0.05/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.7iOlwCDkZY true 0.11/0.32 % Computer : n005.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 1920 0.11/0.32 % WCLimit : 240 0.11/0.32 % DateTime : Wed Jul 30 03:52:49 EDT 2025 0.11/0.32 % CPUTime : 0.11/0.32 % Running portfolio for 1920 s 0.11/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.11/0.32 % Number of cores: 8 0.11/0.32 % Python version: Python 3.6.8 0.11/0.32 % Running in HO mode 0.49/0.63 % Total configuration time : 828 0.49/0.63 % Estimated wc time : 1656 0.49/0.63 % Estimated cpu time (8 cpus) : 207.0 0.49/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 14.86/2.45 % Solved by lams/40_b.comb.sh. 14.86/2.45 % done 145 iterations in 1.674s 14.86/2.45 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 14.86/2.45 % SZS output start Refutation 14.86/2.45 thf(complementT_lem_type, type, complementT_lem: $o). 14.86/2.45 thf(setminus_type, type, setminus: $i > $i > $i). 14.86/2.45 thf(in_type, type, in: $i > $i > $o). 14.86/2.45 thf(setextT_type, type, setextT: $o). 14.86/2.45 thf(binunion_type, type, binunion: $i > $i > $i). 14.86/2.45 thf(binunionT_lem_type, type, binunionT_lem: $o). 14.86/2.45 thf('#sk1_type', type, '#sk1': $i). 14.86/2.45 thf(binintersectT_lem_type, type, binintersectT_lem: $o). 14.86/2.45 thf(binintersect_type, type, binintersect: $i > $i > $i). 14.86/2.45 thf(demorgan1a_type, type, demorgan1a: $o). 14.86/2.45 thf(powerset_type, type, powerset: $i > $i). 14.86/2.45 thf('#sk2_type', type, '#sk2': $i). 14.86/2.45 thf('#sk3_type', type, '#sk3': $i). 14.86/2.45 thf(demorgan1b_type, type, demorgan1b: $o). 14.86/2.45 thf('#sk4_type', type, '#sk4': $i > $i > $i > $i). 14.86/2.45 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 14.86/2.45 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 14.86/2.45 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 14.86/2.45 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 14.86/2.45 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 14.86/2.45 thf(demorgan1, conjecture, 14.86/2.45 (( binintersectT_lem ) => 14.86/2.45 ( ( binunionT_lem ) => 14.86/2.45 ( ( complementT_lem ) => 14.86/2.45 ( ( setextT ) => 14.86/2.45 ( ( demorgan1a ) => 14.86/2.45 ( ( demorgan1b ) => 14.86/2.45 ( ![A:$i,X:$i]: 14.86/2.45 ( ( in @ X @ ( powerset @ A ) ) => 14.86/2.45 ( ![Y:$i]: 14.86/2.45 ( ( in @ Y @ ( powerset @ A ) ) => 14.86/2.45 ( ( setminus @ A @ ( binintersect @ X @ Y ) ) = 14.86/2.45 ( binunion @ 14.86/2.45 ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ))). 14.86/2.45 thf(zf_stmt_0, negated_conjecture, 14.86/2.45 (~( ( binintersectT_lem ) => 14.86/2.45 ( ( binunionT_lem ) => 14.86/2.45 ( ( complementT_lem ) => 14.86/2.45 ( ( setextT ) => 14.86/2.45 ( ( demorgan1a ) => 14.86/2.45 ( ( demorgan1b ) => 14.86/2.45 ( ![A:$i,X:$i]: 14.86/2.45 ( ( in @ X @ ( powerset @ A ) ) => 14.86/2.45 ( ![Y:$i]: 14.86/2.45 ( ( in @ Y @ ( powerset @ A ) ) => 14.86/2.45 ( ( setminus @ A @ ( binintersect @ X @ Y ) ) = 14.86/2.45 ( binunion @ 14.86/2.45 ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ) )), 14.86/2.45 inference('cnf.neg', [status(esa)], [demorgan1])). 14.86/2.45 thf(zip_derived_cl0, plain, 14.86/2.45 (~ (((binintersectT_lem) => 14.86/2.45 (((binunionT_lem) => 14.86/2.45 (((complementT_lem) => 14.86/2.45 (((setextT) => 14.86/2.45 (((demorgan1a) => 14.86/2.45 (((demorgan1b) => 14.86/2.45 (((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y2 : $i]: 14.86/2.45 (((in @ Y2 @ 14.86/2.45 (powerset @ Y0)) => 14.86/2.45 (((setminus @ 14.86/2.45 Y0 @ 14.86/2.45 (binintersect @ 14.86/2.45 Y1 @ Y2)) = 14.86/2.45 (binunion @ 14.86/2.45 (setminus @ 14.86/2.45 Y0 @ Y1) @ 14.86/2.45 (setminus @ 14.86/2.45 Y0 @ Y2)))))))))))))))))))))))))))))), 14.86/2.45 inference('cnf', [status(esa)], [zf_stmt_0])). 14.86/2.45 thf(zip_derived_cl1, plain, 14.86/2.45 (~ (((binintersectT_lem) => 14.86/2.45 (((binunionT_lem) => 14.86/2.45 (((complementT_lem) => 14.86/2.45 (((setextT) => 14.86/2.45 (((demorgan1a) => 14.86/2.45 (((demorgan1b) => 14.86/2.45 (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 powerset)))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 powerset)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ( 14.86/2.45 (('#B') @ (=))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ( 14.86/2.45 '#B') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 '#B') @ 14.86/2.45 setminus)))) @ 14.86/2.45 binintersect)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ ( 14.86/2.45 '#B'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ binunion)) @ 14.86/2.45 setminus)))))) @ 14.86/2.45 setminus))))))))))))))))))))))))))), 14.86/2.45 inference('lams2combs', [status(thm)], [zip_derived_cl0])). 14.86/2.45 thf(zip_derived_cl3, plain, 14.86/2.45 (~ (((binunionT_lem) => 14.86/2.45 (((complementT_lem) => 14.86/2.45 (((setextT) => 14.86/2.45 (((demorgan1a) => 14.86/2.45 (((demorgan1b) => 14.86/2.45 (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 powerset)))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 powerset)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ( 14.86/2.45 (('#B') @ (=))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ( 14.86/2.45 '#B') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 '#B') @ 14.86/2.45 setminus)))) @ 14.86/2.45 binintersect)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#B'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ binunion)) @ 14.86/2.45 setminus)))))) @ 14.86/2.45 setminus))))))))))))))))))))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 14.86/2.45 thf(zip_derived_cl6, plain, 14.86/2.45 (~ (((complementT_lem) => 14.86/2.45 (((setextT) => 14.86/2.45 (((demorgan1a) => 14.86/2.45 (((demorgan1b) => 14.86/2.45 (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 powerset)))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 powerset)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ( 14.86/2.45 (('#B') @ (=))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ( 14.86/2.45 '#B') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 '#B') @ 14.86/2.45 setminus)))) @ 14.86/2.45 binintersect)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#B'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ binunion)) @ 14.86/2.45 setminus)))))) @ 14.86/2.45 setminus))))))))))))))))))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])). 14.86/2.45 thf(zip_derived_cl11, plain, 14.86/2.45 (~ (((setextT) => 14.86/2.45 (((demorgan1a) => 14.86/2.45 (((demorgan1b) => 14.86/2.45 (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 powerset)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (( 14.86/2.45 ('#B') @ ( 14.86/2.45 =))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ( 14.86/2.45 '#B') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 '#B') @ 14.86/2.45 setminus)))) @ 14.86/2.45 binintersect)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#B'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ binunion)) @ 14.86/2.45 setminus)))))) @ 14.86/2.45 setminus))))))))))))))))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 14.86/2.45 thf(zip_derived_cl16, plain, ( (setextT)), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 14.86/2.45 thf(setextT, axiom, (setextT) => 14.86/2.45 ((((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y2 : $i]: 14.86/2.45 (((in @ Y2 @ (powerset @ Y0)) => 14.86/2.45 (((((!!) @ (^[Y3 : $i]: 14.86/2.45 (((in @ Y3 @ Y0) => 14.86/2.45 (((in @ Y3 @ 14.86/2.45 Y1) => (in @ 14.86/2.45 Y3 @ Y2)))))))) => 14.86/2.45 (((((!!) @ (^[Y3 : $i]: 14.86/2.45 (((in @ Y3 @ 14.86/2.45 Y0) => 14.86/2.45 (((in @ Y3 @ 14.86/2.45 Y2) => (in @ 14.86/2.45 Y3 @ Y1)))))))) => 14.86/2.45 (((Y1) = (Y2)))))))))))))))))))) 14.86/2.45 = ($true))). 14.86/2.45 thf('0', plain, 14.86/2.45 (( setextT ) <=> 14.86/2.45 ( ![X5:$i,X7:$i]: 14.86/2.45 ( ( in @ X7 @ ( powerset @ X5 ) ) => 14.86/2.45 ( ![X9:$i]: 14.86/2.45 ( ( in @ X9 @ ( powerset @ X5 ) ) => 14.86/2.45 ( ( ![X11:$i]: 14.86/2.45 ( ( in @ X11 @ X5 ) => 14.86/2.45 ( ( in @ X11 @ X7 ) => ( in @ X11 @ X9 ) ) ) ) => 14.86/2.45 ( ( ![X13:$i]: 14.86/2.45 ( ( in @ X13 @ X5 ) => 14.86/2.45 ( ( in @ X13 @ X9 ) => ( in @ X13 @ X7 ) ) ) ) => 14.86/2.45 ( ( X7 ) = ( X9 ) ) ) ) ) ) ) )), 14.86/2.45 inference('rw.lit', [status(esa)], [setextT])). 14.86/2.45 thf(zip_derived_cl22, plain, 14.86/2.45 ( (((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y2 : $i]: 14.86/2.45 (((in @ Y2 @ (powerset @ Y0)) => 14.86/2.45 (((((!!) @ (^[Y3 : $i]: 14.86/2.45 (((in @ Y3 @ 14.86/2.45 Y0) => 14.86/2.45 (((in @ Y3 @ 14.86/2.45 Y1) => (in @ 14.86/2.45 Y3 @ Y2)))))))) => 14.86/2.45 (((((!!) @ (^[Y3 : $i]: 14.86/2.45 (((in @ Y3 @ 14.86/2.45 Y0) => 14.86/2.45 (((in @ Y3 @ 14.86/2.45 Y2) => 14.86/2.45 (in @ Y3 @ 14.86/2.45 Y1)))))))) => 14.86/2.45 (((Y1) = (Y2))))))))))))))))))))), 14.86/2.45 inference('rw_clause', [status(thm)], [zip_derived_cl16, '0'])). 14.86/2.45 thf(zip_derived_cl28, plain, 14.86/2.45 ( (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 '#S') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 (('#B') @ (=>))) @ 14.86/2.45 ((('#C') @ in)))))))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 '#S') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 (('#B') @ (=>))) @ 14.86/2.45 ((('#C') @ in)))))))) @ 14.86/2.45 ((('#C') @ in)))))))))))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ ( 14.86/2.45 !!))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 '#B') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 '#S') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 (('#B') @ (=>))) @ 14.86/2.45 ((('#C') @ in)))))))))) @ 14.86/2.45 ((('#B') @ ((('#C') @ ( 14.86/2.45 (('#B') @ ( 14.86/2.45 '#S') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 (('#B') @ (=>))) @ 14.86/2.45 ((('#C') @ in)))))))) @ 14.86/2.45 ((('#C') @ in)))))))))))))) @ 14.86/2.45 (=)))))))))))))))), 14.86/2.45 inference('comb-normalize', [status(thm)], [zip_derived_cl22])). 14.86/2.45 thf(zip_derived_cl29, plain, 14.86/2.45 (![X2 : $i]: 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#S') @ ( 14.86/2.45 (('#B') @ ( 14.86/2.45 =>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 X2)))))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 (('#B') @ (=>))) @ 14.86/2.45 ((('#C') @ in)))))))) @ 14.86/2.45 ((('#C') @ in)))))))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#S') @ ( 14.86/2.45 (('#B') @ ( 14.86/2.45 =>) @ 14.86/2.45 (( 14.86/2.45 ('#C') @ in @ 14.86/2.45 X2)))))))) @ 14.86/2.45 ((('#B') @ ((('#C') @ ((('#B') @ ( 14.86/2.45 '#S') @ 14.86/2.45 ( 14.86/2.45 ( 14.86/2.45 ('#B') @ ( 14.86/2.45 ( 14.86/2.45 ('#B') @ ( 14.86/2.45 =>))) @ 14.86/2.45 ( 14.86/2.45 ( 14.86/2.45 ('#C') @ in)))))))) @ 14.86/2.45 ((('#C') @ in)))))))))))) @ 14.86/2.45 (=)))))))))))))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 14.86/2.45 thf(zip_derived_cl36, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (((in @ X4 @ (powerset @ X2)) => 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ ( 14.86/2.45 =>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 X2)))))) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ ( 14.86/2.45 =>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 X4)))))) @ 14.86/2.45 ((('#C') @ in)))))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ ( 14.86/2.45 =>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 X2)))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ( 14.86/2.45 =>))) @ 14.86/2.45 ((('#C') @ in)))))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))))) @ 14.86/2.45 ((($i) = (X4)))))))))))))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 14.86/2.45 thf(zip_derived_cl42, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ ( 14.86/2.45 =>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 X2)))))) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ ( 14.86/2.45 =>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 X4)))))) @ 14.86/2.45 ((('#C') @ in)))))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ ( 14.86/2.45 =>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 X2)))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ( 14.86/2.45 =>))) @ 14.86/2.45 ((('#C') @ in)))))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))))) @ 14.86/2.45 ((($i) = (X4))))))))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 14.86/2.45 thf(zip_derived_cl47, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 ( (((in @ X6 @ (powerset @ X2)) => 14.86/2.45 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X4)))) @ 14.86/2.45 ((('#C') @ in @ X6)))))))) => 14.86/2.45 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) => 14.86/2.45 (((X4) = (X6))))))))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 14.86/2.45 thf(zip_derived_cl52, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X4)))) @ 14.86/2.45 ((('#C') @ in @ X6)))))))) => 14.86/2.45 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) => 14.86/2.45 (((X4) = (X6))))))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 14.86/2.45 thf(zip_derived_cl56, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X4)))) @ 14.86/2.45 ((('#C') @ in @ X6)))))))) 14.86/2.45 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) => 14.86/2.45 (((X4) = (X6))))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 14.86/2.45 thf(zip_derived_cl61, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) => 14.86/2.45 (((in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) => (in @ 14.86/2.45 ('#sk4' @ X2 @ X4 @ X6) @ X6))))) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) => 14.86/2.45 (((X4) = (X6))))))), 14.86/2.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl56])). 14.86/2.45 thf(zip_derived_cl65, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 ( (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) 14.86/2.45 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) => 14.86/2.45 (((X4) = (X6))))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 14.86/2.45 thf(zip_derived_cl69, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) 14.86/2.45 | (((X4) = (X6))) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])). 14.86/2.45 thf(zip_derived_cl74, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) 14.86/2.45 | ((X4) = (X6)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2))), 14.86/2.45 inference('simplify nested equalities', [status(thm)], [zip_derived_cl69])). 14.86/2.45 thf(zip_derived_cl75, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X2) => 14.86/2.45 (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) => (in @ 14.86/2.45 ('#sk4' @ X2 @ X6 @ X4) @ X4))))) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ((X4) = (X6)))), 14.86/2.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl74])). 14.86/2.45 thf(zip_derived_cl80, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) => (in @ 14.86/2.45 ('#sk4' @ X2 @ X6 @ X4) @ X4))) 14.86/2.45 | ((X4) = (X6)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 14.86/2.45 thf(zip_derived_cl85, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 ( (in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ((X4) = (X6)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 14.86/2.45 thf(zip_derived_cl86, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (in @ ('#sk4' @ X2 @ X6 @ X4) @ X4) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ((X4) = (X6)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 14.86/2.45 thf(zip_derived_cl17, plain, 14.86/2.45 (~ (((demorgan1a) => 14.86/2.45 (((demorgan1b) => 14.86/2.45 (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 powerset)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ ( 14.86/2.45 =))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 '#B') @ setminus)))) @ 14.86/2.45 binintersect)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#B'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ binunion)) @ 14.86/2.45 setminus)))))) @ 14.86/2.45 setminus))))))))))))))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 14.86/2.45 thf(zip_derived_cl23, plain, ( (demorgan1a)), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 14.86/2.45 thf(demorgan1a, axiom, (demorgan1a) => 14.86/2.45 ((((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y2 : $i]: 14.86/2.45 (((in @ Y2 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y3 : $i]: 14.86/2.45 (((in @ Y3 @ Y0) => 14.86/2.45 (((in @ Y3 @ 14.86/2.45 (setminus @ Y0 @ 14.86/2.45 (binintersect @ 14.86/2.45 Y1 @ Y2))) => 14.86/2.45 (in @ Y3 @ 14.86/2.45 (binunion @ 14.86/2.45 (setminus @ Y0 @ 14.86/2.45 Y1) @ 14.86/2.45 (setminus @ Y0 @ 14.86/2.45 Y2))))))))))))))))))))))) 14.86/2.45 = ($true))). 14.86/2.45 thf('1', plain, 14.86/2.45 (( demorgan1a ) <=> 14.86/2.45 ( ![X5:$i,X7:$i]: 14.86/2.45 ( ( in @ X7 @ ( powerset @ X5 ) ) => 14.86/2.45 ( ![X9:$i]: 14.86/2.45 ( ( in @ X9 @ ( powerset @ X5 ) ) => 14.86/2.45 ( ![X11:$i]: 14.86/2.45 ( ( in @ X11 @ X5 ) => 14.86/2.45 ( ( in @ 14.86/2.45 X11 @ ( setminus @ X5 @ ( binintersect @ X7 @ X9 ) ) ) => 14.86/2.45 ( in @ 14.86/2.45 X11 @ 14.86/2.45 ( binunion @ 14.86/2.45 ( setminus @ X5 @ X7 ) @ ( setminus @ X5 @ X9 ) ) ) ) ) ) ) ) ) )), 14.86/2.45 inference('rw.lit', [status(esa)], [demorgan1a])). 14.86/2.45 thf(zip_derived_cl30, plain, 14.86/2.45 ( (((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y2 : $i]: 14.86/2.45 (((in @ Y2 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y3 : $i]: 14.86/2.45 (((in @ Y3 @ Y0) => 14.86/2.45 (((in @ Y3 @ 14.86/2.45 (setminus @ 14.86/2.45 Y0 @ 14.86/2.45 (binintersect @ 14.86/2.45 Y1 @ Y2))) => 14.86/2.45 (in @ Y3 @ 14.86/2.45 (binunion @ 14.86/2.45 (setminus @ 14.86/2.45 Y0 @ Y1) @ 14.86/2.45 (setminus @ 14.86/2.45 Y0 @ Y2)))))))))))))))))))))))), 14.86/2.45 inference('rw_clause', [status(thm)], [zip_derived_cl23, '1'])). 14.86/2.45 thf(zip_derived_cl37, plain, 14.86/2.45 ( (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#C') @ in)))))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ ( 14.86/2.45 '#S'))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ ( 14.86/2.45 ( 14.86/2.45 ('#B') @ ( 14.86/2.45 =>))))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ( 14.86/2.45 (('#B') @ ( 14.86/2.45 (('#C') @ in)))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ( 14.86/2.45 '#B') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 '#B') @ 14.86/2.45 setminus)))) @ 14.86/2.45 binintersect)))))))))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ ((('#C') @ in)))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#B'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ binunion)) @ 14.86/2.45 setminus)))))) @ 14.86/2.45 setminus))))))))))))))))))))), 14.86/2.45 inference('comb-normalize', [status(thm)], [zip_derived_cl30])). 14.86/2.45 thf(zip_derived_cl38, plain, 14.86/2.45 (![X2 : $i]: 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 14.86/2.45 =>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 X2)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ ( 14.86/2.45 =>))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ( 14.86/2.45 setminus @ X2))) @ 14.86/2.45 binintersect)))))))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ binunion @ 14.86/2.45 (setminus @ X2))))) @ 14.86/2.45 (setminus @ X2)))))))))))))))))))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 14.86/2.45 thf(zip_derived_cl43, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (((in @ X4 @ (powerset @ X2)) => 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ X2)))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 ((('#B') @ (setminus @ X2) @ 14.86/2.45 (binintersect @ X4))))))))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 ((('#B') @ (binunion @ (setminus @ X2 @ X4)) @ 14.86/2.45 (setminus @ X2)))))))))))))))))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 14.86/2.45 thf(zip_derived_cl48, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ X2)))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 ((('#B') @ (setminus @ X2) @ 14.86/2.45 (binintersect @ X4))))))))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 ((('#B') @ (binunion @ (setminus @ X2 @ X4)) @ 14.86/2.45 (setminus @ X2))))))))))))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl43])). 14.86/2.45 thf(zip_derived_cl53, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 ( (((in @ X6 @ (powerset @ X2)) => 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 (setminus @ X2 @ 14.86/2.45 (binintersect @ X4 @ X6)))))) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 (binunion @ (setminus @ X2 @ X4) @ 14.86/2.45 (setminus @ X2 @ X6)))))))))))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl48])). 14.86/2.45 thf(zip_derived_cl57, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 (setminus @ X2 @ 14.86/2.45 (binintersect @ X4 @ X6)))))) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 (binunion @ (setminus @ X2 @ X4) @ 14.86/2.45 (setminus @ X2 @ X6)))))))))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 14.86/2.45 thf(zip_derived_cl62, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 14.86/2.45 ( (((in @ X8 @ X2) => 14.86/2.45 (((in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) => (in @ 14.86/2.45 X8 @ (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))))))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 14.86/2.45 thf(zip_derived_cl67, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 14.86/2.45 (~ (in @ X8 @ X2) 14.86/2.45 | (((in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) => (in @ 14.86/2.45 X8 @ (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))))) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 14.86/2.45 thf(zip_derived_cl72, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 14.86/2.45 (~ (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) 14.86/2.45 | (in @ X8 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X8 @ X2))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 14.86/2.45 thf(zip_derived_cl103, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 14.86/2.45 (((binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) = (X3)) 14.86/2.45 | ~ (in @ X3 @ (powerset @ X4)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 14.86/2.45 (powerset @ X4)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X4 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 14.86/2.45 X4) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ X3 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 14.86/2.45 X1) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ X3 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 14.86/2.45 (setminus @ X1 @ (binintersect @ X2 @ X0))))), 14.86/2.45 inference('sup+', [status(thm)], [zip_derived_cl86, zip_derived_cl72])). 14.86/2.45 thf(zip_derived_cl476, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 14.86/2.45 (((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 14.86/2.45 = (setminus @ X2 @ (binintersect @ X1 @ X0))) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X3 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 14.86/2.45 X3) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 X2) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X3 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 14.86/2.45 X3) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 14.86/2.45 = (setminus @ X2 @ (binintersect @ X1 @ X0))))), 14.86/2.45 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl103])). 14.86/2.45 thf(zip_derived_cl493, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 14.86/2.45 (~ (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 X2) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X2)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X3 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 14.86/2.45 X3) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 14.86/2.45 = (setminus @ X2 @ (binintersect @ X1 @ X0))))), 14.86/2.45 inference('simplify', [status(thm)], [zip_derived_cl476])). 14.86/2.45 thf(zip_derived_cl66, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) => (in @ 14.86/2.45 ('#sk4' @ X2 @ X4 @ X6) @ X6))) 14.86/2.45 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) => 14.86/2.45 (((X4) = (X6))))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 14.86/2.45 thf(zip_derived_cl71, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (in @ ('#sk4' @ X2 @ X4 @ X6) @ X6) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) => 14.86/2.45 (((X4) = (X6))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 14.86/2.45 thf(zip_derived_cl77, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) 14.86/2.45 | (((X4) = (X6))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ ('#sk4' @ X2 @ X4 @ X6) @ X6))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 14.86/2.45 thf(zip_derived_cl83, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) 14.86/2.45 | ((X4) = (X6)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ ('#sk4' @ X2 @ X4 @ X6) @ X6))), 14.86/2.45 inference('simplify nested equalities', [status(thm)], [zip_derived_cl77])). 14.86/2.45 thf(zip_derived_cl84, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X2) => 14.86/2.45 (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) => (in @ 14.86/2.45 ('#sk4' @ X2 @ X6 @ X4) @ X4))))) 14.86/2.45 | ~ (in @ ('#sk4' @ X2 @ X4 @ X6) @ X6) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ((X4) = (X6)))), 14.86/2.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl83])). 14.86/2.45 thf(zip_derived_cl90, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) => (in @ 14.86/2.45 ('#sk4' @ X2 @ X6 @ X4) @ X4))) 14.86/2.45 | ((X4) = (X6)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ ('#sk4' @ X2 @ X4 @ X6) @ X6))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl84])). 14.86/2.45 thf(zip_derived_cl94, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (in @ ('#sk4' @ X2 @ X6 @ X4) @ X4) 14.86/2.45 | ~ (in @ ('#sk4' @ X2 @ X4 @ X6) @ X6) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ((X4) = (X6)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl90])). 14.86/2.45 thf(zip_derived_cl72, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 14.86/2.45 (~ (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) 14.86/2.45 | (in @ X8 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X8 @ X2))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 14.86/2.45 thf(zip_derived_cl95, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 14.86/2.45 (((binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) = (X3)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 14.86/2.45 (powerset @ X4)) 14.86/2.45 | ~ (in @ X3 @ (powerset @ X4)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 14.86/2.45 X3) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ X3 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 14.86/2.45 X1) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ X3 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 14.86/2.45 (setminus @ X1 @ (binintersect @ X2 @ X0))))), 14.86/2.45 inference('sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl72])). 14.86/2.45 thf(zip_derived_cl72, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 14.86/2.45 (~ (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) 14.86/2.45 | (in @ X8 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X8 @ X2))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 14.86/2.45 thf(zip_derived_cl70, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 ( (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) => 14.86/2.45 (((X4) = (X6))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 14.86/2.45 thf(zip_derived_cl76, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) 14.86/2.45 | (((X4) = (X6))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])). 14.86/2.45 thf(zip_derived_cl81, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X6)))) @ 14.86/2.45 ((('#C') @ in @ X4)))))))) 14.86/2.45 | ((X4) = (X6)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4))), 14.86/2.45 inference('simplify nested equalities', [status(thm)], [zip_derived_cl76])). 14.86/2.45 thf(zip_derived_cl82, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X2) => 14.86/2.45 (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) => (in @ 14.86/2.45 ('#sk4' @ X2 @ X6 @ X4) @ X4))))) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ((X4) = (X6)))), 14.86/2.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 14.86/2.45 thf(zip_derived_cl88, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (((in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) => (in @ 14.86/2.45 ('#sk4' @ X2 @ X6 @ X4) @ X4))) 14.86/2.45 | ((X4) = (X6)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 14.86/2.45 thf(zip_derived_cl92, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (in @ ('#sk4' @ X2 @ X6 @ X4) @ X4) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ((X4) = (X6)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])). 14.86/2.45 thf(zip_derived_cl24, plain, 14.86/2.45 (~ (((demorgan1b) => 14.86/2.45 (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 powerset)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#B') @ 14.86/2.45 setminus)))) @ 14.86/2.45 binintersect)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#B'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ binunion)) @ 14.86/2.45 setminus)))))) @ 14.86/2.45 setminus))))))))))))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 14.86/2.45 thf(zip_derived_cl31, plain, ( (demorgan1b)), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 14.86/2.45 thf(demorgan1b, axiom, (demorgan1b) => 14.86/2.45 ((((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y2 : $i]: 14.86/2.45 (((in @ Y2 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y3 : $i]: 14.86/2.45 (((in @ Y3 @ Y0) => 14.86/2.45 (((in @ Y3 @ 14.86/2.45 (binunion @ 14.86/2.45 (setminus @ Y0 @ 14.86/2.45 Y1) @ 14.86/2.45 (setminus @ Y0 @ 14.86/2.45 Y2))) => 14.86/2.45 (in @ Y3 @ 14.86/2.45 (setminus @ Y0 @ 14.86/2.45 (binintersect @ 14.86/2.45 Y1 @ Y2))))))))))))))))))))))) 14.86/2.45 = ($true))). 14.86/2.45 thf('2', plain, 14.86/2.45 (( demorgan1b ) <=> 14.86/2.45 ( ![X5:$i,X7:$i]: 14.86/2.45 ( ( in @ X7 @ ( powerset @ X5 ) ) => 14.86/2.45 ( ![X9:$i]: 14.86/2.45 ( ( in @ X9 @ ( powerset @ X5 ) ) => 14.86/2.45 ( ![X11:$i]: 14.86/2.45 ( ( in @ X11 @ X5 ) => 14.86/2.45 ( ( in @ 14.86/2.45 X11 @ 14.86/2.45 ( binunion @ 14.86/2.45 ( setminus @ X5 @ X7 ) @ ( setminus @ X5 @ X9 ) ) ) => 14.86/2.45 ( in @ 14.86/2.45 X11 @ ( setminus @ X5 @ ( binintersect @ X7 @ X9 ) ) ) ) ) ) ) ) ) )), 14.86/2.45 inference('rw.lit', [status(esa)], [demorgan1b])). 14.86/2.45 thf(zip_derived_cl39, plain, 14.86/2.45 ( (((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y2 : $i]: 14.86/2.45 (((in @ Y2 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y3 : $i]: 14.86/2.45 (((in @ Y3 @ Y0) => 14.86/2.45 (((in @ Y3 @ 14.86/2.45 (binunion @ 14.86/2.45 (setminus @ 14.86/2.45 Y0 @ Y1) @ 14.86/2.45 (setminus @ 14.86/2.45 Y0 @ Y2))) => 14.86/2.45 (in @ Y3 @ 14.86/2.45 (setminus @ 14.86/2.45 Y0 @ 14.86/2.45 (binintersect @ 14.86/2.45 Y1 @ Y2)))))))))))))))))))))))), 14.86/2.45 inference('rw_clause', [status(thm)], [zip_derived_cl31, '2'])). 14.86/2.45 thf(zip_derived_cl44, plain, 14.86/2.45 ( (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#C') @ in)))))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ ( 14.86/2.45 '#S'))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ ( 14.86/2.45 ( 14.86/2.45 ('#B') @ ( 14.86/2.45 =>))))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ( 14.86/2.45 (('#B') @ ( 14.86/2.45 (('#C') @ in)))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ( 14.86/2.45 '#C') @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 (('#B') @ ( 14.86/2.45 '#B'))) @ 14.86/2.45 ((('#B') @ ( 14.86/2.45 (('#B') @ binunion)) @ 14.86/2.45 setminus)))))) @ 14.86/2.45 setminus)))))))))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ ((('#C') @ in)))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#B') @ setminus)))) @ 14.86/2.45 binintersect))))))))))))))))))))), 14.86/2.45 inference('comb-normalize', [status(thm)], [zip_derived_cl39])). 14.86/2.45 thf(zip_derived_cl45, plain, 14.86/2.45 (![X2 : $i]: 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 14.86/2.45 =>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 X2)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ ( 14.86/2.45 =>))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ( 14.86/2.45 '#B') @ 14.86/2.45 ((('#B') @ binunion @ 14.86/2.45 (setminus @ X2))))) @ 14.86/2.45 (setminus @ X2))))))))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (setminus @ X2))) @ 14.86/2.45 binintersect))))))))))))))))))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl44])). 14.86/2.45 thf(zip_derived_cl49, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (((in @ X4 @ (powerset @ X2)) => 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ X2)))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 ((('#B') @ (binunion @ 14.86/2.45 (setminus @ X2 @ X4)) @ 14.86/2.45 (setminus @ X2))))))))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 ((('#B') @ (setminus @ X2) @ (binintersect @ X4)))))))))))))))))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl45])). 14.86/2.45 thf(zip_derived_cl54, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ X2)))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 ((('#B') @ (binunion @ 14.86/2.45 (setminus @ X2 @ X4)) @ 14.86/2.45 (setminus @ X2))))))))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ 14.86/2.45 ((('#B') @ (setminus @ X2) @ 14.86/2.45 (binintersect @ X4))))))))))))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 14.86/2.45 thf(zip_derived_cl58, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 ( (((in @ X6 @ (powerset @ X2)) => 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 (binunion @ (setminus @ X2 @ X4) @ 14.86/2.45 (setminus @ X2 @ X6)))))) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X4 @ X6)))))))))))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl54])). 14.86/2.45 thf(zip_derived_cl63, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 (binunion @ (setminus @ X2 @ X4) @ 14.86/2.45 (setminus @ X2 @ X6)))))) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X4 @ X6)))))))))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 14.86/2.45 thf(zip_derived_cl68, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 14.86/2.45 ( (((in @ X8 @ X2) => 14.86/2.45 (((in @ X8 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) => 14.86/2.45 (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))))))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 14.86/2.45 thf(zip_derived_cl73, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 14.86/2.45 (~ (in @ X8 @ X2) 14.86/2.45 | (((in @ X8 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) => 14.86/2.45 (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))))) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 14.86/2.45 thf(zip_derived_cl78, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 14.86/2.45 (~ (in @ X8 @ (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) 14.86/2.45 | (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X8 @ X2))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 14.86/2.45 thf(zip_derived_cl133, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 14.86/2.45 (((binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) = (X3)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 14.86/2.45 (powerset @ X4)) 14.86/2.45 | ~ (in @ X3 @ (powerset @ X4)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ X3 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 14.86/2.45 X1) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X1)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X4 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 14.86/2.45 (setminus @ X1 @ (binintersect @ X2 @ X0))))), 14.86/2.45 inference('sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl78])). 14.86/2.45 thf(zip_derived_cl419, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 14.86/2.45 (~ (in @ 14.86/2.45 ('#sk4' @ X4 @ X3 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 14.86/2.45 X1) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ X3 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 14.86/2.45 (setminus @ X1 @ (binintersect @ X2 @ X0))) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X4 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 14.86/2.45 (setminus @ X1 @ (binintersect @ X2 @ X0))) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 14.86/2.45 X1) 14.86/2.45 | ~ (in @ X3 @ (powerset @ X4)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 14.86/2.45 (powerset @ X4)) 14.86/2.45 | ((binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) = (X3)))), 14.86/2.45 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl133])). 14.86/2.45 thf(zip_derived_cl428, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 14.86/2.45 (((binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) = (X3)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 14.86/2.45 (powerset @ X4)) 14.86/2.45 | ~ (in @ X3 @ (powerset @ X4)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 14.86/2.45 X1) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X4 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 14.86/2.45 (setminus @ X1 @ (binintersect @ X2 @ X0))) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ X3 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 14.86/2.45 (setminus @ X1 @ (binintersect @ X2 @ X0))) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ X3 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 14.86/2.45 X1))), 14.86/2.45 inference('simplify', [status(thm)], [zip_derived_cl419])). 14.86/2.45 thf(zip_derived_cl1082, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 14.86/2.45 (~ (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 X2) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 14.86/2.45 = (setminus @ X2 @ (binintersect @ X1 @ X0))) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 X2) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X3 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 14.86/2.45 X2) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 14.86/2.45 = (setminus @ X2 @ (binintersect @ X1 @ X0))))), 14.86/2.45 inference('sup+', [status(thm)], [zip_derived_cl95, zip_derived_cl428])). 14.86/2.45 thf(zip_derived_cl1098, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 14.86/2.45 (~ (in @ 14.86/2.45 ('#sk4' @ X3 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 14.86/2.45 X2) 14.86/2.45 | ((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 14.86/2.45 = (setminus @ X2 @ (binintersect @ X1 @ X0))) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 X2) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))))), 14.86/2.45 inference('simplify', [status(thm)], [zip_derived_cl1082])). 14.86/2.45 thf(zip_derived_cl92, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (in @ ('#sk4' @ X2 @ X6 @ X4) @ X4) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ((X4) = (X6)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])). 14.86/2.45 thf(zip_derived_cl91, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 ( (in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X4) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ((X4) = (X6)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])). 14.86/2.45 thf(zip_derived_cl78, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 14.86/2.45 (~ (in @ X8 @ (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) 14.86/2.45 | (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X8 @ X2))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 14.86/2.45 thf(zip_derived_cl259, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 14.86/2.45 (((X3) = (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) 14.86/2.45 | ~ (in @ X3 @ (powerset @ X4)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 14.86/2.45 (powerset @ X4)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X4 @ X3 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 14.86/2.45 X3) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 14.86/2.45 X1) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X1)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X4 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 14.86/2.45 (setminus @ X1 @ (binintersect @ X2 @ X0))))), 14.86/2.45 inference('sup-', [status(thm)], [zip_derived_cl91, zip_derived_cl78])). 14.86/2.45 thf(zip_derived_cl1018, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 14.86/2.45 (((setminus @ X2 @ (binintersect @ X1 @ X0)) 14.86/2.45 = (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X3 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 14.86/2.45 X2) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ((setminus @ X2 @ (binintersect @ X1 @ X0)) 14.86/2.45 = (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))))), 14.86/2.45 inference('sup+', [status(thm)], [zip_derived_cl92, zip_derived_cl259])). 14.86/2.45 thf(zip_derived_cl1033, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 14.86/2.45 (~ (in @ 14.86/2.45 ('#sk4' @ X3 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 14.86/2.45 X2) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X2)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ((setminus @ X2 @ (binintersect @ X1 @ X0)) 14.86/2.45 = (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))))), 14.86/2.45 inference('simplify', [status(thm)], [zip_derived_cl1018])). 14.86/2.45 thf(zip_derived_cl1123, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 14.86/2.45 (~ (in @ X1 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 X2) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ((binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) 14.86/2.45 = (setminus @ X2 @ (binintersect @ X1 @ X0))) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X3 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 14.86/2.45 X2))), 14.86/2.45 inference('clc', [status(thm)], [zip_derived_cl1098, zip_derived_cl1033])). 14.86/2.45 thf(zip_derived_cl1132, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i]: 14.86/2.45 (((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 14.86/2.45 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 14.86/2.45 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X0 @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) @ 14.86/2.45 X0) 14.86/2.45 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 14.86/2.45 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X0 @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) @ 14.86/2.45 X0) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X0)))), 14.86/2.45 inference('sup-', [status(thm)], [zip_derived_cl493, zip_derived_cl1123])). 14.86/2.45 thf(zip_derived_cl1136, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i]: 14.86/2.45 (~ (in @ 14.86/2.45 ('#sk4' @ X0 @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) @ 14.86/2.45 X0) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 14.86/2.45 = (setminus @ X0 @ (binintersect @ X2 @ X1))))), 14.86/2.45 inference('simplify', [status(thm)], [zip_derived_cl1132])). 14.86/2.45 thf(zip_derived_cl79, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 ( (in @ ('#sk4' @ X2 @ X6 @ X4) @ X2) 14.86/2.45 | ((X4) = (X6)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 14.86/2.45 thf(zip_derived_cl86, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (in @ ('#sk4' @ X2 @ X6 @ X4) @ X4) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ((X4) = (X6)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 14.86/2.45 thf(zip_derived_cl85, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 ( (in @ ('#sk4' @ X2 @ X6 @ X4) @ X6) 14.86/2.45 | (in @ ('#sk4' @ X2 @ X4 @ X6) @ X2) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ((X4) = (X6)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 14.86/2.45 thf(zip_derived_cl78, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 14.86/2.45 (~ (in @ X8 @ (binunion @ (setminus @ X2 @ X4) @ (setminus @ X2 @ X6))) 14.86/2.45 | (in @ X8 @ (setminus @ X2 @ (binintersect @ X4 @ X6))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X8 @ X2))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 14.86/2.45 thf(zip_derived_cl211, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 14.86/2.45 (((X3) = (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ 14.86/2.45 (powerset @ X4)) 14.86/2.45 | ~ (in @ X3 @ (powerset @ X4)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X4 @ X3 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))) @ 14.86/2.45 X4) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X4 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 14.86/2.45 X1) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X1)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X1)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X4 @ 14.86/2.45 (binunion @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)) @ X3) @ 14.86/2.45 (setminus @ X1 @ (binintersect @ X2 @ X0))))), 14.86/2.45 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl78])). 14.86/2.45 thf(zip_derived_cl700, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 14.86/2.45 (((setminus @ X2 @ (binintersect @ X1 @ X0)) 14.86/2.45 = (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 X3) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ 14.86/2.45 ('#sk4' @ X3 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 14.86/2.45 X2) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 X3) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ((setminus @ X2 @ (binintersect @ X1 @ X0)) 14.86/2.45 = (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))))), 14.86/2.45 inference('sup+', [status(thm)], [zip_derived_cl86, zip_derived_cl211])). 14.86/2.45 thf(zip_derived_cl721, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 14.86/2.45 (~ (in @ 14.86/2.45 ('#sk4' @ X3 @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (setminus @ X2 @ (binintersect @ X1 @ X0))) @ 14.86/2.45 X2) 14.86/2.45 | ~ (in @ X0 @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X2)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X3 @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))) @ 14.86/2.45 X3) 14.86/2.45 | ~ (in @ (setminus @ X2 @ (binintersect @ X1 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0)) @ 14.86/2.45 (powerset @ X3)) 14.86/2.45 | ((setminus @ X2 @ (binintersect @ X1 @ X0)) 14.86/2.45 = (binunion @ (setminus @ X2 @ X1) @ (setminus @ X2 @ X0))))), 14.86/2.45 inference('simplify', [status(thm)], [zip_derived_cl700])). 14.86/2.45 thf(zip_derived_cl756, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i]: 14.86/2.45 (~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 14.86/2.45 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X0 @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) @ 14.86/2.45 X0) 14.86/2.45 | ((setminus @ X0 @ (binintersect @ X2 @ X1)) 14.86/2.45 = (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X0 @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) @ 14.86/2.45 X0) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X0)))), 14.86/2.45 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl721])). 14.86/2.45 thf(zip_derived_cl766, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i]: 14.86/2.45 (~ (in @ X1 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X0)) 14.86/2.45 | (in @ 14.86/2.45 ('#sk4' @ X0 @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) @ 14.86/2.45 X0) 14.86/2.45 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 14.86/2.45 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 14.86/2.45 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 14.86/2.45 (powerset @ X0)))), 14.86/2.45 inference('simplify', [status(thm)], [zip_derived_cl756])). 14.86/2.45 thf(zip_derived_cl1142, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i]: 14.86/2.45 (((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 14.86/2.45 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 14.86/2.45 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ~ (in @ (binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X0)))), 14.86/2.45 inference('clc', [status(thm)], [zip_derived_cl1136, zip_derived_cl766])). 14.86/2.45 thf(zip_derived_cl5, plain, ( (binunionT_lem)), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])). 14.86/2.45 thf(binunionT_lem, axiom, (binunionT_lem) => 14.86/2.45 ((((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y2 : $i]: 14.86/2.45 (((in @ Y2 @ (powerset @ Y0)) => 14.86/2.45 (in @ (binunion @ Y1 @ Y2) @ 14.86/2.45 (powerset @ Y0))))))))))))))) 14.86/2.45 = ($true))). 14.86/2.45 thf('3', plain, 14.86/2.45 (( binunionT_lem ) <=> 14.86/2.45 ( ![X5:$i,X7:$i]: 14.86/2.45 ( ( in @ X7 @ ( powerset @ X5 ) ) => 14.86/2.45 ( ![X9:$i]: 14.86/2.45 ( ( in @ X9 @ ( powerset @ X5 ) ) => 14.86/2.45 ( in @ ( binunion @ X7 @ X9 ) @ ( powerset @ X5 ) ) ) ) ) )), 14.86/2.45 inference('rw.lit', [status(esa)], [binunionT_lem])). 14.86/2.45 thf(zip_derived_cl9, plain, 14.86/2.45 ( (((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y2 : $i]: 14.86/2.45 (((in @ Y2 @ (powerset @ Y0)) => 14.86/2.45 (in @ (binunion @ Y1 @ Y2) @ 14.86/2.45 (powerset @ Y0)))))))))))))))), 14.86/2.45 inference('rw_clause', [status(thm)], [zip_derived_cl5, '3'])). 14.86/2.45 thf(zip_derived_cl13, plain, 14.86/2.45 ( (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 14.86/2.45 ((('#B') @ ((('#C') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ in)) @ 14.86/2.45 binunion)))))) @ 14.86/2.45 powerset))))))))))))), 14.86/2.45 inference('comb-normalize', [status(thm)], [zip_derived_cl9])). 14.86/2.45 thf(zip_derived_cl14, plain, 14.86/2.45 (![X2 : $i]: 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ in)) @ binunion)))) @ 14.86/2.45 (powerset @ X2)))))))))))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 14.86/2.45 thf(zip_derived_cl19, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (((in @ X4 @ (powerset @ X2)) => 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ in @ (binunion @ X4))) @ 14.86/2.45 (powerset @ X2)))))))))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 14.86/2.45 thf(zip_derived_cl26, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ in @ (binunion @ X4))) @ 14.86/2.45 (powerset @ X2))))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 14.86/2.45 thf(zip_derived_cl34, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 ( (((in @ X6 @ (powerset @ X2)) => (in @ (binunion @ X4 @ X6) @ 14.86/2.45 (powerset @ X2)))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 14.86/2.45 thf(zip_derived_cl41, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | (in @ (binunion @ X4 @ X6) @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 14.86/2.45 thf(zip_derived_cl1143, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i]: 14.86/2.45 (~ (in @ X1 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 14.86/2.45 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 14.86/2.45 | ~ (in @ (setminus @ X0 @ X2) @ (powerset @ X0)) 14.86/2.45 | ~ (in @ (setminus @ X0 @ X1) @ (powerset @ X0)))), 14.86/2.45 inference('sup+', [status(thm)], [zip_derived_cl1142, zip_derived_cl41])). 14.86/2.45 thf(zip_derived_cl10, plain, ( (complementT_lem)), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 14.86/2.45 thf(complementT_lem, axiom, (complementT_lem) => 14.86/2.45 ((((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => (in @ 14.86/2.45 (setminus @ Y0 @ Y1) @ (powerset @ Y0)))))))))) 14.86/2.45 = ($true))). 14.86/2.45 thf('4', plain, 14.86/2.45 (( complementT_lem ) <=> 14.86/2.45 ( ![X5:$i,X7:$i]: 14.86/2.45 ( ( in @ X7 @ ( powerset @ X5 ) ) => 14.86/2.45 ( in @ ( setminus @ X5 @ X7 ) @ ( powerset @ X5 ) ) ) )), 14.86/2.45 inference('rw.lit', [status(esa)], [complementT_lem])). 14.86/2.45 thf(zip_derived_cl15, plain, 14.86/2.45 ( (((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => (in @ 14.86/2.45 (setminus @ Y0 @ Y1) @ (powerset @ Y0))))))))))), 14.86/2.45 inference('rw_clause', [status(thm)], [zip_derived_cl10, '4'])). 14.86/2.45 thf(zip_derived_cl20, plain, 14.86/2.45 ( (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ in)) @ setminus)))) @ 14.86/2.45 powerset))))))))), 14.86/2.45 inference('comb-normalize', [status(thm)], [zip_derived_cl15])). 14.86/2.45 thf(zip_derived_cl21, plain, 14.86/2.45 (![X2 : $i]: 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ in @ (setminus @ X2))) @ 14.86/2.45 (powerset @ X2)))))))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 14.86/2.45 thf(zip_derived_cl27, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (((in @ X4 @ (powerset @ X2)) => (in @ (setminus @ X2 @ X4) @ 14.86/2.45 (powerset @ X2))))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 14.86/2.45 thf(zip_derived_cl35, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (in @ (setminus @ X2 @ X4) @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 14.86/2.45 thf(zip_derived_cl1145, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i]: 14.86/2.45 (~ (in @ (setminus @ X0 @ X1) @ (powerset @ X0)) 14.86/2.45 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 14.86/2.45 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 14.86/2.45 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X0)))), 14.86/2.45 inference('clc', [status(thm)], [zip_derived_cl1143, zip_derived_cl35])). 14.86/2.45 thf(zip_derived_cl35, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (in @ (setminus @ X2 @ X4) @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 14.86/2.45 thf(zip_derived_cl1146, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i]: 14.86/2.45 (~ (in @ X1 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ (setminus @ X0 @ (binintersect @ X2 @ X1)) @ 14.86/2.45 (powerset @ X0)) 14.86/2.45 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 14.86/2.45 = (setminus @ X0 @ (binintersect @ X2 @ X1))))), 14.86/2.45 inference('clc', [status(thm)], [zip_derived_cl1145, zip_derived_cl35])). 14.86/2.45 thf(zip_derived_cl35, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (in @ (setminus @ X2 @ X4) @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 14.86/2.45 thf(zip_derived_cl1147, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i]: 14.86/2.45 (((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 14.86/2.45 = (setminus @ X0 @ (binintersect @ X2 @ X1))) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ X1 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ (binintersect @ X2 @ X1) @ (powerset @ X0)))), 14.86/2.45 inference('sup+', [status(thm)], [zip_derived_cl1146, zip_derived_cl35])). 14.86/2.45 thf(zip_derived_cl2, plain, ( (binintersectT_lem)), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 14.86/2.45 thf(binintersectT_lem, axiom, (binintersectT_lem) => 14.86/2.45 ((((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y2 : $i]: 14.86/2.45 (((in @ Y2 @ (powerset @ Y0)) => 14.86/2.45 (in @ (binintersect @ Y1 @ Y2) @ 14.86/2.45 (powerset @ Y0))))))))))))))) 14.86/2.45 = ($true))). 14.86/2.45 thf('5', plain, 14.86/2.45 (( binintersectT_lem ) <=> 14.86/2.45 ( ![X5:$i,X7:$i]: 14.86/2.45 ( ( in @ X7 @ ( powerset @ X5 ) ) => 14.86/2.45 ( ![X9:$i]: 14.86/2.45 ( ( in @ X9 @ ( powerset @ X5 ) ) => 14.86/2.45 ( in @ ( binintersect @ X7 @ X9 ) @ ( powerset @ X5 ) ) ) ) ) )), 14.86/2.45 inference('rw.lit', [status(esa)], [binintersectT_lem])). 14.86/2.45 thf(zip_derived_cl4, plain, 14.86/2.45 ( (((!!) @ (^[Y0 : $i]: 14.86/2.45 (((!!) @ (^[Y1 : $i]: 14.86/2.45 (((in @ Y1 @ (powerset @ Y0)) => 14.86/2.45 (((!!) @ (^[Y2 : $i]: 14.86/2.45 (((in @ Y2 @ (powerset @ Y0)) => 14.86/2.45 (in @ 14.86/2.45 (binintersect @ Y1 @ Y2) @ 14.86/2.45 (powerset @ Y0)))))))))))))))), 14.86/2.45 inference('rw_clause', [status(thm)], [zip_derived_cl2, '5'])). 14.86/2.45 thf(zip_derived_cl7, plain, 14.86/2.45 ( (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 14.86/2.45 ((('#B') @ ((('#C') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ in)) @ 14.86/2.45 binintersect)))))) @ 14.86/2.45 powerset))))))))))))), 14.86/2.45 inference('comb-normalize', [status(thm)], [zip_derived_cl4])). 14.86/2.45 thf(zip_derived_cl8, plain, 14.86/2.45 (![X2 : $i]: 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ in)) @ binintersect)))) @ 14.86/2.45 (powerset @ X2)))))))))))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 14.86/2.45 thf(zip_derived_cl12, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (((in @ X4 @ (powerset @ X2)) => 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ in @ (binintersect @ X4))) @ 14.86/2.45 (powerset @ X2)))))))))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 14.86/2.45 thf(zip_derived_cl18, plain, 14.86/2.45 (![X2 : $i, X4 : $i]: 14.86/2.45 (~ (in @ X4 @ (powerset @ X2)) 14.86/2.45 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ X2))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ in @ (binintersect @ X4))) @ 14.86/2.45 (powerset @ X2))))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 14.86/2.45 thf(zip_derived_cl25, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 ( (((in @ X6 @ (powerset @ X2)) => (in @ (binintersect @ X4 @ X6) @ 14.86/2.45 (powerset @ X2)))) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 14.86/2.45 thf(zip_derived_cl33, plain, 14.86/2.45 (![X2 : $i, X4 : $i, X6 : $i]: 14.86/2.45 (~ (in @ X6 @ (powerset @ X2)) 14.86/2.45 | (in @ (binintersect @ X4 @ X6) @ (powerset @ X2)) 14.86/2.45 | ~ (in @ X4 @ (powerset @ X2)))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 14.86/2.45 thf(zip_derived_cl1149, plain, 14.86/2.45 (![X0 : $i, X1 : $i, X2 : $i]: 14.86/2.45 (~ (in @ X1 @ (powerset @ X0)) 14.86/2.45 | ~ (in @ X2 @ (powerset @ X0)) 14.86/2.45 | ((binunion @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) 14.86/2.45 = (setminus @ X0 @ (binintersect @ X2 @ X1))))), 14.86/2.45 inference('clc', [status(thm)], [zip_derived_cl1147, zip_derived_cl33])). 14.86/2.45 thf(zip_derived_cl32, plain, 14.86/2.45 (~ (((!!) @ ((('#B') @ (!!) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (!!))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=>))) @ 14.86/2.45 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#S'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ ('#B') @ 14.86/2.45 setminus)))) @ 14.86/2.45 binintersect)))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#C') @ 14.86/2.45 ((('#B') @ ((('#B') @ ('#B'))) @ 14.86/2.45 ((('#B') @ ((('#B') @ binunion)) @ 14.86/2.45 setminus)))))) @ 14.86/2.45 setminus))))))))))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 14.86/2.45 thf(zip_derived_cl40, plain, 14.86/2.45 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ '#sk1'))))) @ 14.86/2.45 ((('#B') @ (!!) @ 14.86/2.45 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ 14.86/2.45 (powerset @ '#sk1'))))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ ('#S') @ 14.86/2.45 ((('#B') @ ((('#B') @ (=))) @ 14.86/2.45 ((('#B') @ ((('#B') @ (setminus @ '#sk1'))) @ 14.86/2.45 binintersect)))))) @ 14.86/2.45 ((('#C') @ ((('#B') @ ('#B') @ 14.86/2.45 ((('#B') @ binunion @ 14.86/2.45 (setminus @ '#sk1'))))) @ 14.86/2.45 (setminus @ '#sk1')))))))))))))), 14.86/2.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 14.86/2.45 thf(zip_derived_cl46, plain, 14.86/2.45 (~ (((in @ '#sk2' @ (powerset @ '#sk1')) => 14.86/2.45 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ '#sk1'))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=) @ 14.86/2.45 ((('#B') @ (setminus @ '#sk1') @ 14.86/2.45 (binintersect @ '#sk2'))))) @ 14.86/2.45 ((('#B') @ (binunion @ (setminus @ '#sk1' @ '#sk2')) @ 14.86/2.45 (setminus @ '#sk1')))))))))))), 14.86/2.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl40])). 14.86/2.45 thf(zip_derived_cl51, plain, 14.86/2.45 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 14.86/2.45 ((('#C') @ in @ (powerset @ '#sk1'))))) @ 14.86/2.45 ((('#S') @ ((('#B') @ (=) @ 14.86/2.45 ((('#B') @ (setminus @ '#sk1') @ 14.86/2.45 (binintersect @ '#sk2'))))) @ 14.86/2.45 ((('#B') @ (binunion @ (setminus @ '#sk1' @ '#sk2')) @ 14.86/2.45 (setminus @ '#sk1')))))))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 14.86/2.45 thf(zip_derived_cl55, plain, 14.86/2.45 (~ (((in @ '#sk3' @ (powerset @ '#sk1')) => 14.86/2.45 (((setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3')) = 14.86/2.45 (binunion @ (setminus @ '#sk1' @ '#sk2') @ 14.86/2.45 (setminus @ '#sk1' @ '#sk3'))))))), 14.86/2.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl51])). 14.86/2.45 thf(zip_derived_cl60, plain, 14.86/2.45 (~ (((setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3')) = 14.86/2.45 (binunion @ (setminus @ '#sk1' @ '#sk2') @ 14.86/2.45 (setminus @ '#sk1' @ '#sk3'))))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 14.86/2.45 thf(zip_derived_cl64, plain, 14.86/2.45 (((setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3')) 14.86/2.45 != (binunion @ (setminus @ '#sk1' @ '#sk2') @ 14.86/2.45 (setminus @ '#sk1' @ '#sk3')))), 14.86/2.45 inference('simplify nested equalities', [status(thm)], [zip_derived_cl60])). 14.86/2.45 thf(zip_derived_cl1180, plain, 14.86/2.45 ((((setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3')) 14.86/2.45 != (setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3'))) 14.86/2.45 | ~ (in @ '#sk2' @ (powerset @ '#sk1')) 14.86/2.45 | ~ (in @ '#sk3' @ (powerset @ '#sk1')))), 14.86/2.45 inference('sup-', [status(thm)], [zip_derived_cl1149, zip_derived_cl64])). 14.86/2.45 thf(zip_derived_cl50, plain, ( (in @ '#sk2' @ (powerset @ '#sk1'))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 14.86/2.45 thf(zip_derived_cl59, plain, ( (in @ '#sk3' @ (powerset @ '#sk1'))), 14.86/2.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 14.86/2.45 thf(zip_derived_cl1210, plain, 14.86/2.45 (((setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3')) 14.86/2.45 != (setminus @ '#sk1' @ (binintersect @ '#sk2' @ '#sk3')))), 14.86/2.45 inference('demod', [status(thm)], 14.86/2.45 [zip_derived_cl1180, zip_derived_cl50, zip_derived_cl59])). 14.86/2.45 thf(zip_derived_cl1211, plain, ($false), 14.86/2.45 inference('simplify', [status(thm)], [zip_derived_cl1210])). 14.86/2.45 14.86/2.45 % SZS output end Refutation 14.86/2.45 14.86/2.45 14.86/2.45 % Terminating... 15.28/2.55 % Runner terminated. 15.29/2.57 % Zipperpin 1.5 exiting 15.29/2.57 EOF