/1.67 =>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 X2)))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ( 7.36/1.67 =>))) @ 7.36/1.67 ((('#C') @ in)))))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))))) @ 7.36/1.67 ((($i) = (X4)))))))))))))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 7.36/1.67 thf(zip_derived_cl42, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ ( 7.36/1.67 =>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 X2)))))) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ ( 7.36/1.67 =>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 X4)))))) @ 7.36/1.67 ((('#C') @ in)))))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ ( 7.36/1.67 =>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 X2)))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ( 7.36/1.67 =>))) @ 7.36/1.67 ((('#C') @ in)))))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))))) @ 7.36/1.67 ((($i) = (X4))))))))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 7.36/1.67 thf(zip_derived_cl47, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 ( (((in @ X6 @ (powerset @ X2)) => 7.36/1.67 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X4)))) @ 7.36/1.67 ((('#C') @ in @ X6)))))))) => 7.36/1.67 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) => 7.36/1.67 (((X4) = (X6))))))))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 7.36/1.67 thf(zip_derived_cl52, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X4)))) @ 7.36/1.67 ((('#C') @ in @ X6)))))))) => 7.36/1.67 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) => 7.36/1.67 (((X4) = (X6))))))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 7.36/1.67 thf(zip_derived_cl56, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X4)))) @ 7.36/1.67 ((('#C') @ in @ X6)))))))) 7.36/1.67 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) => 7.36/1.67 (((X4) = (X6))))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 7.36/1.67 thf(zip_derived_cl61, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) => 7.36/1.67 (((in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) => (in @ 7.36/1.67 ('#sk4' @ X2 @ X4 @ X6) @ X6))))) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) => 7.36/1.67 (((X4) = (X6))))))), 7.36/1.67 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl56])). 7.36/1.67 thf(zip_derived_cl65, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 ( (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) 7.36/1.67 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) => 7.36/1.67 (((X4) = (X6))))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 7.36/1.67 thf(zip_derived_cl69, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) 7.36/1.67 | (((X4) = (X6))) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])). 7.36/1.67 thf(zip_derived_cl74, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) 7.36/1.67 | ((X4) = (X6)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2))), 7.36/1.67 inference('simplify nested equalities', [status(thm)], [zip_derived_cl69])). 7.36/1.67 thf(zip_derived_cl75, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X2) => 7.36/1.67 (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) => (in @ 7.36/1.67 ('#sk4' @ X2 @ X6 @ X4) @ X4))))) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ((X4) = (X6)))), 7.36/1.67 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl74])). 7.36/1.67 thf(zip_derived_cl80, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) => (in @ 7.36/1.67 ('#sk4' @ X2 @ X6 @ X4) @ X4))) 7.36/1.67 | ((X4) = (X6)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 7.36/1.67 thf(zip_derived_cl85, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 ( (in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ((X4) = (X6)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 7.36/1.67 thf(zip_derived_cl86, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (in @ ('#sk4' @ X2 @ X6 @ X4) @ X4) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ((X4) = (X6)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 7.36/1.67 thf(zip_derived_cl17, plain, 7.36/1.67 (~ (((demorgan1a) => 7.36/1.67 (((demorgan1b) => 7.36/1.67 (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 powerset)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ ( 7.36/1.67 =))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 '#B') @ setminus)))) @ 7.36/1.67 binintersect)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#B'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ binunion)) @ 7.36/1.67 setminus)))))) @ 7.36/1.67 setminus))))))))))))))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 7.36/1.67 thf(zip_derived_cl23, plain, ( (demorgan1a)), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 7.36/1.67 thf(demorgan1a, axiom, (demorgan1a) => 7.36/1.67 ((((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y2 : $i]: 7.36/1.67 (((in @ Y2 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y3 : $i]: 7.36/1.67 (((in @ Y3 @ Y0) => 7.36/1.67 (((in @ Y3 @ 7.36/1.67 (setminus @ Y0 @ 7.36/1.67 (binintersect @ 7.36/1.67 Y1 @ Y2))) => 7.36/1.67 (in @ Y3 @ 7.36/1.67 (binunion @ 7.36/1.67 (setminus @ Y0 @ 7.36/1.67 Y1) @ 7.36/1.67 (setminus @ Y0 @ 7.36/1.67 Y2))))))))))))))))))))))) 7.36/1.67 = ($true))). 7.36/1.67 thf('1', plain, 7.36/1.67 (( demorgan1a ) <=> 7.36/1.67 ( ![X5:$i,X7:$i]: 7.36/1.67 ( ( in @ X7 @ ( powerset @ X5 ) ) => 7.36/1.67 ( ![X9:$i]: 7.36/1.67 ( ( in @ X9 @ ( powerset @ X5 ) ) => 7.36/1.67 ( ![X11:$i]: 7.36/1.67 ( ( in @ X11 @ X5 ) => 7.36/1.67 ( ( in @ 7.36/1.67 X11 @ ( setminus @ X5 @ ( binintersect @ X7 @ X9 ) ) ) => 7.36/1.67 ( in @ 7.36/1.67 X11 @ 7.36/1.67 ( binunion @ 7.36/1.67 ( setminus @ X5 @ X7 ) @ ( setminus @ X5 @ X9 ) ) ) ) ) ) ) ) ) )), 7.36/1.67 inference('rw.lit', [status(esa)], [demorgan1a])). 7.36/1.67 thf(zip_derived_cl30, plain, 7.36/1.67 ( (((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y2 : $i]: 7.36/1.67 (((in @ Y2 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y3 : $i]: 7.36/1.67 (((in @ Y3 @ Y0) => 7.36/1.67 (((in @ Y3 @ 7.36/1.67 (setminus @ 7.36/1.67 Y0 @ 7.36/1.67 (binintersect @ 7.36/1.67 Y1 @ Y2))) => 7.36/1.67 (in @ Y3 @ 7.36/1.67 (binunion @ 7.36/1.67 (setminus @ 7.36/1.67 Y0 @ Y1) @ 7.36/1.67 (setminus @ 7.36/1.67 Y0 @ Y2)))))))))))))))))))))))), 7.36/1.67 inference('rw_clause', [status(thm)], [zip_derived_cl23, '1'])). 7.36/1.67 thf(zip_derived_cl37, plain, 7.36/1.67 ( (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#C') @ in)))))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ ( 7.36/1.67 '#S'))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ ( 7.36/1.67 ( 7.36/1.67 ('#B') @ ( 7.36/1.67 =>))))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ( 7.36/1.67 (('#B') @ ( 7.36/1.67 (('#C') @ in)))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ( 7.36/1.67 '#B') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 '#B') @ 7.36/1.67 setminus)))) @ 7.36/1.67 binintersect)))))))))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ ((('#C') @ in)))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#B'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ binunion)) @ 7.36/1.67 setminus)))))) @ 7.36/1.67 setminus))))))))))))))))))))), 7.36/1.67 inference('comb-normalize', [status(thm)], [zip_derived_cl30])). 7.36/1.67 thf(zip_derived_cl38, plain, 7.36/1.67 (![X2 : $i]: 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 7.36/1.67 =>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 X2)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ ( 7.36/1.67 =>))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ( 7.36/1.67 setminus @ X2))) @ 7.36/1.67 binintersect)))))))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ binunion @ 7.36/1.67 (setminus @ X2))))) @ 7.36/1.67 (setminus @ X2)))))))))))))))))))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 7.36/1.67 thf(zip_derived_cl43, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (((in @ X4 @ (powerset @ X2)) => 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ X2)))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 ((('#B') @ (setminus @ X2) @ 7.36/1.67 (binintersect @ X4))))))))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 ((('#B') @ (binunion @ (setminus @ X2 @ X4)) @ 7.36/1.67 (setminus @ X2)))))))))))))))))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 7.36/1.67 thf(zip_derived_cl48, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ X2)))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 ((('#B') @ (setminus @ X2) @ 7.36/1.67 (binintersect @ X4))))))))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 ((('#B') @ (binunion @ (setminus @ X2 @ X4)) @ 7.36/1.67 (setminus @ X2))))))))))))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl43])). 7.36/1.67 thf(zip_derived_cl53, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 ( (((in @ X6 @ (powerset @ X2)) => 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 (setminus @ X2 @ 7.36/1.67 (binintersect @ X4 @ X6)))))) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 (binunion @ (setminus @ X2 @ X4) @ 7.36/1.67 (setminus @ X2 @ X6)))))))))))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl48])). 7.36/1.67 thf(zip_derived_cl57, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 (setminus @ X2 @ 7.36/1.67 (binintersect @ X4 @ X6)))))) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 (binunion @ (setminus @ X2 @ X4) @ 7.36/1.67 (setminus @ X2 @ X6)))))))))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 7.36/1.67 thf(zip_derived_cl62, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 7.36/1.67 ( (((in @ X8 @ X2) => 7.36/1.67 (((in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) => (in @ 7.36/1.67 X8 @ (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))))))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 7.36/1.67 thf(zip_derived_cl67, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 7.36/1.67 (~ (in @ X8 @ X2) 7.36/1.67 | (((in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) => (in @ 7.36/1.67 X8 @ (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))))) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 7.36/1.67 thf(zip_derived_cl72, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 7.36/1.67 (~ (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) 7.36/1.67 | (in @ X8 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X8 @ X2))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 7.36/1.67 thf(zip_derived_cl103, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 7.36/1.67 (((binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) = (X3)) 7.36/1.67 | ~ (in @ X3 @ (powerset @ X4)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 7.36/1.67 (powerset @ X4)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X4 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 7.36/1.67 X4) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ X3 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 7.36/1.67 X1) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ X3 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 7.36/1.67 (setminus @ X1 @ (binintersect @ X2 @ X0))))), 7.36/1.67 inference('sup+', [status(thm)], [zip_derived_cl86, zip_derived_cl72])). 7.36/1.67 thf(zip_derived_cl520, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 7.36/1.67 (((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 7.36/1.67 = (setminus @ X2 @ (binintersect @ X1 @ X0))) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X3 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 7.36/1.67 X3) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 X2) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X3 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 7.36/1.67 X3) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 7.36/1.67 = (setminus @ X2 @ (binintersect @ X1 @ X0))))), 7.36/1.67 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl103])). 7.36/1.67 thf(zip_derived_cl539, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 7.36/1.67 (~ (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 X2) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X2)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X3 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 7.36/1.67 X3) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 7.36/1.67 = (setminus @ X2 @ (binintersect @ X1 @ X0))))), 7.36/1.67 inference('simplify', [status(thm)], [zip_derived_cl520])). 7.36/1.67 thf(zip_derived_cl66, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) => (in @ 7.36/1.67 ('#sk4' @ X2 @ X4 @ X6) @ X6))) 7.36/1.67 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) => 7.36/1.67 (((X4) = (X6))))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 7.36/1.67 thf(zip_derived_cl71, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (in @ ('#sk4' @ X2 @ X4 @ X6) @ X6) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) => 7.36/1.67 (((X4) = (X6))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 7.36/1.67 thf(zip_derived_cl77, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) 7.36/1.67 | (((X4) = (X6))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ ('#sk4' @ X2 @ X4 @ X6) @ X6))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 7.36/1.67 thf(zip_derived_cl83, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) 7.36/1.67 | ((X4) = (X6)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ ('#sk4' @ X2 @ X4 @ X6) @ X6))), 7.36/1.67 inference('simplify nested equalities', [status(thm)], [zip_derived_cl77])). 7.36/1.67 thf(zip_derived_cl84, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X2) => 7.36/1.67 (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) => (in @ 7.36/1.67 ('#sk4' @ X2 @ X6 @ X4) @ X4))))) 7.36/1.67 | ~ (in @ ('#sk4' @ X2 @ X4 @ X6) @ X6) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ((X4) = (X6)))), 7.36/1.67 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl83])). 7.36/1.67 thf(zip_derived_cl90, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) => (in @ 7.36/1.67 ('#sk4' @ X2 @ X6 @ X4) @ X4))) 7.36/1.67 | ((X4) = (X6)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ ('#sk4' @ X2 @ X4 @ X6) @ X6))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl84])). 7.36/1.67 thf(zip_derived_cl94, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (in @ ('#sk4' @ X2 @ X6 @ X4) @ X4) 7.36/1.67 | ~ (in @ ('#sk4' @ X2 @ X4 @ X6) @ X6) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ((X4) = (X6)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl90])). 7.36/1.67 thf(zip_derived_cl72, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 7.36/1.67 (~ (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) 7.36/1.67 | (in @ X8 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X8 @ X2))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 7.36/1.67 thf(zip_derived_cl95, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 7.36/1.67 (((binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) = (X3)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 7.36/1.67 (powerset @ X4)) 7.36/1.67 | ~ (in @ X3 @ (powerset @ X4)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 7.36/1.67 X3) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ X3 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 7.36/1.67 X1) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ X3 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 7.36/1.67 (setminus @ X1 @ (binintersect @ X2 @ X0))))), 7.36/1.67 inference('sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl72])). 7.36/1.67 thf(zip_derived_cl72, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 7.36/1.67 (~ (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) 7.36/1.67 | (in @ X8 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X8 @ X2))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 7.36/1.67 thf(zip_derived_cl70, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 ( (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) => 7.36/1.67 (((X4) = (X6))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 7.36/1.67 thf(zip_derived_cl76, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) 7.36/1.67 | (((X4) = (X6))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])). 7.36/1.67 thf(zip_derived_cl81, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 7.36/1.67 ((('#C') @ in @ X4)))))))) 7.36/1.67 | ((X4) = (X6)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4))), 7.36/1.67 inference('simplify nested equalities', [status(thm)], [zip_derived_cl76])). 7.36/1.67 thf(zip_derived_cl82, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X2) => 7.36/1.67 (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) => (in @ 7.36/1.67 ('#sk4' @ X2 @ X6 @ X4) @ X4))))) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ((X4) = (X6)))), 7.36/1.67 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 7.36/1.67 thf(zip_derived_cl88, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) => (in @ 7.36/1.67 ('#sk4' @ X2 @ X6 @ X4) @ X4))) 7.36/1.67 | ((X4) = (X6)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 7.36/1.67 thf(zip_derived_cl92, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (in @ ('#sk4' @ X2 @ X6 @ X4) @ X4) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ((X4) = (X6)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])). 7.36/1.67 thf(zip_derived_cl24, plain, 7.36/1.67 (~ (((demorgan1b) => 7.36/1.67 (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 powerset)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#B') @ 7.36/1.67 setminus)))) @ 7.36/1.67 binintersect)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#B'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ binunion)) @ 7.36/1.67 setminus)))))) @ 7.36/1.67 setminus))))))))))))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 7.36/1.67 thf(zip_derived_cl31, plain, ( (demorgan1b)), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 7.36/1.67 thf(demorgan1b, axiom, (demorgan1b) => 7.36/1.67 ((((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y2 : $i]: 7.36/1.67 (((in @ Y2 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y3 : $i]: 7.36/1.67 (((in @ Y3 @ Y0) => 7.36/1.67 (((in @ Y3 @ 7.36/1.67 (binunion @ 7.36/1.67 (setminus @ Y0 @ 7.36/1.67 Y1) @ 7.36/1.67 (setminus @ Y0 @ 7.36/1.67 Y2))) => 7.36/1.67 (in @ Y3 @ 7.36/1.67 (setminus @ Y0 @ 7.36/1.67 (binintersect @ 7.36/1.67 Y1 @ Y2))))))))))))))))))))))) 7.36/1.67 = ($true))). 7.36/1.67 thf('2', plain, 7.36/1.67 (( demorgan1b ) <=> 7.36/1.67 ( ![X5:$i,X7:$i]: 7.36/1.67 ( ( in @ X7 @ ( powerset @ X5 ) ) => 7.36/1.67 ( ![X9:$i]: 7.36/1.67 ( ( in @ X9 @ ( powerset @ X5 ) ) => 7.36/1.67 ( ![X11:$i]: 7.36/1.67 ( ( in @ X11 @ X5 ) => 7.36/1.67 ( ( in @ 7.36/1.67 X11 @ 7.36/1.67 ( binunion @ 7.36/1.67 ( setminus @ X5 @ X7 ) @ ( setminus @ X5 @ X9 ) ) ) => 7.36/1.67 ( in @ 7.36/1.67 X11 @ ( setminus @ X5 @ ( binintersect @ X7 @ X9 ) ) ) ) ) ) ) ) ) )), 7.36/1.67 inference('rw.lit', [status(esa)], [demorgan1b])). 7.36/1.67 thf(zip_derived_cl39, plain, 7.36/1.67 ( (((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y2 : $i]: 7.36/1.67 (((in @ Y2 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y3 : $i]: 7.36/1.67 (((in @ Y3 @ Y0) => 7.36/1.67 (((in @ Y3 @ 7.36/1.67 (binunion @ 7.36/1.67 (setminus @ 7.36/1.67 Y0 @ Y1) @ 7.36/1.67 (setminus @ 7.36/1.67 Y0 @ Y2))) => 7.36/1.67 (in @ Y3 @ 7.36/1.67 (setminus @ 7.36/1.67 Y0 @ 7.36/1.67 (binintersect @ 7.36/1.67 Y1 @ Y2)))))))))))))))))))))))), 7.36/1.67 inference('rw_clause', [status(thm)], [zip_derived_cl31, '2'])). 7.36/1.67 thf(zip_derived_cl44, plain, 7.36/1.67 ( (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#C') @ in)))))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ ( 7.36/1.67 '#S'))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ ( 7.36/1.67 ( 7.36/1.67 ('#B') @ ( 7.36/1.67 =>))))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ( 7.36/1.67 (('#B') @ ( 7.36/1.67 (('#C') @ in)))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ( 7.36/1.67 '#C') @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 (('#B') @ ( 7.36/1.67 '#B'))) @ 7.36/1.67 ((('#B') @ ( 7.36/1.67 (('#B') @ binunion)) @ 7.36/1.67 setminus)))))) @ 7.36/1.67 setminus)))))))))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ ((('#C') @ in)))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#B') @ setminus)))) @ 7.36/1.67 binintersect))))))))))))))))))))), 7.36/1.67 inference('comb-normalize', [status(thm)], [zip_derived_cl39])). 7.36/1.67 thf(zip_derived_cl45, plain, 7.36/1.67 (![X2 : $i]: 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 7.36/1.67 =>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 X2)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ ( 7.36/1.67 =>))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ( 7.36/1.67 '#B') @ 7.36/1.67 ((('#B') @ binunion @ 7.36/1.67 (setminus @ X2))))) @ 7.36/1.67 (setminus @ X2))))))))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (setminus @ X2))) @ 7.36/1.67 binintersect))))))))))))))))))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl44])). 7.36/1.67 thf(zip_derived_cl49, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (((in @ X4 @ (powerset @ X2)) => 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ X2)))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 ((('#B') @ (binunion @ 7.36/1.67 (setminus @ X2 @ X4)) @ 7.36/1.67 (setminus @ X2))))))))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 ((('#B') @ (setminus @ X2) @ (binintersect @ X4)))))))))))))))))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl45])). 7.36/1.67 thf(zip_derived_cl54, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ X2)))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 ((('#B') @ (binunion @ 7.36/1.67 (setminus @ X2 @ X4)) @ 7.36/1.67 (setminus @ X2))))))))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ 7.36/1.67 ((('#B') @ (setminus @ X2) @ 7.36/1.67 (binintersect @ X4))))))))))))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 7.36/1.67 thf(zip_derived_cl58, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 ( (((in @ X6 @ (powerset @ X2)) => 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 (binunion @ (setminus @ X2 @ X4) @ 7.36/1.67 (setminus @ X2 @ X6)))))) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X4 @ X6)))))))))))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl54])). 7.36/1.67 thf(zip_derived_cl63, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 (binunion @ (setminus @ X2 @ X4) @ 7.36/1.67 (setminus @ X2 @ X6)))))) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X4 @ X6)))))))))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 7.36/1.67 thf(zip_derived_cl68, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 7.36/1.67 ( (((in @ X8 @ X2) => 7.36/1.67 (((in @ X8 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) => 7.36/1.67 (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))))))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 7.36/1.67 thf(zip_derived_cl73, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 7.36/1.67 (~ (in @ X8 @ X2) 7.36/1.67 | (((in @ X8 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) => 7.36/1.67 (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))))) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 7.36/1.67 thf(zip_derived_cl78, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 7.36/1.67 (~ (in @ X8 @ (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) 7.36/1.67 | (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X8 @ X2))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 7.36/1.67 thf(zip_derived_cl140, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 7.36/1.67 (((binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) = (X3)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 7.36/1.67 (powerset @ X4)) 7.36/1.67 | ~ (in @ X3 @ (powerset @ X4)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ X3 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 7.36/1.67 X1) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X1)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X4 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 7.36/1.67 (setminus @ X1 @ (binintersect @ X2 @ X0))))), 7.36/1.67 inference('sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl78])). 7.36/1.67 thf(zip_derived_cl460, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 7.36/1.67 (~ (in @ 7.36/1.67 ('#sk4' @ X4 @ X3 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 7.36/1.67 X1) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ X3 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 7.36/1.67 (setminus @ X1 @ (binintersect @ X2 @ X0))) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X4 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 7.36/1.67 (setminus @ X1 @ (binintersect @ X2 @ X0))) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 7.36/1.67 X1) 7.36/1.67 | ~ (in @ X3 @ (powerset @ X4)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 7.36/1.67 (powerset @ X4)) 7.36/1.67 | ((binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) = (X3)))), 7.36/1.67 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl140])). 7.36/1.67 thf(zip_derived_cl470, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 7.36/1.67 (((binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) = (X3)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 7.36/1.67 (powerset @ X4)) 7.36/1.67 | ~ (in @ X3 @ (powerset @ X4)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 7.36/1.67 X1) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X4 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 7.36/1.67 (setminus @ X1 @ (binintersect @ X2 @ X0))) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ X3 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 7.36/1.67 (setminus @ X1 @ (binintersect @ X2 @ X0))) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ X3 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 7.36/1.67 X1))), 7.36/1.67 inference('simplify', [status(thm)], [zip_derived_cl460])). 7.36/1.67 thf(zip_derived_cl1146, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 7.36/1.67 (~ (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 X2) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 7.36/1.67 = (setminus @ X2 @ (binintersect @ X1 @ X0))) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 X2) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X3 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 7.36/1.67 X2) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 7.36/1.67 = (setminus @ X2 @ (binintersect @ X1 @ X0))))), 7.36/1.67 inference('sup+', [status(thm)], [zip_derived_cl95, zip_derived_cl470])). 7.36/1.67 thf(zip_derived_cl1168, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 7.36/1.67 (~ (in @ 7.36/1.67 ('#sk4' @ X3 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 7.36/1.67 X2) 7.36/1.67 | ((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 7.36/1.67 = (setminus @ X2 @ (binintersect @ X1 @ X0))) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 X2) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))))), 7.36/1.67 inference('simplify', [status(thm)], [zip_derived_cl1146])). 7.36/1.67 thf(zip_derived_cl92, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (in @ ('#sk4' @ X2 @ X6 @ X4) @ X4) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ((X4) = (X6)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])). 7.36/1.67 thf(zip_derived_cl91, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 ( (in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ((X4) = (X6)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])). 7.36/1.67 thf(zip_derived_cl78, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 7.36/1.67 (~ (in @ X8 @ (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) 7.36/1.67 | (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X8 @ X2))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 7.36/1.67 thf(zip_derived_cl291, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 7.36/1.67 (((X3) = (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) 7.36/1.67 | ~ (in @ X3 @ (powerset @ X4)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 7.36/1.67 (powerset @ X4)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X4 @ X3 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 7.36/1.67 X3) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 7.36/1.67 X1) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X1)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X4 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 7.36/1.67 (setminus @ X1 @ (binintersect @ X2 @ X0))))), 7.36/1.67 inference('sup-', [status(thm)], [zip_derived_cl91, zip_derived_cl78])). 7.36/1.67 thf(zip_derived_cl1078, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 7.36/1.67 (((setminus @ X2 @ (binintersect @ X1 @ X0)) 7.36/1.67 = (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X3 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 7.36/1.67 X2) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ((setminus @ X2 @ (binintersect @ X1 @ X0)) 7.36/1.67 = (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))))), 7.36/1.67 inference('sup+', [status(thm)], [zip_derived_cl92, zip_derived_cl291])). 7.36/1.67 thf(zip_derived_cl1093, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 7.36/1.67 (~ (in @ 7.36/1.67 ('#sk4' @ X3 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 7.36/1.67 X2) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X2)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ((setminus @ X2 @ (binintersect @ X1 @ X0)) 7.36/1.67 = (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))))), 7.36/1.67 inference('simplify', [status(thm)], [zip_derived_cl1078])). 7.36/1.67 thf(zip_derived_cl1201, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 7.36/1.67 (~ (in @ X1 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 X2) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 7.36/1.67 = (setminus @ X2 @ (binintersect @ X1 @ X0))) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X3 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 7.36/1.67 X2))), 7.36/1.67 inference('clc', [status(thm)], [zip_derived_cl1168, zip_derived_cl1093])). 7.36/1.67 thf(zip_derived_cl1210, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i]: 7.36/1.67 (((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 7.36/1.67 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 7.36/1.67 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X0 @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) @ 7.36/1.67 X0) 7.36/1.67 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 7.36/1.67 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X0 @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) @ 7.36/1.67 X0) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X0)))), 7.36/1.67 inference('sup-', [status(thm)], [zip_derived_cl539, zip_derived_cl1201])). 7.36/1.67 thf(zip_derived_cl1214, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i]: 7.36/1.67 (~ (in @ 7.36/1.67 ('#sk4' @ X0 @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) @ 7.36/1.67 X0) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 7.36/1.67 = (setminus @ X0 @ (binintersect @ X2 @ X1))))), 7.36/1.67 inference('simplify', [status(thm)], [zip_derived_cl1210])). 7.36/1.67 thf(zip_derived_cl79, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 ( (in @ ('#sk4' @ X2 @ X6 @ X4) @ X2) 7.36/1.67 | ((X4) = (X6)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 7.36/1.67 thf(zip_derived_cl86, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (in @ ('#sk4' @ X2 @ X6 @ X4) @ X4) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ((X4) = (X6)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 7.36/1.67 thf(zip_derived_cl85, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 ( (in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) 7.36/1.67 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ((X4) = (X6)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 7.36/1.67 thf(zip_derived_cl78, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 7.36/1.67 (~ (in @ X8 @ (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) 7.36/1.67 | (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X8 @ X2))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 7.36/1.67 thf(zip_derived_cl243, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 7.36/1.67 (((X3) = (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 7.36/1.67 (powerset @ X4)) 7.36/1.67 | ~ (in @ X3 @ (powerset @ X4)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X4 @ X3 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 7.36/1.67 X4) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X4 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 7.36/1.67 X1) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X1)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X1)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X4 @ 7.36/1.67 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 7.36/1.67 (setminus @ X1 @ (binintersect @ X2 @ X0))))), 7.36/1.67 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl78])). 7.36/1.67 thf(zip_derived_cl760, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 7.36/1.67 (((setminus @ X2 @ (binintersect @ X1 @ X0)) 7.36/1.67 = (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 X3) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ 7.36/1.67 ('#sk4' @ X3 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 7.36/1.67 X2) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 X3) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ((setminus @ X2 @ (binintersect @ X1 @ X0)) 7.36/1.67 = (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))))), 7.36/1.67 inference('sup+', [status(thm)], [zip_derived_cl86, zip_derived_cl243])). 7.36/1.67 thf(zip_derived_cl781, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 7.36/1.67 (~ (in @ 7.36/1.67 ('#sk4' @ X3 @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 7.36/1.67 X2) 7.36/1.67 | ~ (in @ X0 @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X2)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 7.36/1.67 X3) 7.36/1.67 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 7.36/1.67 (powerset @ X3)) 7.36/1.67 | ((setminus @ X2 @ (binintersect @ X1 @ X0)) 7.36/1.67 = (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))))), 7.36/1.67 inference('simplify', [status(thm)], [zip_derived_cl760])). 7.36/1.67 thf(zip_derived_cl816, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i]: 7.36/1.67 (~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 7.36/1.67 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X0 @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) @ 7.36/1.67 X0) 7.36/1.67 | ((setminus @ X0 @ (binintersect @ X2 @ X1)) 7.36/1.67 = (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X0 @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) @ 7.36/1.67 X0) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X0)))), 7.36/1.67 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl781])). 7.36/1.67 thf(zip_derived_cl826, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i]: 7.36/1.67 (~ (in @ X1 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X0)) 7.36/1.67 | (in @ 7.36/1.67 ('#sk4' @ X0 @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) @ 7.36/1.67 X0) 7.36/1.67 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 7.36/1.67 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 7.36/1.67 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 7.36/1.67 (powerset @ X0)))), 7.36/1.67 inference('simplify', [status(thm)], [zip_derived_cl816])). 7.36/1.67 thf(zip_derived_cl1220, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i]: 7.36/1.67 (((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 7.36/1.67 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 7.36/1.67 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X0)))), 7.36/1.67 inference('clc', [status(thm)], [zip_derived_cl1214, zip_derived_cl826])). 7.36/1.67 thf(zip_derived_cl5, plain, ( (binunionT_lem)), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])). 7.36/1.67 thf(binunionT_lem, axiom, (binunionT_lem) => 7.36/1.67 ((((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y2 : $i]: 7.36/1.67 (((in @ Y2 @ (powerset @ Y0)) => 7.36/1.67 (in @ (binunion @ Y1 @ Y2) @ 7.36/1.67 (powerset @ Y0))))))))))))))) 7.36/1.67 = ($true))). 7.36/1.67 thf('3', plain, 7.36/1.67 (( binunionT_lem ) <=> 7.36/1.67 ( ![X5:$i,X7:$i]: 7.36/1.67 ( ( in @ X7 @ ( powerset @ X5 ) ) => 7.36/1.67 ( ![X9:$i]: 7.36/1.67 ( ( in @ X9 @ ( powerset @ X5 ) ) => 7.36/1.67 ( in @ ( binunion @ X7 @ X9 ) @ ( powerset @ X5 ) ) ) ) ) )), 7.36/1.67 inference('rw.lit', [status(esa)], [binunionT_lem])). 7.36/1.67 thf(zip_derived_cl9, plain, 7.36/1.67 ( (((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y2 : $i]: 7.36/1.67 (((in @ Y2 @ (powerset @ Y0)) => 7.36/1.67 (in @ (binunion @ Y1 @ Y2) @ 7.36/1.67 (powerset @ Y0)))))))))))))))), 7.36/1.67 inference('rw_clause', [status(thm)], [zip_derived_cl5, '3'])). 7.36/1.67 thf(zip_derived_cl13, plain, 7.36/1.67 ( (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 7.36/1.67 ((('#B') @ ((('#C') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ in)) @ 7.36/1.67 binunion)))))) @ 7.36/1.67 powerset))))))))))))), 7.36/1.67 inference('comb-normalize', [status(thm)], [zip_derived_cl9])). 7.36/1.67 thf(zip_derived_cl14, plain, 7.36/1.67 (![X2 : $i]: 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ in)) @ binunion)))) @ 7.36/1.67 (powerset @ X2)))))))))))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 7.36/1.67 thf(zip_derived_cl19, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (((in @ X4 @ (powerset @ X2)) => 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ in @ (binunion @ X4))) @ 7.36/1.67 (powerset @ X2)))))))))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 7.36/1.67 thf(zip_derived_cl26, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ in @ (binunion @ X4))) @ 7.36/1.67 (powerset @ X2))))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 7.36/1.67 thf(zip_derived_cl34, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 ( (((in @ X6 @ (powerset @ X2)) => (in @ (binunion @ X4 @ X6) @ 7.36/1.67 (powerset @ X2)))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 7.36/1.67 thf(zip_derived_cl41, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | (in @ (binunion @ X4 @ X6) @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 7.36/1.67 thf(zip_derived_cl1221, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i]: 7.36/1.67 (~ (in @ X1 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 7.36/1.67 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 7.36/1.67 | ~ (in @ (setminus @ X0 @ X2) @ (powerset @ X0)) 7.36/1.67 | ~ (in @ (setminus @ X0 @ X1) @ (powerset @ X0)))), 7.36/1.67 inference('sup+', [status(thm)], [zip_derived_cl1220, zip_derived_cl41])). 7.36/1.67 thf(zip_derived_cl10, plain, ( (complementT_lem)), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 7.36/1.67 thf(complementT_lem, axiom, (complementT_lem) => 7.36/1.67 ((((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => (in @ 7.36/1.67 (setminus @ Y0 @ Y1) @ (powerset @ Y0)))))))))) 7.36/1.67 = ($true))). 7.36/1.67 thf('4', plain, 7.36/1.67 (( complementT_lem ) <=> 7.36/1.67 ( ![X5:$i,X7:$i]: 7.36/1.67 ( ( in @ X7 @ ( powerset @ X5 ) ) => 7.36/1.67 ( in @ ( setminus @ X5 @ X7 ) @ ( powerset @ X5 ) ) ) )), 7.36/1.67 inference('rw.lit', [status(esa)], [complementT_lem])). 7.36/1.67 thf(zip_derived_cl15, plain, 7.36/1.67 ( (((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => (in @ 7.36/1.67 (setminus @ Y0 @ Y1) @ (powerset @ Y0))))))))))), 7.36/1.67 inference('rw_clause', [status(thm)], [zip_derived_cl10, '4'])). 7.36/1.67 thf(zip_derived_cl20, plain, 7.36/1.67 ( (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ in)) @ setminus)))) @ 7.36/1.67 powerset))))))))), 7.36/1.67 inference('comb-normalize', [status(thm)], [zip_derived_cl15])). 7.36/1.67 thf(zip_derived_cl21, plain, 7.36/1.67 (![X2 : $i]: 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ in @ (setminus @ X2))) @ 7.36/1.67 (powerset @ X2)))))))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 7.36/1.67 thf(zip_derived_cl27, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (((in @ X4 @ (powerset @ X2)) => (in @ (setminus @ X2 @ X4) @ 7.36/1.67 (powerset @ X2))))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 7.36/1.67 thf(zip_derived_cl35, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (in @ (setminus @ X2 @ X4) @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 7.36/1.67 thf(zip_derived_cl1223, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i]: 7.36/1.67 (~ (in @ (setminus @ X0 @ X1) @ (powerset @ X0)) 7.36/1.67 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 7.36/1.67 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 7.36/1.67 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X0)))), 7.36/1.67 inference('clc', [status(thm)], [zip_derived_cl1221, zip_derived_cl35])). 7.36/1.67 thf(zip_derived_cl35, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (in @ (setminus @ X2 @ X4) @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 7.36/1.67 thf(zip_derived_cl1224, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i]: 7.36/1.67 (~ (in @ X1 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 7.36/1.67 (powerset @ X0)) 7.36/1.67 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 7.36/1.67 = (setminus @ X0 @ (binintersect @ X2 @ X1))))), 7.36/1.67 inference('clc', [status(thm)], [zip_derived_cl1223, zip_derived_cl35])). 7.36/1.67 thf(zip_derived_cl35, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (in @ (setminus @ X2 @ X4) @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 7.36/1.67 thf(zip_derived_cl1225, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i]: 7.36/1.67 (((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 7.36/1.67 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ X1 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ (binintersect @ X2 @ X1) @ (powerset @ X0)))), 7.36/1.67 inference('sup+', [status(thm)], [zip_derived_cl1224, zip_derived_cl35])). 7.36/1.67 thf(zip_derived_cl2, plain, ( (binintersectT_lem)), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 7.36/1.67 thf(binintersectT_lem, axiom, (binintersectT_lem) => 7.36/1.67 ((((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y2 : $i]: 7.36/1.67 (((in @ Y2 @ (powerset @ Y0)) => 7.36/1.67 (in @ (binintersect @ Y1 @ Y2) @ 7.36/1.67 (powerset @ Y0))))))))))))))) 7.36/1.67 = ($true))). 7.36/1.67 thf('5', plain, 7.36/1.67 (( binintersectT_lem ) <=> 7.36/1.67 ( ![X5:$i,X7:$i]: 7.36/1.67 ( ( in @ X7 @ ( powerset @ X5 ) ) => 7.36/1.67 ( ![X9:$i]: 7.36/1.67 ( ( in @ X9 @ ( powerset @ X5 ) ) => 7.36/1.67 ( in @ ( binintersect @ X7 @ X9 ) @ ( powerset @ X5 ) ) ) ) ) )), 7.36/1.67 inference('rw.lit', [status(esa)], [binintersectT_lem])). 7.36/1.67 thf(zip_derived_cl4, plain, 7.36/1.67 ( (((!!) @ (^[Y0 : $i]: 7.36/1.67 (((!!) @ (^[Y1 : $i]: 7.36/1.67 (((in @ Y1 @ (powerset @ Y0)) => 7.36/1.67 (((!!) @ (^[Y2 : $i]: 7.36/1.67 (((in @ Y2 @ (powerset @ Y0)) => 7.36/1.67 (in @ 7.36/1.67 (binintersect @ Y1 @ Y2) @ 7.36/1.67 (powerset @ Y0)))))))))))))))), 7.36/1.67 inference('rw_clause', [status(thm)], [zip_derived_cl2, '5'])). 7.36/1.67 thf(zip_derived_cl7, plain, 7.36/1.67 ( (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 7.36/1.67 ((('#B') @ ((('#C') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ in)) @ 7.36/1.67 binintersect)))))) @ 7.36/1.67 powerset))))))))))))), 7.36/1.67 inference('comb-normalize', [status(thm)], [zip_derived_cl4])). 7.36/1.67 thf(zip_derived_cl8, plain, 7.36/1.67 (![X2 : $i]: 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ in)) @ binintersect)))) @ 7.36/1.67 (powerset @ X2)))))))))))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 7.36/1.67 thf(zip_derived_cl12, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (((in @ X4 @ (powerset @ X2)) => 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ in @ (binintersect @ X4))) @ 7.36/1.67 (powerset @ X2)))))))))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 7.36/1.67 thf(zip_derived_cl18, plain, 7.36/1.67 (![X2 : $i, X4 : $i]: 7.36/1.67 (~ (in @ X4 @ (powerset @ X2)) 7.36/1.67 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ X2))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ in @ (binintersect @ X4))) @ 7.36/1.67 (powerset @ X2))))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 7.36/1.67 thf(zip_derived_cl25, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 ( (((in @ X6 @ (powerset @ X2)) => (in @ (binintersect @ X4 @ X6) @ 7.36/1.67 (powerset @ X2)))) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 7.36/1.67 thf(zip_derived_cl33, plain, 7.36/1.67 (![X2 : $i, X4 : $i, X6 : $i]: 7.36/1.67 (~ (in @ X6 @ (powerset @ X2)) 7.36/1.67 | (in @ (binintersect @ X4 @ X6) @ (powerset @ X2)) 7.36/1.67 | ~ (in @ X4 @ (powerset @ X2)))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 7.36/1.67 thf(zip_derived_cl1227, plain, 7.36/1.67 (![X0 : $i, X1 : $i, X2 : $i]: 7.36/1.67 (~ (in @ X1 @ (powerset @ X0)) 7.36/1.67 | ~ (in @ X2 @ (powerset @ X0)) 7.36/1.67 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 7.36/1.67 = (setminus @ X0 @ (binintersect @ X2 @ X1))))), 7.36/1.67 inference('clc', [status(thm)], [zip_derived_cl1225, zip_derived_cl33])). 7.36/1.67 thf(zip_derived_cl32, plain, 7.36/1.67 (~ (((!!) @ ((('#B') @ (!!) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (!!))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=>))) @ 7.36/1.67 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#S'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ ('#B') @ 7.36/1.67 setminus)))) @ 7.36/1.67 binintersect)))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#C') @ 7.36/1.67 ((('#B') @ ((('#B') @ ('#B'))) @ 7.36/1.67 ((('#B') @ ((('#B') @ binunion)) @ 7.36/1.67 setminus)))))) @ 7.36/1.67 setminus))))))))))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 7.36/1.67 thf(zip_derived_cl40, plain, 7.36/1.67 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ '#sk1'))))) @ 7.36/1.67 ((('#B') @ (!!) @ 7.36/1.67 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ 7.36/1.67 (powerset @ '#sk1'))))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ ('#S') @ 7.36/1.67 ((('#B') @ ((('#B') @ (=))) @ 7.36/1.67 ((('#B') @ ((('#B') @ (setminus @ '#sk1'))) @ 7.36/1.67 binintersect)))))) @ 7.36/1.67 ((('#C') @ ((('#B') @ ('#B') @ 7.36/1.67 ((('#B') @ binunion @ 7.36/1.67 (setminus @ '#sk1'))))) @ 7.36/1.67 (setminus @ '#sk1')))))))))))))), 7.36/1.67 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 7.36/1.67 thf(zip_derived_cl46, plain, 7.36/1.67 (~ (((in @ '#sk2' @ (powerset @ '#sk1')) => 7.36/1.67 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ '#sk1'))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=) @ 7.36/1.67 ((('#B') @ (setminus @ '#sk1') @ 7.36/1.67 (binintersect @ '#sk2'))))) @ 7.36/1.67 ((('#B') @ (binunion @ (setminus @ '#sk1' @ '#sk2')) @ 7.36/1.67 (setminus @ '#sk1')))))))))))), 7.36/1.67 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl40])). 7.36/1.67 thf(zip_derived_cl51, plain, 7.36/1.67 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 7.36/1.67 ((('#C') @ in @ (powerset @ '#sk1'))))) @ 7.36/1.67 ((('#S') @ ((('#B') @ (=) @ 7.36/1.67 ((('#B') @ (setminus @ '#sk1') @ 7.36/1.67 (binintersect @ '#sk2'))))) @ 7.36/1.67 ((('#B') @ (binunion @ (setminus @ '#sk1' @ '#sk2')) @ 7.36/1.67 (setminus @ '#sk1')))))))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 7.36/1.67 thf(zip_derived_cl55, plain, 7.36/1.67 (~ (((in @ '#sk3' @ (powerset @ '#sk1')) => 7.36/1.67 (((setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3')) = 7.36/1.67 (binunion @ (setminus @ '#sk1' @ '#sk2') @ 7.36/1.67 (setminus @ '#sk1' @ '#sk3'))))))), 7.36/1.67 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl51])). 7.36/1.67 thf(zip_derived_cl60, plain, 7.36/1.67 (~ (((setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3')) = 7.36/1.67 (binunion @ (setminus @ '#sk1' @ '#sk2') @ 7.36/1.67 (setminus @ '#sk1' @ '#sk3'))))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 7.36/1.67 thf(zip_derived_cl64, plain, 7.36/1.67 (((setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3')) 7.36/1.67 != (binunion @ (setminus @ '#sk1' @ '#sk2') @ 7.36/1.67 (setminus @ '#sk1' @ '#sk3')))), 7.36/1.67 inference('simplify nested equalities', [status(thm)], [zip_derived_cl60])). 7.36/1.67 thf(zip_derived_cl1258, plain, 7.36/1.67 ((((setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3')) 7.36/1.67 != (setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3'))) 7.36/1.67 | ~ (in @ '#sk2' @ (powerset @ '#sk1')) 7.36/1.67 | ~ (in @ '#sk3' @ (powerset @ '#sk1')))), 7.36/1.67 inference('sup-', [status(thm)], [zip_derived_cl1227, zip_derived_cl64])). 7.36/1.67 thf(zip_derived_cl50, plain, ( (in @ '#sk2' @ (powerset @ '#sk1'))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 7.36/1.67 thf(zip_derived_cl59, plain, ( (in @ '#sk3' @ (powerset @ '#sk1'))), 7.36/1.67 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 7.36/1.67 thf(zip_derived_cl1288, plain, 7.36/1.67 (((setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3')) 7.36/1.67 != (setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3')))), 7.36/1.67 inference('demod', [status(thm)], 7.36/1.67 [zip_derived_cl1258, zip_derived_cl50, zip_derived_cl59])). 7.36/1.67 thf(zip_derived_cl1289, plain, ($false), 7.36/1.67 inference('simplify', [status(thm)], [zip_derived_cl1288])). 7.36/1.67 7.36/1.67 % SZS output end Refutation 7.36/1.67 7.36/1.67 7.36/1.67 % Terminating... 8.50/1.84 % Runner terminated. 8.50/1.84 % Zipperpin 1.5 exiting 8.50/1.84 EOF