0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.14/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Ii8AcXopX4 true 0.14/0.35 % Computer : n008.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1200 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Tue Jul 13 15:48:14 EDT 2021 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 120 s 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.58/0.68 % Total configuration time : 828 0.58/0.68 % Estimated wc time : 983 0.58/0.68 % Estimated cpu time (8 cpus) : 122.875 0.58/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.58/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.58/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.58/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.58/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.58/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 30.27/4.49 % Solved by lams/20_acsne_simpl.sh. 30.27/4.49 % running E: timeout 13 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.Ii8AcXopX4/e_input224e64 --cpu-limit=11 --auto -s -p 30.27/4.49 % done 370 iterations in 3.627s 30.27/4.49 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 30.27/4.49 % SZS output start Refutation 30.27/4.49 thf('#l_lift11586_type', type, '#l_lift11586': $i > $i > $o). 30.27/4.49 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 30.27/4.49 thf(func_type, type, func: $i > $i > $i > $o). 30.27/4.49 thf('#sk16_type', type, '#sk16': $i). 30.27/4.49 thf(ex1_type, type, ex1: $i > ($i > $o) > $o). 30.27/4.49 thf(singleton_type, type, singleton: $i > $o). 30.27/4.49 thf('#sk29_type', type, '#sk29': $i > ($i > $o) > $i > $i). 30.27/4.49 thf('#l_lift11587_type', type, '#l_lift11587': $i > $o). 30.27/4.49 thf('#sk60_type', type, '#sk60': $i). 30.27/4.49 thf(ex1I_type, type, ex1I: $o). 30.27/4.49 thf(emptyset_type, type, emptyset: $i). 30.27/4.49 thf(kpair_type, type, kpair: $i > $i > $i). 30.27/4.49 thf(breln_type, type, breln: $i > $i > $i > $o). 30.27/4.49 thf(cartprod_type, type, cartprod: $i > $i > $i). 30.27/4.49 thf('#sk25_type', type, '#sk25': $i > $i). 30.27/4.49 thf('#sk8_type', type, '#sk8': $i). 30.27/4.49 thf(subset_type, type, subset: $i > $i > $o). 30.27/4.49 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 30.27/4.49 thf('#sk50_type', type, '#sk50': $i > ($i > $o) > $i). 30.27/4.49 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o). 30.27/4.49 thf(dpsetconstrI_type, type, dpsetconstrI: $o). 30.27/4.49 thf(in_type, type, in: $i > $i > $o). 30.27/4.49 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o). 30.27/4.49 thf(dpsetconstr_type, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 30.27/4.49 thf(func, axiom,(( func ) = 30.27/4.49 (^[A:$i,B:$i,R:$i]: 30.27/4.49 ( ( breln @ A @ B @ R ) & 30.27/4.49 ( ![Xx:$i]: 30.27/4.49 ( ( in @ Xx @ A ) => 30.27/4.49 ( ex1 @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )))). 30.27/4.49 thf(breln, axiom,(( breln ) = 30.27/4.49 (^[A:$i,B:$i,C:$i]: ( subset @ C @ ( cartprod @ A @ B ) )))). 30.27/4.49 thf('0', plain, 30.27/4.49 (( breln ) = ( ^[A:$i,B:$i,C:$i]: ( subset @ C @ ( cartprod @ A @ B ) ) )), 30.27/4.49 inference('simplify_rw_rule', [status(thm)], [breln])). 30.27/4.49 thf('1', plain, 30.27/4.49 (( breln ) = 30.27/4.49 ( ^[V_1:$i,V_2:$i,V_3:$i]: ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) )), 30.27/4.49 define([status(thm)])). 30.27/4.49 thf(ex1, axiom,(( ex1 ) = 30.27/4.49 (^[A:$i,Xphi:( $i > $o )]: 30.27/4.49 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) )))). 30.27/4.49 thf(singleton, axiom,(( singleton ) = 30.27/4.49 (^[A:$i]: 30.27/4.49 ( ?[Xx:$i]: 30.27/4.49 ( ( ( A ) = ( setadjoin @ Xx @ emptyset ) ) & ( in @ Xx @ A ) ) )))). 30.27/4.49 thf('2', plain, 30.27/4.49 (( singleton ) = 30.27/4.49 ( ^[A:$i]: 30.27/4.49 ( ?[Xx:$i]: 30.27/4.49 ( ( ( A ) = ( setadjoin @ Xx @ emptyset ) ) & ( in @ Xx @ A ) ) ) )), 30.27/4.49 inference('simplify_rw_rule', [status(thm)], [singleton])). 30.27/4.49 thf('3', plain, 30.27/4.49 (( singleton ) = 30.27/4.49 ( ^[V_1:$i]: 30.27/4.49 ( ?[X4:$i]: 30.27/4.49 ( ( ( V_1 ) = ( setadjoin @ X4 @ emptyset ) ) & ( in @ X4 @ V_1 ) ) ) )), 30.27/4.49 define([status(thm)])). 30.27/4.49 thf('4', plain, 30.27/4.49 (( ex1 ) = 30.27/4.49 ( ^[A:$i,Xphi:( $i > $o )]: 30.27/4.49 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) )), 30.27/4.49 inference('simplify_rw_rule', [status(thm)], [ex1, '3'])). 30.27/4.49 thf('5', plain, 30.27/4.49 (( ex1 ) = 30.27/4.49 ( ^[V_1:$i,V_2:( $i > $o )]: 30.27/4.49 ( singleton @ ( dsetconstr @ V_1 @ ( ^[V_3:$i]: ( V_2 @ V_3 ) ) ) ) )), 30.27/4.49 define([status(thm)])). 30.27/4.49 thf('6', plain, 30.27/4.49 (( func ) = 30.27/4.49 ( ^[A:$i,B:$i,R:$i]: 30.27/4.49 ( ( breln @ A @ B @ R ) & 30.27/4.49 ( ![Xx:$i]: 30.27/4.49 ( ( in @ Xx @ A ) => 30.27/4.49 ( ex1 @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) )), 30.27/4.49 inference('simplify_rw_rule', [status(thm)], [func, '1', '5', '3'])). 30.27/4.49 thf('7', plain, 30.27/4.49 (( func ) = 30.27/4.49 ( ^[V_1:$i,V_2:$i,V_3:$i]: 30.27/4.49 ( ( breln @ V_1 @ V_2 @ V_3 ) & 30.27/4.49 ( ![X4:$i]: 30.27/4.49 ( ( in @ X4 @ V_1 ) => 30.27/4.49 ( ex1 @ V_2 @ ( ^[V_4:$i]: ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ) )), 30.27/4.49 define([status(thm)])). 30.27/4.49 thf(dpsetconstrERa, axiom, dpsetconstrERa = 30.27/4.49 (![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i]: 30.27/4.49 ( ( in @ Xx @ A ) => 30.27/4.49 ( ![Xy:$i]: 30.27/4.49 ( ( in @ Xy @ B ) => 30.27/4.49 ( ( in @ 30.27/4.49 ( kpair @ Xx @ Xy ) @ 30.27/4.49 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) => 30.27/4.49 ( Xphi @ Xx @ Xy ) ) ) ) ))). 30.27/4.49 thf('8', plain, 30.27/4.49 (( dpsetconstrERa ) = 30.27/4.49 ( ![X4:$i,X6:$i,X8:( $i > $i > $o ),X10:$i]: 30.27/4.49 ( ( in @ X10 @ X4 ) => 30.27/4.49 ( ![X12:$i]: 30.27/4.49 ( ( in @ X12 @ X6 ) => 30.27/4.49 ( ( in @ 30.27/4.49 ( kpair @ X10 @ X12 ) @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) => 30.27/4.49 ( X8 @ X10 @ X12 ) ) ) ) ) )), 30.27/4.49 define([status(thm)])). 30.27/4.49 thf(setOfPairsIsBReln, axiom, setOfPairsIsBReln = 30.27/4.49 (![A:$i,B:$i,Xphi:( $i > $i > $o )]: 30.27/4.49 ( breln @ 30.27/4.49 A @ B @ ( dpsetconstr @ A @ B @ ( ^[Xx:$i,Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ))). 30.27/4.49 thf('9', plain, 30.27/4.49 (( setOfPairsIsBReln ) = 30.27/4.49 ( ![X4:$i,X6:$i,X8:( $i > $i > $o )]: 30.27/4.49 ( breln @ 30.27/4.49 X4 @ X6 @ 30.27/4.49 ( dpsetconstr @ X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) )), 30.27/4.49 define([status(thm)])). 30.27/4.49 thf(dpsetconstrI, axiom, dpsetconstrI = 30.27/4.49 (![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i]: 30.27/4.49 ( ( in @ Xx @ A ) => 30.27/4.49 ( ![Xy:$i]: 30.27/4.49 ( ( in @ Xy @ B ) => 30.27/4.49 ( ( Xphi @ Xx @ Xy ) => 30.27/4.49 ( in @ 30.27/4.49 ( kpair @ Xx @ Xy ) @ 30.27/4.49 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ))). 30.27/4.49 thf('10', plain, 30.27/4.49 (( dpsetconstrI ) = 30.27/4.49 ( ![X4:$i,X6:$i,X8:( $i > $i > $o ),X10:$i]: 30.27/4.49 ( ( in @ X10 @ X4 ) => 30.27/4.49 ( ![X12:$i]: 30.27/4.49 ( ( in @ X12 @ X6 ) => 30.27/4.49 ( ( X8 @ X10 @ X12 ) => 30.27/4.49 ( in @ 30.27/4.49 ( kpair @ X10 @ X12 ) @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) ) ) ) ) )), 30.27/4.49 define([status(thm)])). 30.27/4.49 thf(ex1I, axiom, ex1I = 30.27/4.49 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 30.27/4.49 ( ( in @ Xx @ A ) => 30.27/4.49 ( ( Xphi @ Xx ) => 30.27/4.49 ( ( ![Xy:$i]: 30.27/4.49 ( ( in @ Xy @ A ) => ( ( Xphi @ Xy ) => ( ( Xy ) = ( Xx ) ) ) ) ) => 30.27/4.49 ( ex1 @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))). 30.27/4.49 thf('11', plain, 30.27/4.49 (( ex1I ) = 30.27/4.49 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 30.27/4.49 ( ( in @ X8 @ X4 ) => 30.27/4.49 ( ( X6 @ X8 ) => 30.27/4.49 ( ( ![X10:$i]: 30.27/4.49 ( ( in @ X10 @ X4 ) => 30.27/4.49 ( ( X6 @ X10 ) => ( ( X10 ) = ( X8 ) ) ) ) ) => 30.27/4.49 ( ex1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )), 30.27/4.49 define([status(thm)])). 30.27/4.49 thf(lamProp, conjecture, 30.27/4.49 (( ex1I ) => 30.27/4.49 ( ( dpsetconstrI ) => 30.27/4.49 ( ( setOfPairsIsBReln ) => 30.27/4.49 ( ( dpsetconstrERa ) => 30.27/4.49 ( ![A:$i,B:$i,Xf:( $i > $i )]: 30.27/4.49 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) => 30.27/4.49 ( func @ 30.27/4.49 A @ B @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 A @ B @ ( ^[Xx:$i,Xy:$i]: ( ( Xf @ Xx ) = ( Xy ) ) ) ) ) ) ) ) ) ))). 30.27/4.49 thf(zf_stmt_0, conjecture, 30.27/4.49 (( ![X4:$i,X6:( $i > $o ),X8:$i]: 30.27/4.49 ( ( in @ X8 @ X4 ) => 30.27/4.49 ( ( X6 @ X8 ) => 30.27/4.49 ( ( ![X10:$i]: 30.27/4.49 ( ( in @ X10 @ X4 ) => ( ( X6 @ X10 ) => ( ( X10 ) = ( X8 ) ) ) ) ) => 30.27/4.49 ( ?[X12:$i]: 30.27/4.49 ( ( in @ X12 @ ( dsetconstr @ X4 @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) ) & 30.27/4.49 ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = 30.27/4.49 ( setadjoin @ X12 @ emptyset ) ) ) ) ) ) ) ) => 30.27/4.49 ( ( ![X14:$i,X16:$i,X18:( $i > $i > $o ),X20:$i]: 30.27/4.49 ( ( in @ X20 @ X14 ) => 30.27/4.49 ( ![X22:$i]: 30.27/4.49 ( ( in @ X22 @ X16 ) => 30.27/4.49 ( ( X18 @ X20 @ X22 ) => 30.27/4.49 ( in @ 30.27/4.49 ( kpair @ X20 @ X22 ) @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X14 @ X16 @ ( ^[V_3:$i,V_4:$i]: ( X18 @ V_3 @ V_4 ) ) ) ) ) ) ) ) ) => 30.27/4.49 ( ( ![X24:$i,X26:$i,X28:( $i > $i > $o )]: 30.27/4.49 ( subset @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X24 @ X26 @ ( ^[V_5:$i,V_6:$i]: ( X28 @ V_5 @ V_6 ) ) ) @ 30.27/4.49 ( cartprod @ X24 @ X26 ) ) ) => 30.27/4.49 ( ( ![X30:$i,X32:$i,X34:( $i > $i > $o ),X36:$i]: 30.27/4.49 ( ( in @ X36 @ X30 ) => 30.27/4.49 ( ![X38:$i]: 30.27/4.49 ( ( in @ X38 @ X32 ) => 30.27/4.49 ( ( in @ 30.27/4.49 ( kpair @ X36 @ X38 ) @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X30 @ X32 @ ( ^[V_7:$i,V_8:$i]: ( X34 @ V_7 @ V_8 ) ) ) ) => 30.27/4.49 ( X34 @ X36 @ X38 ) ) ) ) ) ) => 30.27/4.49 ( ![X40:$i,X42:$i,X44:( $i > $i )]: 30.27/4.49 ( ( ![X46:$i]: 30.27/4.49 ( ( in @ X46 @ X40 ) => ( in @ ( X44 @ X46 ) @ X42 ) ) ) => 30.27/4.49 ( ( ![X48:$i]: 30.27/4.49 ( ( in @ X48 @ X40 ) => 30.27/4.49 ( ?[X50:$i]: 30.27/4.49 ( ( in @ 30.27/4.49 X50 @ 30.27/4.49 ( dsetconstr @ 30.27/4.49 X42 @ 30.27/4.49 ( ^[V_14:$i]: 30.27/4.49 ( in @ 30.27/4.49 ( kpair @ X48 @ V_14 ) @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X40 @ X42 @ 30.27/4.49 ( ^[V_15:$i,V_16:$i]: 30.27/4.49 ( ( X44 @ V_15 ) = ( V_16 ) ) ) ) ) ) ) ) & 30.27/4.49 ( ( dsetconstr @ 30.27/4.49 X42 @ 30.27/4.49 ( ^[V_11:$i]: 30.27/4.49 ( in @ 30.27/4.49 ( kpair @ X48 @ V_11 ) @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X40 @ X42 @ 30.27/4.49 ( ^[V_12:$i,V_13:$i]: 30.27/4.49 ( ( X44 @ V_12 ) = ( V_13 ) ) ) ) ) ) ) = 30.27/4.49 ( setadjoin @ X50 @ emptyset ) ) ) ) ) ) & 30.27/4.49 ( subset @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X40 @ X42 @ 30.27/4.49 ( ^[V_9:$i,V_10:$i]: ( ( X44 @ V_9 ) = ( V_10 ) ) ) ) @ 30.27/4.49 ( cartprod @ X40 @ X42 ) ) ) ) ) ) ) ))). 30.27/4.49 thf(zf_stmt_1, negated_conjecture, 30.27/4.49 (~( ( ![X4:$i,X6:( $i > $o ),X8:$i]: 30.27/4.49 ( ( in @ X8 @ X4 ) => 30.27/4.49 ( ( X6 @ X8 ) => 30.27/4.49 ( ( ![X10:$i]: 30.27/4.49 ( ( in @ X10 @ X4 ) => 30.27/4.49 ( ( X6 @ X10 ) => ( ( X10 ) = ( X8 ) ) ) ) ) => 30.27/4.49 ( ?[X12:$i]: 30.27/4.49 ( ( in @ 30.27/4.49 X12 @ ( dsetconstr @ X4 @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) ) & 30.27/4.49 ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = 30.27/4.49 ( setadjoin @ X12 @ emptyset ) ) ) ) ) ) ) ) => 30.27/4.49 ( ( ![X14:$i,X16:$i,X18:( $i > $i > $o ),X20:$i]: 30.27/4.49 ( ( in @ X20 @ X14 ) => 30.27/4.49 ( ![X22:$i]: 30.27/4.49 ( ( in @ X22 @ X16 ) => 30.27/4.49 ( ( X18 @ X20 @ X22 ) => 30.27/4.49 ( in @ 30.27/4.49 ( kpair @ X20 @ X22 ) @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X14 @ X16 @ ( ^[V_3:$i,V_4:$i]: ( X18 @ V_3 @ V_4 ) ) ) ) ) ) ) ) ) => 30.27/4.49 ( ( ![X24:$i,X26:$i,X28:( $i > $i > $o )]: 30.27/4.49 ( subset @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X24 @ X26 @ ( ^[V_5:$i,V_6:$i]: ( X28 @ V_5 @ V_6 ) ) ) @ 30.27/4.49 ( cartprod @ X24 @ X26 ) ) ) => 30.27/4.49 ( ( ![X30:$i,X32:$i,X34:( $i > $i > $o ),X36:$i]: 30.27/4.49 ( ( in @ X36 @ X30 ) => 30.27/4.49 ( ![X38:$i]: 30.27/4.49 ( ( in @ X38 @ X32 ) => 30.27/4.49 ( ( in @ 30.27/4.49 ( kpair @ X36 @ X38 ) @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X30 @ X32 @ 30.27/4.49 ( ^[V_7:$i,V_8:$i]: ( X34 @ V_7 @ V_8 ) ) ) ) => 30.27/4.49 ( X34 @ X36 @ X38 ) ) ) ) ) ) => 30.27/4.49 ( ![X40:$i,X42:$i,X44:( $i > $i )]: 30.27/4.49 ( ( ![X46:$i]: 30.27/4.49 ( ( in @ X46 @ X40 ) => ( in @ ( X44 @ X46 ) @ X42 ) ) ) => 30.27/4.49 ( ( ![X48:$i]: 30.27/4.49 ( ( in @ X48 @ X40 ) => 30.27/4.49 ( ?[X50:$i]: 30.27/4.49 ( ( in @ 30.27/4.49 X50 @ 30.27/4.49 ( dsetconstr @ 30.27/4.49 X42 @ 30.27/4.49 ( ^[V_14:$i]: 30.27/4.49 ( in @ 30.27/4.49 ( kpair @ X48 @ V_14 ) @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X40 @ X42 @ 30.27/4.49 ( ^[V_15:$i,V_16:$i]: 30.27/4.49 ( ( X44 @ V_15 ) = ( V_16 ) ) ) ) ) ) ) ) & 30.27/4.49 ( ( dsetconstr @ 30.27/4.49 X42 @ 30.27/4.49 ( ^[V_11:$i]: 30.27/4.49 ( in @ 30.27/4.49 ( kpair @ X48 @ V_11 ) @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X40 @ X42 @ 30.27/4.49 ( ^[V_12:$i,V_13:$i]: 30.27/4.49 ( ( X44 @ V_12 ) = ( V_13 ) ) ) ) ) ) ) = 30.27/4.49 ( setadjoin @ X50 @ emptyset ) ) ) ) ) ) & 30.27/4.49 ( subset @ 30.27/4.49 ( dpsetconstr @ 30.27/4.49 X40 @ X42 @ 30.27/4.49 ( ^[V_9:$i,V_10:$i]: ( ( X44 @ V_9 ) = ( V_10 ) ) ) ) @ 30.27/4.49 ( cartprod @ X40 @ X42 ) ) ) ) ) ) ) ) )), 30.27/4.49 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 30.27/4.49 thf(zip_derived_cl0, plain, 30.27/4.49 (~ (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i > $o]: 30.27/4.49 (((!!) @ (^[Y2 : $i]: 30.27/4.49 (((in @ Y2 @ Y0) => 30.27/4.49 (((Y1 @ Y2) => 30.27/4.49 (((((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (((Y1 @ 30.27/4.49 Y3) => 30.27/4.49 (( 30.27/4.49 (Y3) = 30.27/4.49 (Y2)))))))))) => 30.27/4.49 (((??) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 (dsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 (^[Y4 : $i]: 30.27/4.49 (Y1 @ Y4)))) & 30.27/4.49 (((dsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 (^[Y4 : $i]: 30.27/4.49 (Y1 @ Y4))) = 30.27/4.49 (setadjoin @ 30.27/4.49 Y3 @ 30.27/4.49 emptyset))))))))))))))))))))))) => 30.27/4.49 (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.49 (((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (((!!) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (((in @ 30.27/4.49 Y4 @ 30.27/4.49 Y1) => 30.27/4.49 (( 30.27/4.49 (Y2 @ 30.27/4.49 Y3 @ 30.27/4.49 Y4) => 30.27/4.49 (in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y4) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 ( 30.27/4.49 ^[Y5 : $i, 30.27/4.49 Y6 : $i]: 30.27/4.49 (Y2 @ 30.27/4.49 Y5 @ Y6))))))))))))))))))))))))) => 30.27/4.49 (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.49 (subset @ 30.27/4.49 (dpsetconstr @ Y0 @ Y1 @ 30.27/4.49 (^[Y3 : $i,Y4 : $i]: 30.27/4.49 (Y2 @ Y3 @ Y4))) @ 30.27/4.49 (cartprod @ Y0 @ Y1))))))))))) => 30.27/4.49 (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.49 (((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (((!!) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 Y4 @ 30.27/4.49 Y1) => 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 ( 30.27/4.49 kpair @ 30.27/4.49 Y3 @ Y4) @ 30.27/4.49 ( 30.27/4.49 dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 ( 30.27/4.49 ^[Y5 : $i, 30.27/4.49 Y6 : $i]: 30.27/4.49 (Y2 @ 30.27/4.49 Y5 @ Y6)))) => 30.27/4.49 (Y2 @ 30.27/4.49 Y3 @ Y4)))))))))))))))))))))) => 30.27/4.49 (((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i]: 30.27/4.49 (((((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ 30.27/4.49 Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (in @ 30.27/4.49 (Y2 @ Y3) @ 30.27/4.49 Y1)))))) => 30.27/4.49 (((((!!) @ (^[Y3 : $i]: 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (( 30.27/4.49 (??) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 Y4 @ 30.27/4.49 ( 30.27/4.49 dsetconstr @ 30.27/4.49 Y1 @ 30.27/4.49 ( 30.27/4.49 ^[Y5 : $i]: 30.27/4.49 (in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y5) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 (^[Y6 : $i, 30.27/4.49 Y7 : $i]: 30.27/4.49 (( 30.27/4.49 (Y2 @ 30.27/4.49 Y6) = 30.27/4.49 (Y7))))))))) & 30.27/4.49 (( 30.27/4.49 (dsetconstr @ 30.27/4.49 Y1 @ 30.27/4.49 ( 30.27/4.49 ^[Y5 : $i]: 30.27/4.49 (in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y5) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 (^[Y6 : $i, 30.27/4.49 Y7 : $i]: 30.27/4.49 (( 30.27/4.49 (Y2 @ 30.27/4.49 Y6) = 30.27/4.49 (Y7)))))))) = 30.27/4.49 (setadjoin @ 30.27/4.49 Y4 @ 30.27/4.49 emptyset))))))))))))) & 30.27/4.49 (subset @ 30.27/4.49 (dpsetconstr @ Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 (^[Y3 : $i,Y4 : $i]: 30.27/4.49 (((Y2 @ Y3) = (Y4))))) @ 30.27/4.49 (cartprod @ Y0 @ Y1)))))))))))))))))))))))), 30.27/4.49 inference('cnf', [status(esa)], [zf_stmt_1])). 30.27/4.49 thf(zip_derived_cl1, plain, 30.27/4.49 (~ (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i > $o]: 30.27/4.49 (((!!) @ (^[Y2 : $i]: 30.27/4.49 (((in @ Y2 @ Y0) => 30.27/4.49 (((Y1 @ Y2) => 30.27/4.49 (((((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (((Y1 @ 30.27/4.49 Y3) => 30.27/4.49 (( 30.27/4.49 (Y3) = 30.27/4.49 (Y2)))))))))) => 30.27/4.49 (((??) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 (dsetconstr @ 30.27/4.49 Y0 @ Y1)) & 30.27/4.49 (((dsetconstr @ 30.27/4.49 Y0 @ Y1) = 30.27/4.49 (setadjoin @ 30.27/4.49 Y3 @ 30.27/4.49 emptyset))))))))))))))))))))))) => 30.27/4.49 (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.49 (((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (((!!) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (((in @ 30.27/4.49 Y4 @ 30.27/4.49 Y1) => 30.27/4.49 (( 30.27/4.49 (Y2 @ 30.27/4.49 Y3 @ 30.27/4.49 Y4) => 30.27/4.49 (in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y4) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ Y2))))))))))))))))))))))) => 30.27/4.49 (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.49 (subset @ 30.27/4.49 (dpsetconstr @ Y0 @ Y1 @ Y2) @ 30.27/4.49 (cartprod @ Y0 @ Y1))))))))))) => 30.27/4.49 (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.49 (((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (((!!) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 Y4 @ 30.27/4.49 Y1) => 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 ( 30.27/4.49 kpair @ 30.27/4.49 Y3 @ Y4) @ 30.27/4.49 ( 30.27/4.49 dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ Y2)) => 30.27/4.49 (Y2 @ 30.27/4.49 Y3 @ Y4)))))))))))))))))))))) => 30.27/4.49 (((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i]: 30.27/4.49 (((((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ 30.27/4.49 Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (in @ 30.27/4.49 (Y2 @ Y3) @ 30.27/4.49 Y1)))))) => 30.27/4.49 (((((!!) @ (^[Y3 : $i]: 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (( 30.27/4.49 (??) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 Y4 @ 30.27/4.49 ( 30.27/4.49 dsetconstr @ 30.27/4.49 Y1 @ 30.27/4.49 ( 30.27/4.49 ^[Y5 : $i]: 30.27/4.49 (in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y5) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 (^[Y6 : $i]: 30.27/4.49 (( 30.27/4.49 ($i) = 30.27/4.49 (Y2 @ Y6))))))))) & 30.27/4.49 (( 30.27/4.49 (dsetconstr @ 30.27/4.49 Y1 @ 30.27/4.49 ( 30.27/4.49 ^[Y5 : $i]: 30.27/4.49 (in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y5) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 (^[Y6 : $i]: 30.27/4.49 (( 30.27/4.49 ($i) = 30.27/4.49 (Y2 @ Y6)))))))) = 30.27/4.49 (setadjoin @ 30.27/4.49 Y4 @ 30.27/4.49 emptyset))))))))))))) & 30.27/4.49 (subset @ 30.27/4.49 (dpsetconstr @ Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 (^[Y3 : $i]: 30.27/4.49 ((($i) = (Y2 @ Y3))))) @ 30.27/4.49 (cartprod @ Y0 @ Y1)))))))))))))))))))))))), 30.27/4.49 inference('ho_norm', [status(thm)], [zip_derived_cl0])). 30.27/4.49 thf(zip_derived_cl3, plain, 30.27/4.49 (~ (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.49 (((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ Y0) => 30.27/4.49 (((!!) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (((in @ Y4 @ 30.27/4.49 Y1) => 30.27/4.49 (((Y2 @ 30.27/4.49 Y3 @ 30.27/4.49 Y4) => 30.27/4.49 (in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y4) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ Y2))))))))))))))))))))))) => 30.27/4.49 (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.49 (subset @ 30.27/4.49 (dpsetconstr @ Y0 @ Y1 @ Y2) @ 30.27/4.49 (cartprod @ Y0 @ Y1))))))))))) => 30.27/4.49 (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.49 (((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (((!!) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 Y4 @ 30.27/4.49 Y1) => 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 ( 30.27/4.49 kpair @ 30.27/4.49 Y3 @ Y4) @ 30.27/4.49 ( 30.27/4.49 dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ Y2)) => 30.27/4.49 (Y2 @ 30.27/4.49 Y3 @ Y4)))))))))))))))))))))) => 30.27/4.49 (((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i]: 30.27/4.49 (((((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (in @ 30.27/4.49 (Y2 @ Y3) @ 30.27/4.49 Y1)))))) => 30.27/4.49 (((((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ 30.27/4.49 Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (( 30.27/4.49 (??) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 Y4 @ 30.27/4.49 ( 30.27/4.49 dsetconstr @ 30.27/4.49 Y1 @ 30.27/4.49 ( 30.27/4.49 ^[Y5 : $i]: 30.27/4.49 (in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y5) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 (^[Y6 : $i]: 30.27/4.49 (( 30.27/4.49 ($i) = 30.27/4.49 (Y2 @ Y6))))))))) & 30.27/4.49 (( 30.27/4.49 (dsetconstr @ 30.27/4.49 Y1 @ 30.27/4.49 ( 30.27/4.49 ^[Y5 : $i]: 30.27/4.49 (in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y5) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 (^[Y6 : $i]: 30.27/4.49 (( 30.27/4.49 ($i) = 30.27/4.49 (Y2 @ Y6)))))))) = 30.27/4.49 (setadjoin @ 30.27/4.49 Y4 @ 30.27/4.49 emptyset))))))))))))) & 30.27/4.49 (subset @ 30.27/4.49 (dpsetconstr @ Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 (^[Y3 : $i]: 30.27/4.49 ((($i) = (Y2 @ Y3))))) @ 30.27/4.49 (cartprod @ Y0 @ Y1)))))))))))))))))))))), 30.27/4.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 30.27/4.49 thf(zip_derived_cl6, plain, 30.27/4.49 (~ (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.49 (subset @ 30.27/4.49 (dpsetconstr @ Y0 @ Y1 @ Y2) @ 30.27/4.49 (cartprod @ Y0 @ Y1))))))))))) => 30.27/4.49 (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.49 (((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (((!!) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (((in @ 30.27/4.49 Y4 @ 30.27/4.49 Y1) => 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y4) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ Y2)) => 30.27/4.49 (Y2 @ 30.27/4.49 Y3 @ Y4)))))))))))))))))))))) => 30.27/4.49 (((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i]: 30.27/4.49 (((((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => (in @ 30.27/4.49 (Y2 @ Y3) @ 30.27/4.49 Y1)))))) => 30.27/4.49 (((((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (((??) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 Y4 @ 30.27/4.49 ( 30.27/4.49 dsetconstr @ 30.27/4.49 Y1 @ 30.27/4.49 ( 30.27/4.49 ^[Y5 : $i]: 30.27/4.49 (in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y5) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 (^[Y6 : $i]: 30.27/4.49 (( 30.27/4.49 ($i) = 30.27/4.49 (Y2 @ Y6))))))))) & 30.27/4.49 (( 30.27/4.49 (dsetconstr @ 30.27/4.49 Y1 @ 30.27/4.49 ( 30.27/4.49 ^[Y5 : $i]: 30.27/4.49 (in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y5) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ 30.27/4.49 (^[Y6 : $i]: 30.27/4.49 (( 30.27/4.49 ($i) = 30.27/4.49 (Y2 @ Y6)))))))) = 30.27/4.49 (setadjoin @ 30.27/4.49 Y4 @ 30.27/4.49 emptyset))))))))))))) & 30.27/4.49 (subset @ 30.27/4.49 (dpsetconstr @ Y0 @ Y1 @ 30.27/4.49 (^[Y3 : $i]: 30.27/4.49 ((($i) = (Y2 @ Y3))))) @ 30.27/4.49 (cartprod @ Y0 @ Y1)))))))))))))))))))), 30.27/4.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])). 30.27/4.49 thf(zip_derived_cl10, plain, 30.27/4.49 (~ (((((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.49 (((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ Y0) => 30.27/4.49 (((!!) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (((in @ Y4 @ 30.27/4.49 Y1) => 30.27/4.49 (((in @ 30.27/4.49 (kpair @ 30.27/4.49 Y3 @ Y4) @ 30.27/4.49 (dpsetconstr @ 30.27/4.49 Y0 @ 30.27/4.49 Y1 @ Y2)) => 30.27/4.49 (Y2 @ 30.27/4.49 Y3 @ Y4)))))))))))))))))))))) => 30.27/4.49 (((!!) @ (^[Y0 : $i]: 30.27/4.49 (((!!) @ (^[Y1 : $i]: 30.27/4.49 (((!!) @ (^[Y2 : $i > $i]: 30.27/4.49 (((((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => (in @ 30.27/4.49 (Y2 @ Y3) @ Y1)))))) => 30.27/4.49 (((((!!) @ (^[Y3 : $i]: 30.27/4.49 (((in @ Y3 @ 30.27/4.49 Y0) => 30.27/4.49 (((??) @ ( 30.27/4.49 ^[Y4 : $i]: 30.27/4.49 (( 30.27/4.49 (in @ 30.27/4.49 Y4 @ 30.27/4.49 ( 30.27/4.49 dsetconstr @ 30.27/4.49 Y1 @ 30.27/4.49 ( 30.27/4.49 ^[Y5 : $i]: 30.27/4.50 (in @ 30.27/4.50 (kpair @ 30.27/4.50 Y3 @ Y5) @ 30.27/4.50 (dpsetconstr @ 30.27/4.50 Y0 @ 30.27/4.50 Y1 @ 30.27/4.50 (^[Y6 : $i]: 30.27/4.50 (( 30.27/4.50 ($i) = 30.27/4.50 (Y2 @ Y6))))))))) & 30.27/4.50 (( 30.27/4.50 (dsetconstr @ 30.27/4.50 Y1 @ 30.27/4.50 ( 30.27/4.50 ^[Y5 : $i]: 30.27/4.50 (in @ 30.27/4.50 (kpair @ 30.27/4.50 Y3 @ Y5) @ 30.27/4.50 (dpsetconstr @ 30.27/4.50 Y0 @ 30.27/4.50 Y1 @ 30.27/4.50 (^[Y6 : $i]: 30.27/4.50 (( 30.27/4.50 ($i) = 30.27/4.50 (Y2 @ Y6)))))))) = 30.27/4.50 (setadjoin @ 30.27/4.50 Y4 @ 30.27/4.50 emptyset))))))))))))) & 30.27/4.50 (subset @ 30.27/4.50 (dpsetconstr @ Y0 @ Y1 @ 30.27/4.50 (^[Y3 : $i]: 30.27/4.50 ((($i) = (Y2 @ Y3))))) @ 30.27/4.50 (cartprod @ Y0 @ Y1)))))))))))))))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 30.27/4.50 thf(zip_derived_cl15, plain, 30.27/4.50 (~ (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((!!) @ (^[Y1 : $i]: 30.27/4.50 (((!!) @ (^[Y2 : $i > $i]: 30.27/4.50 (((((!!) @ (^[Y3 : $i]: 30.27/4.50 (((in @ Y3 @ Y0) => 30.27/4.50 (in @ (Y2 @ Y3) @ 30.27/4.50 Y1)))))) => 30.27/4.50 (((((!!) @ (^[Y3 : $i]: 30.27/4.50 (((in @ Y3 @ 30.27/4.50 Y0) => 30.27/4.50 (((??) @ ( 30.27/4.50 ^[Y4 : $i]: 30.27/4.50 (((in @ 30.27/4.50 Y4 @ 30.27/4.50 (dsetconstr @ 30.27/4.50 Y1 @ 30.27/4.50 ( 30.27/4.50 ^[Y5 : $i]: 30.27/4.50 (in @ 30.27/4.50 (kpair @ 30.27/4.50 Y3 @ Y5) @ 30.27/4.50 (dpsetconstr @ 30.27/4.50 Y0 @ 30.27/4.50 Y1 @ 30.27/4.50 (^[Y6 : $i]: 30.27/4.50 (( 30.27/4.50 ($i) = 30.27/4.50 (Y2 @ Y6))))))))) & 30.27/4.50 (( 30.27/4.50 (dsetconstr @ 30.27/4.50 Y1 @ 30.27/4.50 (^[Y5 : $i]: 30.27/4.50 (in @ 30.27/4.50 (kpair @ 30.27/4.50 Y3 @ Y5) @ 30.27/4.50 (dpsetconstr @ 30.27/4.50 Y0 @ 30.27/4.50 Y1 @ 30.27/4.50 (^[Y6 : $i]: 30.27/4.50 (( 30.27/4.50 ($i) = 30.27/4.50 (Y2 @ Y6)))))))) = 30.27/4.50 (setadjoin @ 30.27/4.50 Y4 @ 30.27/4.50 emptyset))))))))))))) & 30.27/4.50 (subset @ 30.27/4.50 (dpsetconstr @ Y0 @ Y1 @ 30.27/4.50 (^[Y3 : $i]: 30.27/4.50 ((($i) = (Y2 @ Y3))))) @ 30.27/4.50 (cartprod @ Y0 @ Y1)))))))))))))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10])). 30.27/4.50 thf(zip_derived_cl20, plain, 30.27/4.50 (~ (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((!!) @ (^[Y1 : $i > $i]: 30.27/4.50 (((((!!) @ (^[Y2 : $i]: 30.27/4.50 (((in @ Y2 @ '#sk8') => (in @ 30.27/4.50 (Y1 @ Y2) @ Y0)))))) => 30.27/4.50 (((((!!) @ (^[Y2 : $i]: 30.27/4.50 (((in @ Y2 @ '#sk8') => 30.27/4.50 (((??) @ (^[Y3 : $i]: 30.27/4.50 (((in @ Y3 @ 30.27/4.50 (dsetconstr @ 30.27/4.50 Y0 @ 30.27/4.50 (^[Y4 : $i]: 30.27/4.50 (in @ 30.27/4.50 ( 30.27/4.50 kpair @ 30.27/4.50 Y2 @ Y4) @ 30.27/4.50 ( 30.27/4.50 dpsetconstr @ 30.27/4.50 '#sk8' @ 30.27/4.50 Y0 @ 30.27/4.50 ( 30.27/4.50 ^[Y5 : $i]: 30.27/4.50 (( 30.27/4.50 ($i) = 30.27/4.50 (Y1 @ Y5))))))))) & 30.27/4.50 (((dsetconstr @ 30.27/4.50 Y0 @ 30.27/4.50 (^[Y4 : $i]: 30.27/4.50 ( 30.27/4.50 in @ 30.27/4.50 ( 30.27/4.50 kpair @ 30.27/4.50 Y2 @ Y4) @ 30.27/4.50 ( 30.27/4.50 dpsetconstr @ 30.27/4.50 '#sk8' @ 30.27/4.50 Y0 @ 30.27/4.50 ( 30.27/4.50 ^[Y5 : $i]: 30.27/4.50 (( 30.27/4.50 ($i) = 30.27/4.50 (Y1 @ Y5)))))))) = 30.27/4.50 (setadjoin @ 30.27/4.50 Y3 @ 30.27/4.50 emptyset))))))))))))) & 30.27/4.50 (subset @ 30.27/4.50 (dpsetconstr @ '#sk8' @ Y0 @ 30.27/4.50 (^[Y2 : $i]: ((($i) = (Y1 @ Y2))))) @ 30.27/4.50 (cartprod @ '#sk8' @ Y0))))))))))))), 30.27/4.50 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 30.27/4.50 thf(zip_derived_cl25, plain, 30.27/4.50 (~ (((!!) @ (^[Y0 : $i > $i]: 30.27/4.50 (((((!!) @ (^[Y1 : $i]: 30.27/4.50 (((in @ Y1 @ '#sk8') => (in @ (Y0 @ Y1) @ 30.27/4.50 '#sk16')))))) => 30.27/4.50 (((((!!) @ (^[Y1 : $i]: 30.27/4.50 (((in @ Y1 @ '#sk8') => 30.27/4.50 (((??) @ (^[Y2 : $i]: 30.27/4.50 (((in @ Y2 @ 30.27/4.50 (dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y3 : $i]: 30.27/4.50 (in @ 30.27/4.50 (kpair @ Y1 @ Y3) @ 30.27/4.50 (dpsetconstr @ 30.27/4.50 '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y4 : $i]: 30.27/4.50 ((($i) = (Y0 @ 30.27/4.50 Y4))))))))) & 30.27/4.50 (((dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y3 : $i]: 30.27/4.50 (in @ 30.27/4.50 (kpair @ Y1 @ Y3) @ 30.27/4.50 (dpsetconstr @ 30.27/4.50 '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y4 : $i]: 30.27/4.50 ((($i) = (Y0 @ 30.27/4.50 Y4)))))))) = 30.27/4.50 (setadjoin @ Y2 @ 30.27/4.50 emptyset))))))))))))) & 30.27/4.50 (subset @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = (Y0 @ Y1))))) @ 30.27/4.50 (cartprod @ '#sk8' @ '#sk16')))))))))), 30.27/4.50 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl20])). 30.27/4.50 thf(zip_derived_cl29, plain, 30.27/4.50 (~ (((((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ '#sk8') => (in @ ('#sk25' @ Y0) @ '#sk16')))))) => 30.27/4.50 (((((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ '#sk8') => 30.27/4.50 (((??) @ (^[Y1 : $i]: 30.27/4.50 (((in @ Y1 @ 30.27/4.50 (dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y2 : $i]: 30.27/4.50 (in @ (kpair @ Y0 @ Y2) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ 30.27/4.50 '#sk16' @ 30.27/4.50 (^[Y3 : $i]: 30.27/4.50 ((($i) = ('#sk25' @ Y3))))))))) & 30.27/4.50 (((dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y2 : $i]: 30.27/4.50 (in @ (kpair @ Y0 @ Y2) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ 30.27/4.50 '#sk16' @ 30.27/4.50 (^[Y3 : $i]: 30.27/4.50 ((($i) = ('#sk25' @ Y3)))))))) = 30.27/4.50 (setadjoin @ Y1 @ emptyset))))))))))))) & 30.27/4.50 (subset @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: ((($i) = ('#sk25' @ Y0))))) @ 30.27/4.50 (cartprod @ '#sk8' @ '#sk16'))))))), 30.27/4.50 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl25])). 30.27/4.50 thf(zip_derived_cl33, plain, 30.27/4.50 ( (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ '#sk8') => (in @ ('#sk25' @ Y0) @ '#sk16'))))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl29])). 30.27/4.50 thf(zip_derived_cl39, plain, 30.27/4.50 (![X2 : $i]: (((in @ X2 @ '#sk8') => (in @ ('#sk25' @ X2) @ '#sk16')))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])). 30.27/4.50 thf(zip_derived_cl46, plain, 30.27/4.50 (![X2 : $i]: (~ (in @ X2 @ '#sk8') | (in @ ('#sk25' @ X2) @ '#sk16'))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 30.27/4.50 thf(zip_derived_cl2, plain, 30.27/4.50 ( (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((!!) @ (^[Y1 : $i > $o]: 30.27/4.50 (((!!) @ (^[Y2 : $i]: 30.27/4.50 (((in @ Y2 @ Y0) => 30.27/4.50 (((Y1 @ Y2) => 30.27/4.50 (((((!!) @ (^[Y3 : $i]: 30.27/4.50 (((in @ Y3 @ 30.27/4.50 Y0) => 30.27/4.50 (((Y1 @ Y3) => 30.27/4.50 (((Y3) = (Y2)))))))))) => 30.27/4.50 (((??) @ (^[Y3 : $i]: 30.27/4.50 (((in @ Y3 @ 30.27/4.50 (dsetconstr @ 30.27/4.50 Y0 @ Y1)) & 30.27/4.50 (((dsetconstr @ 30.27/4.50 Y0 @ Y1) = 30.27/4.50 (setadjoin @ 30.27/4.50 Y3 @ 30.27/4.50 emptyset)))))))))))))))))))))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 30.27/4.50 thf(zip_derived_cl4, plain, 30.27/4.50 (![X2 : $i]: 30.27/4.50 (((!!) @ (^[Y0 : $i > $o]: 30.27/4.50 (((!!) @ (^[Y1 : $i]: 30.27/4.50 (((in @ Y1 @ X2) => 30.27/4.50 (((Y0 @ Y1) => 30.27/4.50 (((((!!) @ (^[Y2 : $i]: 30.27/4.50 (((in @ Y2 @ X2) => 30.27/4.50 (((Y0 @ Y2) => 30.27/4.50 (((Y2) = (Y1)))))))))) => 30.27/4.50 (((??) @ (^[Y2 : $i]: 30.27/4.50 (((in @ Y2 @ 30.27/4.50 (dsetconstr @ X2 @ Y0)) & 30.27/4.50 (((dsetconstr @ X2 @ 30.27/4.50 Y0) = (setadjoin @ 30.27/4.50 Y2 @ emptyset))))))))))))))))))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 30.27/4.50 thf(zip_derived_cl7, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o]: 30.27/4.50 (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ X2) => 30.27/4.50 (((X4 @ Y0) => 30.27/4.50 (((((!!) @ (^[Y1 : $i]: 30.27/4.50 (((in @ Y1 @ X2) => 30.27/4.50 (((X4 @ Y1) => (((Y1) = (Y0)))))))))) => 30.27/4.50 (((??) @ (^[Y1 : $i]: 30.27/4.50 (((in @ Y1 @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = 30.27/4.50 (setadjoin @ Y1 @ emptyset)))))))))))))))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 30.27/4.50 thf(zip_derived_cl11, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 (((in @ X6 @ X2) => 30.27/4.50 (((X4 @ X6) => 30.27/4.50 (((((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ X2) => 30.27/4.50 (((X4 @ Y0) => (((Y0) = (X6)))))))))) => 30.27/4.50 (((??) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ Y0 @ 30.27/4.50 emptyset))))))))))))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 30.27/4.50 thf(zip_derived_cl16, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 (~ (in @ X6 @ X2) 30.27/4.50 | (((X4 @ X6) => 30.27/4.50 (((((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ X2) => 30.27/4.50 (((X4 @ Y0) => (((Y0) = (X6)))))))))) => 30.27/4.50 (((??) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ Y0 @ 30.27/4.50 emptyset)))))))))))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 30.27/4.50 thf(zip_derived_cl21, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 (~ (X4 @ X6) 30.27/4.50 | (((((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ X2) => (((X4 @ Y0) => (((Y0) = (X6)))))))))) => 30.27/4.50 (((??) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ Y0 @ 30.27/4.50 emptyset)))))))))) 30.27/4.50 | ~ (in @ X6 @ X2))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 30.27/4.50 thf(zip_derived_cl26, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 (~ (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ X2) => (((X4 @ Y0) => (((Y0) = (X6)))))))))) 30.27/4.50 | (((??) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ Y0 @ 30.27/4.50 emptyset)))))))) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | ~ (X4 @ X6))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 30.27/4.50 thf(zip_derived_cl30, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 (~ (((in @ ('#sk29' @ X2 @ X4 @ X6) @ X2) => 30.27/4.50 (((X4 @ ('#sk29' @ X2 @ X4 @ X6)) => 30.27/4.50 ((('#sk29' @ X2 @ X4 @ X6) = (X6))))))) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | (((??) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ Y0 @ 30.27/4.50 emptyset)))))))))), 30.27/4.50 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl26])). 30.27/4.50 thf(zip_derived_cl36, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 (~ (((X4 @ ('#sk29' @ X2 @ X4 @ X6)) => 30.27/4.50 ((('#sk29' @ X2 @ X4 @ X6) = (X6))))) 30.27/4.50 | (((??) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ Y0 @ 30.27/4.50 emptyset)))))))) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | ~ (X4 @ X6))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 30.27/4.50 thf(zip_derived_cl43, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 (~ ((('#sk29' @ X2 @ X4 @ X6) = (X6))) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | (((??) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ Y0 @ 30.27/4.50 emptyset)))))))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 30.27/4.50 thf(zip_derived_cl51, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 ((('#sk29' @ X2 @ X4 @ X6) != (X6)) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | (((??) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ Y0 @ 30.27/4.50 emptyset)))))))))), 30.27/4.50 inference('simplify nested equalities', [status(thm)], [zip_derived_cl43])). 30.27/4.50 thf(zip_derived_cl52, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 ( (((in @ ('#sk50' @ X2 @ X4) @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ ('#sk50' @ X2 @ X4) @ 30.27/4.50 emptyset))))) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | (('#sk29' @ X2 @ X4 @ X6) != (X6)))), 30.27/4.50 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl51])). 30.27/4.50 thf(zip_derived_cl60, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 ( (((dsetconstr @ X2 @ X4) = (setadjoin @ ('#sk50' @ X2 @ X4) @ 30.27/4.50 emptyset))) 30.27/4.50 | (('#sk29' @ X2 @ X4 @ X6) != (X6)) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | ~ (in @ X6 @ X2))), 30.27/4.50 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl52])). 30.27/4.50 thf(zip_derived_cl64, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 (((dsetconstr @ X2 @ X4) 30.27/4.50 = (setadjoin @ ('#sk50' @ X2 @ X4) @ emptyset)) 30.27/4.50 | (('#sk29' @ X2 @ X4 @ X6) != (X6)) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | ~ (in @ X6 @ X2))), 30.27/4.50 inference('simplify nested equalities', [status(thm)], [zip_derived_cl60])). 30.27/4.50 thf(zip_derived_cl203, plain, 30.27/4.50 (![X0 : $i, X1 : $i > $o]: 30.27/4.50 (~ (in @ X0 @ '#sk8') 30.27/4.50 | ~ (X1 @ ('#sk25' @ X0)) 30.27/4.50 | (('#sk29' @ '#sk16' @ X1 @ ('#sk25' @ X0)) != ('#sk25' @ X0)) 30.27/4.50 | ((dsetconstr @ '#sk16' @ X1) 30.27/4.50 = (setadjoin @ ('#sk50' @ '#sk16' @ X1) @ emptyset)))), 30.27/4.50 inference('sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl64])). 30.27/4.50 thf(zip_derived_cl46, plain, 30.27/4.50 (![X2 : $i]: (~ (in @ X2 @ '#sk8') | (in @ ('#sk25' @ X2) @ '#sk16'))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 30.27/4.50 thf(zip_derived_cl59, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 ( (in @ ('#sk50' @ X2 @ X4) @ (dsetconstr @ X2 @ X4)) 30.27/4.50 | (('#sk29' @ X2 @ X4 @ X6) != (X6)) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | ~ (in @ X6 @ X2))), 30.27/4.50 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl52])). 30.27/4.50 thf(zip_derived_cl373, plain, 30.27/4.50 (![X0 : $i, X1 : $i > $o]: 30.27/4.50 (~ (in @ X0 @ '#sk8') 30.27/4.50 | ~ (X1 @ ('#sk25' @ X0)) 30.27/4.50 | (('#sk29' @ '#sk16' @ X1 @ ('#sk25' @ X0)) != ('#sk25' @ X0)) 30.27/4.50 | (in @ ('#sk50' @ '#sk16' @ X1) @ (dsetconstr @ '#sk16' @ X1)))), 30.27/4.50 inference('sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl59])). 30.27/4.50 thf(zip_derived_cl34, plain, 30.27/4.50 (~ (((((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ '#sk8') => 30.27/4.50 (((??) @ (^[Y1 : $i]: 30.27/4.50 (((in @ Y1 @ 30.27/4.50 (dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y2 : $i]: 30.27/4.50 (in @ (kpair @ Y0 @ Y2) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y3 : $i]: 30.27/4.50 ((($i) = ('#sk25' @ Y3))))))))) & 30.27/4.50 (((dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y2 : $i]: 30.27/4.50 (in @ (kpair @ Y0 @ Y2) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y3 : $i]: 30.27/4.50 ((($i) = ('#sk25' @ Y3)))))))) = 30.27/4.50 (setadjoin @ Y1 @ emptyset))))))))))))) & 30.27/4.50 (subset @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: ((($i) = ('#sk25' @ Y0))))) @ 30.27/4.50 (cartprod @ '#sk8' @ '#sk16'))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl29])). 30.27/4.50 thf(zip_derived_cl40, plain, 30.27/4.50 ((~ (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ '#sk8') => 30.27/4.50 (((??) @ (^[Y1 : $i]: 30.27/4.50 (((in @ Y1 @ 30.27/4.50 (dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y2 : $i]: 30.27/4.50 (in @ (kpair @ Y0 @ Y2) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y3 : $i]: 30.27/4.50 ((($i) = ('#sk25' @ Y3))))))))) & 30.27/4.50 (((dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y2 : $i]: 30.27/4.50 (in @ (kpair @ Y0 @ Y2) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y3 : $i]: 30.27/4.50 ((($i) = ('#sk25' @ Y3)))))))) = 30.27/4.50 (setadjoin @ Y1 @ emptyset))))))))))))) 30.27/4.50 | ~ (subset @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: ((($i) = ('#sk25' @ Y0))))) @ 30.27/4.50 (cartprod @ '#sk8' @ '#sk16')))), 30.27/4.50 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl34])). 30.27/4.50 thf(zip_derived_cl47, plain, 30.27/4.50 ((~ (((in @ '#sk60' @ '#sk8') => 30.27/4.50 (((??) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ 30.27/4.50 (dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y1) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y2 : $i]: ((($i) = ('#sk25' @ Y2))))))))) & 30.27/4.50 (((dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y1) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y2 : $i]: ((($i) = ('#sk25' @ Y2)))))))) = 30.27/4.50 (setadjoin @ Y0 @ emptyset)))))))))) 30.27/4.50 | ~ (subset @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: ((($i) = ('#sk25' @ Y0))))) @ 30.27/4.50 (cartprod @ '#sk8' @ '#sk16')))), 30.27/4.50 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl40])). 30.27/4.50 thf(zip_derived_cl55, plain, 30.27/4.50 ((~ (((??) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ 30.27/4.50 (dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y1) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y2 : $i]: ((($i) = ('#sk25' @ Y2))))))))) & 30.27/4.50 (((dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y1) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y2 : $i]: ((($i) = ('#sk25' @ Y2)))))))) = 30.27/4.50 (setadjoin @ Y0 @ emptyset)))))))) 30.27/4.50 | ~ (subset @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: ((($i) = ('#sk25' @ Y0))))) @ 30.27/4.50 (cartprod @ '#sk8' @ '#sk16')))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 30.27/4.50 thf(zip_derived_cl62, plain, 30.27/4.50 (![X2 : $i]: 30.27/4.50 (~ (((in @ X2 @ 30.27/4.50 (dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y0) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = ('#sk25' @ Y1))))))))) & 30.27/4.50 (((dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y0) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = ('#sk25' @ Y1)))))))) = 30.27/4.50 (setadjoin @ X2 @ emptyset))))) 30.27/4.50 | ~ (subset @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: ((($i) = ('#sk25' @ Y0))))) @ 30.27/4.50 (cartprod @ '#sk8' @ '#sk16')))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl55])). 30.27/4.50 thf(zip_derived_cl65, plain, 30.27/4.50 (![X2 : $i]: 30.27/4.50 (~ (in @ X2 @ 30.27/4.50 (dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y0) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = ('#sk25' @ Y1))))))))) 30.27/4.50 | ~ (((dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y0) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = ('#sk25' @ Y1)))))))) = 30.27/4.50 (setadjoin @ X2 @ emptyset))) 30.27/4.50 | ~ (subset @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: ((($i) = ('#sk25' @ Y0))))) @ 30.27/4.50 (cartprod @ '#sk8' @ '#sk16')))), 30.27/4.50 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 30.27/4.50 thf(zip_derived_cl66, plain, 30.27/4.50 (![X2 : $i]: 30.27/4.50 (~ (in @ X2 @ 30.27/4.50 (dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y0) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = ('#sk25' @ Y1))))))))) 30.27/4.50 | ((dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y0) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = ('#sk25' @ Y1)))))))) 30.27/4.50 != (setadjoin @ X2 @ emptyset)) 30.27/4.50 | ~ (subset @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: ((($i) = ('#sk25' @ Y0))))) @ 30.27/4.50 (cartprod @ '#sk8' @ '#sk16')))), 30.27/4.50 inference('simplify nested equalities', [status(thm)], [zip_derived_cl65])). 30.27/4.50 thf(zip_derived_cl9, plain, 30.27/4.50 ( (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((!!) @ (^[Y1 : $i]: 30.27/4.50 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.50 (subset @ 30.27/4.50 (dpsetconstr @ Y0 @ Y1 @ Y2) @ 30.27/4.50 (cartprod @ Y0 @ Y1)))))))))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 30.27/4.50 thf(zip_derived_cl13, plain, 30.27/4.50 (![X2 : $i]: 30.27/4.50 (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((!!) @ (^[Y1 : $i > $i > $o]: 30.27/4.50 (subset @ (dpsetconstr @ X2 @ Y0 @ Y1) @ 30.27/4.50 (cartprod @ X2 @ Y0))))))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 30.27/4.50 thf(zip_derived_cl18, plain, 30.27/4.50 (![X2 : $i, X4 : $i]: 30.27/4.50 (((!!) @ (^[Y0 : $i > $i > $o]: 30.27/4.50 (subset @ (dpsetconstr @ X2 @ X4 @ Y0) @ 30.27/4.50 (cartprod @ X2 @ X4)))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 30.27/4.50 thf(zip_derived_cl23, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o]: 30.27/4.50 (subset @ (dpsetconstr @ X2 @ X4 @ X6) @ (cartprod @ X2 @ X4))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 30.27/4.50 thf(zip_derived_cl68, plain, 30.27/4.50 (![X2 : $i]: 30.27/4.50 (~ (in @ X2 @ 30.27/4.50 (dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y0) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = ('#sk25' @ Y1))))))))) 30.27/4.50 | ((dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y0) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = ('#sk25' @ Y1)))))))) 30.27/4.50 != (setadjoin @ X2 @ emptyset)))), 30.27/4.50 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl23])). 30.27/4.50 thf(zip_derived_cl68, plain, 30.27/4.50 (![X2 : $i]: 30.27/4.50 (~ (in @ X2 @ 30.27/4.50 (dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y0) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = ('#sk25' @ Y1))))))))) 30.27/4.50 | ((dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y0) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = ('#sk25' @ Y1)))))))) 30.27/4.50 != (setadjoin @ X2 @ emptyset)))), 30.27/4.50 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl23])). 30.27/4.50 thf(zip_derived_cl5601, plain, 30.27/4.50 (![X5 : $i]: 30.27/4.50 (('#l_lift11587' @ X5) 30.27/4.50 = (in @ (kpair @ '#sk60' @ X5) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ '#l_lift11586')))), 30.27/4.50 define([status(thm)])). 30.27/4.50 thf(zip_derived_cl68, plain, 30.27/4.50 (![X2 : $i]: 30.27/4.50 (~ (in @ X2 @ 30.27/4.50 (dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y0) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = ('#sk25' @ Y1))))))))) 30.27/4.50 | ((dsetconstr @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: 30.27/4.50 (in @ (kpair @ '#sk60' @ Y0) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y1 : $i]: ((($i) = ('#sk25' @ Y1)))))))) 30.27/4.50 != (setadjoin @ X2 @ emptyset)))), 30.27/4.50 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl23])). 30.27/4.50 thf(zip_derived_cl5600, plain, 30.27/4.50 (![X3 : $i, X4 : $i]: 30.27/4.50 (('#l_lift11586' @ X3 @ X4) = ((('#sk25' @ X3) = (X4))))), 30.27/4.50 define([status(thm)])). 30.27/4.50 thf(zip_derived_cl5601, plain, 30.27/4.50 (![X5 : $i]: 30.27/4.50 (('#l_lift11587' @ X5) 30.27/4.50 = (in @ (kpair @ '#sk60' @ X5) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ '#l_lift11586')))), 30.27/4.50 define([status(thm)])). 30.27/4.50 thf(zip_derived_cl5600, plain, 30.27/4.50 (![X3 : $i, X4 : $i]: 30.27/4.50 (('#l_lift11586' @ X3 @ X4) = ((('#sk25' @ X3) = (X4))))), 30.27/4.50 define([status(thm)])). 30.27/4.50 thf(zip_derived_cl5602, plain, 30.27/4.50 (![X2 : $i]: 30.27/4.50 (~ (in @ X2 @ (dsetconstr @ '#sk16' @ '#l_lift11587')) 30.27/4.50 | ((dsetconstr @ '#sk16' @ '#l_lift11587') 30.27/4.50 != (setadjoin @ X2 @ emptyset)))), 30.27/4.50 inference('lambda_lifting', [status(thm)], 30.27/4.50 [zip_derived_cl68, zip_derived_cl5601, zip_derived_cl5600, 30.27/4.50 zip_derived_cl5601, zip_derived_cl5600])). 30.27/4.50 thf(zip_derived_cl46, plain, 30.27/4.50 (![X2 : $i]: (~ (in @ X2 @ '#sk8') | (in @ ('#sk25' @ X2) @ '#sk16'))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 30.27/4.50 thf(zip_derived_cl42, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 ( (X4 @ ('#sk29' @ X2 @ X4 @ X6)) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | (((??) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ Y0 @ 30.27/4.50 emptyset)))))))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 30.27/4.50 thf(zip_derived_cl50, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 ( (((in @ ('#sk50' @ X2 @ X4) @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ ('#sk50' @ X2 @ X4) @ 30.27/4.50 emptyset))))) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | (X4 @ ('#sk29' @ X2 @ X4 @ X6)))), 30.27/4.50 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl42])). 30.27/4.50 thf(zip_derived_cl58, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 ( (((dsetconstr @ X2 @ X4) = (setadjoin @ ('#sk50' @ X2 @ X4) @ 30.27/4.50 emptyset))) 30.27/4.50 | (X4 @ ('#sk29' @ X2 @ X4 @ X6)) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | ~ (in @ X6 @ X2))), 30.27/4.50 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl50])). 30.27/4.50 thf(zip_derived_cl63, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 (((dsetconstr @ X2 @ X4) 30.27/4.50 = (setadjoin @ ('#sk50' @ X2 @ X4) @ emptyset)) 30.27/4.50 | (X4 @ ('#sk29' @ X2 @ X4 @ X6)) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | ~ (in @ X6 @ X2))), 30.27/4.50 inference('simplify nested equalities', [status(thm)], [zip_derived_cl58])). 30.27/4.50 thf(zip_derived_cl529, plain, 30.27/4.50 (![X0 : $i, X1 : $i > $o]: 30.27/4.50 (~ (in @ X0 @ '#sk8') 30.27/4.50 | ~ (X1 @ ('#sk25' @ X0)) 30.27/4.50 | (X1 @ ('#sk29' @ '#sk16' @ X1 @ ('#sk25' @ X0))) 30.27/4.50 | ((dsetconstr @ '#sk16' @ X1) 30.27/4.50 = (setadjoin @ ('#sk50' @ '#sk16' @ X1) @ emptyset)))), 30.27/4.50 inference('sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl63])). 30.27/4.50 thf(zip_derived_cl46, plain, 30.27/4.50 (![X2 : $i]: (~ (in @ X2 @ '#sk8') | (in @ ('#sk25' @ X2) @ '#sk16'))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 30.27/4.50 thf(zip_derived_cl54, plain, 30.27/4.50 (( (in @ '#sk60' @ '#sk8') 30.27/4.50 | ~ (subset @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ 30.27/4.50 (^[Y0 : $i]: ((($i) = ('#sk25' @ Y0))))) @ 30.27/4.50 (cartprod @ '#sk8' @ '#sk16')))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 30.27/4.50 thf(zip_derived_cl23, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o]: 30.27/4.50 (subset @ (dpsetconstr @ X2 @ X4 @ X6) @ (cartprod @ X2 @ X4))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 30.27/4.50 thf(zip_derived_cl67, plain, ( (in @ '#sk60' @ '#sk8')), 30.27/4.50 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl23])). 30.27/4.50 thf(zip_derived_cl14, plain, 30.27/4.50 ( (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((!!) @ (^[Y1 : $i]: 30.27/4.50 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.50 (((!!) @ (^[Y3 : $i]: 30.27/4.50 (((in @ Y3 @ Y0) => 30.27/4.50 (((!!) @ (^[Y4 : $i]: 30.27/4.50 ( 30.27/4.50 ( 30.27/4.50 (in @ 30.27/4.50 Y4 @ 30.27/4.50 Y1) => 30.27/4.50 (( 30.27/4.50 (in @ 30.27/4.50 ( 30.27/4.50 kpair @ 30.27/4.50 Y3 @ Y4) @ 30.27/4.50 ( 30.27/4.50 dpsetconstr @ 30.27/4.50 Y0 @ 30.27/4.50 Y1 @ Y2)) => 30.27/4.50 (Y2 @ 30.27/4.50 Y3 @ Y4))))))))))))))))))))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10])). 30.27/4.50 thf(zip_derived_cl19, plain, 30.27/4.50 (![X2 : $i]: 30.27/4.50 (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((!!) @ (^[Y1 : $i > $i > $o]: 30.27/4.50 (((!!) @ (^[Y2 : $i]: 30.27/4.50 (((in @ Y2 @ X2) => 30.27/4.50 (((!!) @ (^[Y3 : $i]: 30.27/4.50 (((in @ Y3 @ Y0) => 30.27/4.50 (((in @ 30.27/4.50 (kpair @ Y2 @ 30.27/4.50 Y3) @ 30.27/4.50 (dpsetconstr @ 30.27/4.50 X2 @ Y0 @ Y1)) => 30.27/4.50 (Y1 @ Y2 @ Y3)))))))))))))))))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 30.27/4.50 thf(zip_derived_cl24, plain, 30.27/4.50 (![X2 : $i, X4 : $i]: 30.27/4.50 (((!!) @ (^[Y0 : $i > $i > $o]: 30.27/4.50 (((!!) @ (^[Y1 : $i]: 30.27/4.50 (((in @ Y1 @ X2) => 30.27/4.50 (((!!) @ (^[Y2 : $i]: 30.27/4.50 (((in @ Y2 @ X4) => 30.27/4.50 (((in @ (kpair @ Y1 @ Y2) @ 30.27/4.50 (dpsetconstr @ X2 @ X4 @ Y0)) => 30.27/4.50 (Y0 @ Y1 @ Y2))))))))))))))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 30.27/4.50 thf(zip_derived_cl28, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o]: 30.27/4.50 (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ X2) => 30.27/4.50 (((!!) @ (^[Y1 : $i]: 30.27/4.50 (((in @ Y1 @ X4) => 30.27/4.50 (((in @ (kpair @ Y0 @ Y1) @ 30.27/4.50 (dpsetconstr @ X2 @ X4 @ X6)) => (X6 @ 30.27/4.50 Y0 @ Y1)))))))))))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl24])). 30.27/4.50 thf(zip_derived_cl32, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o, X8 : $i]: 30.27/4.50 (((in @ X8 @ X2) => 30.27/4.50 (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ X4) => 30.27/4.50 (((in @ (kpair @ X8 @ Y0) @ 30.27/4.50 (dpsetconstr @ X2 @ X4 @ X6)) => (X6 @ X8 @ Y0))))))))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 30.27/4.50 thf(zip_derived_cl38, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o, X8 : $i]: 30.27/4.50 (~ (in @ X8 @ X2) 30.27/4.50 | (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ X4) => 30.27/4.50 (((in @ (kpair @ X8 @ Y0) @ 30.27/4.50 (dpsetconstr @ X2 @ X4 @ X6)) => (X6 @ X8 @ Y0)))))))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl32])). 30.27/4.50 thf(zip_derived_cl45, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o, X8 : $i, X10 : $i]: 30.27/4.50 ( (((in @ X10 @ X4) => 30.27/4.50 (((in @ (kpair @ X8 @ X10) @ (dpsetconstr @ X2 @ X4 @ X6)) => 30.27/4.50 (X6 @ X8 @ X10))))) 30.27/4.50 | ~ (in @ X8 @ X2))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 30.27/4.50 thf(zip_derived_cl53, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o, X8 : $i, X10 : $i]: 30.27/4.50 (~ (in @ X10 @ X4) 30.27/4.50 | (((in @ (kpair @ X8 @ X10) @ (dpsetconstr @ X2 @ X4 @ X6)) => 30.27/4.50 (X6 @ X8 @ X10))) 30.27/4.50 | ~ (in @ X8 @ X2))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 30.27/4.50 thf(zip_derived_cl61, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o, X8 : $i, X10 : $i]: 30.27/4.50 (~ (in @ (kpair @ X8 @ X10) @ (dpsetconstr @ X2 @ X4 @ X6)) 30.27/4.50 | (X6 @ X8 @ X10) 30.27/4.50 | ~ (in @ X8 @ X2) 30.27/4.50 | ~ (in @ X10 @ X4))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 30.27/4.50 thf(zip_derived_cl46, plain, 30.27/4.50 (![X2 : $i]: (~ (in @ X2 @ '#sk8') | (in @ ('#sk25' @ X2) @ '#sk16'))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 30.27/4.50 thf(zip_derived_cl35, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 ( (in @ ('#sk29' @ X2 @ X4 @ X6) @ X2) 30.27/4.50 | (((??) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ Y0 @ 30.27/4.50 emptyset)))))))) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | ~ (X4 @ X6))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 30.27/4.50 thf(zip_derived_cl41, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 ( (((in @ ('#sk50' @ X2 @ X4) @ (dsetconstr @ X2 @ X4)) & 30.27/4.50 (((dsetconstr @ X2 @ X4) = (setadjoin @ ('#sk50' @ X2 @ X4) @ 30.27/4.50 emptyset))))) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | (in @ ('#sk29' @ X2 @ X4 @ X6) @ X2))), 30.27/4.50 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl35])). 30.27/4.50 thf(zip_derived_cl49, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 ( (((dsetconstr @ X2 @ X4) = (setadjoin @ ('#sk50' @ X2 @ X4) @ 30.27/4.50 emptyset))) 30.27/4.50 | (in @ ('#sk29' @ X2 @ X4 @ X6) @ X2) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | ~ (X4 @ X6))), 30.27/4.50 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl41])). 30.27/4.50 thf(zip_derived_cl56, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 (((dsetconstr @ X2 @ X4) 30.27/4.50 = (setadjoin @ ('#sk50' @ X2 @ X4) @ emptyset)) 30.27/4.50 | (in @ ('#sk29' @ X2 @ X4 @ X6) @ X2) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | ~ (X4 @ X6))), 30.27/4.50 inference('simplify nested equalities', [status(thm)], [zip_derived_cl49])). 30.27/4.50 thf(zip_derived_cl282, plain, 30.27/4.50 (![X0 : $i, X1 : $i > $o]: 30.27/4.50 (~ (in @ X0 @ '#sk8') 30.27/4.50 | ~ (X1 @ ('#sk25' @ X0)) 30.27/4.50 | (in @ ('#sk29' @ '#sk16' @ X1 @ ('#sk25' @ X0)) @ '#sk16') 30.27/4.50 | ((dsetconstr @ '#sk16' @ X1) 30.27/4.50 = (setadjoin @ ('#sk50' @ '#sk16' @ X1) @ emptyset)))), 30.27/4.50 inference('sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl56])). 30.27/4.50 thf(zip_derived_cl46, plain, 30.27/4.50 (![X2 : $i]: (~ (in @ X2 @ '#sk8') | (in @ ('#sk25' @ X2) @ '#sk16'))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 30.27/4.50 thf(zip_derived_cl48, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 ( (in @ ('#sk50' @ X2 @ X4) @ (dsetconstr @ X2 @ X4)) 30.27/4.50 | (in @ ('#sk29' @ X2 @ X4 @ X6) @ X2) 30.27/4.50 | ~ (in @ X6 @ X2) 30.27/4.50 | ~ (X4 @ X6))), 30.27/4.50 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl41])). 30.27/4.50 thf(zip_derived_cl157, plain, 30.27/4.50 (![X0 : $i, X1 : $i > $o]: 30.27/4.50 (~ (in @ X0 @ '#sk8') 30.27/4.50 | ~ (X1 @ ('#sk25' @ X0)) 30.27/4.50 | (in @ ('#sk29' @ '#sk16' @ X1 @ ('#sk25' @ X0)) @ '#sk16') 30.27/4.50 | (in @ ('#sk50' @ '#sk16' @ X1) @ (dsetconstr @ '#sk16' @ X1)))), 30.27/4.50 inference('sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl48])). 30.27/4.50 thf(zip_derived_cl5600, plain, 30.27/4.50 (![X3 : $i, X4 : $i]: 30.27/4.50 (('#l_lift11586' @ X3 @ X4) = ((('#sk25' @ X3) = (X4))))), 30.27/4.50 define([status(thm)])). 30.27/4.50 thf(zip_derived_cl5601, plain, 30.27/4.50 (![X5 : $i]: 30.27/4.50 (('#l_lift11587' @ X5) 30.27/4.50 = (in @ (kpair @ '#sk60' @ X5) @ 30.27/4.50 (dpsetconstr @ '#sk8' @ '#sk16' @ '#l_lift11586')))), 30.27/4.50 define([status(thm)])). 30.27/4.50 thf(zip_derived_cl46, plain, 30.27/4.50 (![X2 : $i]: (~ (in @ X2 @ '#sk8') | (in @ ('#sk25' @ X2) @ '#sk16'))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 30.27/4.50 thf(zip_derived_cl57, plain, 30.27/4.50 (![X2 : $i, X4 : $i > $o, X6 : $i]: 30.27/4.50 ( (in @ ('#sk50' @ X2 @ X4) @ (dsetconstr @ X2 @ X4)) 30.27/4.50 | (X4 @ ('#sk29' @ X2 @ X4 @ X6)) 30.27/4.50 | ~ (X4 @ X6) 30.27/4.50 | ~ (in @ X6 @ X2))), 30.27/4.50 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl50])). 30.27/4.50 thf(zip_derived_cl416, plain, 30.27/4.50 (![X0 : $i, X1 : $i > $o]: 30.27/4.50 (~ (in @ X0 @ '#sk8') 30.27/4.50 | ~ (X1 @ ('#sk25' @ X0)) 30.27/4.50 | (X1 @ ('#sk29' @ '#sk16' @ X1 @ ('#sk25' @ X0))) 30.27/4.50 | (in @ ('#sk50' @ '#sk16' @ X1) @ (dsetconstr @ '#sk16' @ X1)))), 30.27/4.50 inference('sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl57])). 30.27/4.50 thf(zip_derived_cl67, plain, ( (in @ '#sk60' @ '#sk8')), 30.27/4.50 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl23])). 30.27/4.50 thf(zip_derived_cl5, plain, 30.27/4.50 ( (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((!!) @ (^[Y1 : $i]: 30.27/4.50 (((!!) @ (^[Y2 : $i > $i > $o]: 30.27/4.50 (((!!) @ (^[Y3 : $i]: 30.27/4.50 (((in @ Y3 @ Y0) => 30.27/4.50 (((!!) @ (^[Y4 : $i]: 30.27/4.50 ( 30.27/4.50 ( 30.27/4.50 (in @ 30.27/4.50 Y4 @ 30.27/4.50 Y1) => 30.27/4.50 (( 30.27/4.50 (Y2 @ 30.27/4.50 Y3 @ 30.27/4.50 Y4) => 30.27/4.50 (in @ 30.27/4.50 ( 30.27/4.50 kpair @ 30.27/4.50 Y3 @ Y4) @ 30.27/4.50 ( 30.27/4.50 dpsetconstr @ 30.27/4.50 Y0 @ 30.27/4.50 Y1 @ Y2)))))))))))))))))))))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])). 30.27/4.50 thf(zip_derived_cl8, plain, 30.27/4.50 (![X2 : $i]: 30.27/4.50 (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((!!) @ (^[Y1 : $i > $i > $o]: 30.27/4.50 (((!!) @ (^[Y2 : $i]: 30.27/4.50 (((in @ Y2 @ X2) => 30.27/4.50 (((!!) @ (^[Y3 : $i]: 30.27/4.50 (((in @ Y3 @ Y0) => 30.27/4.50 (((Y1 @ Y2 @ 30.27/4.50 Y3) => (in @ 30.27/4.50 (kpair @ Y2 @ 30.27/4.50 Y3) @ 30.27/4.50 (dpsetconstr @ 30.27/4.50 X2 @ Y0 @ Y1))))))))))))))))))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 30.27/4.50 thf(zip_derived_cl12, plain, 30.27/4.50 (![X2 : $i, X4 : $i]: 30.27/4.50 (((!!) @ (^[Y0 : $i > $i > $o]: 30.27/4.50 (((!!) @ (^[Y1 : $i]: 30.27/4.50 (((in @ Y1 @ X2) => 30.27/4.50 (((!!) @ (^[Y2 : $i]: 30.27/4.50 (((in @ Y2 @ X4) => 30.27/4.50 (((Y0 @ Y1 @ Y2) => (in @ 30.27/4.50 (kpair @ Y1 @ Y2) @ 30.27/4.50 (dpsetconstr @ X2 @ X4 @ Y0)))))))))))))))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 30.27/4.50 thf(zip_derived_cl17, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o]: 30.27/4.50 (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ X2) => 30.27/4.50 (((!!) @ (^[Y1 : $i]: 30.27/4.50 (((in @ Y1 @ X4) => 30.27/4.50 (((X6 @ Y0 @ Y1) => (in @ 30.27/4.50 (kpair @ Y0 @ Y1) @ 30.27/4.50 (dpsetconstr @ X2 @ X4 @ X6))))))))))))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 30.27/4.50 thf(zip_derived_cl22, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o, X8 : $i]: 30.27/4.50 (((in @ X8 @ X2) => 30.27/4.50 (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ X4) => 30.27/4.50 (((X6 @ X8 @ Y0) => (in @ (kpair @ X8 @ Y0) @ 30.27/4.50 (dpsetconstr @ X2 @ X4 @ X6)))))))))))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 30.27/4.50 thf(zip_derived_cl27, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o, X8 : $i]: 30.27/4.50 (~ (in @ X8 @ X2) 30.27/4.50 | (((!!) @ (^[Y0 : $i]: 30.27/4.50 (((in @ Y0 @ X4) => 30.27/4.50 (((X6 @ X8 @ Y0) => (in @ (kpair @ X8 @ Y0) @ 30.27/4.50 (dpsetconstr @ X2 @ X4 @ X6))))))))))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 30.27/4.50 thf(zip_derived_cl31, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o, X8 : $i, X10 : $i]: 30.27/4.50 ( (((in @ X10 @ X4) => 30.27/4.50 (((X6 @ X8 @ X10) => (in @ (kpair @ X8 @ X10) @ 30.27/4.50 (dpsetconstr @ X2 @ X4 @ X6)))))) 30.27/4.50 | ~ (in @ X8 @ X2))), 30.27/4.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl27])). 30.27/4.50 thf(zip_derived_cl37, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o, X8 : $i, X10 : $i]: 30.27/4.50 (~ (in @ X10 @ X4) 30.27/4.50 | (((X6 @ X8 @ X10) => (in @ (kpair @ X8 @ X10) @ 30.27/4.50 (dpsetconstr @ X2 @ X4 @ X6)))) 30.27/4.50 | ~ (in @ X8 @ X2))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl31])). 30.27/4.50 thf(zip_derived_cl44, plain, 30.27/4.50 (![X2 : $i, X4 : $i, X6 : $i > $i > $o, X8 : $i, X10 : $i]: 30.27/4.50 (~ (X6 @ X8 @ X10) 30.27/4.50 | (in @ (kpair @ X8 @ X10) @ (dpsetconstr @ X2 @ X4 @ X6)) 30.27/4.50 | ~ (in @ X8 @ X2) 30.27/4.50 | ~ (in @ X10 @ X4))), 30.27/4.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 30.27/4.50 thf(zip_derived_cl96, plain, 30.27/4.50 (![X0 : $i, X1 : $i, X2 : $i > $i > $o]: 30.27/4.50 (~ (in @ X1 @ X0) 30.27/4.50 | (in @ (kpair @ '#sk60' @ X1) @ (dpsetconstr @ '#sk8' @ X0 @ X2)) 30.27/4.50 | ~ (X2 @ '#sk60' @ X1))), 30.27/4.50 inference('sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl44])). 30.27/4.50 thf(zip_derived_cl5605, plain, ($false), 30.27/4.50 inference('eprover', [status(thm)], 30.27/4.50 [zip_derived_cl203, zip_derived_cl373, zip_derived_cl5602, 30.27/4.50 zip_derived_cl529, zip_derived_cl46, zip_derived_cl67, 30.27/4.50 zip_derived_cl61, zip_derived_cl282, zip_derived_cl157, 30.27/4.50 zip_derived_cl5600, zip_derived_cl5601, zip_derived_cl416, 30.27/4.50 zip_derived_cl96])). 30.27/4.50 30.27/4.50 % SZS output end Refutation 30.27/4.50 30.27/4.50 30.27/4.50 % Terminating... 30.82/4.60 % Runner terminated. 30.82/4.61 % Zipperpin 1.5 exiting 30.82/4.61 EOF