0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.t1k04Q51fa true 0.13/0.35 % Computer : n015.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Aug 9 06:04:41 EDT 2022 0.13/0.35 % CPUTime : 0.13/0.35 % Running portfolio for 960 s 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.35 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.60/0.70 % Total configuration time : 828 0.60/0.70 % Estimated wc time : 1656 0.60/0.70 % Estimated cpu time (8 cpus) : 207.0 0.62/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.62/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.62/0.80 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.62/0.80 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.62/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.62/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.62/0.81 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.62/0.81 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.64/1.13 % Solved by lams/35_full_unif4.sh. 0.64/1.13 % done 45 iterations in 0.231s 0.64/1.13 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 0.64/1.13 % SZS output start Refutation 0.64/1.13 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 0.64/1.13 thf('#sk32_type', type, '#sk32': $i). 0.64/1.13 thf(ex1_type, type, ex1: $i > ($i > $o) > $o). 0.64/1.13 thf(singleton_type, type, singleton: $i > $o). 0.64/1.13 thf(breln_type, type, breln: $i > $i > $i > $o). 0.64/1.13 thf('#sk1_type', type, '#sk1': $i). 0.64/1.13 thf('#sk6_type', type, '#sk6': $i). 0.64/1.13 thf(emptyset_type, type, emptyset: $i). 0.64/1.13 thf(kpair_type, type, kpair: $i > $i > $i). 0.64/1.13 thf(func_type, type, func: $i > $i > $i > $o). 0.64/1.13 thf('#sk11_type', type, '#sk11': $i). 0.64/1.13 thf(cartprod_type, type, cartprod: $i > $i > $i). 0.64/1.13 thf(subset_type, type, subset: $i > $i > $o). 0.64/1.13 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 0.64/1.13 thf('#sk25_type', type, '#sk25': $i). 0.64/1.13 thf(app_type, type, app: $o). 0.64/1.13 thf(in_type, type, in: $i > $i > $o). 0.64/1.13 thf(funcGraphProp1_type, type, funcGraphProp1: $o). 0.64/1.13 thf(ap_type, type, ap: $i > $i > $i > $i > $i). 0.64/1.13 thf('#sk35_type', type, '#sk35': $i > $i). 0.64/1.13 thf(ex1E2_type, type, ex1E2: $o). 0.64/1.13 thf('#sk12_type', type, '#sk12': $i > $i > $i > $i). 0.64/1.13 thf(funcGraphProp1, axiom, funcGraphProp1 = 0.64/1.13 (![A:$i,B:$i,Xf:$i]: 0.64/1.13 ( ( func @ A @ B @ Xf ) => 0.64/1.13 ( ![Xx:$i]: 0.64/1.13 ( ( in @ Xx @ A ) => 0.64/1.13 ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ))). 0.64/1.13 thf('0', plain, 0.64/1.13 (( funcGraphProp1 ) = 0.64/1.13 ( ![X4:$i,X6:$i,X8:$i]: 0.64/1.13 ( ( func @ X4 @ X6 @ X8 ) => 0.64/1.13 ( ![X10:$i]: 0.64/1.13 ( ( in @ X10 @ X4 ) => 0.64/1.13 ( in @ ( kpair @ X10 @ ( ap @ X4 @ X6 @ X8 @ X10 ) ) @ X8 ) ) ) ) )), 0.64/1.13 define([status(thm)])). 0.64/1.13 thf(ex1E2, axiom, ex1E2 = 0.64/1.13 (![A:$i,Xphi:( $i > $o )]: 0.64/1.13 ( ( ex1 @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) => 0.64/1.13 ( ![Xx:$i]: 0.64/1.13 ( ( in @ Xx @ A ) => 0.64/1.13 ( ![Xy:$i]: 0.64/1.13 ( ( in @ Xy @ A ) => 0.64/1.13 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ) ) ) ))). 0.64/1.13 thf('1', plain, 0.64/1.13 (( ex1E2 ) = 0.64/1.13 ( ![X4:$i,X6:( $i > $o )]: 0.64/1.13 ( ( ex1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) => 0.64/1.13 ( ![X8:$i]: 0.64/1.13 ( ( in @ X8 @ X4 ) => 0.64/1.13 ( ![X10:$i]: 0.64/1.13 ( ( in @ X10 @ X4 ) => 0.64/1.13 ( ( X6 @ X8 ) => ( ( X6 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) ) ) ) ) )), 0.64/1.13 define([status(thm)])). 0.64/1.13 thf(app, axiom, app = 0.64/1.13 (![A:$i,B:$i,Xf:$i]: 0.64/1.13 ( ( func @ A @ B @ Xf ) => 0.64/1.13 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ))). 0.64/1.13 thf('2', plain, 0.64/1.13 (( app ) = 0.64/1.13 ( ![X4:$i,X6:$i,X8:$i]: 0.64/1.13 ( ( func @ X4 @ X6 @ X8 ) => 0.64/1.13 ( ![X10:$i]: 0.64/1.13 ( ( in @ X10 @ X4 ) => ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) )), 0.64/1.13 define([status(thm)])). 0.64/1.13 thf(func, axiom,(( func ) = 0.64/1.13 (^[A:$i,B:$i,R:$i]: 0.64/1.13 ( ( breln @ A @ B @ R ) & 0.64/1.13 ( ![Xx:$i]: 0.64/1.13 ( ( in @ Xx @ A ) => 0.64/1.13 ( ex1 @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )))). 0.64/1.13 thf(breln, axiom,(( breln ) = 0.64/1.13 (^[A:$i,B:$i,C:$i]: ( subset @ C @ ( cartprod @ A @ B ) )))). 0.64/1.13 thf('3', plain, 0.64/1.13 (( breln ) = ( ^[A:$i,B:$i,C:$i]: ( subset @ C @ ( cartprod @ A @ B ) ) )), 0.64/1.13 inference('simplify_rw_rule', [status(thm)], [breln])). 0.64/1.13 thf('4', plain, 0.64/1.13 (( breln ) = 0.64/1.13 ( ^[V_1:$i,V_2:$i,V_3:$i]: ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) )), 0.64/1.13 define([status(thm)])). 0.64/1.13 thf(ex1, axiom,(( ex1 ) = 0.64/1.13 (^[A:$i,Xphi:( $i > $o )]: 0.64/1.13 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) )))). 0.64/1.13 thf(singleton, axiom,(( singleton ) = 0.64/1.13 (^[A:$i]: 0.64/1.13 ( ?[Xx:$i]: 0.64/1.13 ( ( ( A ) = ( setadjoin @ Xx @ emptyset ) ) & ( in @ Xx @ A ) ) )))). 0.64/1.13 thf('5', plain, 0.64/1.13 (( singleton ) = 0.64/1.13 ( ^[A:$i]: 0.64/1.13 ( ?[Xx:$i]: 0.64/1.13 ( ( ( A ) = ( setadjoin @ Xx @ emptyset ) ) & ( in @ Xx @ A ) ) ) )), 0.64/1.13 inference('simplify_rw_rule', [status(thm)], [singleton])). 0.64/1.13 thf('6', plain, 0.64/1.13 (( singleton ) = 0.64/1.13 ( ^[V_1:$i]: 0.64/1.13 ( ?[X4:$i]: 0.64/1.13 ( ( ( V_1 ) = ( setadjoin @ X4 @ emptyset ) ) & ( in @ X4 @ V_1 ) ) ) )), 0.64/1.13 define([status(thm)])). 0.64/1.13 thf('7', plain, 0.64/1.13 (( ex1 ) = 0.64/1.13 ( ^[A:$i,Xphi:( $i > $o )]: 0.64/1.13 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) )), 0.64/1.13 inference('simplify_rw_rule', [status(thm)], [ex1, '6'])). 0.64/1.13 thf('8', plain, 0.64/1.13 (( ex1 ) = 0.64/1.13 ( ^[V_1:$i,V_2:( $i > $o )]: 0.64/1.13 ( singleton @ ( dsetconstr @ V_1 @ ( ^[V_3:$i]: ( V_2 @ V_3 ) ) ) ) )), 0.64/1.13 define([status(thm)])). 0.64/1.13 thf('9', plain, 0.64/1.13 (( func ) = 0.64/1.13 ( ^[A:$i,B:$i,R:$i]: 0.64/1.13 ( ( breln @ A @ B @ R ) & 0.64/1.13 ( ![Xx:$i]: 0.64/1.13 ( ( in @ Xx @ A ) => 0.64/1.13 ( ex1 @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) )), 0.64/1.13 inference('simplify_rw_rule', [status(thm)], [func, '4', '8', '6'])). 0.64/1.13 thf('10', plain, 0.64/1.13 (( func ) = 0.64/1.13 ( ^[V_1:$i,V_2:$i,V_3:$i]: 0.64/1.13 ( ( breln @ V_1 @ V_2 @ V_3 ) & 0.64/1.13 ( ![X4:$i]: 0.64/1.13 ( ( in @ X4 @ V_1 ) => 0.64/1.13 ( ex1 @ V_2 @ ( ^[V_4:$i]: ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ) )), 0.64/1.13 define([status(thm)])). 0.64/1.13 thf(funcGraphProp2, conjecture, 0.64/1.13 (( app ) => 0.64/1.13 ( ( ex1E2 ) => 0.64/1.13 ( ( funcGraphProp1 ) => 0.64/1.13 ( ![A:$i,B:$i,Xf:$i]: 0.64/1.13 ( ( func @ A @ B @ Xf ) => 0.64/1.13 ( ![Xx:$i]: 0.64/1.13 ( ( in @ Xx @ A ) => 0.64/1.13 ( ![Xy:$i]: 0.64/1.13 ( ( in @ Xy @ B ) => 0.64/1.13 ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) => 0.64/1.13 ( ( ap @ A @ B @ Xf @ Xx ) = ( Xy ) ) ) ) ) ) ) ) ) ) ))). 0.64/1.13 thf(zf_stmt_0, conjecture, 0.64/1.13 (( ![X4:$i,X6:$i,X8:$i]: 0.64/1.13 ( ( ( ![X10:$i]: 0.64/1.13 ( ( in @ X10 @ X4 ) => 0.64/1.13 ( ?[X12:$i]: 0.64/1.13 ( ( in @ 0.64/1.13 X12 @ 0.64/1.13 ( dsetconstr @ 0.64/1.13 X6 @ ( ^[V_2:$i]: ( in @ ( kpair @ X10 @ V_2 ) @ X8 ) ) ) ) & 0.64/1.13 ( ( dsetconstr @ 0.64/1.13 X6 @ ( ^[V_1:$i]: ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) = 0.64/1.13 ( setadjoin @ X12 @ emptyset ) ) ) ) ) ) & 0.64/1.13 ( subset @ X8 @ ( cartprod @ X4 @ X6 ) ) ) => 0.64/1.13 ( ![X14:$i]: 0.64/1.13 ( ( in @ X14 @ X4 ) => ( in @ ( ap @ X4 @ X6 @ X8 @ X14 ) @ X6 ) ) ) ) ) => 0.64/1.13 ( ( ![X16:$i,X18:( $i > $o )]: 0.64/1.13 ( ( ?[X20:$i]: 0.64/1.13 ( ( in @ X20 @ ( dsetconstr @ X16 @ ( ^[V_4:$i]: ( X18 @ V_4 ) ) ) ) & 0.64/1.13 ( ( dsetconstr @ X16 @ ( ^[V_3:$i]: ( X18 @ V_3 ) ) ) = 0.64/1.13 ( setadjoin @ X20 @ emptyset ) ) ) ) => 0.64/1.13 ( ![X22:$i]: 0.64/1.13 ( ( in @ X22 @ X16 ) => 0.64/1.13 ( ![X24:$i]: 0.64/1.13 ( ( in @ X24 @ X16 ) => 0.64/1.13 ( ( X18 @ X22 ) => 0.64/1.13 ( ( X18 @ X24 ) => ( ( X22 ) = ( X24 ) ) ) ) ) ) ) ) ) ) => 0.64/1.13 ( ( ![X26:$i,X28:$i,X30:$i]: 0.64/1.13 ( ( ( ![X32:$i]: 0.64/1.13 ( ( in @ X32 @ X26 ) => 0.64/1.13 ( ?[X34:$i]: 0.64/1.13 ( ( in @ 0.64/1.13 X34 @ 0.64/1.13 ( dsetconstr @ 0.64/1.13 X28 @ 0.64/1.13 ( ^[V_6:$i]: ( in @ ( kpair @ X32 @ V_6 ) @ X30 ) ) ) ) & 0.64/1.13 ( ( dsetconstr @ 0.64/1.13 X28 @ 0.64/1.13 ( ^[V_5:$i]: ( in @ ( kpair @ X32 @ V_5 ) @ X30 ) ) ) = 0.64/1.13 ( setadjoin @ X34 @ emptyset ) ) ) ) ) ) & 0.64/1.13 ( subset @ X30 @ ( cartprod @ X26 @ X28 ) ) ) => 0.64/1.13 ( ![X36:$i]: 0.64/1.13 ( ( in @ X36 @ X26 ) => 0.64/1.13 ( in @ ( kpair @ X36 @ ( ap @ X26 @ X28 @ X30 @ X36 ) ) @ X30 ) ) ) ) ) => 0.64/1.13 ( ![X38:$i,X40:$i,X42:$i]: 0.64/1.13 ( ( ( ![X44:$i]: 0.64/1.13 ( ( in @ X44 @ X38 ) => 0.64/1.13 ( ?[X46:$i]: 0.64/1.13 ( ( in @ 0.64/1.13 X46 @ 0.64/1.13 ( dsetconstr @ 0.64/1.13 X40 @ 0.64/1.13 ( ^[V_8:$i]: ( in @ ( kpair @ X44 @ V_8 ) @ X42 ) ) ) ) & 0.64/1.13 ( ( dsetconstr @ 0.64/1.13 X40 @ 0.64/1.13 ( ^[V_7:$i]: ( in @ ( kpair @ X44 @ V_7 ) @ X42 ) ) ) = 0.64/1.13 ( setadjoin @ X46 @ emptyset ) ) ) ) ) ) & 0.64/1.13 ( subset @ X42 @ ( cartprod @ X38 @ X40 ) ) ) => 0.64/1.13 ( ![X48:$i]: 0.64/1.13 ( ( in @ X48 @ X38 ) => 0.64/1.13 ( ![X50:$i]: 0.64/1.13 ( ( in @ X50 @ X40 ) => 0.64/1.13 ( ( in @ ( kpair @ X48 @ X50 ) @ X42 ) => 0.64/1.13 ( ( ap @ X38 @ X40 @ X42 @ X48 ) = ( X50 ) ) ) ) ) ) ) ) ) ) ))). 0.64/1.13 thf(zf_stmt_1, negated_conjecture, 0.64/1.13 (~( ( ![X4:$i,X6:$i,X8:$i]: 0.64/1.13 ( ( ( ![X10:$i]: 0.64/1.13 ( ( in @ X10 @ X4 ) => 0.64/1.13 ( ?[X12:$i]: 0.64/1.13 ( ( in @ 0.64/1.13 X12 @ 0.64/1.13 ( dsetconstr @ 0.64/1.13 X6 @ 0.64/1.13 ( ^[V_2:$i]: ( in @ ( kpair @ X10 @ V_2 ) @ X8 ) ) ) ) & 0.64/1.13 ( ( dsetconstr @ 0.64/1.13 X6 @ 0.64/1.13 ( ^[V_1:$i]: ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) = 0.64/1.13 ( setadjoin @ X12 @ emptyset ) ) ) ) ) ) & 0.64/1.13 ( subset @ X8 @ ( cartprod @ X4 @ X6 ) ) ) => 0.64/1.13 ( ![X14:$i]: 0.64/1.13 ( ( in @ X14 @ X4 ) => ( in @ ( ap @ X4 @ X6 @ X8 @ X14 ) @ X6 ) ) ) ) ) => 0.64/1.13 ( ( ![X16:$i,X18:( $i > $o )]: 0.64/1.13 ( ( ?[X20:$i]: 0.64/1.13 ( ( in @ 0.64/1.13 X20 @ ( dsetconstr @ X16 @ ( ^[V_4:$i]: ( X18 @ V_4 ) ) ) ) & 0.64/1.13 ( ( dsetconstr @ X16 @ ( ^[V_3:$i]: ( X18 @ V_3 ) ) ) = 0.64/1.13 ( setadjoin @ X20 @ emptyset ) ) ) ) => 0.64/1.13 ( ![X22:$i]: 0.64/1.13 ( ( in @ X22 @ X16 ) => 0.64/1.13 ( ![X24:$i]: 0.64/1.13 ( ( in @ X24 @ X16 ) => 0.64/1.13 ( ( X18 @ X22 ) => 0.64/1.13 ( ( X18 @ X24 ) => ( ( X22 ) = ( X24 ) ) ) ) ) ) ) ) ) ) => 0.64/1.13 ( ( ![X26:$i,X28:$i,X30:$i]: 0.64/1.13 ( ( ( ![X32:$i]: 0.64/1.13 ( ( in @ X32 @ X26 ) => 0.64/1.13 ( ?[X34:$i]: 0.64/1.13 ( ( in @ 0.64/1.13 X34 @ 0.64/1.13 ( dsetconstr @ 0.64/1.13 X28 @ 0.64/1.13 ( ^[V_6:$i]: ( in @ ( kpair @ X32 @ V_6 ) @ X30 ) ) ) ) & 0.64/1.13 ( ( dsetconstr @ 0.64/1.13 X28 @ 0.64/1.13 ( ^[V_5:$i]: ( in @ ( kpair @ X32 @ V_5 ) @ X30 ) ) ) = 0.64/1.13 ( setadjoin @ X34 @ emptyset ) ) ) ) ) ) & 0.64/1.13 ( subset @ X30 @ ( cartprod @ X26 @ X28 ) ) ) => 0.64/1.13 ( ![X36:$i]: 0.64/1.13 ( ( in @ X36 @ X26 ) => 0.64/1.13 ( in @ 0.64/1.13 ( kpair @ X36 @ ( ap @ X26 @ X28 @ X30 @ X36 ) ) @ X30 ) ) ) ) ) => 0.64/1.13 ( ![X38:$i,X40:$i,X42:$i]: 0.64/1.13 ( ( ( ![X44:$i]: 0.64/1.13 ( ( in @ X44 @ X38 ) => 0.64/1.13 ( ?[X46:$i]: 0.64/1.13 ( ( in @ 0.64/1.13 X46 @ 0.64/1.13 ( dsetconstr @ 0.64/1.13 X40 @ 0.64/1.13 ( ^[V_8:$i]: ( in @ ( kpair @ X44 @ V_8 ) @ X42 ) ) ) ) & 0.64/1.13 ( ( dsetconstr @ 0.64/1.13 X40 @ 0.64/1.13 ( ^[V_7:$i]: ( in @ ( kpair @ X44 @ V_7 ) @ X42 ) ) ) = 0.64/1.13 ( setadjoin @ X46 @ emptyset ) ) ) ) ) ) & 0.64/1.13 ( subset @ X42 @ ( cartprod @ X38 @ X40 ) ) ) => 0.64/1.13 ( ![X48:$i]: 0.64/1.13 ( ( in @ X48 @ X38 ) => 0.64/1.13 ( ![X50:$i]: 0.64/1.13 ( ( in @ X50 @ X40 ) => 0.64/1.13 ( ( in @ ( kpair @ X48 @ X50 ) @ X42 ) => 0.64/1.13 ( ( ap @ X38 @ X40 @ X42 @ X48 ) = ( X50 ) ) ) ) ) ) ) ) ) ) ) )), 0.64/1.13 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 0.64/1.13 thf(zip_derived_cl0, plain, 0.64/1.13 (~ (((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 ( 0.64/1.13 dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (( 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => (in @ 0.64/1.13 (ap @ Y0 @ Y1 @ 0.64/1.13 Y2 @ Y3) @ 0.64/1.13 Y1))))))))))))))))) => 0.64/1.13 (((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i > $o]: 0.64/1.13 (((((??) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ 0.64/1.13 (dsetconstr @ Y0 @ 0.64/1.13 (^[Y3 : $i]: (Y1 @ Y3)))) & 0.64/1.13 (((dsetconstr @ Y0 @ 0.64/1.13 (^[Y3 : $i]: (Y1 @ Y3))) = 0.64/1.13 (setadjoin @ Y2 @ 0.64/1.13 emptyset)))))))) => 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ Y0) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((Y1 @ 0.64/1.13 Y2) => 0.64/1.13 (( 0.64/1.13 (Y1 @ 0.64/1.13 Y3) => 0.64/1.13 (( 0.64/1.13 (Y2) = 0.64/1.13 (Y3))))))))))))))))))))))))) => 0.64/1.13 (((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ 0.64/1.13 Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (( 0.64/1.13 (??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 ( 0.64/1.13 dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (( 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ 0.64/1.13 (ap @ Y0 @ 0.64/1.13 Y1 @ Y2 @ 0.64/1.13 Y3)) @ 0.64/1.13 Y2))))))))))))))))) => 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ 0.64/1.13 Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (( 0.64/1.13 (??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 ( 0.64/1.13 dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (( 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((!!) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 Y1) => 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 ( 0.64/1.13 kpair @ 0.64/1.13 Y3 @ Y4) @ 0.64/1.13 Y2) => 0.64/1.13 (( 0.64/1.13 (ap @ 0.64/1.13 Y0 @ 0.64/1.13 Y1 @ 0.64/1.13 Y2 @ 0.64/1.13 Y3) = 0.64/1.13 (Y4))))))))))))))))))))))))))))))))), 0.64/1.13 inference('cnf', [status(esa)], [zf_stmt_1])). 0.64/1.13 thf(zip_derived_cl1, plain, 0.64/1.13 (~ (((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 ( 0.64/1.13 dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (( 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => (in @ 0.64/1.13 (ap @ Y0 @ Y1 @ 0.64/1.13 Y2 @ Y3) @ 0.64/1.13 Y1))))))))))))))))) => 0.64/1.13 (((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i > $o]: 0.64/1.13 (((((??) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ 0.64/1.13 (dsetconstr @ Y0 @ Y1)) & 0.64/1.13 (((dsetconstr @ Y0 @ Y1) = 0.64/1.13 (setadjoin @ Y2 @ 0.64/1.13 emptyset)))))))) => 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ Y0) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((Y1 @ 0.64/1.13 Y2) => 0.64/1.13 (( 0.64/1.13 (Y1 @ 0.64/1.13 Y3) => 0.64/1.13 (( 0.64/1.13 (Y2) = 0.64/1.13 (Y3))))))))))))))))))))))))) => 0.64/1.13 (((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ 0.64/1.13 Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (( 0.64/1.13 (??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 ( 0.64/1.13 dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (( 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ 0.64/1.13 (ap @ Y0 @ 0.64/1.13 Y1 @ Y2 @ 0.64/1.13 Y3)) @ 0.64/1.13 Y2))))))))))))))))) => 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ 0.64/1.13 Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (( 0.64/1.13 (??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 ( 0.64/1.13 dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (( 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((!!) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 Y1) => 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 ( 0.64/1.13 kpair @ 0.64/1.13 Y3 @ Y4) @ 0.64/1.13 Y2) => 0.64/1.13 (( 0.64/1.13 (ap @ 0.64/1.13 Y0 @ 0.64/1.13 Y1 @ 0.64/1.13 Y2 @ 0.64/1.13 Y3) = 0.64/1.13 (Y4))))))))))))))))))))))))))))))))), 0.64/1.13 inference('ho_norm', [status(thm)], [zip_derived_cl0])). 0.64/1.13 thf(zip_derived_cl3, plain, 0.64/1.13 (~ (((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i > $o]: 0.64/1.13 (((((??) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ 0.64/1.13 (dsetconstr @ Y0 @ Y1)) & 0.64/1.13 (((dsetconstr @ Y0 @ Y1) = 0.64/1.13 (setadjoin @ Y2 @ 0.64/1.13 emptyset)))))))) => 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ Y0) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((Y1 @ Y2) => 0.64/1.13 (((Y1 @ 0.64/1.13 Y3) => 0.64/1.13 (( 0.64/1.13 (Y2) = 0.64/1.13 (Y3))))))))))))))))))))))))) => 0.64/1.13 (((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 ( 0.64/1.13 dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (( 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => (in @ 0.64/1.13 (kpair @ Y3 @ 0.64/1.13 (ap @ Y0 @ 0.64/1.13 Y1 @ Y2 @ Y3)) @ 0.64/1.13 Y2))))))))))))))))) => 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 ( 0.64/1.13 dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (( 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((!!) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 Y1) => 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 ( 0.64/1.13 kpair @ 0.64/1.13 Y3 @ Y4) @ 0.64/1.13 Y2) => 0.64/1.13 (( 0.64/1.13 (ap @ 0.64/1.13 Y0 @ 0.64/1.13 Y1 @ 0.64/1.13 Y2 @ 0.64/1.13 Y3) = 0.64/1.13 (Y4))))))))))))))))))))))))))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 0.64/1.13 thf(zip_derived_cl6, plain, 0.64/1.13 (~ (((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 ( 0.64/1.13 dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (( 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => (in @ 0.64/1.13 (kpair @ Y3 @ 0.64/1.13 (ap @ Y0 @ 0.64/1.13 Y1 @ Y2 @ Y3)) @ 0.64/1.13 Y2))))))))))))))))) => 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 Y4 @ 0.64/1.13 ( 0.64/1.13 dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (( 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((!!) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (((in @ 0.64/1.13 Y4 @ 0.64/1.13 Y1) => 0.64/1.13 (( 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y4) @ 0.64/1.13 Y2) => 0.64/1.13 (( 0.64/1.13 (ap @ 0.64/1.13 Y0 @ Y1 @ 0.64/1.13 Y2 @ Y3) = 0.64/1.13 (Y4))))))))))))))))))))))))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])). 0.64/1.13 thf(zip_derived_cl10, plain, 0.64/1.13 (~ (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (((in @ 0.64/1.13 Y4 @ 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (( 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 (^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ Y0) => 0.64/1.13 (((!!) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (((in @ Y4 @ 0.64/1.13 Y1) => 0.64/1.13 (((in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y4) @ 0.64/1.13 Y2) => 0.64/1.13 (( 0.64/1.13 (ap @ 0.64/1.13 Y0 @ Y1 @ 0.64/1.13 Y2 @ Y3) = 0.64/1.13 (Y4))))))))))))))))))))))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 0.64/1.13 thf(zip_derived_cl14, plain, 0.64/1.13 (~ (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((((((!!) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ '#sk1') => 0.64/1.13 (((??) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 (dsetconstr @ 0.64/1.13 Y0 @ 0.64/1.13 (^[Y4 : $i]: 0.64/1.13 (in @ 0.64/1.13 ( 0.64/1.13 kpair @ 0.64/1.13 Y2 @ Y4) @ 0.64/1.13 Y1)))) & 0.64/1.13 (((dsetconstr @ 0.64/1.13 Y0 @ 0.64/1.13 (^[Y4 : $i]: 0.64/1.13 ( 0.64/1.13 in @ 0.64/1.13 ( 0.64/1.13 kpair @ 0.64/1.13 Y2 @ Y4) @ 0.64/1.13 Y1))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y3 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y1 @ (cartprod @ '#sk1' @ Y0)))) => 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ '#sk1') => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 Y0) => 0.64/1.13 (((in @ 0.64/1.13 (kpair @ Y2 @ 0.64/1.13 Y3) @ 0.64/1.13 Y1) => 0.64/1.13 (((ap @ 0.64/1.13 '#sk1' @ 0.64/1.13 Y0 @ Y1 @ 0.64/1.13 Y2) = (Y3)))))))))))))))))))))))), 0.64/1.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl10])). 0.64/1.13 thf(zip_derived_cl18, plain, 0.64/1.13 (~ (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((((((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ '#sk1') => 0.64/1.13 (((??) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ 0.64/1.13 (dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y3 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ Y1 @ Y3) @ 0.64/1.13 Y0)))) & 0.64/1.13 (((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y3 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ Y1 @ Y3) @ 0.64/1.13 Y0))) = 0.64/1.13 (setadjoin @ Y2 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y0 @ (cartprod @ '#sk1' @ '#sk6')))) => 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ '#sk1') => 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ '#sk6') => 0.64/1.13 (((in @ (kpair @ Y1 @ Y2) @ 0.64/1.13 Y0) => 0.64/1.13 (((ap @ '#sk1' @ '#sk6' @ 0.64/1.13 Y0 @ Y1) = (Y2))))))))))))))))))))), 0.64/1.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])). 0.64/1.13 thf(zip_derived_cl22, plain, 0.64/1.13 (~ (((((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ '#sk1') => 0.64/1.13 (((??) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ 0.64/1.13 (dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ '#sk11')))) & 0.64/1.13 (((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ '#sk11'))) = 0.64/1.13 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.64/1.13 (subset @ '#sk11' @ (cartprod @ '#sk1' @ '#sk6')))) => 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ '#sk1') => 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ '#sk6') => 0.64/1.13 (((in @ (kpair @ Y0 @ Y1) @ '#sk11') => 0.64/1.13 (((ap @ '#sk1' @ '#sk6' @ '#sk11' @ 0.64/1.13 Y0) = (Y1)))))))))))))))))), 0.64/1.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl18])). 0.64/1.13 thf(zip_derived_cl26, plain, 0.64/1.13 ( (((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ '#sk1') => 0.64/1.13 (((??) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ 0.64/1.13 (dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ '#sk11')))) & 0.64/1.13 (((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ '#sk11'))) = 0.64/1.13 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.64/1.13 (subset @ '#sk11' @ (cartprod @ '#sk1' @ '#sk6'))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 0.64/1.13 thf(zip_derived_cl34, plain, 0.64/1.13 ( (subset @ '#sk11' @ (cartprod @ '#sk1' @ '#sk6'))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 0.64/1.13 thf(zip_derived_cl33, plain, 0.64/1.13 ( (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ '#sk1') => 0.64/1.13 (((??) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ 0.64/1.13 (dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ '#sk11')))) & 0.64/1.13 (((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ '#sk11'))) = 0.64/1.13 (setadjoin @ Y1 @ emptyset)))))))))))))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 0.64/1.13 thf(zip_derived_cl40, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 (((in @ X2 @ '#sk1') => 0.64/1.13 (((??) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ 0.64/1.13 (dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y1 : $i]: (in @ (kpair @ X2 @ Y1) @ '#sk11')))) & 0.64/1.13 (((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y1 : $i]: (in @ (kpair @ X2 @ Y1) @ '#sk11'))) = 0.64/1.13 (setadjoin @ Y0 @ emptyset))))))))))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])). 0.64/1.13 thf(zip_derived_cl48, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 (~ (in @ X2 @ '#sk1') 0.64/1.13 | (((??) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ 0.64/1.13 (dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y1 : $i]: (in @ (kpair @ X2 @ Y1) @ '#sk11')))) & 0.64/1.13 (((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y1 : $i]: (in @ (kpair @ X2 @ Y1) @ '#sk11'))) = 0.64/1.13 (setadjoin @ Y0 @ emptyset)))))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 0.64/1.13 thf(zip_derived_cl55, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 ( (((in @ ('#sk35' @ X2) @ 0.64/1.13 (dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ X2 @ Y0) @ '#sk11')))) & 0.64/1.13 (((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ X2 @ Y0) @ '#sk11'))) = 0.64/1.13 (setadjoin @ ('#sk35' @ X2) @ emptyset))))) 0.64/1.13 | ~ (in @ X2 @ '#sk1'))), 0.64/1.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl48])). 0.64/1.13 thf(zip_derived_cl62, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 ( (in @ ('#sk35' @ X2) @ 0.64/1.13 (dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ X2 @ Y0) @ '#sk11')))) 0.64/1.13 | ~ (in @ X2 @ '#sk1'))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 0.64/1.13 thf(zip_derived_cl2, plain, 0.64/1.13 ( (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ Y0) => 0.64/1.13 (((??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (((in @ Y4 @ 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 (^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (((dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ Y0) => 0.64/1.13 (in @ 0.64/1.13 (ap @ Y0 @ Y1 @ 0.64/1.13 Y2 @ Y3) @ 0.64/1.13 Y1)))))))))))))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 0.64/1.13 thf(zip_derived_cl4, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((((((!!) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ X2) => 0.64/1.13 (((??) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 (dsetconstr @ 0.64/1.13 Y0 @ 0.64/1.13 (^[Y4 : $i]: 0.64/1.13 ( 0.64/1.13 in @ 0.64/1.13 ( 0.64/1.13 kpair @ 0.64/1.13 Y2 @ Y4) @ 0.64/1.13 Y1)))) & 0.64/1.13 (((dsetconstr @ 0.64/1.13 Y0 @ 0.64/1.13 (^[Y4 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y2 @ Y4) @ 0.64/1.13 Y1))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y3 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y1 @ (cartprod @ X2 @ Y0)))) => 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ X2) => (in @ 0.64/1.13 (ap @ X2 @ Y0 @ Y1 @ Y2) @ 0.64/1.13 Y0))))))))))))))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 0.64/1.13 thf(zip_derived_cl7, plain, 0.64/1.13 (![X2 : $i, X4 : $i]: 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((((((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ X2) => 0.64/1.13 (((??) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y3 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ Y1 @ Y3) @ 0.64/1.13 Y0)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y3 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ Y1 @ Y3) @ 0.64/1.13 Y0))) = 0.64/1.13 (setadjoin @ Y2 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y0 @ (cartprod @ X2 @ X4)))) => 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ X2) => (in @ 0.64/1.13 (ap @ X2 @ X4 @ Y0 @ Y1) @ X4)))))))))))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 0.64/1.13 thf(zip_derived_cl11, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i]: 0.64/1.13 (((((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((??) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ X6)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ X6))) = 0.64/1.13 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.64/1.13 (subset @ X6 @ (cartprod @ X2 @ X4)))) => 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ (ap @ X2 @ X4 @ X6 @ Y0) @ 0.64/1.13 X4))))))))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 0.64/1.13 thf(zip_derived_cl15, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i]: 0.64/1.13 (~ (((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((??) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ X6)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ X6))) = 0.64/1.13 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.64/1.13 (subset @ X6 @ (cartprod @ X2 @ X4)))) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ (ap @ X2 @ X4 @ X6 @ Y0) @ 0.64/1.13 X4)))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 0.64/1.13 thf(zip_derived_cl19, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i]: 0.64/1.13 (~ (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((??) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ X6)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ X6))) = 0.64/1.13 (setadjoin @ Y1 @ emptyset))))))))))))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ (ap @ X2 @ X4 @ X6 @ Y0) @ 0.64/1.13 X4)))))))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl15])). 0.64/1.13 thf(zip_derived_cl23, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i]: 0.64/1.13 (~ (((in @ ('#sk12' @ X2 @ X4 @ X6) @ X2) => 0.64/1.13 (((??) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y1 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y1) @ X6)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y1 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y1) @ X6))) = 0.64/1.13 (setadjoin @ Y0 @ emptyset)))))))))) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ (ap @ X2 @ X4 @ X6 @ Y0) @ 0.64/1.13 X4)))))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.64/1.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 0.64/1.13 thf(zip_derived_cl29, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i]: 0.64/1.13 (~ (((??) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y1 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y1) @ 0.64/1.13 X6)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y1 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y1) @ 0.64/1.13 X6))) = 0.64/1.13 (setadjoin @ Y0 @ emptyset)))))))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ (ap @ X2 @ X4 @ X6 @ Y0) @ 0.64/1.13 X4)))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 0.64/1.13 thf(zip_derived_cl37, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.64/1.13 (~ (((in @ X8 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6))) = 0.64/1.13 (setadjoin @ X8 @ emptyset))))) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ (ap @ X2 @ X4 @ X6 @ Y0) @ 0.64/1.13 X4)))))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 0.64/1.13 thf(zip_derived_cl44, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.64/1.13 (~ (in @ X8 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.64/1.13 | ~ (((dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6))) = 0.64/1.13 (setadjoin @ X8 @ emptyset))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ (ap @ X2 @ X4 @ X6 @ Y0) @ 0.64/1.13 X4)))))))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl37])). 0.64/1.13 thf(zip_derived_cl50, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.64/1.13 (~ (in @ X8 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.64/1.13 | ((dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.64/1.13 != (setadjoin @ X8 @ emptyset)) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ (ap @ X2 @ X4 @ X6 @ Y0) @ 0.64/1.13 X4)))))))), 0.64/1.13 inference('simplify nested equalities', [status(thm)], [zip_derived_cl44])). 0.64/1.13 thf(zip_derived_cl51, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 0.64/1.13 ( (((in @ X10 @ X2) => (in @ (ap @ X2 @ X4 @ X6 @ X10) @ X4))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | ((dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.64/1.13 != (setadjoin @ X8 @ emptyset)) 0.64/1.13 | ~ (in @ X8 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6)))))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl50])). 0.64/1.13 thf(zip_derived_cl58, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 0.64/1.13 (~ (in @ X10 @ X2) 0.64/1.13 | (in @ (ap @ X2 @ X4 @ X6 @ X10) @ X4) 0.64/1.13 | ~ (in @ X8 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.64/1.13 | ((dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.64/1.13 != (setadjoin @ X8 @ emptyset)) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 0.64/1.13 thf(zip_derived_cl113, plain, 0.64/1.13 (![X0 : $i, X1 : $i]: 0.64/1.13 (~ (in @ ('#sk12' @ X0 @ '#sk6' @ '#sk11') @ '#sk1') 0.64/1.13 | ~ (subset @ '#sk11' @ (cartprod @ X0 @ '#sk6')) 0.64/1.13 | ((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X0 @ '#sk6' @ '#sk11') @ Y0) @ 0.64/1.13 '#sk11'))) 0.64/1.13 != (setadjoin @ ('#sk35' @ ('#sk12' @ X0 @ '#sk6' @ '#sk11')) @ 0.64/1.13 emptyset)) 0.64/1.13 | (in @ (ap @ X0 @ '#sk6' @ '#sk11' @ X1) @ '#sk6') 0.64/1.13 | ~ (in @ X1 @ X0))), 0.64/1.13 inference('sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl58])). 0.64/1.13 thf(zip_derived_cl63, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 ( (((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ X2 @ Y0) @ '#sk11'))) = (setadjoin @ 0.64/1.13 ('#sk35' @ X2) @ emptyset))) 0.64/1.13 | ~ (in @ X2 @ '#sk1'))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 0.64/1.13 thf(zip_derived_cl69, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 (((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ X2 @ Y0) @ '#sk11'))) 0.64/1.13 = (setadjoin @ ('#sk35' @ X2) @ emptyset)) 0.64/1.13 | ~ (in @ X2 @ '#sk1'))), 0.64/1.13 inference('simplify nested equalities', [status(thm)], [zip_derived_cl63])). 0.64/1.13 thf(zip_derived_cl125, plain, 0.64/1.13 (![X0 : $i, X1 : $i]: 0.64/1.13 (~ (in @ X1 @ X0) 0.64/1.13 | (in @ (ap @ X0 @ '#sk6' @ '#sk11' @ X1) @ '#sk6') 0.64/1.13 | ~ (subset @ '#sk11' @ (cartprod @ X0 @ '#sk6')) 0.64/1.13 | ~ (in @ ('#sk12' @ X0 @ '#sk6' @ '#sk11') @ '#sk1'))), 0.64/1.13 inference('clc', [status(thm)], [zip_derived_cl113, zip_derived_cl69])). 0.64/1.13 thf(zip_derived_cl126, plain, 0.64/1.13 (![X0 : $i]: 0.64/1.13 (~ (in @ ('#sk12' @ '#sk1' @ '#sk6' @ '#sk11') @ '#sk1') 0.64/1.13 | (in @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0) @ '#sk6') 0.64/1.13 | ~ (in @ X0 @ '#sk1'))), 0.64/1.13 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl125])). 0.64/1.13 thf(zip_derived_cl34, plain, 0.64/1.13 ( (subset @ '#sk11' @ (cartprod @ '#sk1' @ '#sk6'))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 0.64/1.13 thf(zip_derived_cl28, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i]: 0.64/1.13 ( (in @ ('#sk12' @ X2 @ X4 @ X6) @ X2) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ (ap @ X2 @ X4 @ X6 @ Y0) @ 0.64/1.13 X4)))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 0.64/1.13 thf(zip_derived_cl36, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.64/1.13 ( (((in @ X8 @ X2) => (in @ (ap @ X2 @ X4 @ X6 @ X8) @ X4))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | (in @ ('#sk12' @ X2 @ X4 @ X6) @ X2))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 0.64/1.13 thf(zip_derived_cl43, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.64/1.13 (~ (in @ X8 @ X2) 0.64/1.13 | (in @ (ap @ X2 @ X4 @ X6 @ X8) @ X4) 0.64/1.13 | (in @ ('#sk12' @ X2 @ X4 @ X6) @ X2) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 0.64/1.13 thf(zip_derived_cl96, plain, 0.64/1.13 (![X0 : $i]: 0.64/1.13 ( (in @ ('#sk12' @ '#sk1' @ '#sk6' @ '#sk11') @ '#sk1') 0.64/1.13 | (in @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0) @ '#sk6') 0.64/1.13 | ~ (in @ X0 @ '#sk1'))), 0.64/1.13 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl43])). 0.64/1.13 thf(zip_derived_cl128, plain, 0.64/1.13 (![X0 : $i]: 0.64/1.13 (~ (in @ X0 @ '#sk1') 0.64/1.13 | (in @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0) @ '#sk6'))), 0.64/1.13 inference('clc', [status(thm)], [zip_derived_cl126, zip_derived_cl96])). 0.64/1.13 thf(zip_derived_cl27, plain, 0.64/1.13 (~ (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ '#sk1') => 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ '#sk6') => 0.64/1.13 (((in @ (kpair @ Y0 @ Y1) @ '#sk11') => 0.64/1.13 (((ap @ '#sk1' @ '#sk6' @ '#sk11' @ 0.64/1.13 Y0) = (Y1)))))))))))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 0.64/1.13 thf(zip_derived_cl35, plain, 0.64/1.13 (~ (((in @ '#sk25' @ '#sk1') => 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ '#sk6') => 0.64/1.13 (((in @ (kpair @ '#sk25' @ Y0) @ '#sk11') => 0.64/1.13 (((ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') = (Y0))))))))))))), 0.64/1.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl27])). 0.64/1.13 thf(zip_derived_cl42, plain, 0.64/1.13 (~ (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ '#sk6') => 0.64/1.13 (((in @ (kpair @ '#sk25' @ Y0) @ '#sk11') => 0.64/1.13 (((ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') = (Y0))))))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 0.64/1.13 thf(zip_derived_cl49, plain, 0.64/1.13 (~ (((in @ '#sk32' @ '#sk6') => 0.64/1.13 (((in @ (kpair @ '#sk25' @ '#sk32') @ '#sk11') => 0.64/1.13 (((ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') = ('#sk32')))))))), 0.64/1.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl42])). 0.64/1.13 thf(zip_derived_cl57, plain, 0.64/1.13 (~ (((in @ (kpair @ '#sk25' @ '#sk32') @ '#sk11') => 0.64/1.13 (((ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') = ('#sk32')))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 0.64/1.13 thf(zip_derived_cl64, plain, ( (in @ (kpair @ '#sk25' @ '#sk32') @ '#sk11')), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 0.64/1.13 thf(zip_derived_cl62, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 ( (in @ ('#sk35' @ X2) @ 0.64/1.13 (dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ X2 @ Y0) @ '#sk11')))) 0.64/1.13 | ~ (in @ X2 @ '#sk1'))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 0.64/1.13 thf(zip_derived_cl5, plain, 0.64/1.13 ( (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i > $o]: 0.64/1.13 (((((??) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ 0.64/1.13 (dsetconstr @ Y0 @ Y1)) & 0.64/1.13 (((dsetconstr @ Y0 @ Y1) = 0.64/1.13 (setadjoin @ Y2 @ emptyset)))))))) => 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ Y0) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ Y0) => 0.64/1.13 (((Y1 @ Y2) => 0.64/1.13 (((Y1 @ Y3) => 0.64/1.13 (((Y2) = (Y3)))))))))))))))))))))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])). 0.64/1.13 thf(zip_derived_cl8, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 (((!!) @ (^[Y0 : $i > $o]: 0.64/1.13 (((((??) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ (dsetconstr @ X2 @ Y0)) & 0.64/1.13 (((dsetconstr @ X2 @ Y0) = (setadjoin @ 0.64/1.13 Y1 @ emptyset)))))))) => 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ X2) => 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ X2) => 0.64/1.13 (((Y0 @ Y1) => 0.64/1.13 (((Y0 @ Y2) => 0.64/1.13 (((Y1) = (Y2))))))))))))))))))))))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 0.64/1.13 thf(zip_derived_cl12, plain, 0.64/1.13 (![X2 : $i, X4 : $i > $o]: 0.64/1.13 (((((??) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) & 0.64/1.13 (((dsetconstr @ X2 @ X4) = (setadjoin @ Y0 @ 0.64/1.13 emptyset)))))))) => 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ X2) => 0.64/1.13 (((X4 @ Y0) => 0.64/1.13 (((X4 @ Y1) => (((Y0) = (Y1)))))))))))))))))))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 0.64/1.13 thf(zip_derived_cl16, plain, 0.64/1.13 (![X2 : $i, X4 : $i > $o]: 0.64/1.13 (~ (((??) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) & 0.64/1.13 (((dsetconstr @ X2 @ X4) = (setadjoin @ Y0 @ 0.64/1.13 emptyset)))))))) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ X2) => 0.64/1.13 (((X4 @ Y0) => 0.64/1.13 (((X4 @ Y1) => (((Y0) = (Y1))))))))))))))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 0.64/1.13 thf(zip_derived_cl20, plain, 0.64/1.13 (![X2 : $i, X4 : $i > $o, X6 : $i]: 0.64/1.13 (~ (((in @ X6 @ (dsetconstr @ X2 @ X4)) & 0.64/1.13 (((dsetconstr @ X2 @ X4) = (setadjoin @ X6 @ emptyset))))) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ X2) => 0.64/1.13 (((X4 @ Y0) => 0.64/1.13 (((X4 @ Y1) => (((Y0) = (Y1))))))))))))))))))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 0.64/1.13 thf(zip_derived_cl24, plain, 0.64/1.13 (![X2 : $i, X4 : $i > $o, X6 : $i]: 0.64/1.13 (~ (in @ X6 @ (dsetconstr @ X2 @ X4)) 0.64/1.13 | ~ (((dsetconstr @ X2 @ X4) = (setadjoin @ X6 @ emptyset))) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ X2) => 0.64/1.13 (((X4 @ Y0) => 0.64/1.13 (((X4 @ Y1) => (((Y0) = (Y1))))))))))))))))))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl20])). 0.64/1.13 thf(zip_derived_cl30, plain, 0.64/1.13 (![X2 : $i, X4 : $i > $o, X6 : $i]: 0.64/1.13 (~ (in @ X6 @ (dsetconstr @ X2 @ X4)) 0.64/1.13 | ((dsetconstr @ X2 @ X4) != (setadjoin @ X6 @ emptyset)) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ X2) => 0.64/1.13 (((X4 @ Y0) => 0.64/1.13 (((X4 @ Y1) => (((Y0) = (Y1))))))))))))))))))), 0.64/1.13 inference('simplify nested equalities', [status(thm)], [zip_derived_cl24])). 0.64/1.13 thf(zip_derived_cl31, plain, 0.64/1.13 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 0.64/1.13 ( (((in @ X8 @ X2) => 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((X4 @ X8) => (((X4 @ Y0) => (((X8) = (Y0)))))))))))))) 0.64/1.13 | ((dsetconstr @ X2 @ X4) != (setadjoin @ X6 @ emptyset)) 0.64/1.13 | ~ (in @ X6 @ (dsetconstr @ X2 @ X4)))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl30])). 0.64/1.13 thf(zip_derived_cl38, plain, 0.64/1.13 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 0.64/1.13 (~ (in @ X8 @ X2) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((X4 @ X8) => (((X4 @ Y0) => (((X8) = (Y0)))))))))))) 0.64/1.13 | ~ (in @ X6 @ (dsetconstr @ X2 @ X4)) 0.64/1.13 | ((dsetconstr @ X2 @ X4) != (setadjoin @ X6 @ emptyset)))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl31])). 0.64/1.13 thf(zip_derived_cl45, plain, 0.64/1.13 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i, X10 : $i]: 0.64/1.13 ( (((in @ X10 @ X2) => 0.64/1.13 (((X4 @ X8) => (((X4 @ X10) => (((X8) = (X10))))))))) 0.64/1.13 | ((dsetconstr @ X2 @ X4) != (setadjoin @ X6 @ emptyset)) 0.64/1.13 | ~ (in @ X6 @ (dsetconstr @ X2 @ X4)) 0.64/1.13 | ~ (in @ X8 @ X2))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 0.64/1.13 thf(zip_derived_cl52, plain, 0.64/1.13 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i, X10 : $i]: 0.64/1.13 (~ (in @ X10 @ X2) 0.64/1.13 | (((X4 @ X8) => (((X4 @ X10) => (((X8) = (X10))))))) 0.64/1.13 | ~ (in @ X8 @ X2) 0.64/1.13 | ~ (in @ X6 @ (dsetconstr @ X2 @ X4)) 0.64/1.13 | ((dsetconstr @ X2 @ X4) != (setadjoin @ X6 @ emptyset)))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 0.64/1.13 thf(zip_derived_cl59, plain, 0.64/1.13 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i, X10 : $i]: 0.64/1.13 (~ (X4 @ X8) 0.64/1.13 | (((X4 @ X10) => (((X8) = (X10))))) 0.64/1.13 | ((dsetconstr @ X2 @ X4) != (setadjoin @ X6 @ emptyset)) 0.64/1.13 | ~ (in @ X6 @ (dsetconstr @ X2 @ X4)) 0.64/1.13 | ~ (in @ X8 @ X2) 0.64/1.13 | ~ (in @ X10 @ X2))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 0.64/1.13 thf(zip_derived_cl66, plain, 0.64/1.13 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i, X10 : $i]: 0.64/1.13 (~ (X4 @ X10) 0.64/1.13 | (((X8) = (X10))) 0.64/1.13 | ~ (in @ X10 @ X2) 0.64/1.13 | ~ (in @ X8 @ X2) 0.64/1.13 | ~ (in @ X6 @ (dsetconstr @ X2 @ X4)) 0.64/1.13 | ((dsetconstr @ X2 @ X4) != (setadjoin @ X6 @ emptyset)) 0.64/1.13 | ~ (X4 @ X8))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl59])). 0.64/1.13 thf(zip_derived_cl71, plain, 0.64/1.13 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i, X10 : $i]: 0.64/1.13 (~ (X4 @ X10) 0.64/1.13 | ((X8) = (X10)) 0.64/1.13 | ~ (in @ X10 @ X2) 0.64/1.13 | ~ (in @ X8 @ X2) 0.64/1.13 | ~ (in @ X6 @ (dsetconstr @ X2 @ X4)) 0.64/1.13 | ((dsetconstr @ X2 @ X4) != (setadjoin @ X6 @ emptyset)) 0.64/1.13 | ~ (X4 @ X8))), 0.64/1.13 inference('simplify nested equalities', [status(thm)], [zip_derived_cl66])). 0.64/1.13 thf(zip_derived_cl81, plain, 0.64/1.13 (![X0 : $i, X1 : $i, X2 : $i]: 0.64/1.13 (~ (in @ X0 @ '#sk1') 0.64/1.13 | ~ ((^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ '#sk11')) @ X1) 0.64/1.13 | ((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ '#sk11'))) 0.64/1.13 != (setadjoin @ ('#sk35' @ X0) @ emptyset)) 0.64/1.13 | ~ (in @ X1 @ '#sk6') 0.64/1.13 | ~ (in @ X2 @ '#sk6') 0.64/1.13 | ((X1) = (X2)) 0.64/1.13 | ~ ((^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ '#sk11')) @ X2))), 0.64/1.13 inference('sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl71])). 0.64/1.13 thf(zip_derived_cl95, plain, 0.64/1.13 (![X0 : $i, X1 : $i, X2 : $i]: 0.64/1.13 (~ (in @ X0 @ '#sk1') 0.64/1.13 | ~ (in @ (kpair @ X0 @ X1) @ '#sk11') 0.64/1.13 | ((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ '#sk11'))) 0.64/1.13 != (setadjoin @ ('#sk35' @ X0) @ emptyset)) 0.64/1.13 | ~ (in @ X1 @ '#sk6') 0.64/1.13 | ~ (in @ X2 @ '#sk6') 0.64/1.13 | ((X1) = (X2)) 0.64/1.13 | ~ (in @ (kpair @ X0 @ X2) @ '#sk11'))), 0.64/1.13 inference('ho_norm', [status(thm)], [zip_derived_cl81])). 0.64/1.13 thf(zip_derived_cl69, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 (((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ X2 @ Y0) @ '#sk11'))) 0.64/1.13 = (setadjoin @ ('#sk35' @ X2) @ emptyset)) 0.64/1.13 | ~ (in @ X2 @ '#sk1'))), 0.64/1.13 inference('simplify nested equalities', [status(thm)], [zip_derived_cl63])). 0.64/1.13 thf(zip_derived_cl130, plain, 0.64/1.13 (![X0 : $i, X1 : $i, X2 : $i]: 0.64/1.13 (~ (in @ (kpair @ X0 @ X2) @ '#sk11') 0.64/1.13 | ((X1) = (X2)) 0.64/1.13 | ~ (in @ X2 @ '#sk6') 0.64/1.13 | ~ (in @ X1 @ '#sk6') 0.64/1.13 | ~ (in @ (kpair @ X0 @ X1) @ '#sk11') 0.64/1.13 | ~ (in @ X0 @ '#sk1'))), 0.64/1.13 inference('clc', [status(thm)], [zip_derived_cl95, zip_derived_cl69])). 0.64/1.13 thf(zip_derived_cl131, plain, 0.64/1.13 (![X0 : $i]: 0.64/1.13 (~ (in @ '#sk25' @ '#sk1') 0.64/1.13 | ~ (in @ (kpair @ '#sk25' @ X0) @ '#sk11') 0.64/1.13 | ~ (in @ X0 @ '#sk6') 0.64/1.13 | ~ (in @ '#sk32' @ '#sk6') 0.64/1.13 | ((X0) = ('#sk32')))), 0.64/1.13 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl130])). 0.64/1.13 thf(zip_derived_cl41, plain, ( (in @ '#sk25' @ '#sk1')), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 0.64/1.13 thf(zip_derived_cl56, plain, ( (in @ '#sk32' @ '#sk6')), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 0.64/1.13 thf(zip_derived_cl138, plain, 0.64/1.13 (![X0 : $i]: 0.64/1.13 (~ (in @ (kpair @ '#sk25' @ X0) @ '#sk11') 0.64/1.13 | ~ (in @ X0 @ '#sk6') 0.64/1.13 | ((X0) = ('#sk32')))), 0.64/1.13 inference('demod', [status(thm)], 0.64/1.13 [zip_derived_cl131, zip_derived_cl41, zip_derived_cl56])). 0.64/1.13 thf(zip_derived_cl34, plain, 0.64/1.13 ( (subset @ '#sk11' @ (cartprod @ '#sk1' @ '#sk6'))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 0.64/1.13 thf(zip_derived_cl62, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 ( (in @ ('#sk35' @ X2) @ 0.64/1.13 (dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ X2 @ Y0) @ '#sk11')))) 0.64/1.13 | ~ (in @ X2 @ '#sk1'))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 0.64/1.13 thf(zip_derived_cl9, plain, 0.64/1.13 ( (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((((((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ Y0) => 0.64/1.13 (((??) @ ( 0.64/1.13 ^[Y4 : $i]: 0.64/1.13 (((in @ Y4 @ 0.64/1.13 (dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 (^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2)))) & 0.64/1.13 (((dsetconstr @ 0.64/1.13 Y1 @ 0.64/1.13 ( 0.64/1.13 ^[Y5 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y3 @ Y5) @ 0.64/1.13 Y2))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y4 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y2 @ 0.64/1.13 (cartprod @ Y0 @ Y1)))) => 0.64/1.13 (((!!) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ Y0) => 0.64/1.13 (in @ 0.64/1.13 (kpair @ Y3 @ 0.64/1.13 (ap @ Y0 @ Y1 @ 0.64/1.13 Y2 @ Y3)) @ 0.64/1.13 Y2)))))))))))))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 0.64/1.13 thf(zip_derived_cl13, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((((((!!) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ X2) => 0.64/1.13 (((??) @ (^[Y3 : $i]: 0.64/1.13 (((in @ Y3 @ 0.64/1.13 (dsetconstr @ 0.64/1.13 Y0 @ 0.64/1.13 (^[Y4 : $i]: 0.64/1.13 ( 0.64/1.13 in @ 0.64/1.13 ( 0.64/1.13 kpair @ 0.64/1.13 Y2 @ Y4) @ 0.64/1.13 Y1)))) & 0.64/1.13 (((dsetconstr @ 0.64/1.13 Y0 @ 0.64/1.13 (^[Y4 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ 0.64/1.13 Y2 @ Y4) @ 0.64/1.13 Y1))) = 0.64/1.13 (setadjoin @ 0.64/1.13 Y3 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y1 @ (cartprod @ X2 @ Y0)))) => 0.64/1.13 (((!!) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ X2) => (in @ 0.64/1.13 (kpair @ Y2 @ 0.64/1.13 (ap @ X2 @ Y0 @ Y1 @ Y2)) @ 0.64/1.13 Y1))))))))))))))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 0.64/1.13 thf(zip_derived_cl17, plain, 0.64/1.13 (![X2 : $i, X4 : $i]: 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((((((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ X2) => 0.64/1.13 (((??) @ (^[Y2 : $i]: 0.64/1.13 (((in @ Y2 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y3 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ Y1 @ Y3) @ 0.64/1.13 Y0)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y3 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ Y1 @ Y3) @ 0.64/1.13 Y0))) = 0.64/1.13 (setadjoin @ Y2 @ 0.64/1.13 emptyset))))))))))))) & 0.64/1.13 (subset @ Y0 @ (cartprod @ X2 @ X4)))) => 0.64/1.13 (((!!) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ X2) => (in @ 0.64/1.13 (kpair @ Y1 @ (ap @ X2 @ X4 @ Y0 @ Y1)) @ 0.64/1.13 Y0)))))))))))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 0.64/1.13 thf(zip_derived_cl21, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i]: 0.64/1.13 (((((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((??) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ X6)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ X6))) = 0.64/1.13 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.64/1.13 (subset @ X6 @ (cartprod @ X2 @ X4)))) => 0.64/1.13 (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ 0.64/1.13 (kpair @ Y0 @ (ap @ X2 @ X4 @ X6 @ Y0)) @ X6))))))))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 0.64/1.13 thf(zip_derived_cl25, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i]: 0.64/1.13 (~ (((((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((??) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ X6)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ X6))) = 0.64/1.13 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.64/1.13 (subset @ X6 @ (cartprod @ X2 @ X4)))) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ 0.64/1.13 (kpair @ Y0 @ (ap @ X2 @ X4 @ X6 @ Y0)) @ X6)))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 0.64/1.13 thf(zip_derived_cl32, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i]: 0.64/1.13 (~ (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => 0.64/1.13 (((??) @ (^[Y1 : $i]: 0.64/1.13 (((in @ Y1 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ X6)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y2 : $i]: 0.64/1.13 (in @ (kpair @ Y0 @ Y2) @ X6))) = 0.64/1.13 (setadjoin @ Y1 @ emptyset))))))))))))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ 0.64/1.13 (kpair @ Y0 @ (ap @ X2 @ X4 @ X6 @ Y0)) @ X6)))))))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])). 0.64/1.13 thf(zip_derived_cl39, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i]: 0.64/1.13 (~ (((in @ ('#sk12' @ X2 @ X4 @ X6) @ X2) => 0.64/1.13 (((??) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y1 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y1) @ X6)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y1 : $i]: 0.64/1.13 (in @ 0.64/1.13 (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y1) @ X6))) = 0.64/1.13 (setadjoin @ Y0 @ emptyset)))))))))) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ 0.64/1.13 (kpair @ Y0 @ (ap @ X2 @ X4 @ X6 @ Y0)) @ X6)))))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.64/1.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 0.64/1.13 thf(zip_derived_cl47, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i]: 0.64/1.13 (~ (((??) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y1 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y1) @ 0.64/1.13 X6)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y1 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y1) @ 0.64/1.13 X6))) = 0.64/1.13 (setadjoin @ Y0 @ emptyset)))))))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ 0.64/1.13 (kpair @ Y0 @ (ap @ X2 @ X4 @ X6 @ Y0)) @ X6)))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 0.64/1.13 thf(zip_derived_cl54, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.64/1.13 (~ (((in @ X8 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6)))) & 0.64/1.13 (((dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6))) = 0.64/1.13 (setadjoin @ X8 @ emptyset))))) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ 0.64/1.13 (kpair @ Y0 @ (ap @ X2 @ X4 @ X6 @ Y0)) @ X6)))))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 0.64/1.13 thf(zip_derived_cl61, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.64/1.13 (~ (in @ X8 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.64/1.13 | ~ (((dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6))) = 0.64/1.13 (setadjoin @ X8 @ emptyset))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ 0.64/1.13 (kpair @ Y0 @ (ap @ X2 @ X4 @ X6 @ Y0)) @ X6)))))))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl54])). 0.64/1.13 thf(zip_derived_cl67, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.64/1.13 (~ (in @ X8 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.64/1.13 | ((dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.64/1.13 != (setadjoin @ X8 @ emptyset)) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ 0.64/1.13 (kpair @ Y0 @ (ap @ X2 @ X4 @ X6 @ Y0)) @ X6)))))))), 0.64/1.13 inference('simplify nested equalities', [status(thm)], [zip_derived_cl61])). 0.64/1.13 thf(zip_derived_cl68, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 0.64/1.13 ( (((in @ X10 @ X2) => (in @ 0.64/1.13 (kpair @ X10 @ (ap @ X2 @ X4 @ X6 @ X10)) @ X6))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | ((dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.64/1.13 != (setadjoin @ X8 @ emptyset)) 0.64/1.13 | ~ (in @ X8 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6)))))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl67])). 0.64/1.13 thf(zip_derived_cl72, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 0.64/1.13 (~ (in @ X10 @ X2) 0.64/1.13 | (in @ (kpair @ X10 @ (ap @ X2 @ X4 @ X6 @ X10)) @ X6) 0.64/1.13 | ~ (in @ X8 @ 0.64/1.13 (dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.64/1.13 | ((dsetconstr @ X4 @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ ('#sk12' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.64/1.13 != (setadjoin @ X8 @ emptyset)) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 0.64/1.13 thf(zip_derived_cl144, plain, 0.64/1.13 (![X0 : $i, X1 : $i]: 0.64/1.13 (~ (in @ ('#sk12' @ X0 @ '#sk6' @ '#sk11') @ '#sk1') 0.64/1.13 | ~ (subset @ '#sk11' @ (cartprod @ X0 @ '#sk6')) 0.64/1.13 | ((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: 0.64/1.13 (in @ (kpair @ ('#sk12' @ X0 @ '#sk6' @ '#sk11') @ Y0) @ 0.64/1.13 '#sk11'))) 0.64/1.13 != (setadjoin @ ('#sk35' @ ('#sk12' @ X0 @ '#sk6' @ '#sk11')) @ 0.64/1.13 emptyset)) 0.64/1.13 | (in @ (kpair @ X1 @ (ap @ X0 @ '#sk6' @ '#sk11' @ X1)) @ '#sk11') 0.64/1.13 | ~ (in @ X1 @ X0))), 0.64/1.13 inference('sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl72])). 0.64/1.13 thf(zip_derived_cl69, plain, 0.64/1.13 (![X2 : $i]: 0.64/1.13 (((dsetconstr @ '#sk6' @ 0.64/1.13 (^[Y0 : $i]: (in @ (kpair @ X2 @ Y0) @ '#sk11'))) 0.64/1.13 = (setadjoin @ ('#sk35' @ X2) @ emptyset)) 0.64/1.13 | ~ (in @ X2 @ '#sk1'))), 0.64/1.13 inference('simplify nested equalities', [status(thm)], [zip_derived_cl63])). 0.64/1.13 thf(zip_derived_cl201, plain, 0.64/1.13 (![X0 : $i, X1 : $i]: 0.64/1.13 (~ (in @ X1 @ X0) 0.64/1.13 | (in @ (kpair @ X1 @ (ap @ X0 @ '#sk6' @ '#sk11' @ X1)) @ '#sk11') 0.64/1.13 | ~ (subset @ '#sk11' @ (cartprod @ X0 @ '#sk6')) 0.64/1.13 | ~ (in @ ('#sk12' @ X0 @ '#sk6' @ '#sk11') @ '#sk1'))), 0.64/1.13 inference('clc', [status(thm)], [zip_derived_cl144, zip_derived_cl69])). 0.64/1.13 thf(zip_derived_cl202, plain, 0.64/1.13 (![X0 : $i]: 0.64/1.13 (~ (in @ ('#sk12' @ '#sk1' @ '#sk6' @ '#sk11') @ '#sk1') 0.64/1.13 | (in @ (kpair @ X0 @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0)) @ 0.64/1.13 '#sk11') 0.64/1.13 | ~ (in @ X0 @ '#sk1'))), 0.64/1.13 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl201])). 0.64/1.13 thf(zip_derived_cl128, plain, 0.64/1.13 (![X0 : $i]: 0.64/1.13 (~ (in @ X0 @ '#sk1') 0.64/1.13 | (in @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0) @ '#sk6'))), 0.64/1.13 inference('clc', [status(thm)], [zip_derived_cl126, zip_derived_cl96])). 0.64/1.13 thf(zip_derived_cl34, plain, 0.64/1.13 ( (subset @ '#sk11' @ (cartprod @ '#sk1' @ '#sk6'))), 0.64/1.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 0.64/1.13 thf(zip_derived_cl46, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i]: 0.64/1.13 ( (in @ ('#sk12' @ X2 @ X4 @ X6) @ X2) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | (((!!) @ (^[Y0 : $i]: 0.64/1.13 (((in @ Y0 @ X2) => (in @ 0.64/1.13 (kpair @ Y0 @ (ap @ X2 @ X4 @ X6 @ Y0)) @ X6)))))))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 0.64/1.13 thf(zip_derived_cl53, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.64/1.13 ( (((in @ X8 @ X2) => (in @ (kpair @ X8 @ (ap @ X2 @ X4 @ X6 @ X8)) @ 0.64/1.13 X6))) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.64/1.13 | (in @ ('#sk12' @ X2 @ X4 @ X6) @ X2))), 0.64/1.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl46])). 0.64/1.13 thf(zip_derived_cl60, plain, 0.64/1.13 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.64/1.13 (~ (in @ X8 @ X2) 0.64/1.13 | (in @ (kpair @ X8 @ (ap @ X2 @ X4 @ X6 @ X8)) @ X6) 0.64/1.13 | (in @ ('#sk12' @ X2 @ X4 @ X6) @ X2) 0.64/1.13 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 0.64/1.13 thf(zip_derived_cl98, plain, 0.64/1.13 (![X0 : $i]: 0.64/1.13 ( (in @ ('#sk12' @ '#sk1' @ '#sk6' @ '#sk11') @ '#sk1') 0.64/1.13 | (in @ (kpair @ X0 @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0)) @ 0.64/1.13 '#sk11') 0.64/1.13 | ~ (in @ X0 @ '#sk1'))), 0.64/1.13 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl60])). 0.64/1.13 thf(zip_derived_cl138, plain, 0.64/1.13 (![X0 : $i]: 0.64/1.13 (~ (in @ (kpair @ '#sk25' @ X0) @ '#sk11') 0.64/1.13 | ~ (in @ X0 @ '#sk6') 0.64/1.13 | ((X0) = ('#sk32')))), 0.64/1.13 inference('demod', [status(thm)], 0.64/1.13 [zip_derived_cl131, zip_derived_cl41, zip_derived_cl56])). 0.64/1.13 thf(zip_derived_cl148, plain, 0.64/1.13 ((~ (in @ '#sk25' @ '#sk1') 0.64/1.13 | (in @ ('#sk12' @ '#sk1' @ '#sk6' @ '#sk11') @ '#sk1') 0.64/1.13 | ((ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') = ('#sk32')) 0.64/1.13 | ~ (in @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') @ '#sk6'))), 0.64/1.13 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl138])). 0.64/1.13 thf(zip_derived_cl41, plain, ( (in @ '#sk25' @ '#sk1')), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 0.64/1.13 thf(zip_derived_cl154, plain, 0.64/1.13 (( (in @ ('#sk12' @ '#sk1' @ '#sk6' @ '#sk11') @ '#sk1') 0.64/1.13 | ((ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') = ('#sk32')) 0.64/1.13 | ~ (in @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') @ '#sk6'))), 0.64/1.13 inference('demod', [status(thm)], [zip_derived_cl148, zip_derived_cl41])). 0.64/1.13 thf(zip_derived_cl65, plain, 0.64/1.13 (~ (((ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') = ('#sk32')))), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 0.64/1.13 thf(zip_derived_cl70, plain, 0.64/1.13 (((ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') != ('#sk32'))), 0.64/1.13 inference('simplify nested equalities', [status(thm)], [zip_derived_cl65])). 0.64/1.13 thf(zip_derived_cl155, plain, 0.64/1.13 (( (in @ ('#sk12' @ '#sk1' @ '#sk6' @ '#sk11') @ '#sk1') 0.64/1.13 | ~ (in @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') @ '#sk6'))), 0.64/1.13 inference('simplify_reflect-', [status(thm)], 0.64/1.13 [zip_derived_cl154, zip_derived_cl70])). 0.64/1.13 thf(zip_derived_cl166, plain, 0.64/1.13 ((~ (in @ '#sk25' @ '#sk1') 0.64/1.13 | (in @ ('#sk12' @ '#sk1' @ '#sk6' @ '#sk11') @ '#sk1'))), 0.64/1.13 inference('sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl155])). 0.64/1.13 thf(zip_derived_cl41, plain, ( (in @ '#sk25' @ '#sk1')), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 0.64/1.13 thf(zip_derived_cl169, plain, 0.64/1.13 ( (in @ ('#sk12' @ '#sk1' @ '#sk6' @ '#sk11') @ '#sk1')), 0.64/1.13 inference('demod', [status(thm)], [zip_derived_cl166, zip_derived_cl41])). 0.64/1.13 thf(zip_derived_cl204, plain, 0.64/1.13 (![X0 : $i]: 0.64/1.13 ( (in @ (kpair @ X0 @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0)) @ '#sk11') 0.64/1.13 | ~ (in @ X0 @ '#sk1'))), 0.64/1.13 inference('demod', [status(thm)], [zip_derived_cl202, zip_derived_cl169])). 0.64/1.13 thf(zip_derived_cl208, plain, 0.64/1.13 ((((ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') = ('#sk32')) 0.64/1.13 | ~ (in @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') @ '#sk6') 0.64/1.13 | ~ (in @ '#sk25' @ '#sk1'))), 0.64/1.13 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl204])). 0.64/1.13 thf(zip_derived_cl41, plain, ( (in @ '#sk25' @ '#sk1')), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 0.64/1.13 thf(zip_derived_cl212, plain, 0.64/1.13 ((((ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') = ('#sk32')) 0.64/1.13 | ~ (in @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') @ '#sk6'))), 0.64/1.13 inference('demod', [status(thm)], [zip_derived_cl208, zip_derived_cl41])). 0.64/1.13 thf(zip_derived_cl70, plain, 0.64/1.13 (((ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') != ('#sk32'))), 0.64/1.13 inference('simplify nested equalities', [status(thm)], [zip_derived_cl65])). 0.64/1.13 thf(zip_derived_cl213, plain, 0.64/1.13 (~ (in @ (ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25') @ '#sk6')), 0.64/1.13 inference('simplify_reflect-', [status(thm)], 0.64/1.13 [zip_derived_cl212, zip_derived_cl70])). 0.64/1.13 thf(zip_derived_cl223, plain, (~ (in @ '#sk25' @ '#sk1')), 0.64/1.13 inference('sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl213])). 0.64/1.13 thf(zip_derived_cl41, plain, ( (in @ '#sk25' @ '#sk1')), 0.64/1.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 0.64/1.13 thf(zip_derived_cl227, plain, ($false), 0.64/1.13 inference('demod', [status(thm)], [zip_derived_cl223, zip_derived_cl41])). 0.64/1.13 0.64/1.13 % SZS output end Refutation 0.64/1.13 0.64/1.13 0.64/1.13 % Terminating... 4.40/1.27 % Runner terminated. 4.40/1.29 % Zipperpin 1.5 exiting 4.40/1.31 EOF