0.06/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Dt9yA4YE31 true 0.11/0.32 % Computer : n006.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Tue Aug 9 07:48:14 EDT 2022 0.11/0.32 % CPUTime : 0.11/0.32 % Running portfolio for 960 s 0.11/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.11/0.32 % Number of cores: 8 0.17/0.32 % Python version: Python 3.6.8 0.17/0.32 % Running in HO mode 0.47/0.63 % Total configuration time : 828 0.47/0.63 % Estimated wc time : 1656 0.47/0.63 % Estimated cpu time (8 cpus) : 207.0 0.52/0.67 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.53/0.68 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.53/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.53/0.72 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.53/0.72 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.54/0.89 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 5.72/1.30 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 39.62/5.56 % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 30s 238.22/30.67 % /export/starexec/sandbox/solver/bin/lams/15_lifting3.sh running for 30s 276.55/35.66 % /export/starexec/sandbox/solver/bin/lams/33_shallow_sine.sh running for 66s 295.87/38.15 % /export/starexec/sandbox/solver/bin/lams/40_e_lift.sh running for 80s 444.75/57.21 % /export/starexec/sandbox/solver/bin/lams/15_lifting1.sh running for 30s 472.07/60.66 % /export/starexec/sandbox/solver/bin/lams/8_new_cnf.sh running for 16s 473.94/60.91 % /export/starexec/sandbox/solver/bin/lams/10_e_short2.sh running for 20s 477.92/61.57 % /export/starexec/sandbox/solver/bin/lams/8_add_var_l_av.sh running for 16s 481.30/62.02 % Solved by lams/10_e_short2.sh. 481.30/62.02 % running E: timeout 8 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.Dt9yA4YE31/e_input2127a4 --cpu-limit=6 --auto -s -p 481.30/62.02 % done 0 iterations in 0.901s 481.30/62.02 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 481.30/62.02 % SZS output start Refutation 481.30/62.02 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 481.30/62.02 thf('#sk5_type', type, '#sk5': $i). 481.30/62.02 thf('#sk42_type', type, '#sk42': $i). 481.30/62.02 thf('#form7_type', type, '#form7': $o). 481.30/62.02 thf('#sk32_type', type, '#sk32': $i). 481.30/62.02 thf('#sk12_type', type, '#sk12': $i). 481.30/62.02 thf('#sk30_type', type, '#sk30': $i). 481.30/62.02 thf('#sk38_type', type, '#sk38': $i). 481.30/62.02 thf('#sk36_type', type, '#sk36': $i). 481.30/62.02 thf('#sk37_type', type, '#sk37': $i > $o). 481.30/62.02 thf('#sk43_type', type, '#sk43': $i). 481.30/62.02 thf('#sk31_type', type, '#sk31': $i > $o). 481.30/62.02 thf('#sk4_type', type, '#sk4': $i). 481.30/62.02 thf('#sk2_type', type, '#sk2': $i > $o). 481.30/62.02 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 481.30/62.02 thf('#sk89_type', type, '#sk89': ($i > $o) > $i > $i). 481.30/62.02 thf('#sk27_type', type, '#sk27': $i). 481.30/62.02 thf('#sk3_type', type, '#sk3': $i). 481.30/62.02 thf('#sk39_type', type, '#sk39': $i). 481.30/62.02 thf(mforall_prop_type, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o). 481.30/62.02 thf('#form14_type', type, '#form14': $o). 481.30/62.02 thf('#sk21_type', type, '#sk21': $i > $o). 481.30/62.02 thf('#sk52_type', type, '#sk52': ($i > $o) > $i > $i). 481.30/62.02 thf('#sk15_type', type, '#sk15': $i). 481.30/62.02 thf('#sk40_type', type, '#sk40': $i). 481.30/62.02 thf(r1_type, type, r1: $i > $i > $o). 481.30/62.02 thf(mbox_type, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o). 481.30/62.02 thf('#sk28_type', type, '#sk28': $i > $o). 481.30/62.02 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 481.30/62.02 thf(r2_type, type, r2: $i > $i > $o). 481.30/62.02 thf('#form26_type', type, '#form26': $o). 481.30/62.02 thf('#sk33_type', type, '#sk33': $i). 481.30/62.02 thf('#sk1_type', type, '#sk1': $i). 481.30/62.02 thf('#sk35_type', type, '#sk35': $i). 481.30/62.02 thf(r3_type, type, r3: $i > $i > $o). 481.30/62.02 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 481.30/62.02 thf('#form9_type', type, '#form9': $o). 481.30/62.02 thf('#sk29_type', type, '#sk29': $i). 481.30/62.02 thf('#sk20_type', type, '#sk20': $i > $o). 481.30/62.02 thf('#form34_type', type, '#form34': $o). 481.30/62.02 thf('#sk6_type', type, '#sk6': $i > $o). 481.30/62.02 thf('#sk17_type', type, '#sk17': $i). 481.30/62.02 thf('#sk75_type', type, '#sk75': $i > ($i > $o) > $i). 481.30/62.02 thf('#form24_type', type, '#form24': $o). 481.30/62.02 thf('#sk25_type', type, '#sk25': $i). 481.30/62.02 thf('#sk41_type', type, '#sk41': $i). 481.30/62.02 thf('#form16_type', type, '#form16': $o). 481.30/62.02 thf(mvalid, axiom,(( mvalid ) = 481.30/62.02 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 481.30/62.02 thf('0', plain, 481.30/62.02 (( mvalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 481.30/62.02 inference('simplify_rw_rule', [status(thm)], [mvalid])). 481.30/62.02 thf('1', plain, 481.30/62.02 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 481.30/62.02 define([status(thm)])). 481.30/62.02 thf(mbox, axiom,(( mbox ) = 481.30/62.02 (^[R:( $i > $i > $o ),Phi:( $i > $o ),W:$i]: 481.30/62.02 ( ![V:$i]: ( ( Phi @ V ) | ( ~( R @ W @ V ) ) ) )))). 481.30/62.02 thf('2', plain, 481.30/62.02 (( mbox ) = 481.30/62.02 ( ^[R:( $i > $i > $o ),Phi:( $i > $o ),W:$i]: 481.30/62.02 ( ![V:$i]: ( ( Phi @ V ) | ( ~( R @ W @ V ) ) ) ) )), 481.30/62.02 inference('simplify_rw_rule', [status(thm)], [mbox])). 481.30/62.02 thf('3', plain, 481.30/62.02 (( mbox ) = 481.30/62.02 ( ^[V_1:( $i > $i > $o ),V_2:( $i > $o ),V_3:$i]: 481.30/62.02 ( ![X4:$i]: ( ( V_2 @ X4 ) | ( ~( V_1 @ V_3 @ X4 ) ) ) ) )), 481.30/62.02 define([status(thm)])). 481.30/62.02 thf(mforall_prop, axiom,(( mforall_prop ) = 481.30/62.02 (^[Phi:( ( $i > $o ) > $i > $o ),W:$i]: 481.30/62.02 ( ![P:( $i > $o )]: ( Phi @ P @ W ) )))). 481.30/62.02 thf('4', plain, 481.30/62.02 (( mforall_prop ) = 481.30/62.02 ( ^[Phi:( ( $i > $o ) > $i > $o ),W:$i]: 481.30/62.02 ( ![P:( $i > $o )]: ( Phi @ P @ W ) ) )), 481.30/62.02 inference('simplify_rw_rule', [status(thm)], [mforall_prop])). 481.30/62.02 thf('5', plain, 481.30/62.02 (( mforall_prop ) = 481.30/62.02 ( ^[V_1:( ( $i > $o ) > $i > $o ),V_2:$i]: 481.30/62.02 ( ![X4:( $i > $o )]: ( V_1 @ X4 @ V_2 ) ) )), 481.30/62.02 define([status(thm)])). 481.30/62.02 thf(mimplies, axiom,(( mimplies ) = 481.30/62.02 (^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi )))). 481.30/62.02 thf(mor, axiom,(( mor ) = 481.30/62.02 (^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) )))). 481.30/62.02 thf('6', plain, 481.30/62.02 (( mor ) = 481.30/62.02 ( ^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) ) )), 481.30/62.02 inference('simplify_rw_rule', [status(thm)], [mor])). 481.30/62.02 thf('7', plain, 481.30/62.02 (( mor ) = 481.30/62.02 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 481.30/62.02 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 481.30/62.02 define([status(thm)])). 481.30/62.02 thf(mnot, axiom,(( mnot ) = (^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) )))). 481.30/62.02 thf('8', plain, (( mnot ) = ( ^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) ) )), 481.30/62.02 inference('simplify_rw_rule', [status(thm)], [mnot])). 481.30/62.02 thf('9', plain, 481.30/62.02 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 481.30/62.02 define([status(thm)])). 481.30/62.02 thf('10', plain, 481.30/62.02 (( mimplies ) = 481.30/62.02 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi ) )), 481.30/62.02 inference('simplify_rw_rule', [status(thm)], [mimplies, '7', '9'])). 481.30/62.02 thf('11', plain, 481.30/62.02 (( mimplies ) = 481.30/62.02 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 481.30/62.02 define([status(thm)])). 481.30/62.02 thf(conj, conjecture, 481.30/62.02 (( mvalid @ 481.30/62.02 ( mforall_prop @ 481.30/62.02 ( ^[Phi:( $i > $o )]: 481.30/62.02 ( mimplies @ 481.30/62.02 ( mnot @ ( mbox @ r1 @ Phi ) ) @ 481.30/62.02 ( mbox @ r1 @ ( mnot @ ( mbox @ r1 @ Phi ) ) ) ) ) ) ) & 481.30/62.02 ( mvalid @ 481.30/62.02 ( mforall_prop @ 481.30/62.02 ( ^[Phi:( $i > $o )]: 481.30/62.02 ( mimplies @ 481.30/62.02 ( mnot @ ( mbox @ r1 @ Phi ) ) @ 481.30/62.02 ( mbox @ r3 @ ( mnot @ ( mbox @ r1 @ Phi ) ) ) ) ) ) ) & 481.30/62.02 ( mvalid @ 481.30/62.02 ( mforall_prop @ 481.30/62.02 ( ^[Phi:( $i > $o )]: 481.30/62.02 ( mimplies @ 481.30/62.02 ( mnot @ ( mbox @ r2 @ Phi ) ) @ 481.30/62.02 ( mbox @ r1 @ ( mnot @ ( mbox @ r2 @ Phi ) ) ) ) ) ) ) & 481.30/62.02 ( mvalid @ 481.30/62.02 ( mforall_prop @ 481.30/62.02 ( ^[Phi:( $i > $o )]: 481.30/62.02 ( mimplies @ 481.30/62.02 ( mnot @ ( mbox @ r2 @ Phi ) ) @ 481.30/62.02 ( mbox @ r3 @ ( mnot @ ( mbox @ r2 @ Phi ) ) ) ) ) ) ) & 481.30/62.02 ( mvalid @ 481.30/62.02 ( mforall_prop @ 481.30/62.02 ( ^[Phi:( $i > $o )]: 481.30/62.02 ( mimplies @ 481.30/62.02 ( mnot @ ( mbox @ r3 @ Phi ) ) @ 481.30/62.02 ( mbox @ r1 @ ( mnot @ ( mbox @ r3 @ Phi ) ) ) ) ) ) ) & 481.30/62.02 ( mvalid @ 481.30/62.02 ( mforall_prop @ 481.30/62.02 ( ^[Phi:( $i > $o )]: 481.30/62.02 ( mimplies @ 481.30/62.02 ( mnot @ ( mbox @ r3 @ Phi ) ) @ 481.30/62.02 ( mbox @ r3 @ ( mnot @ ( mbox @ r3 @ Phi ) ) ) ) ) ) ) & 481.30/62.02 ( mvalid @ 481.30/62.02 ( mforall_prop @ 481.30/62.02 ( ^[Phi:( $i > $o )]: 481.30/62.02 ( mimplies @ 481.30/62.02 ( mnot @ ( mbox @ r3 @ Phi ) ) @ 481.30/62.02 ( mbox @ r2 @ ( mnot @ ( mbox @ r3 @ Phi ) ) ) ) ) ) ) & 481.30/62.02 ( mvalid @ 481.30/62.02 ( mforall_prop @ 481.30/62.02 ( ^[Phi:( $i > $o )]: 481.30/62.02 ( mimplies @ 481.30/62.02 ( mnot @ ( mbox @ r2 @ Phi ) ) @ 481.30/62.02 ( mbox @ r2 @ ( mnot @ ( mbox @ r2 @ Phi ) ) ) ) ) ) ) & 481.30/62.02 ( mvalid @ 481.30/62.02 ( mforall_prop @ 481.30/62.02 ( ^[Phi:( $i > $o )]: 481.30/62.02 ( mimplies @ 481.30/62.02 ( mnot @ ( mbox @ r1 @ Phi ) ) @ 481.30/62.02 ( mbox @ r2 @ ( mnot @ ( mbox @ r1 @ Phi ) ) ) ) ) ) ))). 481.30/62.02 thf(zf_stmt_0, conjecture, 481.30/62.02 (( ![X4:$i,X6:( $i > $o )]: 481.30/62.02 ( ( ![X10:$i]: 481.30/62.02 ( ( ~( r1 @ X4 @ X10 ) ) | 481.30/62.02 ( ~( ![X12:$i]: ( ( ~( r1 @ X10 @ X12 ) ) | ( X6 @ X12 ) ) ) ) ) ) | 481.30/62.02 ( ![X8:$i]: ( ( ~( r1 @ X4 @ X8 ) ) | ( X6 @ X8 ) ) ) ) ) & 481.30/62.02 ( ![X14:$i,X16:( $i > $o )]: 481.30/62.02 ( ( ![X20:$i]: 481.30/62.02 ( ( ~( r3 @ X14 @ X20 ) ) | 481.30/62.02 ( ~( ![X22:$i]: ( ( ~( r1 @ X20 @ X22 ) ) | ( X16 @ X22 ) ) ) ) ) ) | 481.30/62.02 ( ![X18:$i]: ( ( ~( r1 @ X14 @ X18 ) ) | ( X16 @ X18 ) ) ) ) ) & 481.30/62.02 ( ![X24:$i,X26:( $i > $o )]: 481.30/62.02 ( ( ![X30:$i]: 481.30/62.02 ( ( ~( r1 @ X24 @ X30 ) ) | 481.30/62.02 ( ~( ![X32:$i]: ( ( ~( r2 @ X30 @ X32 ) ) | ( X26 @ X32 ) ) ) ) ) ) | 481.30/62.02 ( ![X28:$i]: ( ( ~( r2 @ X24 @ X28 ) ) | ( X26 @ X28 ) ) ) ) ) & 481.30/62.02 ( ![X34:$i,X36:( $i > $o )]: 481.30/62.02 ( ( ![X40:$i]: 481.30/62.02 ( ( ~( r3 @ X34 @ X40 ) ) | 481.30/62.02 ( ~( ![X42:$i]: ( ( ~( r2 @ X40 @ X42 ) ) | ( X36 @ X42 ) ) ) ) ) ) | 481.30/62.02 ( ![X38:$i]: ( ( ~( r2 @ X34 @ X38 ) ) | ( X36 @ X38 ) ) ) ) ) & 481.30/62.02 ( ![X44:$i,X46:( $i > $o )]: 481.30/62.02 ( ( ![X50:$i]: 481.30/62.02 ( ( ~( r1 @ X44 @ X50 ) ) | 481.30/62.02 ( ~( ![X52:$i]: ( ( ~( r3 @ X50 @ X52 ) ) | ( X46 @ X52 ) ) ) ) ) ) | 481.30/62.02 ( ![X48:$i]: ( ( ~( r3 @ X44 @ X48 ) ) | ( X46 @ X48 ) ) ) ) ) & 481.30/62.02 ( ![X54:$i,X56:( $i > $o )]: 481.30/62.02 ( ( ![X60:$i]: 481.30/62.02 ( ( ~( r3 @ X54 @ X60 ) ) | 481.30/62.02 ( ~( ![X62:$i]: ( ( ~( r3 @ X60 @ X62 ) ) | ( X56 @ X62 ) ) ) ) ) ) | 481.30/62.02 ( ![X58:$i]: ( ( ~( r3 @ X54 @ X58 ) ) | ( X56 @ X58 ) ) ) ) ) & 481.30/62.02 ( ![X64:$i,X66:( $i > $o )]: 481.30/62.02 ( ( ![X70:$i]: 481.30/62.02 ( ( ~( r2 @ X64 @ X70 ) ) | 481.30/62.02 ( ~( ![X72:$i]: ( ( ~( r3 @ X70 @ X72 ) ) | ( X66 @ X72 ) ) ) ) ) ) | 481.30/62.02 ( ![X68:$i]: ( ( ~( r3 @ X64 @ X68 ) ) | ( X66 @ X68 ) ) ) ) ) & 481.30/62.02 ( ![X74:$i,X76:( $i > $o )]: 481.30/62.02 ( ( ![X80:$i]: 481.30/62.02 ( ( ~( r2 @ X74 @ X80 ) ) | 481.30/62.02 ( ~( ![X82:$i]: ( ( ~( r2 @ X80 @ X82 ) ) | ( X76 @ X82 ) ) ) ) ) ) | 481.30/62.02 ( ![X78:$i]: ( ( ~( r2 @ X74 @ X78 ) ) | ( X76 @ X78 ) ) ) ) ) & 481.30/62.02 ( ![X84:$i,X86:( $i > $o )]: 481.30/62.02 ( ( ![X90:$i]: 481.30/62.02 ( ( ~( r2 @ X84 @ X90 ) ) | 481.30/62.02 ( ~( ![X92:$i]: ( ( ~( r1 @ X90 @ X92 ) ) | ( X86 @ X92 ) ) ) ) ) ) | 481.30/62.02 ( ![X88:$i]: ( ( ~( r1 @ X84 @ X88 ) ) | ( X86 @ X88 ) ) ) ) ))). 481.30/62.02 thf(zf_stmt_1, negated_conjecture, 481.30/62.02 (~( ( ![X4:$i,X6:( $i > $o )]: 481.30/62.02 ( ( ![X10:$i]: 481.30/62.02 ( ( ~( r1 @ X4 @ X10 ) ) | 481.30/62.02 ( ~( ![X12:$i]: ( ( ~( r1 @ X10 @ X12 ) ) | ( X6 @ X12 ) ) ) ) ) ) | 481.30/62.02 ( ![X8:$i]: ( ( ~( r1 @ X4 @ X8 ) ) | ( X6 @ X8 ) ) ) ) ) & 481.30/62.02 ( ![X14:$i,X16:( $i > $o )]: 481.30/62.02 ( ( ![X20:$i]: 481.30/62.02 ( ( ~( r3 @ X14 @ X20 ) ) | 481.30/62.02 ( ~( ![X22:$i]: ( ( ~( r1 @ X20 @ X22 ) ) | ( X16 @ X22 ) ) ) ) ) ) | 481.30/62.02 ( ![X18:$i]: ( ( ~( r1 @ X14 @ X18 ) ) | ( X16 @ X18 ) ) ) ) ) & 481.30/62.02 ( ![X24:$i,X26:( $i > $o )]: 481.30/62.02 ( ( ![X30:$i]: 481.30/62.02 ( ( ~( r1 @ X24 @ X30 ) ) | 481.30/62.02 ( ~( ![X32:$i]: ( ( ~( r2 @ X30 @ X32 ) ) | ( X26 @ X32 ) ) ) ) ) ) | 481.30/62.02 ( ![X28:$i]: ( ( ~( r2 @ X24 @ X28 ) ) | ( X26 @ X28 ) ) ) ) ) & 481.30/62.02 ( ![X34:$i,X36:( $i > $o )]: 481.30/62.02 ( ( ![X40:$i]: 481.30/62.02 ( ( ~( r3 @ X34 @ X40 ) ) | 481.30/62.02 ( ~( ![X42:$i]: ( ( ~( r2 @ X40 @ X42 ) ) | ( X36 @ X42 ) ) ) ) ) ) | 481.30/62.02 ( ![X38:$i]: ( ( ~( r2 @ X34 @ X38 ) ) | ( X36 @ X38 ) ) ) ) ) & 481.30/62.02 ( ![X44:$i,X46:( $i > $o )]: 481.30/62.02 ( ( ![X50:$i]: 481.30/62.02 ( ( ~( r1 @ X44 @ X50 ) ) | 481.30/62.02 ( ~( ![X52:$i]: ( ( ~( r3 @ X50 @ X52 ) ) | ( X46 @ X52 ) ) ) ) ) ) | 481.30/62.02 ( ![X48:$i]: ( ( ~( r3 @ X44 @ X48 ) ) | ( X46 @ X48 ) ) ) ) ) & 481.30/62.02 ( ![X54:$i,X56:( $i > $o )]: 481.30/62.02 ( ( ![X60:$i]: 481.30/62.02 ( ( ~( r3 @ X54 @ X60 ) ) | 481.30/62.02 ( ~( ![X62:$i]: ( ( ~( r3 @ X60 @ X62 ) ) | ( X56 @ X62 ) ) ) ) ) ) | 481.30/62.02 ( ![X58:$i]: ( ( ~( r3 @ X54 @ X58 ) ) | ( X56 @ X58 ) ) ) ) ) & 481.30/62.02 ( ![X64:$i,X66:( $i > $o )]: 481.30/62.02 ( ( ![X70:$i]: 481.30/62.02 ( ( ~( r2 @ X64 @ X70 ) ) | 481.30/62.02 ( ~( ![X72:$i]: ( ( ~( r3 @ X70 @ X72 ) ) | ( X66 @ X72 ) ) ) ) ) ) | 481.30/62.02 ( ![X68:$i]: ( ( ~( r3 @ X64 @ X68 ) ) | ( X66 @ X68 ) ) ) ) ) & 481.30/62.02 ( ![X74:$i,X76:( $i > $o )]: 481.30/62.02 ( ( ![X80:$i]: 481.30/62.02 ( ( ~( r2 @ X74 @ X80 ) ) | 481.30/62.02 ( ~( ![X82:$i]: ( ( ~( r2 @ X80 @ X82 ) ) | ( X76 @ X82 ) ) ) ) ) ) | 481.30/62.02 ( ![X78:$i]: ( ( ~( r2 @ X74 @ X78 ) ) | ( X76 @ X78 ) ) ) ) ) & 481.30/62.02 ( ![X84:$i,X86:( $i > $o )]: 481.30/62.02 ( ( ![X90:$i]: 481.30/62.02 ( ( ~( r2 @ X84 @ X90 ) ) | 481.30/62.02 ( ~( ![X92:$i]: ( ( ~( r1 @ X90 @ X92 ) ) | ( X86 @ X92 ) ) ) ) ) ) | 481.30/62.02 ( ![X88:$i]: ( ( ~( r1 @ X84 @ X88 ) ) | ( X86 @ X88 ) ) ) ) ) )), 481.30/62.02 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 481.30/62.02 thf(zip_derived_cl18, plain, 481.30/62.02 (~ (((((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) & 481.30/62.02 (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) & 481.30/62.02 (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) & 481.30/62.02 (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) & 481.30/62.02 (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) & 481.30/62.02 (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) & 481.30/62.02 (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) & 481.30/62.02 (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) & 481.30/62.02 (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2))))))))))))))))), 481.30/62.02 inference('cnf', [status(esa)], [zf_stmt_1])). 481.30/62.02 thf(zip_derived_cl19, plain, 481.30/62.02 ((~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 ( 481.30/62.02 ( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 481.30/62.02 thf(zip_derived_cl20, plain, 481.30/62.02 ((~ (((!!) @ (^[Y0 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk1' @ Y1))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y1 @ 481.30/62.02 Y2))) | 481.30/62.02 (Y0 @ Y2))))))))))))) | 481.30/62.02 (((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk1' @ Y1))) | (Y0 @ Y1))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 481.30/62.02 thf(zip_derived_cl21, plain, 481.30/62.02 ((~ (((((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk1' @ Y0))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y1))) | 481.30/62.02 ('#sk2' @ Y1))))))))))))) | 481.30/62.02 (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk1' @ Y0))) | ('#sk2' @ Y0)))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl20])). 481.30/62.02 thf(zip_derived_cl23, plain, 481.30/62.02 ((~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk1' @ Y0))) | ('#sk2' @ Y0)))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl21])). 481.30/62.02 thf(zip_derived_cl25, plain, 481.30/62.02 ((~ (((((~) @ (r1 @ '#sk1' @ '#sk4'))) | ('#sk2' @ '#sk4'))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl23])). 481.30/62.02 thf(zip_derived_cl29, plain, 481.30/62.02 ((~ ('#sk2' @ '#sk4') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl25])). 481.30/62.02 thf(zip_derived_cl33, plain, 481.30/62.02 ((~ (((!!) @ (^[Y0 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r2 @ '#sk5' @ Y1))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y1 @ 481.30/62.02 Y2))) | 481.30/62.02 (Y0 @ Y2))))))))))))) | 481.30/62.02 (((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk5' @ Y1))) | (Y0 @ Y1))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ ('#sk2' @ '#sk4'))), 481.30/62.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])). 481.30/62.02 thf(zip_derived_cl37, plain, 481.30/62.02 ((~ (((((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y1))) | 481.30/62.02 ('#sk6' @ Y1))))))))))))) | 481.30/62.02 (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))))) 481.30/62.02 | ~ ('#sk2' @ '#sk4') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl33])). 481.30/62.02 thf(zip_derived_cl44, plain, 481.30/62.02 ((~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ ('#sk2' @ '#sk4'))), 481.30/62.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl37])). 481.30/62.02 thf(zip_derived_cl22, plain, 481.30/62.02 ((~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk1' @ Y0))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y1))) | 481.30/62.02 ('#sk2' @ Y1))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl21])). 481.30/62.02 thf(zip_derived_cl24, plain, 481.30/62.02 ((~ (((((~) @ (r1 @ '#sk1' @ '#sk3'))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk3' @ Y0))) | ('#sk2' @ Y0)))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl22])). 481.30/62.02 thf(zip_derived_cl26, plain, 481.30/62.02 (( (r1 @ '#sk1' @ '#sk3') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])). 481.30/62.02 thf(zip_derived_cl30, plain, 481.30/62.02 ((~ (((!!) @ (^[Y0 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r2 @ '#sk5' @ Y1))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y1 @ 481.30/62.02 Y2))) | 481.30/62.02 (Y0 @ Y2))))))))))))) | 481.30/62.02 (((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk5' @ Y1))) | (Y0 @ Y1))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | (r1 @ '#sk1' @ '#sk3'))), 481.30/62.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl26])). 481.30/62.02 thf(zip_derived_cl34, plain, 481.30/62.02 ((~ (((((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y1))) | 481.30/62.02 ('#sk6' @ Y1))))))))))))) | 481.30/62.02 (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))))) 481.30/62.02 | (r1 @ '#sk1' @ '#sk3') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 481.30/62.02 thf(zip_derived_cl38, plain, 481.30/62.02 ((~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y1))) | 481.30/62.02 ('#sk6' @ Y1))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | (r1 @ '#sk1' @ '#sk3'))), 481.30/62.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 481.30/62.02 thf(zip_derived_cl45, plain, 481.30/62.02 (( ('#form7') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 define([status(thm)])). 481.30/62.02 thf(zip_derived_cl53, plain, 481.30/62.02 ((~ ('#form7') 481.30/62.02 | ~ ('#sk2' @ '#sk4') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))))), 481.30/62.02 inference('renaming', [status(thm)], [zip_derived_cl44, zip_derived_cl45])). 481.30/62.02 thf(zip_derived_cl38, plain, 481.30/62.02 ((~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y1))) | 481.30/62.02 ('#sk6' @ Y1))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | (r1 @ '#sk1' @ '#sk3'))), 481.30/62.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 481.30/62.02 thf(zip_derived_cl45, plain, 481.30/62.02 (( ('#form7') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 define([status(thm)])). 481.30/62.02 thf(zip_derived_cl47, plain, 481.30/62.02 ((~ ('#form7') 481.30/62.02 | (r1 @ '#sk1' @ '#sk3') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y1 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y1))) | 481.30/62.02 ('#sk6' @ Y1))))))))))))))), 481.30/62.02 inference('renaming', [status(thm)], [zip_derived_cl38, zip_derived_cl45])). 481.30/62.02 thf(zip_derived_cl54, plain, 481.30/62.02 (( ('#form9') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 define([status(thm)])). 481.30/62.02 thf(zip_derived_cl63, plain, 481.30/62.02 ((~ ('#form9') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ ('#sk2' @ '#sk4') 481.30/62.02 | ~ ('#form7'))), 481.30/62.02 inference('renaming', [status(thm)], [zip_derived_cl53, zip_derived_cl54])). 481.30/62.02 thf(zip_derived_cl39, plain, 481.30/62.02 ((~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | (r1 @ '#sk1' @ '#sk3'))), 481.30/62.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 481.30/62.02 thf(zip_derived_cl45, plain, 481.30/62.02 (( ('#form7') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 define([status(thm)])). 481.30/62.02 thf(zip_derived_cl48, plain, 481.30/62.02 ((~ ('#form7') 481.30/62.02 | (r1 @ '#sk1' @ '#sk3') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))))), 481.30/62.02 inference('renaming', [status(thm)], [zip_derived_cl39, zip_derived_cl45])). 481.30/62.02 thf(zip_derived_cl54, plain, 481.30/62.02 (( ('#form9') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 define([status(thm)])). 481.30/62.02 thf(zip_derived_cl58, plain, 481.30/62.02 ((~ ('#form9') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | (r1 @ '#sk1' @ '#sk3') 481.30/62.02 | ~ ('#form7'))), 481.30/62.02 inference('renaming', [status(thm)], [zip_derived_cl48, zip_derived_cl54])). 481.30/62.02 thf(zip_derived_cl68, plain, 481.30/62.02 (( ('#form14') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r1 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))))), 481.30/62.02 define([status(thm)])). 481.30/62.02 thf(zip_derived_cl75, plain, 481.30/62.02 ((~ ('#form14') 481.30/62.02 | ~ ('#form7') 481.30/62.02 | ~ ('#sk2' @ '#sk4') 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r3 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.02 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.02 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.02 (((((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.02 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.02 (( 481.30/62.02 (( 481.30/62.02 (~) @ ( 481.30/62.02 r2 @ 481.30/62.02 Y2 @ Y3))) | 481.30/62.02 (Y1 @ Y3))))))))))))) | 481.30/62.02 (((!!) @ (^[Y2 : $i]: 481.30/62.02 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.02 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.03 | ~ ('#form9'))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl63, zip_derived_cl68])). 481.30/62.03 thf(zip_derived_cl47, plain, 481.30/62.03 ((~ ('#form7') 481.30/62.03 | (r1 @ '#sk1' @ '#sk3') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y1 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y1))) | 481.30/62.03 ('#sk6' @ Y1))))))))))))))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl38, zip_derived_cl45])). 481.30/62.03 thf(zip_derived_cl54, plain, 481.30/62.03 (( ('#form9') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl56, plain, 481.30/62.03 ((~ ('#form9') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y1 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y1))) | 481.30/62.03 ('#sk6' @ Y1))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | (r1 @ '#sk1' @ '#sk3') 481.30/62.03 | ~ ('#form7'))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl47, zip_derived_cl54])). 481.30/62.03 thf(zip_derived_cl64, plain, 481.30/62.03 ((~ (((((~) @ (r2 @ '#sk5' @ '#sk12'))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ Y0)))))))))) 481.30/62.03 | ~ ('#form7') 481.30/62.03 | (r1 @ '#sk1' @ '#sk3') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ ('#form9'))), 481.30/62.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl56])). 481.30/62.03 thf(zip_derived_cl76, plain, 481.30/62.03 (( ('#form16') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl89, plain, 481.30/62.03 ((~ ('#form16') 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ ('#sk2' @ '#sk4') 481.30/62.03 | ~ ('#form7') 481.30/62.03 | ~ ('#form14'))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl75, zip_derived_cl76])). 481.30/62.03 thf(zip_derived_cl58, plain, 481.30/62.03 ((~ ('#form9') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | (r1 @ '#sk1' @ '#sk3') 481.30/62.03 | ~ ('#form7'))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl48, zip_derived_cl54])). 481.30/62.03 thf(zip_derived_cl68, plain, 481.30/62.03 (( ('#form14') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl70, plain, 481.30/62.03 ((~ ('#form14') 481.30/62.03 | ~ ('#form7') 481.30/62.03 | (r1 @ '#sk1' @ '#sk3') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.03 | ~ ('#form9'))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl58, zip_derived_cl68])). 481.30/62.03 thf(zip_derived_cl76, plain, 481.30/62.03 (( ('#form16') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl83, plain, 481.30/62.03 ((~ ('#form16') 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | (r1 @ '#sk1' @ '#sk3') 481.30/62.03 | ~ ('#form7') 481.30/62.03 | ~ ('#form14'))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl70, zip_derived_cl76])). 481.30/62.03 thf(zip_derived_cl98, plain, 481.30/62.03 (( ('#form24') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl107, plain, 481.30/62.03 ((~ ('#form24') 481.30/62.03 | ~ ('#form14') 481.30/62.03 | ~ ('#form7') 481.30/62.03 | ~ ('#sk2' @ '#sk4') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ ('#form16'))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl89, zip_derived_cl98])). 481.30/62.03 thf(zip_derived_cl64, plain, 481.30/62.03 ((~ (((((~) @ (r2 @ '#sk5' @ '#sk12'))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ Y0)))))))))) 481.30/62.03 | ~ ('#form7') 481.30/62.03 | (r1 @ '#sk1' @ '#sk3') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ ('#form9'))), 481.30/62.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl56])). 481.30/62.03 thf(zip_derived_cl76, plain, 481.30/62.03 (( ('#form16') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl78, plain, 481.30/62.03 ((~ ('#form16') 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | (r1 @ '#sk1' @ '#sk3') 481.30/62.03 | ~ ('#form7') 481.30/62.03 | ~ (((((~) @ (r2 @ '#sk5' @ '#sk12'))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ 481.30/62.03 Y0)))))))))))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl64, zip_derived_cl76])). 481.30/62.03 thf(zip_derived_cl68, plain, 481.30/62.03 (( ('#form14') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl90, plain, 481.30/62.03 ((~ ('#form14') 481.30/62.03 | ~ (((((~) @ (r2 @ '#sk5' @ '#sk12'))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ 481.30/62.03 Y0)))))))))) 481.30/62.03 | ~ ('#form7') 481.30/62.03 | (r1 @ '#sk1' @ '#sk3') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ ('#form16'))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl78, zip_derived_cl68])). 481.30/62.03 thf(zip_derived_cl108, plain, 481.30/62.03 (( ('#form26') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl126, plain, 481.30/62.03 ((~ ('#form26') 481.30/62.03 | ~ ('#form16') 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ ('#sk2' @ '#sk4') 481.30/62.03 | ~ ('#form7') 481.30/62.03 | ~ ('#form14') 481.30/62.03 | ~ ('#form24'))), 481.30/62.03 inference('renaming', [status(thm)], 481.30/62.03 [zip_derived_cl107, zip_derived_cl108])). 481.30/62.03 thf(zip_derived_cl83, plain, 481.30/62.03 ((~ ('#form16') 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | (r1 @ '#sk1' @ '#sk3') 481.30/62.03 | ~ ('#form7') 481.30/62.03 | ~ ('#form14'))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl70, zip_derived_cl76])). 481.30/62.03 thf(zip_derived_cl98, plain, 481.30/62.03 (( ('#form24') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl100, plain, 481.30/62.03 ((~ ('#form24') 481.30/62.03 | ~ ('#form14') 481.30/62.03 | ~ ('#form7') 481.30/62.03 | (r1 @ '#sk1' @ '#sk3') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ ('#form16'))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl83, zip_derived_cl98])). 481.30/62.03 thf(zip_derived_cl108, plain, 481.30/62.03 (( ('#form26') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl118, plain, 481.30/62.03 ((~ ('#form26') 481.30/62.03 | ~ ('#form16') 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | (r1 @ '#sk1' @ '#sk3') 481.30/62.03 | ~ ('#form7') 481.30/62.03 | ~ ('#form14') 481.30/62.03 | ~ ('#form24'))), 481.30/62.03 inference('renaming', [status(thm)], 481.30/62.03 [zip_derived_cl100, zip_derived_cl108])). 481.30/62.03 thf(zip_derived_cl133, plain, 481.30/62.03 (( ('#form34') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl146, plain, 481.30/62.03 ((~ ('#form34') 481.30/62.03 | ~ ('#form24') 481.30/62.03 | ~ ('#form14') 481.30/62.03 | ~ ('#form7') 481.30/62.03 | ~ ('#sk2' @ '#sk4') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ ('#form16') 481.30/62.03 | ~ ('#form26'))), 481.30/62.03 inference('renaming', [status(thm)], 481.30/62.03 [zip_derived_cl126, zip_derived_cl133])). 481.30/62.03 thf(zip_derived_cl164, plain, 481.30/62.03 ((~ (((((~) @ (r1 @ '#sk5' @ '#sk36'))) | ('#sk6' @ '#sk36'))) 481.30/62.03 | ~ ('#form26') 481.30/62.03 | ~ ('#form16') 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ ('#sk2' @ '#sk4') 481.30/62.03 | ~ ('#form7') 481.30/62.03 | ~ ('#form14') 481.30/62.03 | ~ ('#form24') 481.30/62.03 | ~ ('#form34'))), 481.30/62.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl146])). 481.30/62.03 thf(zip_derived_cl188, plain, 481.30/62.03 ((~ ('#sk6' @ '#sk36') 481.30/62.03 | ~ ('#form34') 481.30/62.03 | ~ ('#form24') 481.30/62.03 | ~ ('#form14') 481.30/62.03 | ~ ('#form7') 481.30/62.03 | ~ ('#sk2' @ '#sk4') 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ ('#form16') 481.30/62.03 | ~ ('#form26'))), 481.30/62.03 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl164])). 481.30/62.03 thf(axiom_5_for_r3, axiom, 481.30/62.03 (mvalid @ 481.30/62.03 ( mforall_prop @ 481.30/62.03 ( ^[Phi:( $i > $o )]: 481.30/62.03 ( mimplies @ 481.30/62.03 ( mnot @ ( mbox @ r3 @ Phi ) ) @ 481.30/62.03 ( mbox @ r3 @ ( mnot @ ( mbox @ r3 @ Phi ) ) ) ) ) ))). 481.30/62.03 thf(zf_stmt_2, axiom, 481.30/62.03 (![X4:$i,X6:( $i > $o )]: 481.30/62.03 ( ( ![X10:$i]: 481.30/62.03 ( ( ~( r3 @ X4 @ X10 ) ) | 481.30/62.03 ( ~( ![X12:$i]: ( ( ~( r3 @ X10 @ X12 ) ) | ( X6 @ X12 ) ) ) ) ) ) | 481.30/62.03 ( ![X8:$i]: ( ( ~( r3 @ X4 @ X8 ) ) | ( X6 @ X8 ) ) ) ))). 481.30/62.03 thf(zip_derived_cl13, plain, 481.30/62.03 ( (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (((( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2))))))))))))))), 481.30/62.03 inference('cnf', [status(esa)], [zf_stmt_2])). 481.30/62.03 thf(zip_derived_cl13, plain, 481.30/62.03 ( (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (((( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2))))))))))))))), 481.30/62.03 inference('cnf', [status(esa)], [zf_stmt_2])). 481.30/62.03 thf(zip_derived_cl242, plain, 481.30/62.03 ((~ ('#form7') 481.30/62.03 | (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl45, plain, 481.30/62.03 (( ('#form7') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl244, plain, ( ('#form7')), 481.30/62.03 inference('renaming', [status(thm)], 481.30/62.03 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.30/62.03 thf(zip_derived_cl256, plain, 481.30/62.03 ((~ ('#sk6' @ '#sk36') 481.30/62.03 | ~ ('#form34') 481.30/62.03 | ~ ('#form24') 481.30/62.03 | ~ ('#form14') 481.30/62.03 | ~ ('#sk2' @ '#sk4') 481.30/62.03 | ~ ('#form9') 481.30/62.03 | ~ ('#form16') 481.30/62.03 | ~ ('#form26'))), 481.30/62.03 inference('demod', [status(thm)], [zip_derived_cl188, zip_derived_cl244])). 481.30/62.03 thf(axiom_5_for_r2, axiom, 481.30/62.03 (mvalid @ 481.30/62.03 ( mforall_prop @ 481.30/62.03 ( ^[Phi:( $i > $o )]: 481.30/62.03 ( mimplies @ 481.30/62.03 ( mnot @ ( mbox @ r2 @ Phi ) ) @ 481.30/62.03 ( mbox @ r2 @ ( mnot @ ( mbox @ r2 @ Phi ) ) ) ) ) ))). 481.30/62.03 thf(zf_stmt_3, axiom, 481.30/62.03 (![X4:$i,X6:( $i > $o )]: 481.30/62.03 ( ( ![X10:$i]: 481.30/62.03 ( ( ~( r2 @ X4 @ X10 ) ) | 481.30/62.03 ( ~( ![X12:$i]: ( ( ~( r2 @ X10 @ X12 ) ) | ( X6 @ X12 ) ) ) ) ) ) | 481.30/62.03 ( ![X8:$i]: ( ( ~( r2 @ X4 @ X8 ) ) | ( X6 @ X8 ) ) ) ))). 481.30/62.03 thf(zip_derived_cl16, plain, 481.30/62.03 ( (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (((( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2))))))))))))))), 481.30/62.03 inference('cnf', [status(esa)], [zf_stmt_3])). 481.30/62.03 thf(zip_derived_cl16, plain, 481.30/62.03 ( (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (((( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2))))))))))))))), 481.30/62.03 inference('cnf', [status(esa)], [zf_stmt_3])). 481.30/62.03 thf(zip_derived_cl266, plain, 481.30/62.03 ((~ ('#form9') 481.30/62.03 | (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl54, plain, 481.30/62.03 (( ('#form9') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl268, plain, ( ('#form9')), 481.30/62.03 inference('renaming', [status(thm)], 481.30/62.03 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.30/62.03 thf(zip_derived_cl280, plain, 481.30/62.03 ((~ ('#sk6' @ '#sk36') 481.30/62.03 | ~ ('#form34') 481.30/62.03 | ~ ('#form24') 481.30/62.03 | ~ ('#form14') 481.30/62.03 | ~ ('#sk2' @ '#sk4') 481.30/62.03 | ~ ('#form16') 481.30/62.03 | ~ ('#form26'))), 481.30/62.03 inference('demod', [status(thm)], [zip_derived_cl256, zip_derived_cl268])). 481.30/62.03 thf(zip_derived_cl27, plain, 481.30/62.03 (( (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ '#sk3' @ Y0))) | ('#sk2' @ Y0)))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])). 481.30/62.03 thf(zip_derived_cl31, plain, 481.30/62.03 (![X2 : $i]: 481.30/62.03 ( (((((~) @ (r1 @ '#sk3' @ X2))) | ('#sk2' @ X2))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl27])). 481.30/62.03 thf(zip_derived_cl35, plain, 481.30/62.03 (![X2 : $i]: 481.30/62.03 (~ (r1 @ '#sk3' @ X2) 481.30/62.03 | ('#sk2' @ X2) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 481.30/62.03 thf(zip_derived_cl40, plain, 481.30/62.03 (![X2 : $i]: 481.30/62.03 (~ (((!!) @ (^[Y0 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y1 : $i]: 481.30/62.03 (((((~) @ (r2 @ '#sk5' @ Y1))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r1 @ Y1 @ Y2))) | 481.30/62.03 (Y0 @ Y2))))))))))))) | 481.30/62.03 (((!!) @ (^[Y1 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y1))) | (Y0 @ 481.30/62.03 Y1))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ('#sk2' @ X2) 481.30/62.03 | ~ (r1 @ '#sk3' @ X2))), 481.30/62.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl35])). 481.30/62.03 thf(zip_derived_cl45, plain, 481.30/62.03 (( ('#form7') 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y3 : $i]: 481.30/62.03 (( 481.30/62.03 (( 481.30/62.03 (~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))))), 481.30/62.03 define([status(thm)])). 481.30/62.03 thf(zip_derived_cl49, plain, 481.30/62.03 (![X2 : $i]: 481.30/62.03 (~ ('#form7') 481.30/62.03 | ~ (r1 @ '#sk3' @ X2) 481.30/62.03 | ('#sk2' @ X2) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r3 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r2 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r2 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i]: 481.30/62.03 (((!!) @ (^[Y1 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r3 @ Y0 @ Y2))) | 481.30/62.03 (((~) @ (((!!) @ ( 481.30/62.03 ^[Y3 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r1 @ 481.30/62.03 Y2 @ Y3))) | 481.30/62.03 (Y1 @ Y3))))))))))))) | 481.30/62.03 (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ (r1 @ Y0 @ Y2))) | 481.30/62.03 (Y1 @ Y2)))))))))))))) 481.30/62.03 | ~ (((!!) @ (^[Y0 : $i > $o]: 481.30/62.03 (((((!!) @ (^[Y1 : $i]: 481.30/62.03 (((((~) @ (r2 @ '#sk5' @ Y1))) | 481.30/62.03 (((~) @ (((!!) @ (^[Y2 : $i]: 481.30/62.03 (((((~) @ ( 481.30/62.03 r1 @ Y1 @ Y2))) | 481.30/62.03 (Y0 @ Y2))))))))))))) | 481.30/62.03 (((!!) @ (^[Y1 : $i]: 481.30/62.03 (((((~) @ (r1 @ '#sk5' @ Y1))) | (Y0 @ 481.30/62.03 Y1))))))))))))), 481.30/62.03 inference('renaming', [status(thm)], [zip_derived_cl40, zip_derived_cl45])). 481.51/62.04 thf(zip_derived_cl54, plain, 481.51/62.04 (( ('#form9') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))))), 481.51/62.04 define([status(thm)])). 481.51/62.04 thf(zip_derived_cl59, plain, 481.51/62.04 (![X2 : $i]: 481.51/62.04 (~ ('#form9') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r2 @ '#sk5' @ Y1))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r1 @ Y1 @ Y2))) | 481.51/62.04 (Y0 @ Y2))))))))))))) | 481.51/62.04 (((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r1 @ '#sk5' @ Y1))) | (Y0 @ 481.51/62.04 Y1))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r1 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ('#sk2' @ X2) 481.51/62.04 | ~ (r1 @ '#sk3' @ X2) 481.51/62.04 | ~ ('#form7'))), 481.51/62.04 inference('renaming', [status(thm)], [zip_derived_cl49, zip_derived_cl54])). 481.51/62.04 thf(zip_derived_cl68, plain, 481.51/62.04 (( ('#form14') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r1 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))))), 481.51/62.04 define([status(thm)])). 481.51/62.04 thf(zip_derived_cl71, plain, 481.51/62.04 (![X2 : $i]: 481.51/62.04 (~ ('#form14') 481.51/62.04 | ~ ('#form7') 481.51/62.04 | ~ (r1 @ '#sk3' @ X2) 481.51/62.04 | ('#sk2' @ X2) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r2 @ '#sk5' @ Y1))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r1 @ Y1 @ Y2))) | 481.51/62.04 (Y0 @ Y2))))))))))))) | 481.51/62.04 (((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r1 @ '#sk5' @ Y1))) | (Y0 @ 481.51/62.04 Y1))))))))))) 481.51/62.04 | ~ ('#form9'))), 481.51/62.04 inference('renaming', [status(thm)], [zip_derived_cl59, zip_derived_cl68])). 481.51/62.04 thf(zip_derived_cl76, plain, 481.51/62.04 (( ('#form16') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))))), 481.51/62.04 define([status(thm)])). 481.51/62.04 thf(zip_derived_cl85, plain, 481.51/62.04 (![X2 : $i]: 481.51/62.04 (~ ('#form16') 481.51/62.04 | ~ ('#form9') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r2 @ '#sk5' @ Y1))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r1 @ Y1 @ Y2))) | 481.51/62.04 (Y0 @ Y2))))))))))))) | 481.51/62.04 (((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r1 @ '#sk5' @ Y1))) | (Y0 @ 481.51/62.04 Y1))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ('#sk2' @ X2) 481.51/62.04 | ~ (r1 @ '#sk3' @ X2) 481.51/62.04 | ~ ('#form7') 481.51/62.04 | ~ ('#form14'))), 481.51/62.04 inference('renaming', [status(thm)], [zip_derived_cl71, zip_derived_cl76])). 481.51/62.04 thf(zip_derived_cl98, plain, 481.51/62.04 (( ('#form24') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))))), 481.51/62.04 define([status(thm)])). 481.51/62.04 thf(zip_derived_cl103, plain, 481.51/62.04 (![X2 : $i]: 481.51/62.04 (~ ('#form24') 481.51/62.04 | ~ ('#form14') 481.51/62.04 | ~ ('#form7') 481.51/62.04 | ~ (r1 @ '#sk3' @ X2) 481.51/62.04 | ('#sk2' @ X2) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r2 @ '#sk5' @ Y1))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r1 @ Y1 @ Y2))) | 481.51/62.04 (Y0 @ Y2))))))))))))) | 481.51/62.04 (((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r1 @ '#sk5' @ Y1))) | (Y0 @ 481.51/62.04 Y1))))))))))) 481.51/62.04 | ~ ('#form9') 481.51/62.04 | ~ ('#form16'))), 481.51/62.04 inference('renaming', [status(thm)], [zip_derived_cl85, zip_derived_cl98])). 481.51/62.04 thf(zip_derived_cl108, plain, 481.51/62.04 (( ('#form26') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))))), 481.51/62.04 define([status(thm)])). 481.51/62.04 thf(zip_derived_cl122, plain, 481.51/62.04 (![X2 : $i]: 481.51/62.04 (~ ('#form26') 481.51/62.04 | ~ ('#form16') 481.51/62.04 | ~ ('#form9') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r2 @ '#sk5' @ Y1))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r1 @ Y1 @ Y2))) | 481.51/62.04 (Y0 @ Y2))))))))))))) | 481.51/62.04 (((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r1 @ '#sk5' @ Y1))) | (Y0 @ 481.51/62.04 Y1))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ ( 481.51/62.04 ^[Y3 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ('#sk2' @ X2) 481.51/62.04 | ~ (r1 @ '#sk3' @ X2) 481.51/62.04 | ~ ('#form7') 481.51/62.04 | ~ ('#form14') 481.51/62.04 | ~ ('#form24'))), 481.51/62.04 inference('renaming', [status(thm)], 481.51/62.04 [zip_derived_cl103, zip_derived_cl108])). 481.51/62.04 thf(zip_derived_cl133, plain, 481.51/62.04 (( ('#form34') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))))), 481.51/62.04 define([status(thm)])). 481.51/62.04 thf(zip_derived_cl142, plain, 481.51/62.04 (![X2 : $i]: 481.51/62.04 (~ ('#form34') 481.51/62.04 | ~ ('#form24') 481.51/62.04 | ~ ('#form14') 481.51/62.04 | ~ ('#form7') 481.51/62.04 | ~ (r1 @ '#sk3' @ X2) 481.51/62.04 | ('#sk2' @ X2) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r2 @ '#sk5' @ Y1))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ ( 481.51/62.04 r1 @ Y1 @ Y2))) | 481.51/62.04 (Y0 @ Y2))))))))))))) | 481.51/62.04 (((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r1 @ '#sk5' @ Y1))) | (Y0 @ 481.51/62.04 Y1))))))))))) 481.51/62.04 | ~ ('#form9') 481.51/62.04 | ~ ('#form16') 481.51/62.04 | ~ ('#form26'))), 481.51/62.04 inference('renaming', [status(thm)], 481.51/62.04 [zip_derived_cl122, zip_derived_cl133])). 481.51/62.04 thf(zip_derived_cl160, plain, 481.51/62.04 (![X2 : $i]: 481.51/62.04 (~ (((((!!) @ (^[Y0 : $i]: 481.51/62.04 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.04 ('#sk6' @ Y1))))))))))))) | 481.51/62.04 (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))))) 481.51/62.04 | ~ ('#form26') 481.51/62.04 | ~ ('#form16') 481.51/62.04 | ~ ('#form9') 481.51/62.04 | ('#sk2' @ X2) 481.51/62.04 | ~ (r1 @ '#sk3' @ X2) 481.51/62.04 | ~ ('#form7') 481.51/62.04 | ~ ('#form14') 481.51/62.04 | ~ ('#form24') 481.51/62.04 | ~ ('#form34'))), 481.51/62.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl142])). 481.51/62.04 thf(zip_derived_cl180, plain, 481.51/62.04 (![X2 : $i]: 481.51/62.04 (~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.04 | ~ ('#form34') 481.51/62.04 | ~ ('#form24') 481.51/62.04 | ~ ('#form14') 481.51/62.04 | ~ ('#form7') 481.51/62.04 | ~ (r1 @ '#sk3' @ X2) 481.51/62.04 | ('#sk2' @ X2) 481.51/62.04 | ~ ('#form9') 481.51/62.04 | ~ ('#form16') 481.51/62.04 | ~ ('#form26'))), 481.51/62.04 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl160])). 481.51/62.04 thf(zip_derived_cl199, plain, 481.51/62.04 (![X2 : $i]: 481.51/62.04 (~ (((((~) @ (r1 @ '#sk5' @ '#sk36'))) | ('#sk6' @ '#sk36'))) 481.51/62.04 | ~ ('#form26') 481.51/62.04 | ~ ('#form16') 481.51/62.04 | ~ ('#form9') 481.51/62.04 | ('#sk2' @ X2) 481.51/62.04 | ~ (r1 @ '#sk3' @ X2) 481.51/62.04 | ~ ('#form7') 481.51/62.04 | ~ ('#form14') 481.51/62.04 | ~ ('#form24') 481.51/62.04 | ~ ('#form34'))), 481.51/62.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl180])). 481.51/62.04 thf(zip_derived_cl212, plain, 481.51/62.04 (![X2 : $i]: 481.51/62.04 (~ ('#sk6' @ '#sk36') 481.51/62.04 | ~ ('#form34') 481.51/62.04 | ~ ('#form24') 481.51/62.04 | ~ ('#form14') 481.51/62.04 | ~ ('#form7') 481.51/62.04 | ~ (r1 @ '#sk3' @ X2) 481.51/62.04 | ('#sk2' @ X2) 481.51/62.04 | ~ ('#form9') 481.51/62.04 | ~ ('#form16') 481.51/62.04 | ~ ('#form26'))), 481.51/62.04 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl199])). 481.51/62.04 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.04 inference('renaming', [status(thm)], 481.51/62.04 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.04 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.04 inference('renaming', [status(thm)], 481.51/62.04 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.04 thf(zip_derived_cl346, plain, 481.51/62.04 (![X2 : $i]: 481.51/62.04 (~ ('#sk6' @ '#sk36') 481.51/62.04 | ~ ('#form34') 481.51/62.04 | ~ ('#form24') 481.51/62.04 | ~ ('#form14') 481.51/62.04 | ~ (r1 @ '#sk3' @ X2) 481.51/62.04 | ('#sk2' @ X2) 481.51/62.04 | ~ ('#form16') 481.51/62.04 | ~ ('#form26'))), 481.51/62.04 inference('demod', [status(thm)], 481.51/62.04 [zip_derived_cl212, zip_derived_cl244, zip_derived_cl268])). 481.51/62.04 thf(zip_derived_cl43, plain, 481.51/62.04 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.04 ('#sk6' @ Y1))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r1 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ ('#sk2' @ '#sk4'))), 481.51/62.04 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl37])). 481.51/62.04 thf(zip_derived_cl45, plain, 481.51/62.04 (( ('#form7') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))))), 481.51/62.04 define([status(thm)])). 481.51/62.04 thf(zip_derived_cl52, plain, 481.51/62.04 ((~ ('#form7') 481.51/62.04 | ~ ('#sk2' @ '#sk4') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r1 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.04 ('#sk6' @ Y1))))))))))))))), 481.51/62.04 inference('renaming', [status(thm)], [zip_derived_cl43, zip_derived_cl45])). 481.51/62.04 thf(zip_derived_cl54, plain, 481.51/62.04 (( ('#form9') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))))), 481.51/62.04 define([status(thm)])). 481.51/62.04 thf(zip_derived_cl62, plain, 481.51/62.04 ((~ ('#form9') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.04 ('#sk6' @ Y1))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r1 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ ('#sk2' @ '#sk4') 481.51/62.04 | ~ ('#form7'))), 481.51/62.04 inference('renaming', [status(thm)], [zip_derived_cl52, zip_derived_cl54])). 481.51/62.04 thf(zip_derived_cl68, plain, 481.51/62.04 (( ('#form14') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r1 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))))), 481.51/62.04 define([status(thm)])). 481.51/62.04 thf(zip_derived_cl74, plain, 481.51/62.04 ((~ ('#form14') 481.51/62.04 | ~ ('#form7') 481.51/62.04 | ~ ('#sk2' @ '#sk4') 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r3 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.04 (((((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.04 (( 481.51/62.04 (( 481.51/62.04 (~) @ ( 481.51/62.04 r2 @ 481.51/62.04 Y2 @ Y3))) | 481.51/62.04 (Y1 @ Y3))))))))))))) | 481.51/62.04 (((!!) @ (^[Y2 : $i]: 481.51/62.04 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.04 (Y1 @ Y2)))))))))))))) 481.51/62.04 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.04 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.04 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.04 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ ('#form9'))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl62, zip_derived_cl68])). 481.51/62.05 thf(zip_derived_cl76, plain, 481.51/62.05 (( ('#form16') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl88, plain, 481.51/62.05 ((~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14'))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl74, zip_derived_cl76])). 481.51/62.05 thf(zip_derived_cl98, plain, 481.51/62.05 (( ('#form24') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl106, plain, 481.51/62.05 ((~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16'))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl88, zip_derived_cl98])). 481.51/62.05 thf(zip_derived_cl108, plain, 481.51/62.05 (( ('#form26') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl125, plain, 481.51/62.05 ((~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24'))), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl106, zip_derived_cl108])). 481.51/62.05 thf(zip_derived_cl133, plain, 481.51/62.05 (( ('#form34') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl145, plain, 481.51/62.05 ((~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl125, zip_derived_cl133])). 481.51/62.05 thf(zip_derived_cl163, plain, 481.51/62.05 ((~ (((((~) @ (r2 @ '#sk5' @ '#sk12'))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ Y0)))))))))) 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl145])). 481.51/62.05 thf(zip_derived_cl186, plain, 481.51/62.05 (( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl163])). 481.51/62.05 thf(zip_derived_cl201, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (((((~) @ (r1 @ '#sk12' @ X2))) | ('#sk6' @ X2))) 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl186])). 481.51/62.05 thf(zip_derived_cl214, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 (~ (r1 @ '#sk12' @ X2) 481.51/62.05 | ('#sk6' @ X2) 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl201])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl362, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 (~ (r1 @ '#sk12' @ X2) 481.51/62.05 | ('#sk6' @ X2) 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl214, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl179, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 (~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ (r1 @ '#sk3' @ X2) 481.51/62.05 | ('#sk2' @ X2) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl160])). 481.51/62.05 thf(zip_derived_cl198, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 (~ (((((~) @ (r2 @ '#sk5' @ '#sk12'))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ 481.51/62.05 Y0)))))))))) 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ('#sk2' @ X2) 481.51/62.05 | ~ (r1 @ '#sk3' @ X2) 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl179])). 481.51/62.05 thf(zip_derived_cl210, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ (r1 @ '#sk3' @ X2) 481.51/62.05 | ('#sk2' @ X2) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl198])). 481.51/62.05 thf(zip_derived_cl217, plain, 481.51/62.05 (![X2 : $i, X4 : $i]: 481.51/62.05 ( (((((~) @ (r1 @ '#sk12' @ X4))) | ('#sk6' @ X4))) 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ('#sk2' @ X2) 481.51/62.05 | ~ (r1 @ '#sk3' @ X2) 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl210])). 481.51/62.05 thf(zip_derived_cl219, plain, 481.51/62.05 (![X2 : $i, X4 : $i]: 481.51/62.05 (~ (r1 @ '#sk12' @ X4) 481.51/62.05 | ('#sk6' @ X4) 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ (r1 @ '#sk3' @ X2) 481.51/62.05 | ('#sk2' @ X2) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl217])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl377, plain, 481.51/62.05 (![X2 : $i, X4 : $i]: 481.51/62.05 (~ (r1 @ '#sk12' @ X4) 481.51/62.05 | ('#sk6' @ X4) 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ (r1 @ '#sk3' @ X2) 481.51/62.05 | ('#sk2' @ X2) 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl219, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl185, plain, 481.51/62.05 (( (r2 @ '#sk5' @ '#sk12') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl163])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl332, plain, 481.51/62.05 (( (r2 @ '#sk5' @ '#sk12') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl185, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl209, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (r2 @ '#sk5' @ '#sk12') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ (r1 @ '#sk3' @ X2) 481.51/62.05 | ('#sk2' @ X2) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl198])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl378, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (r2 @ '#sk5' @ '#sk12') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ (r1 @ '#sk3' @ X2) 481.51/62.05 | ('#sk2' @ X2) 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl209, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl187, plain, 481.51/62.05 (( (r1 @ '#sk5' @ '#sk36') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl164])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl345, plain, 481.51/62.05 (( (r1 @ '#sk5' @ '#sk36') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#sk2' @ '#sk4') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl187, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl211, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (r1 @ '#sk5' @ '#sk36') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ (r1 @ '#sk3' @ X2) 481.51/62.05 | ('#sk2' @ X2) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl199])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl389, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (r1 @ '#sk5' @ '#sk36') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ (r1 @ '#sk3' @ X2) 481.51/62.05 | ('#sk2' @ X2) 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl211, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(axiom_4s_for_r1_r2, axiom, 481.51/62.05 (mvalid @ 481.51/62.05 ( mforall_prop @ 481.51/62.05 ( ^[Phi:( $i > $o )]: 481.51/62.05 ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mbox @ r2 @ ( mbox @ r1 @ Phi ) ) ) ) ))). 481.51/62.05 thf(zf_stmt_4, axiom, 481.51/62.05 (![X4:$i,X6:( $i > $o )]: 481.51/62.05 ( ( ![X10:$i]: 481.51/62.05 ( ( ~( r2 @ X4 @ X10 ) ) | 481.51/62.05 ( ![X12:$i]: ( ( ~( r1 @ X10 @ X12 ) ) | ( X6 @ X12 ) ) ) ) ) | 481.51/62.05 ( ~( ![X8:$i]: ( ( ~( r1 @ X4 @ X8 ) ) | ( X6 @ X8 ) ) ) ) ))). 481.51/62.05 thf(zip_derived_cl3, plain, 481.51/62.05 ( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((!!) @ (^[Y3 : $i]: 481.51/62.05 (((((~) @ ( 481.51/62.05 r1 @ Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2))))))))))))))))), 481.51/62.05 inference('cnf', [status(esa)], [zf_stmt_4])). 481.51/62.05 thf(zip_derived_cl282, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 (((!!) @ (^[Y0 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ X2 @ Y1))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y1 @ Y2))) | 481.51/62.05 (Y0 @ Y2))))))))))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ X2 @ Y1))) | (Y0 @ 481.51/62.05 Y1)))))))))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 481.51/62.05 thf(zip_derived_cl283, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ X2 @ Y0))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | (X4 @ Y1))))))))))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0))))))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl282])). 481.51/62.05 thf(zip_derived_cl284, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o]: 481.51/62.05 ( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ X2 @ Y0))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | (X4 @ Y1))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl283])). 481.51/62.05 thf(zip_derived_cl285, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 ( (((((~) @ (r2 @ X2 @ X6))) | 481.51/62.05 (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X6 @ Y0))) | (X4 @ Y0)))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl284])). 481.51/62.05 thf(zip_derived_cl286, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 (~ (r2 @ X2 @ X6) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X6 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl285])). 481.51/62.05 thf(zip_derived_cl287, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 ( (((((~) @ (r1 @ X6 @ X8))) | (X4 @ X8))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ (r2 @ X2 @ X6))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl286])). 481.51/62.05 thf(zip_derived_cl288, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 (~ (r1 @ X6 @ X8) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (r2 @ X2 @ X6) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl287])). 481.51/62.05 thf(zip_derived_cl289, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 (~ (((((~) @ (r1 @ X2 @ ('#sk52' @ X4 @ X2)))) | (X4 @ 481.51/62.05 ('#sk52' @ X4 @ X2)))) 481.51/62.05 | ~ (r2 @ X2 @ X6) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (r1 @ X6 @ X8))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl288])). 481.51/62.05 thf(zip_derived_cl291, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 (~ (X4 @ ('#sk52' @ X4 @ X2)) 481.51/62.05 | ~ (r1 @ X6 @ X8) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (r2 @ X2 @ X6))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl289])). 481.51/62.05 thf(zip_derived_cl118, plain, 481.51/62.05 ((~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24'))), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl100, zip_derived_cl108])). 481.51/62.05 thf(zip_derived_cl133, plain, 481.51/62.05 (( ('#form34') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl135, plain, 481.51/62.05 ((~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl118, zip_derived_cl133])). 481.51/62.05 thf(zip_derived_cl155, plain, 481.51/62.05 ((~ (((((~) @ (r1 @ '#sk5' @ '#sk36'))) | ('#sk6' @ '#sk36'))) 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl135])). 481.51/62.05 thf(zip_derived_cl171, plain, 481.51/62.05 ((~ ('#sk6' @ '#sk36') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl155])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl319, plain, 481.51/62.05 ((~ ('#sk6' @ '#sk36') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl171, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl290, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 ( (r1 @ X2 @ ('#sk52' @ X4 @ X2)) 481.51/62.05 | ~ (r1 @ X6 @ X8) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (r2 @ X2 @ X6))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl289])). 481.51/62.05 thf(zip_derived_cl28, plain, 481.51/62.05 (( (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl25])). 481.51/62.05 thf(zip_derived_cl32, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y1))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y1 @ 481.51/62.05 Y2))) | 481.51/62.05 (Y0 @ Y2))))))))))))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk5' @ Y1))) | (Y0 @ Y1))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | (r1 @ '#sk1' @ '#sk4'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])). 481.51/62.05 thf(zip_derived_cl36, plain, 481.51/62.05 ((~ (((((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) | 481.51/62.05 (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))))) 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 481.51/62.05 thf(zip_derived_cl42, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | (r1 @ '#sk1' @ '#sk4'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl36])). 481.51/62.05 thf(zip_derived_cl45, plain, 481.51/62.05 (( ('#form7') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl51, plain, 481.51/62.05 ((~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl42, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl54, plain, 481.51/62.05 (( ('#form9') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl61, plain, 481.51/62.05 ((~ ('#form9') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form7'))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl51, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl68, plain, 481.51/62.05 (( ('#form14') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl73, plain, 481.51/62.05 ((~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ ('#form9'))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl61, zip_derived_cl68])). 481.51/62.05 thf(zip_derived_cl76, plain, 481.51/62.05 (( ('#form16') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl87, plain, 481.51/62.05 ((~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14'))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl73, zip_derived_cl76])). 481.51/62.05 thf(zip_derived_cl98, plain, 481.51/62.05 (( ('#form24') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl105, plain, 481.51/62.05 ((~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16'))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl87, zip_derived_cl98])). 481.51/62.05 thf(zip_derived_cl108, plain, 481.51/62.05 (( ('#form26') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl124, plain, 481.51/62.05 ((~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24'))), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl105, zip_derived_cl108])). 481.51/62.05 thf(zip_derived_cl133, plain, 481.51/62.05 (( ('#form34') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl144, plain, 481.51/62.05 ((~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk5' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl124, zip_derived_cl133])). 481.51/62.05 thf(zip_derived_cl162, plain, 481.51/62.05 ((~ (((((~) @ (r1 @ '#sk5' @ '#sk36'))) | ('#sk6' @ '#sk36'))) 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl144])). 481.51/62.05 thf(zip_derived_cl184, plain, 481.51/62.05 ((~ ('#sk6' @ '#sk36') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl162])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl331, plain, 481.51/62.05 ((~ ('#sk6' @ '#sk36') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl184, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl90, plain, 481.51/62.05 ((~ ('#form14') 481.51/62.05 | ~ (((((~) @ (r2 @ '#sk5' @ '#sk12'))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ 481.51/62.05 Y0)))))))))) 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16'))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl78, zip_derived_cl68])). 481.51/62.05 thf(zip_derived_cl108, plain, 481.51/62.05 (( ('#form26') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl110, plain, 481.51/62.05 ((~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ (((((~) @ (r2 @ '#sk5' @ '#sk12'))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ 481.51/62.05 Y0)))))))))) 481.51/62.05 | ~ ('#form14'))), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl90, zip_derived_cl108])). 481.51/62.05 thf(zip_derived_cl98, plain, 481.51/62.05 (( ('#form24') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl127, plain, 481.51/62.05 ((~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ (((((~) @ (r2 @ '#sk5' @ '#sk12'))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ 481.51/62.05 Y0)))))))))) 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl110, zip_derived_cl98])). 481.51/62.05 thf(zip_derived_cl133, plain, 481.51/62.05 (( ('#form34') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl147, plain, 481.51/62.05 ((~ ('#form34') 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ (((((~) @ (r2 @ '#sk5' @ '#sk12'))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ 481.51/62.05 Y0)))))))))) 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24'))), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl127, zip_derived_cl133])). 481.51/62.05 thf(zip_derived_cl166, plain, 481.51/62.05 (( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl147])). 481.51/62.05 thf(zip_derived_cl189, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (((((~) @ (r1 @ '#sk12' @ X2))) | ('#sk6' @ X2))) 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl166])). 481.51/62.05 thf(zip_derived_cl202, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 (~ (r1 @ '#sk12' @ X2) 481.51/62.05 | ('#sk6' @ X2) 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl189])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl376, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 (~ (r1 @ '#sk12' @ X2) 481.51/62.05 | ('#sk6' @ X2) 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl202, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl41, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | (r1 @ '#sk1' @ '#sk4'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl36])). 481.51/62.05 thf(zip_derived_cl45, plain, 481.51/62.05 (( ('#form7') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl50, plain, 481.51/62.05 ((~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl41, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl54, plain, 481.51/62.05 (( ('#form9') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl60, plain, 481.51/62.05 ((~ ('#form9') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form7'))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl50, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl68, plain, 481.51/62.05 (( ('#form14') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl72, plain, 481.51/62.05 ((~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ ('#form9'))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl60, zip_derived_cl68])). 481.51/62.05 thf(zip_derived_cl76, plain, 481.51/62.05 (( ('#form16') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl86, plain, 481.51/62.05 ((~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14'))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl72, zip_derived_cl76])). 481.51/62.05 thf(zip_derived_cl98, plain, 481.51/62.05 (( ('#form24') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl104, plain, 481.51/62.05 ((~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16'))), 481.51/62.05 inference('renaming', [status(thm)], [zip_derived_cl86, zip_derived_cl98])). 481.51/62.05 thf(zip_derived_cl108, plain, 481.51/62.05 (( ('#form26') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl123, plain, 481.51/62.05 ((~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))) 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24'))), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl104, zip_derived_cl108])). 481.51/62.05 thf(zip_derived_cl133, plain, 481.51/62.05 (( ('#form34') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl143, plain, 481.51/62.05 ((~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk5' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk6' @ Y1))))))))))))) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl123, zip_derived_cl133])). 481.51/62.05 thf(zip_derived_cl161, plain, 481.51/62.05 ((~ (((((~) @ (r2 @ '#sk5' @ '#sk12'))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ Y0)))))))))) 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl143])). 481.51/62.05 thf(zip_derived_cl182, plain, 481.51/62.05 (( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk12' @ Y0))) | ('#sk6' @ Y0)))))) 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl161])). 481.51/62.05 thf(zip_derived_cl200, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (((((~) @ (r1 @ '#sk12' @ X2))) | ('#sk6' @ X2))) 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl182])). 481.51/62.05 thf(zip_derived_cl213, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 (~ (r1 @ '#sk12' @ X2) 481.51/62.05 | ('#sk6' @ X2) 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl200])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl390, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 (~ (r1 @ '#sk12' @ X2) 481.51/62.05 | ('#sk6' @ X2) 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl213, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl165, plain, 481.51/62.05 (( (r2 @ '#sk5' @ '#sk12') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl147])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl359, plain, 481.51/62.05 (( (r2 @ '#sk5' @ '#sk12') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26') 481.51/62.05 | ~ ('#form34'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl165, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl181, plain, 481.51/62.05 (( (r2 @ '#sk5' @ '#sk12') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl161])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl361, plain, 481.51/62.05 (( (r2 @ '#sk5' @ '#sk12') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl181, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl170, plain, 481.51/62.05 (( (r1 @ '#sk5' @ '#sk36') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl155])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl360, plain, 481.51/62.05 (( (r1 @ '#sk5' @ '#sk36') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | (r1 @ '#sk1' @ '#sk3') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl170, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl68, plain, 481.51/62.05 (( ('#form14') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl69, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk15' @ Y1))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y1 @ 481.51/62.05 Y2))) | 481.51/62.05 (Y0 @ Y2))))))))))))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk15' @ Y1))) | (Y0 @ Y1))))))))))) 481.51/62.05 | ('#form14'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl68])). 481.51/62.05 thf(zip_derived_cl84, plain, 481.51/62.05 ((~ (((((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk15' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk20' @ Y1))))))))))))) | 481.51/62.05 (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk15' @ Y0))) | ('#sk20' @ Y0)))))))) 481.51/62.05 | ('#form14'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl69])). 481.51/62.05 thf(zip_derived_cl102, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk15' @ Y0))) | ('#sk20' @ Y0)))))) 481.51/62.05 | ('#form14'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl84])). 481.51/62.05 thf(zip_derived_cl121, plain, 481.51/62.05 ((~ (((((~) @ (r1 @ '#sk15' @ '#sk30'))) | ('#sk20' @ '#sk30'))) 481.51/62.05 | ('#form14'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl102])). 481.51/62.05 thf(zip_derived_cl141, plain, ((~ ('#sk20' @ '#sk30') | ('#form14'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl121])). 481.51/62.05 thf(axiom_4s_for_r1_r3, axiom, 481.51/62.05 (mvalid @ 481.51/62.05 ( mforall_prop @ 481.51/62.05 ( ^[Phi:( $i > $o )]: 481.51/62.05 ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mbox @ r3 @ ( mbox @ r1 @ Phi ) ) ) ) ))). 481.51/62.05 thf(zf_stmt_5, axiom, 481.51/62.05 (![X4:$i,X6:( $i > $o )]: 481.51/62.05 ( ( ![X10:$i]: 481.51/62.05 ( ( ~( r3 @ X4 @ X10 ) ) | 481.51/62.05 ( ![X12:$i]: ( ( ~( r1 @ X10 @ X12 ) ) | ( X6 @ X12 ) ) ) ) ) | 481.51/62.05 ( ~( ![X8:$i]: ( ( ~( r1 @ X4 @ X8 ) ) | ( X6 @ X8 ) ) ) ) ))). 481.51/62.05 thf(zip_derived_cl14, plain, 481.51/62.05 ( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((!!) @ (^[Y3 : $i]: 481.51/62.05 (((((~) @ ( 481.51/62.05 r1 @ Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2))))))))))))))))), 481.51/62.05 inference('cnf', [status(esa)], [zf_stmt_5])). 481.51/62.05 thf(zip_derived_cl413, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 (((!!) @ (^[Y0 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ X2 @ Y1))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y1 @ Y2))) | 481.51/62.05 (Y0 @ Y2))))))))))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ X2 @ Y1))) | (Y0 @ 481.51/62.05 Y1)))))))))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 481.51/62.05 thf(zip_derived_cl414, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ X2 @ Y0))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | (X4 @ Y1))))))))))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0))))))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl413])). 481.51/62.05 thf(zip_derived_cl415, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o]: 481.51/62.05 ( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ X2 @ Y0))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | (X4 @ Y1))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl414])). 481.51/62.05 thf(zip_derived_cl416, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 ( (((((~) @ (r3 @ X2 @ X6))) | 481.51/62.05 (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X6 @ Y0))) | (X4 @ Y0)))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl415])). 481.51/62.05 thf(zip_derived_cl417, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 (~ (r3 @ X2 @ X6) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X6 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl416])). 481.51/62.05 thf(zip_derived_cl418, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 ( (((((~) @ (r1 @ X6 @ X8))) | (X4 @ X8))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ (r3 @ X2 @ X6))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl417])). 481.51/62.05 thf(zip_derived_cl419, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 (~ (r1 @ X6 @ X8) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (r3 @ X2 @ X6) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl418])). 481.51/62.05 thf(zip_derived_cl420, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 (~ (((((~) @ (r1 @ X2 @ ('#sk52' @ X4 @ X2)))) | (X4 @ 481.51/62.05 ('#sk52' @ X4 @ X2)))) 481.51/62.05 | ~ (r3 @ X2 @ X6) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (r1 @ X6 @ X8))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl419])). 481.51/62.05 thf(zip_derived_cl422, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 (~ (X4 @ ('#sk52' @ X4 @ X2)) 481.51/62.05 | ~ (r1 @ X6 @ X8) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (r3 @ X2 @ X6))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl420])). 481.51/62.05 thf(zip_derived_cl133, plain, 481.51/62.05 (( ('#form34') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl134, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk35' @ Y1))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y1 @ 481.51/62.05 Y2))) | 481.51/62.05 (Y0 @ Y2))))))))))))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk35' @ Y1))) | (Y0 @ Y1))))))))))) 481.51/62.05 | ('#form34'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl133])). 481.51/62.05 thf(zip_derived_cl156, plain, 481.51/62.05 ((~ (((((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk35' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y1))) | 481.51/62.05 ('#sk37' @ Y1))))))))))))) | 481.51/62.05 (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk35' @ Y0))) | ('#sk37' @ Y0)))))))) 481.51/62.05 | ('#form34'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl134])). 481.51/62.05 thf(zip_derived_cl173, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk35' @ Y0))) | ('#sk37' @ Y0)))))) 481.51/62.05 | ('#form34'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl156])). 481.51/62.05 thf(zip_derived_cl196, plain, 481.51/62.05 ((~ (((((~) @ (r2 @ '#sk35' @ '#sk43'))) | ('#sk37' @ '#sk43'))) 481.51/62.05 | ('#form34'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl173])). 481.51/62.05 thf(zip_derived_cl207, plain, ((~ ('#sk37' @ '#sk43') | ('#form34'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl196])). 481.51/62.05 thf(zip_derived_cl183, plain, 481.51/62.05 (( (r1 @ '#sk5' @ '#sk36') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form9') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl162])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.05 thf(zip_derived_cl375, plain, 481.51/62.05 (( (r1 @ '#sk5' @ '#sk36') 481.51/62.05 | ~ ('#form34') 481.51/62.05 | ~ ('#form24') 481.51/62.05 | ~ ('#form14') 481.51/62.05 | (r1 @ '#sk1' @ '#sk4') 481.51/62.05 | ~ ('#form16') 481.51/62.05 | ~ ('#form26'))), 481.51/62.05 inference('demod', [status(thm)], 481.51/62.05 [zip_derived_cl183, zip_derived_cl244, zip_derived_cl268])). 481.51/62.05 thf(zip_derived_cl101, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk15' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 ('#sk20' @ Y1))))))))))))) 481.51/62.05 | ('#form14'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl84])). 481.51/62.05 thf(zip_derived_cl120, plain, 481.51/62.05 ((~ (((((~) @ (r3 @ '#sk15' @ '#sk29'))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk29' @ Y0))) | ('#sk20' @ 481.51/62.05 Y0)))))))))) 481.51/62.05 | ('#form14'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])). 481.51/62.05 thf(zip_derived_cl139, plain, 481.51/62.05 (( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk29' @ Y0))) | ('#sk20' @ Y0)))))) 481.51/62.05 | ('#form14'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl120])). 481.51/62.05 thf(zip_derived_cl159, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (((((~) @ (r1 @ '#sk29' @ X2))) | ('#sk20' @ X2))) | ('#form14'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl139])). 481.51/62.05 thf(zip_derived_cl178, plain, 481.51/62.05 (![X2 : $i]: (~ (r1 @ '#sk29' @ X2) | ('#sk20' @ X2) | ('#form14'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl159])). 481.51/62.05 thf(axiom_4s_for_r2_r3, axiom, 481.51/62.05 (mvalid @ 481.51/62.05 ( mforall_prop @ 481.51/62.05 ( ^[Phi:( $i > $o )]: 481.51/62.05 ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mbox @ r3 @ ( mbox @ r2 @ Phi ) ) ) ) ))). 481.51/62.05 thf(zf_stmt_6, axiom, 481.51/62.05 (![X4:$i,X6:( $i > $o )]: 481.51/62.05 ( ( ![X10:$i]: 481.51/62.05 ( ( ~( r3 @ X4 @ X10 ) ) | 481.51/62.05 ( ![X12:$i]: ( ( ~( r2 @ X10 @ X12 ) ) | ( X6 @ X12 ) ) ) ) ) | 481.51/62.05 ( ~( ![X8:$i]: ( ( ~( r2 @ X4 @ X8 ) ) | ( X6 @ X8 ) ) ) ) ))). 481.51/62.05 thf(zip_derived_cl15, plain, 481.51/62.05 ( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((!!) @ (^[Y3 : $i]: 481.51/62.05 (((((~) @ ( 481.51/62.05 r2 @ Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2))))))))))))))))), 481.51/62.05 inference('cnf', [status(esa)], [zf_stmt_6])). 481.51/62.05 thf(zip_derived_cl423, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 (((!!) @ (^[Y0 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ X2 @ Y1))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y1 @ Y2))) | 481.51/62.05 (Y0 @ Y2))))))))))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ X2 @ Y1))) | (Y0 @ 481.51/62.05 Y1)))))))))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 481.51/62.05 thf(zip_derived_cl424, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ X2 @ Y0))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y1))) | (X4 @ Y1))))))))))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0))))))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl423])). 481.51/62.05 thf(zip_derived_cl425, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o]: 481.51/62.05 ( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ X2 @ Y0))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y1))) | (X4 @ Y1))))))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl424])). 481.51/62.05 thf(zip_derived_cl426, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 ( (((((~) @ (r3 @ X2 @ X6))) | 481.51/62.05 (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X6 @ Y0))) | (X4 @ Y0)))))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl425])). 481.51/62.05 thf(zip_derived_cl427, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 (~ (r3 @ X2 @ X6) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X6 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl426])). 481.51/62.05 thf(zip_derived_cl428, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 ( (((((~) @ (r2 @ X6 @ X8))) | (X4 @ X8))) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ (r3 @ X2 @ X6))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl427])). 481.51/62.05 thf(zip_derived_cl429, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 (~ (r2 @ X6 @ X8) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (r3 @ X2 @ X6) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl428])). 481.51/62.05 thf(zip_derived_cl430, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 (~ (((((~) @ (r2 @ X2 @ ('#sk75' @ X2 @ X4)))) | (X4 @ 481.51/62.05 ('#sk75' @ X2 @ X4)))) 481.51/62.05 | ~ (r3 @ X2 @ X6) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (r2 @ X6 @ X8))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl429])). 481.51/62.05 thf(zip_derived_cl432, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 (~ (X4 @ ('#sk75' @ X2 @ X4)) 481.51/62.05 | ~ (r2 @ X6 @ X8) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (r3 @ X2 @ X6))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl430])). 481.51/62.05 thf(zip_derived_cl76, plain, 481.51/62.05 (( ('#form16') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl77, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk17' @ Y1))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y1 @ 481.51/62.05 Y2))) | 481.51/62.05 (Y0 @ Y2))))))))))))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk17' @ Y1))) | (Y0 @ Y1))))))))))) 481.51/62.05 | ('#form16'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl76])). 481.51/62.05 thf(zip_derived_cl91, plain, 481.51/62.05 ((~ (((((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk17' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y1))) | 481.51/62.05 ('#sk21' @ Y1))))))))))))) | 481.51/62.05 (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk17' @ Y0))) | ('#sk21' @ Y0)))))))) 481.51/62.05 | ('#form16'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl77])). 481.51/62.05 thf(zip_derived_cl112, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk17' @ Y0))) | ('#sk21' @ Y0)))))) 481.51/62.05 | ('#form16'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl91])). 481.51/62.05 thf(zip_derived_cl130, plain, 481.51/62.05 ((~ (((((~) @ (r3 @ '#sk17' @ '#sk33'))) | ('#sk21' @ '#sk33'))) 481.51/62.05 | ('#form16'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl112])). 481.51/62.05 thf(zip_derived_cl153, plain, ((~ ('#sk21' @ '#sk33') | ('#form16'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl130])). 481.51/62.05 thf(zip_derived_cl172, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk35' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y1))) | 481.51/62.05 ('#sk37' @ Y1))))))))))))) 481.51/62.05 | ('#form34'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl156])). 481.51/62.05 thf(zip_derived_cl195, plain, 481.51/62.05 ((~ (((((~) @ (r3 @ '#sk35' @ '#sk42'))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk42' @ Y0))) | ('#sk37' @ 481.51/62.05 Y0)))))))))) 481.51/62.05 | ('#form34'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl172])). 481.51/62.05 thf(zip_derived_cl205, plain, 481.51/62.05 (( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk42' @ Y0))) | ('#sk37' @ Y0)))))) 481.51/62.05 | ('#form34'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl195])). 481.51/62.05 thf(zip_derived_cl216, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (((((~) @ (r2 @ '#sk42' @ X2))) | ('#sk37' @ X2))) | ('#form34'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl205])). 481.51/62.05 thf(zip_derived_cl218, plain, 481.51/62.05 (![X2 : $i]: (~ (r2 @ '#sk42' @ X2) | ('#sk37' @ X2) | ('#form34'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl216])). 481.51/62.05 thf(zip_derived_cl152, plain, (( (r3 @ '#sk17' @ '#sk33') | ('#form16'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl130])). 481.51/62.05 thf(zip_derived_cl108, plain, 481.51/62.05 (( ('#form26') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl109, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk27' @ Y1))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y1 @ 481.51/62.05 Y2))) | 481.51/62.05 (Y0 @ Y2))))))))))))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk27' @ Y1))) | (Y0 @ Y1))))))))))) 481.51/62.05 | ('#form26'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl108])). 481.51/62.05 thf(zip_derived_cl128, plain, 481.51/62.05 ((~ (((((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk27' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y1))) | 481.51/62.05 ('#sk31' @ Y1))))))))))))) | 481.51/62.05 (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk27' @ Y0))) | ('#sk31' @ Y0)))))))) 481.51/62.05 | ('#form26'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl109])). 481.51/62.05 thf(zip_derived_cl149, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk27' @ Y0))) | ('#sk31' @ Y0)))))) 481.51/62.05 | ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl128])). 481.51/62.05 thf(zip_derived_cl168, plain, 481.51/62.05 ((~ (((((~) @ (r3 @ '#sk27' @ '#sk41'))) | ('#sk31' @ '#sk41'))) 481.51/62.05 | ('#form26'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl149])). 481.51/62.05 thf(zip_derived_cl193, plain, ((~ ('#sk31' @ '#sk41') | ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl168])). 481.51/62.05 thf(zip_derived_cl421, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 ( (r1 @ X2 @ ('#sk52' @ X4 @ X2)) 481.51/62.05 | ~ (r1 @ X6 @ X8) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (r3 @ X2 @ X6))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl420])). 481.51/62.05 thf(zip_derived_cl111, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk17' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y1))) | 481.51/62.05 ('#sk21' @ Y1))))))))))))) 481.51/62.05 | ('#form16'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl91])). 481.51/62.05 thf(zip_derived_cl129, plain, 481.51/62.05 ((~ (((((~) @ (r2 @ '#sk17' @ '#sk32'))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk32' @ Y0))) | ('#sk21' @ 481.51/62.05 Y0)))))))))) 481.51/62.05 | ('#form16'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl111])). 481.51/62.05 thf(zip_derived_cl151, plain, 481.51/62.05 (( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk32' @ Y0))) | ('#sk21' @ Y0)))))) 481.51/62.05 | ('#form16'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl129])). 481.51/62.05 thf(zip_derived_cl169, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (((((~) @ (r3 @ '#sk32' @ X2))) | ('#sk21' @ X2))) | ('#form16'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl151])). 481.51/62.05 thf(zip_derived_cl194, plain, 481.51/62.05 (![X2 : $i]: (~ (r3 @ '#sk32' @ X2) | ('#sk21' @ X2) | ('#form16'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl169])). 481.51/62.05 thf(zip_derived_cl192, plain, (( (r3 @ '#sk27' @ '#sk41') | ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl168])). 481.51/62.05 thf(zip_derived_cl98, plain, 481.51/62.05 (( ('#form24') 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl99, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk25' @ Y1))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y1 @ 481.51/62.05 Y2))) | 481.51/62.05 (Y0 @ Y2))))))))))))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk25' @ Y1))) | (Y0 @ Y1))))))))))) 481.51/62.05 | ('#form24'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 481.51/62.05 thf(zip_derived_cl119, plain, 481.51/62.05 ((~ (((((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk25' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y1))) | 481.51/62.05 ('#sk28' @ Y1))))))))))))) | 481.51/62.05 (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk25' @ Y0))) | ('#sk28' @ Y0)))))))) 481.51/62.05 | ('#form24'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl99])). 481.51/62.05 thf(zip_derived_cl137, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk25' @ Y0))) | ('#sk28' @ Y0)))))) 481.51/62.05 | ('#form24'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl119])). 481.51/62.05 thf(zip_derived_cl158, plain, 481.51/62.05 ((~ (((((~) @ (r2 @ '#sk25' @ '#sk39'))) | ('#sk28' @ '#sk39'))) 481.51/62.05 | ('#form24'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl137])). 481.51/62.05 thf(zip_derived_cl177, plain, ((~ ('#sk28' @ '#sk39') | ('#form24'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])). 481.51/62.05 thf(zip_derived_cl431, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 ( (r2 @ X2 @ ('#sk75' @ X2 @ X4)) 481.51/62.05 | ~ (r2 @ X6 @ X8) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (r3 @ X2 @ X6))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl430])). 481.51/62.05 thf(zip_derived_cl148, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk27' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y1))) | 481.51/62.05 ('#sk31' @ Y1))))))))))))) 481.51/62.05 | ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl128])). 481.51/62.05 thf(zip_derived_cl167, plain, 481.51/62.05 ((~ (((((~) @ (r1 @ '#sk27' @ '#sk40'))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk40' @ Y0))) | ('#sk31' @ 481.51/62.05 Y0)))))))))) 481.51/62.05 | ('#form26'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl148])). 481.51/62.05 thf(zip_derived_cl191, plain, 481.51/62.05 (( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ '#sk40' @ Y0))) | ('#sk31' @ Y0)))))) 481.51/62.05 | ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl167])). 481.51/62.05 thf(zip_derived_cl203, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (((((~) @ (r3 @ '#sk40' @ X2))) | ('#sk31' @ X2))) | ('#form26'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl191])). 481.51/62.05 thf(zip_derived_cl215, plain, 481.51/62.05 (![X2 : $i]: (~ (r3 @ '#sk40' @ X2) | ('#sk31' @ X2) | ('#form26'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl203])). 481.51/62.05 thf(zip_derived_cl176, plain, (( (r2 @ '#sk25' @ '#sk39') | ('#form24'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])). 481.51/62.05 thf(zip_derived_cl138, plain, (( (r3 @ '#sk15' @ '#sk29') | ('#form14'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl120])). 481.51/62.05 thf(zip_derived_cl136, plain, 481.51/62.05 ((~ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ '#sk25' @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y1))) | 481.51/62.05 ('#sk28' @ Y1))))))))))))) 481.51/62.05 | ('#form24'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl119])). 481.51/62.05 thf(zip_derived_cl157, plain, 481.51/62.05 ((~ (((((~) @ (r1 @ '#sk25' @ '#sk38'))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk38' @ Y0))) | ('#sk28' @ 481.51/62.05 Y0)))))))))) 481.51/62.05 | ('#form24'))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl136])). 481.51/62.05 thf(zip_derived_cl175, plain, 481.51/62.05 (( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ '#sk38' @ Y0))) | ('#sk28' @ Y0)))))) 481.51/62.05 | ('#form24'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl157])). 481.51/62.05 thf(zip_derived_cl197, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (((((~) @ (r2 @ '#sk38' @ X2))) | ('#sk28' @ X2))) | ('#form24'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl175])). 481.51/62.05 thf(zip_derived_cl208, plain, 481.51/62.05 (![X2 : $i]: (~ (r2 @ '#sk38' @ X2) | ('#sk28' @ X2) | ('#form24'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl197])). 481.51/62.05 thf(axiom_5_for_r1, axiom, 481.51/62.05 (mvalid @ 481.51/62.05 ( mforall_prop @ 481.51/62.05 ( ^[Phi:( $i > $o )]: 481.51/62.05 ( mimplies @ 481.51/62.05 ( mnot @ ( mbox @ r1 @ Phi ) ) @ 481.51/62.05 ( mbox @ r1 @ ( mnot @ ( mbox @ r1 @ Phi ) ) ) ) ) ))). 481.51/62.05 thf(zf_stmt_7, axiom, 481.51/62.05 (![X4:$i,X6:( $i > $o )]: 481.51/62.05 ( ( ![X10:$i]: 481.51/62.05 ( ( ~( r1 @ X4 @ X10 ) ) | 481.51/62.05 ( ~( ![X12:$i]: ( ( ~( r1 @ X10 @ X12 ) ) | ( X6 @ X12 ) ) ) ) ) ) | 481.51/62.05 ( ![X8:$i]: ( ( ~( r1 @ X4 @ X8 ) ) | ( X6 @ X8 ) ) ) ))). 481.51/62.05 thf(zip_derived_cl2, plain, 481.51/62.05 ( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (((( 481.51/62.05 (~) @ ( 481.51/62.05 r1 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2))))))))))))))), 481.51/62.05 inference('cnf', [status(esa)], [zf_stmt_7])). 481.51/62.05 thf(zip_derived_cl220, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 (((!!) @ (^[Y0 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ X2 @ Y1))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y1 @ 481.51/62.05 Y2))) | 481.51/62.05 (Y0 @ Y2))))))))))))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ X2 @ Y1))) | (Y0 @ Y1)))))))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 481.51/62.05 thf(zip_derived_cl221, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ X2 @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 (X4 @ Y1))))))))))))) | 481.51/62.05 (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0))))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl220])). 481.51/62.05 thf(zip_derived_cl222, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o]: 481.51/62.05 ( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ X2 @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r1 @ Y0 @ Y1))) | 481.51/62.05 (X4 @ Y1))))))))))))) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl221])). 481.51/62.05 thf(zip_derived_cl223, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 ( (((((~) @ (r1 @ X2 @ X6))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r1 @ X6 @ Y0))) | (X4 @ Y0)))))))))) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl222])). 481.51/62.05 thf(zip_derived_cl224, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 (~ (r1 @ X2 @ X6) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X6 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl223])). 481.51/62.05 thf(zip_derived_cl225, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 (~ (((((~) @ (r1 @ X6 @ ('#sk52' @ X4 @ X6)))) | (X4 @ 481.51/62.05 ('#sk52' @ X4 @ X6)))) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ (r1 @ X2 @ X6))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl224])). 481.51/62.05 thf(zip_derived_cl227, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 (~ (X4 @ ('#sk52' @ X4 @ X6)) 481.51/62.05 | ~ (r1 @ X2 @ X6) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl225])). 481.51/62.05 thf(zip_derived_cl229, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 ( (((((~) @ (r1 @ X2 @ X8))) | (X4 @ X8))) 481.51/62.05 | ~ (r1 @ X2 @ X6) 481.51/62.05 | ~ (X4 @ ('#sk52' @ X4 @ X6)))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl227])). 481.51/62.05 thf(zip_derived_cl231, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 (~ (r1 @ X2 @ X8) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (X4 @ ('#sk52' @ X4 @ X6)) 481.51/62.05 | ~ (r1 @ X2 @ X6))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl229])). 481.51/62.05 thf(zip_derived_cl204, plain, (( (r3 @ '#sk35' @ '#sk42') | ('#form34'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl195])). 481.51/62.05 thf(zip_derived_cl242, plain, 481.51/62.05 ((~ ('#form7') 481.51/62.05 | (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r3 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl243, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (((!!) @ (^[Y0 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ X2 @ Y1))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r3 @ 481.51/62.05 Y1 @ Y2))) | 481.51/62.05 (Y0 @ Y2))))))))))))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ X2 @ Y1))) | (Y0 @ Y1))))))))))) 481.51/62.05 | ~ ('#form7'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl242])). 481.51/62.05 thf(zip_derived_cl245, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o]: 481.51/62.05 ( (((((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ X2 @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y1))) | 481.51/62.05 (X4 @ Y1))))))))))))) | 481.51/62.05 (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))))) 481.51/62.05 | ~ ('#form7'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl243])). 481.51/62.05 thf(zip_derived_cl246, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o]: 481.51/62.05 ( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ X2 @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r3 @ Y0 @ Y1))) | 481.51/62.05 (X4 @ Y1))))))))))))) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ ('#form7'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl245])). 481.51/62.05 thf(zip_derived_cl247, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 ( (((((~) @ (r3 @ X2 @ X6))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r3 @ X6 @ Y0))) | (X4 @ Y0)))))))))) 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl246])). 481.51/62.05 thf(zip_derived_cl248, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 (~ (r3 @ X2 @ X6) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X6 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ ('#form7'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl247])). 481.51/62.05 thf(zip_derived_cl249, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 (~ (((((~) @ (r3 @ X6 @ ('#sk89' @ X4 @ X6)))) | (X4 @ 481.51/62.05 ('#sk89' @ X4 @ X6)))) 481.51/62.05 | ~ ('#form7') 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ (r3 @ X2 @ X6))), 481.51/62.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl248])). 481.51/62.05 thf(zip_derived_cl251, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 (~ (X4 @ ('#sk89' @ X4 @ X6)) 481.51/62.05 | ~ (r3 @ X2 @ X6) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ ('#form7'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl249])). 481.51/62.05 thf(zip_derived_cl253, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 ( (((((~) @ (r3 @ X2 @ X8))) | (X4 @ X8))) 481.51/62.05 | ~ ('#form7') 481.51/62.05 | ~ (r3 @ X2 @ X6) 481.51/62.05 | ~ (X4 @ ('#sk89' @ X4 @ X6)))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl251])). 481.51/62.05 thf(zip_derived_cl255, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 (~ (r3 @ X2 @ X8) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (X4 @ ('#sk89' @ X4 @ X6)) 481.51/62.05 | ~ (r3 @ X2 @ X6) 481.51/62.05 | ~ ('#form7'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl253])). 481.51/62.05 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.05 inference('renaming', [status(thm)], 481.51/62.05 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.05 thf(zip_derived_cl257, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.05 (~ (r3 @ X2 @ X8) 481.51/62.05 | (X4 @ X8) 481.51/62.05 | ~ (X4 @ ('#sk89' @ X4 @ X6)) 481.51/62.05 | ~ (r3 @ X2 @ X6))), 481.51/62.05 inference('demod', [status(thm)], [zip_derived_cl255, zip_derived_cl244])). 481.51/62.05 thf(zip_derived_cl150, plain, (( (r2 @ '#sk17' @ '#sk32') | ('#form16'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl129])). 481.51/62.05 thf(zip_derived_cl140, plain, (( (r1 @ '#sk15' @ '#sk30') | ('#form14'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl121])). 481.51/62.05 thf(zip_derived_cl266, plain, 481.51/62.05 ((~ ('#form9') 481.51/62.05 | (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y3 : $i]: 481.51/62.05 (( 481.51/62.05 (( 481.51/62.05 (~) @ ( 481.51/62.05 r2 @ 481.51/62.05 Y2 @ Y3))) | 481.51/62.05 (Y1 @ Y3))))))))))))) | 481.51/62.05 (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.05 (Y1 @ Y2)))))))))))))))), 481.51/62.05 define([status(thm)])). 481.51/62.05 thf(zip_derived_cl267, plain, 481.51/62.05 (![X2 : $i]: 481.51/62.05 ( (((!!) @ (^[Y0 : $i > $o]: 481.51/62.05 (((((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ X2 @ Y1))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.05 (((((~) @ (r2 @ 481.51/62.05 Y1 @ Y2))) | 481.51/62.05 (Y0 @ Y2))))))))))))) | 481.51/62.05 (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ X2 @ Y1))) | (Y0 @ Y1))))))))))) 481.51/62.05 | ~ ('#form9'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl266])). 481.51/62.05 thf(zip_derived_cl269, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o]: 481.51/62.05 ( (((((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ X2 @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y1))) | 481.51/62.05 (X4 @ Y1))))))))))))) | 481.51/62.05 (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))))) 481.51/62.05 | ~ ('#form9'))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl267])). 481.51/62.05 thf(zip_derived_cl270, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o]: 481.51/62.05 ( (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ X2 @ Y0))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.05 (((((~) @ (r2 @ Y0 @ Y1))) | 481.51/62.05 (X4 @ Y1))))))))))))) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ ('#form9'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl269])). 481.51/62.05 thf(zip_derived_cl271, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 ( (((((~) @ (r2 @ X2 @ X6))) | 481.51/62.05 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.05 (((((~) @ (r2 @ X6 @ Y0))) | (X4 @ Y0)))))))))) 481.51/62.05 | ~ ('#form9') 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl270])). 481.51/62.05 thf(zip_derived_cl272, plain, 481.51/62.05 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.05 (~ (r2 @ X2 @ X6) 481.51/62.05 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X6 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.05 | ~ ('#form9'))), 481.51/62.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl271])). 481.51/62.06 thf(zip_derived_cl273, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 (~ (((((~) @ (r2 @ X6 @ ('#sk75' @ X6 @ X4)))) | (X4 @ 481.51/62.06 ('#sk75' @ X6 @ X4)))) 481.51/62.06 | ~ ('#form9') 481.51/62.06 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.06 | ~ (r2 @ X2 @ X6))), 481.51/62.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl272])). 481.51/62.06 thf(zip_derived_cl275, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 (~ (X4 @ ('#sk75' @ X6 @ X4)) 481.51/62.06 | ~ (r2 @ X2 @ X6) 481.51/62.06 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.06 | ~ ('#form9'))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl273])). 481.51/62.06 thf(zip_derived_cl277, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.06 ( (((((~) @ (r2 @ X2 @ X8))) | (X4 @ X8))) 481.51/62.06 | ~ ('#form9') 481.51/62.06 | ~ (r2 @ X2 @ X6) 481.51/62.06 | ~ (X4 @ ('#sk75' @ X6 @ X4)))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl275])). 481.51/62.06 thf(zip_derived_cl279, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.06 (~ (r2 @ X2 @ X8) 481.51/62.06 | (X4 @ X8) 481.51/62.06 | ~ (X4 @ ('#sk75' @ X6 @ X4)) 481.51/62.06 | ~ (r2 @ X2 @ X6) 481.51/62.06 | ~ ('#form9'))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl277])). 481.51/62.06 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.06 inference('renaming', [status(thm)], 481.51/62.06 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.06 thf(zip_derived_cl281, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.06 (~ (r2 @ X2 @ X8) 481.51/62.06 | (X4 @ X8) 481.51/62.06 | ~ (X4 @ ('#sk75' @ X6 @ X4)) 481.51/62.06 | ~ (r2 @ X2 @ X6))), 481.51/62.06 inference('demod', [status(thm)], [zip_derived_cl279, zip_derived_cl268])). 481.51/62.06 thf(zip_derived_cl190, plain, (( (r1 @ '#sk27' @ '#sk40') | ('#form26'))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl167])). 481.51/62.06 thf(zip_derived_cl226, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 ( (r1 @ X6 @ ('#sk52' @ X4 @ X6)) 481.51/62.06 | ~ (r1 @ X2 @ X6) 481.51/62.06 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl225])). 481.51/62.06 thf(zip_derived_cl228, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.06 ( (((((~) @ (r1 @ X2 @ X8))) | (X4 @ X8))) 481.51/62.06 | ~ (r1 @ X2 @ X6) 481.51/62.06 | (r1 @ X6 @ ('#sk52' @ X4 @ X6)))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl226])). 481.51/62.06 thf(zip_derived_cl230, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.06 (~ (r1 @ X2 @ X8) 481.51/62.06 | (X4 @ X8) 481.51/62.06 | (r1 @ X6 @ ('#sk52' @ X4 @ X6)) 481.51/62.06 | ~ (r1 @ X2 @ X6))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl228])). 481.51/62.06 thf(zip_derived_cl206, plain, (( (r2 @ '#sk35' @ '#sk43') | ('#form34'))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl196])). 481.51/62.06 thf(zip_derived_cl250, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 ( (r3 @ X6 @ ('#sk89' @ X4 @ X6)) 481.51/62.06 | ~ (r3 @ X2 @ X6) 481.51/62.06 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.06 | ~ ('#form7'))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl249])). 481.51/62.06 thf(zip_derived_cl252, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.06 ( (((((~) @ (r3 @ X2 @ X8))) | (X4 @ X8))) 481.51/62.06 | ~ ('#form7') 481.51/62.06 | ~ (r3 @ X2 @ X6) 481.51/62.06 | (r3 @ X6 @ ('#sk89' @ X4 @ X6)))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl250])). 481.51/62.06 thf(zip_derived_cl254, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.06 (~ (r3 @ X2 @ X8) 481.51/62.06 | (X4 @ X8) 481.51/62.06 | (r3 @ X6 @ ('#sk89' @ X4 @ X6)) 481.51/62.06 | ~ (r3 @ X2 @ X6) 481.51/62.06 | ~ ('#form7'))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl252])). 481.51/62.06 thf(zip_derived_cl244, plain, ( ('#form7')), 481.51/62.06 inference('renaming', [status(thm)], 481.51/62.06 [zip_derived_cl13, zip_derived_cl242, zip_derived_cl45])). 481.51/62.06 thf(zip_derived_cl300, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.06 (~ (r3 @ X2 @ X8) 481.51/62.06 | (X4 @ X8) 481.51/62.06 | (r3 @ X6 @ ('#sk89' @ X4 @ X6)) 481.51/62.06 | ~ (r3 @ X2 @ X6))), 481.51/62.06 inference('demod', [status(thm)], [zip_derived_cl254, zip_derived_cl244])). 481.51/62.06 thf(axiom_I_for_r3_r1, axiom, 481.51/62.06 (mvalid @ 481.51/62.06 ( mforall_prop @ 481.51/62.06 ( ^[Phi:( $i > $o )]: 481.51/62.06 ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r1 @ Phi ) ) ) ))). 481.51/62.06 thf(zf_stmt_8, axiom, 481.51/62.06 (![X4:$i,X6:( $i > $o )]: 481.51/62.06 ( ( ![X10:$i]: ( ( ~( r1 @ X4 @ X10 ) ) | ( X6 @ X10 ) ) ) | 481.51/62.06 ( ~( ![X8:$i]: ( ( ~( r3 @ X4 @ X8 ) ) | ( X6 @ X8 ) ) ) ) ))). 481.51/62.06 thf(zip_derived_cl11, plain, 481.51/62.06 ( (((!!) @ (^[Y0 : $i]: 481.51/62.06 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.06 (((((!!) @ (^[Y2 : $i]: 481.51/62.06 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.06 (Y1 @ Y2)))))) | 481.51/62.06 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.06 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.06 (Y1 @ Y2))))))))))))))))), 481.51/62.06 inference('cnf', [status(esa)], [zf_stmt_8])). 481.51/62.06 thf(zip_derived_cl311, plain, 481.51/62.06 (![X2 : $i]: 481.51/62.06 (((!!) @ (^[Y0 : $i > $o]: 481.51/62.06 (((((!!) @ (^[Y1 : $i]: 481.51/62.06 (((((~) @ (r1 @ X2 @ Y1))) | (Y0 @ Y1)))))) | 481.51/62.06 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.06 (((((~) @ (r3 @ X2 @ Y1))) | (Y0 @ 481.51/62.06 Y1)))))))))))))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])). 481.51/62.06 thf(zip_derived_cl312, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o]: 481.51/62.06 (((((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))) | 481.51/62.06 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.06 (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0))))))))))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl311])). 481.51/62.06 thf(zip_derived_cl313, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o]: 481.51/62.06 ( (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.06 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl312])). 481.51/62.06 thf(zip_derived_cl314, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 ( (((((~) @ (r1 @ X2 @ X6))) | (X4 @ X6))) 481.51/62.06 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl313])). 481.51/62.06 thf(zip_derived_cl315, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 (~ (r1 @ X2 @ X6) 481.51/62.06 | (X4 @ X6) 481.51/62.06 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl314])). 481.51/62.06 thf(zip_derived_cl316, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 (~ (((((~) @ (r3 @ X2 @ ('#sk89' @ X4 @ X2)))) | (X4 @ 481.51/62.06 ('#sk89' @ X4 @ X2)))) 481.51/62.06 | (X4 @ X6) 481.51/62.06 | ~ (r1 @ X2 @ X6))), 481.51/62.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl315])). 481.51/62.06 thf(zip_derived_cl318, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 (~ (X4 @ ('#sk89' @ X4 @ X2)) | ~ (r1 @ X2 @ X6) | (X4 @ X6))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl316])). 481.51/62.06 thf(zip_derived_cl174, plain, (( (r1 @ '#sk25' @ '#sk38') | ('#form24'))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl157])). 481.51/62.06 thf(axiom_I_for_r3_r2, axiom, 481.51/62.06 (mvalid @ 481.51/62.06 ( mforall_prop @ 481.51/62.06 ( ^[Phi:( $i > $o )]: 481.51/62.06 ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r2 @ Phi ) ) ) ))). 481.51/62.06 thf(zf_stmt_9, axiom, 481.51/62.06 (![X4:$i,X6:( $i > $o )]: 481.51/62.06 ( ( ![X10:$i]: ( ( ~( r2 @ X4 @ X10 ) ) | ( X6 @ X10 ) ) ) | 481.51/62.06 ( ~( ![X8:$i]: ( ( ~( r3 @ X4 @ X8 ) ) | ( X6 @ X8 ) ) ) ) ))). 481.51/62.06 thf(zip_derived_cl5, plain, 481.51/62.06 ( (((!!) @ (^[Y0 : $i]: 481.51/62.06 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.06 (((((!!) @ (^[Y2 : $i]: 481.51/62.06 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.06 (Y1 @ Y2)))))) | 481.51/62.06 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.06 (((((~) @ (r3 @ Y0 @ Y2))) | 481.51/62.06 (Y1 @ Y2))))))))))))))))), 481.51/62.06 inference('cnf', [status(esa)], [zf_stmt_9])). 481.51/62.06 thf(zip_derived_cl292, plain, 481.51/62.06 (![X2 : $i]: 481.51/62.06 (((!!) @ (^[Y0 : $i > $o]: 481.51/62.06 (((((!!) @ (^[Y1 : $i]: 481.51/62.06 (((((~) @ (r2 @ X2 @ Y1))) | (Y0 @ Y1)))))) | 481.51/62.06 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.06 (((((~) @ (r3 @ X2 @ Y1))) | (Y0 @ 481.51/62.06 Y1)))))))))))))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 481.51/62.06 thf(zip_derived_cl293, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o]: 481.51/62.06 (((((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))) | 481.51/62.06 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.06 (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0))))))))))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl292])). 481.51/62.06 thf(zip_derived_cl294, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o]: 481.51/62.06 ( (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.06 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl293])). 481.51/62.06 thf(zip_derived_cl295, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 ( (((((~) @ (r2 @ X2 @ X6))) | (X4 @ X6))) 481.51/62.06 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl294])). 481.51/62.06 thf(zip_derived_cl296, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 (~ (r2 @ X2 @ X6) 481.51/62.06 | (X4 @ X6) 481.51/62.06 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r3 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl295])). 481.51/62.06 thf(zip_derived_cl297, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 (~ (((((~) @ (r3 @ X2 @ ('#sk89' @ X4 @ X2)))) | (X4 @ 481.51/62.06 ('#sk89' @ X4 @ X2)))) 481.51/62.06 | (X4 @ X6) 481.51/62.06 | ~ (r2 @ X2 @ X6))), 481.51/62.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl296])). 481.51/62.06 thf(zip_derived_cl299, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 (~ (X4 @ ('#sk89' @ X4 @ X2)) | ~ (r2 @ X2 @ X6) | (X4 @ X6))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl297])). 481.51/62.06 thf(zip_derived_cl274, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 ( (r2 @ X6 @ ('#sk75' @ X6 @ X4)) 481.51/62.06 | ~ (r2 @ X2 @ X6) 481.51/62.06 | (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.06 | ~ ('#form9'))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl273])). 481.51/62.06 thf(zip_derived_cl276, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.06 ( (((((~) @ (r2 @ X2 @ X8))) | (X4 @ X8))) 481.51/62.06 | ~ ('#form9') 481.51/62.06 | ~ (r2 @ X2 @ X6) 481.51/62.06 | (r2 @ X6 @ ('#sk75' @ X6 @ X4)))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl274])). 481.51/62.06 thf(zip_derived_cl278, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.06 (~ (r2 @ X2 @ X8) 481.51/62.06 | (X4 @ X8) 481.51/62.06 | (r2 @ X6 @ ('#sk75' @ X6 @ X4)) 481.51/62.06 | ~ (r2 @ X2 @ X6) 481.51/62.06 | ~ ('#form9'))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl276])). 481.51/62.06 thf(zip_derived_cl268, plain, ( ('#form9')), 481.51/62.06 inference('renaming', [status(thm)], 481.51/62.06 [zip_derived_cl16, zip_derived_cl266, zip_derived_cl54])). 481.51/62.06 thf(zip_derived_cl320, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i, X8 : $i]: 481.51/62.06 (~ (r2 @ X2 @ X8) 481.51/62.06 | (X4 @ X8) 481.51/62.06 | (r2 @ X6 @ ('#sk75' @ X6 @ X4)) 481.51/62.06 | ~ (r2 @ X2 @ X6))), 481.51/62.06 inference('demod', [status(thm)], [zip_derived_cl278, zip_derived_cl268])). 481.51/62.06 thf(zip_derived_cl317, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 ( (r3 @ X2 @ ('#sk89' @ X4 @ X2)) | ~ (r1 @ X2 @ X6) | (X4 @ X6))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl316])). 481.51/62.06 thf(axiom_I_for_r2_r1, axiom, 481.51/62.06 (mvalid @ 481.51/62.06 ( mforall_prop @ 481.51/62.06 ( ^[Phi:( $i > $o )]: 481.51/62.06 ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mbox @ r1 @ Phi ) ) ) ))). 481.51/62.06 thf(zf_stmt_10, axiom, 481.51/62.06 (![X4:$i,X6:( $i > $o )]: 481.51/62.06 ( ( ![X10:$i]: ( ( ~( r1 @ X4 @ X10 ) ) | ( X6 @ X10 ) ) ) | 481.51/62.06 ( ~( ![X8:$i]: ( ( ~( r2 @ X4 @ X8 ) ) | ( X6 @ X8 ) ) ) ) ))). 481.51/62.06 thf(zip_derived_cl1, plain, 481.51/62.06 ( (((!!) @ (^[Y0 : $i]: 481.51/62.06 (((!!) @ (^[Y1 : $i > $o]: 481.51/62.06 (((((!!) @ (^[Y2 : $i]: 481.51/62.06 (((((~) @ (r1 @ Y0 @ Y2))) | 481.51/62.06 (Y1 @ Y2)))))) | 481.51/62.06 (((~) @ (((!!) @ (^[Y2 : $i]: 481.51/62.06 (((((~) @ (r2 @ Y0 @ Y2))) | 481.51/62.06 (Y1 @ Y2))))))))))))))))), 481.51/62.06 inference('cnf', [status(esa)], [zf_stmt_10])). 481.51/62.06 thf(zip_derived_cl258, plain, 481.51/62.06 (![X2 : $i]: 481.51/62.06 (((!!) @ (^[Y0 : $i > $o]: 481.51/62.06 (((((!!) @ (^[Y1 : $i]: 481.51/62.06 (((((~) @ (r1 @ X2 @ Y1))) | (Y0 @ Y1)))))) | 481.51/62.06 (((~) @ (((!!) @ (^[Y1 : $i]: 481.51/62.06 (((((~) @ (r2 @ X2 @ Y1))) | (Y0 @ 481.51/62.06 Y1)))))))))))))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 481.51/62.06 thf(zip_derived_cl259, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o]: 481.51/62.06 (((((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))) | 481.51/62.06 (((~) @ (((!!) @ (^[Y0 : $i]: 481.51/62.06 (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0))))))))))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl258])). 481.51/62.06 thf(zip_derived_cl260, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o]: 481.51/62.06 ( (((!!) @ (^[Y0 : $i]: (((((~) @ (r1 @ X2 @ Y0))) | (X4 @ Y0)))))) 481.51/62.06 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl259])). 481.51/62.06 thf(zip_derived_cl261, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 ( (((((~) @ (r1 @ X2 @ X6))) | (X4 @ X6))) 481.51/62.06 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl260])). 481.51/62.06 thf(zip_derived_cl262, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 (~ (r1 @ X2 @ X6) 481.51/62.06 | (X4 @ X6) 481.51/62.06 | ~ (((!!) @ (^[Y0 : $i]: (((((~) @ (r2 @ X2 @ Y0))) | (X4 @ Y0)))))))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl261])). 481.51/62.06 thf(zip_derived_cl263, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 (~ (((((~) @ (r2 @ X2 @ ('#sk75' @ X2 @ X4)))) | (X4 @ 481.51/62.06 ('#sk75' @ X2 @ X4)))) 481.51/62.06 | (X4 @ X6) 481.51/62.06 | ~ (r1 @ X2 @ X6))), 481.51/62.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl262])). 481.51/62.06 thf(zip_derived_cl265, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 (~ (X4 @ ('#sk75' @ X2 @ X4)) | ~ (r1 @ X2 @ X6) | (X4 @ X6))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl263])). 481.51/62.06 thf(zip_derived_cl298, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 ( (r3 @ X2 @ ('#sk89' @ X4 @ X2)) | ~ (r2 @ X2 @ X6) | (X4 @ X6))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl297])). 481.51/62.06 thf(zip_derived_cl264, plain, 481.51/62.06 (![X2 : $i, X4 : $i > $o, X6 : $i]: 481.51/62.06 ( (r2 @ X2 @ ('#sk75' @ X2 @ X4)) | ~ (r1 @ X2 @ X6) | (X4 @ X6))), 481.51/62.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl263])). 481.51/62.06 thf(zip_derived_cl433, plain, ($false), 481.51/62.06 inference('eprover', [status(thm)], 481.51/62.06 [zip_derived_cl280, zip_derived_cl346, zip_derived_cl362, 481.51/62.06 zip_derived_cl377, zip_derived_cl332, zip_derived_cl378, 481.51/62.06 zip_derived_cl345, zip_derived_cl389, zip_derived_cl291, 481.51/62.06 zip_derived_cl319, zip_derived_cl290, zip_derived_cl331, 481.51/62.06 zip_derived_cl376, zip_derived_cl390, zip_derived_cl359, 481.51/62.06 zip_derived_cl361, zip_derived_cl360, zip_derived_cl141, 481.51/62.06 zip_derived_cl422, zip_derived_cl207, zip_derived_cl375, 481.51/62.06 zip_derived_cl178, zip_derived_cl432, zip_derived_cl153, 481.51/62.06 zip_derived_cl218, zip_derived_cl152, zip_derived_cl193, 481.51/62.06 zip_derived_cl421, zip_derived_cl194, zip_derived_cl192, 481.51/62.06 zip_derived_cl177, zip_derived_cl431, zip_derived_cl215, 481.51/62.06 zip_derived_cl176, zip_derived_cl138, zip_derived_cl208, 481.51/62.06 zip_derived_cl231, zip_derived_cl204, zip_derived_cl257, 481.51/62.06 zip_derived_cl150, zip_derived_cl140, zip_derived_cl281, 481.51/62.06 zip_derived_cl190, zip_derived_cl230, zip_derived_cl206, 481.51/62.06 zip_derived_cl300, zip_derived_cl318, zip_derived_cl174, 481.51/62.06 zip_derived_cl299, zip_derived_cl320, zip_derived_cl317, 481.51/62.06 zip_derived_cl265, zip_derived_cl298, zip_derived_cl264])). 481.51/62.06 481.51/62.06 % SZS output end Refutation 481.51/62.06 481.51/62.06 481.51/62.06 % Terminating... 481.51/62.19 % Runner terminated. 481.51/62.20 % Zipperpin 1.5 exiting 481.51/62.21 EOF