0.00/0.05 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.lcgY07ftPl true 0.19/0.45 % Computer : n007.cluster.edu 0.19/0.45 % Model : x86_64 x86_64 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.19/0.45 % Memory : 8046.5625MB 0.19/0.45 % OS : Linux 6.8.0-71-generic 0.19/0.45 % CPULimit : 1440 0.19/0.45 % WCLimit : 180 0.19/0.45 % DateTime : Mon Jul 27 13:55:18 UTC 2026 0.19/0.45 % CPUTime : 0.19/0.45 % Running portfolio for 1440 s 0.19/0.45 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.19/0.46 % Number of cores: 8 0.19/0.46 % Python version: Python 3.12.3 0.19/0.47 % Running in HO mode 0.45/0.92 % Total configuration time : 828 0.45/0.92 % Estimated wc time : 1656 0.45/0.92 % Estimated cpu time (8 cpus) : 207.0 0.45/1.02 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.45/1.09 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 2.16/1.11 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 2.16/1.11 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 2.16/1.12 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 2.16/1.13 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 2.16/1.13 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 2.16/1.13 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 2.31/1.58 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 40.84/6.12 % Solved by lams/35_full_unif4.sh. 40.84/6.12 % done 2769 iterations in 4.829s 40.84/6.12 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 40.84/6.12 % SZS output start Refutation 40.84/6.12 thf(a2_type, type, a2: $i > $o). 40.84/6.12 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 40.84/6.12 thf('#sk9_type', type, '#sk9': $i > $i). 40.84/6.12 thf(iimplies_type, type, iimplies: ($i > $o) > ($i > $o) > $i > $o). 40.84/6.12 thf('#sk10_type', type, '#sk10': $i > $i). 40.84/6.12 thf(a1_type, type, a1: $i > $o). 40.84/6.12 thf(irel_type, type, irel: $i > $i > $o). 40.84/6.12 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 40.84/6.12 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o). 40.84/6.12 thf('#sk7_type', type, '#sk7': $i > $i). 40.84/6.12 thf(iatom_type, type, iatom: ($i > $o) > $i > $o). 40.84/6.12 thf(b1_type, type, b1: $i > $o). 40.84/6.12 thf(a0_type, type, a0: $i > $o). 40.84/6.12 thf(f_type, type, f: $i > $o). 40.84/6.12 thf('#sk4_type', type, '#sk4': $i > $i). 40.84/6.12 thf(b2_type, type, b2: $i > $o). 40.84/6.12 thf('#form3_type', type, '#form3': $o). 40.84/6.12 thf(iand_type, type, iand: ($i > $o) > ($i > $o) > $i > $o). 40.84/6.12 thf('#sk5_type', type, '#sk5': $i > $i). 40.84/6.12 thf(b0_type, type, b0: $i > $o). 40.84/6.12 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 40.84/6.12 thf('#sk1_type', type, '#sk1': $i). 40.84/6.12 thf(ivalid_type, type, ivalid: ($i > $o) > $o). 40.84/6.12 thf('#sk6_type', type, '#sk6': $i > $i). 40.84/6.12 thf('#sk8_type', type, '#sk8': $i > $i). 40.84/6.12 thf('#sk2_type', type, '#sk2': $i). 40.84/6.12 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 40.84/6.12 thf(ivalid, axiom,(( ivalid ) = 40.84/6.12 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 40.84/6.12 thf('0', plain, 40.84/6.12 (( ivalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 40.84/6.12 inference('simplify_rw_rule', [status(thm)], [ivalid])). 40.84/6.12 thf('1', plain, 40.84/6.12 (( ivalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 40.84/6.12 define([status(thm)])). 40.84/6.12 thf(iimplies, axiom,(( iimplies ) = 40.84/6.12 (^[P:( $i > $o ),Q:( $i > $o )]: 40.84/6.12 ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) )))). 40.84/6.12 thf(mbox_s4, axiom,(( mbox_s4 ) = 40.84/6.12 (^[P:( $i > $o ),X:$i]: ( ![Y:$i]: ( ( irel @ X @ Y ) => ( P @ Y ) ) )))). 40.84/6.12 thf('2', plain, 40.84/6.12 (( mbox_s4 ) = 40.84/6.12 ( ^[P:( $i > $o ),X:$i]: ( ![Y:$i]: ( ( irel @ X @ Y ) => ( P @ Y ) ) ) )), 40.84/6.12 inference('simplify_rw_rule', [status(thm)], [mbox_s4])). 40.84/6.12 thf('3', plain, 40.84/6.12 (( mbox_s4 ) = 40.84/6.12 ( ^[V_1:( $i > $o ),V_2:$i]: 40.84/6.12 ( ![X4:$i]: ( ( irel @ V_2 @ X4 ) => ( V_1 @ X4 ) ) ) )), 40.84/6.12 define([status(thm)])). 40.84/6.12 thf(mimplies, axiom,(( mimplies ) = 40.84/6.12 (^[U:( $i > $o ),V:( $i > $o )]: ( mor @ ( mnot @ U ) @ V )))). 40.84/6.12 thf(mor, axiom,(( mor ) = 40.84/6.12 (^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) )))). 40.84/6.12 thf('4', plain, 40.84/6.12 (( mor ) = 40.84/6.12 ( ^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) ) )), 40.84/6.12 inference('simplify_rw_rule', [status(thm)], [mor])). 40.84/6.12 thf('5', plain, 40.84/6.12 (( mor ) = 40.84/6.12 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 40.84/6.12 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 40.84/6.12 define([status(thm)])). 40.84/6.12 thf(mnot, axiom,(( mnot ) = (^[X:( $i > $o ),U:$i]: ( ~( X @ U ) )))). 40.84/6.12 thf('6', plain, (( mnot ) = ( ^[X:( $i > $o ),U:$i]: ( ~( X @ U ) ) )), 40.84/6.12 inference('simplify_rw_rule', [status(thm)], [mnot])). 40.84/6.12 thf('7', plain, 40.84/6.12 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 40.84/6.12 define([status(thm)])). 40.84/6.12 thf('8', plain, 40.84/6.12 (( mimplies ) = 40.84/6.12 ( ^[U:( $i > $o ),V:( $i > $o )]: ( mor @ ( mnot @ U ) @ V ) )), 40.84/6.12 inference('simplify_rw_rule', [status(thm)], [mimplies, '5', '7'])). 40.84/6.12 thf('9', plain, 40.84/6.12 (( mimplies ) = 40.84/6.12 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 40.84/6.12 define([status(thm)])). 40.84/6.12 thf('10', plain, 40.84/6.12 (( iimplies ) = 40.84/6.12 ( ^[P:( $i > $o ),Q:( $i > $o )]: 40.84/6.12 ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) )), 40.84/6.12 inference('simplify_rw_rule', [status(thm)], [iimplies, '3', '9'])). 40.84/6.12 thf('11', plain, 40.84/6.12 (( iimplies ) = 40.84/6.12 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 40.84/6.12 ( mimplies @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) )), 40.84/6.12 define([status(thm)])). 40.84/6.12 thf(iand, axiom,(( iand ) = 40.84/6.12 (^[P:( $i > $o ),Q:( $i > $o )]: ( mand @ P @ Q )))). 40.84/6.12 thf(mand, axiom,(( mand ) = 40.84/6.12 (^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) & ( Y @ U ) )))). 40.84/6.12 thf('12', plain, 40.84/6.12 (( mand ) = 40.84/6.12 ( ^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) & ( Y @ U ) ) )), 40.84/6.12 inference('simplify_rw_rule', [status(thm)], [mand])). 40.84/6.12 thf('13', plain, 40.84/6.12 (( mand ) = 40.84/6.12 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 40.84/6.12 ( ( V_1 @ V_3 ) & ( V_2 @ V_3 ) ) )), 40.84/6.12 define([status(thm)])). 40.84/6.12 thf('14', plain, 40.84/6.12 (( iand ) = ( ^[P:( $i > $o ),Q:( $i > $o )]: ( mand @ P @ Q ) )), 40.84/6.12 inference('simplify_rw_rule', [status(thm)], [iand, '13'])). 40.84/6.12 thf('15', plain, 40.84/6.12 (( iand ) = ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mand @ V_1 @ V_2 ) )), 40.84/6.12 define([status(thm)])). 40.84/6.12 thf(iatom, axiom,(( iatom ) = (^[P:( $i > $o )]: ( P )))). 40.84/6.12 thf('16', plain, (( iatom ) = ( ^[P:( $i > $o )]: ( P ) )), 40.84/6.12 inference('simplify_rw_rule', [status(thm)], [iatom])). 40.84/6.12 thf('17', plain, (( iatom ) = ( ^[V_1:( $i > $o )]: ( V_1 ) )), 40.84/6.12 define([status(thm)])). 40.84/6.12 thf(con, conjecture, 40.84/6.12 (ivalid @ 40.84/6.12 ( iand @ 40.84/6.12 ( iimplies @ 40.84/6.12 ( iand @ 40.84/6.12 ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ 40.84/6.12 ( iand @ 40.84/6.12 ( iimplies @ 40.84/6.12 ( iimplies @ ( iatom @ b2 ) @ ( iatom @ b0 ) ) @ ( iatom @ a2 ) ) @ 40.84/6.12 ( iand @ 40.84/6.12 ( iimplies @ 40.84/6.12 ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ 40.84/6.12 ( iatom @ a0 ) ) @ 40.84/6.12 ( iimplies @ 40.84/6.12 ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ 40.84/6.12 ( iatom @ a1 ) ) ) ) ) @ 40.84/6.12 ( iatom @ f ) ) @ 40.84/6.12 ( iimplies @ 40.84/6.12 ( iand @ 40.84/6.12 ( iimplies @ 40.84/6.12 ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ 40.84/6.12 ( iand @ 40.84/6.12 ( iimplies @ 40.84/6.12 ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ 40.84/6.12 ( iand @ 40.84/6.12 ( iimplies @ 40.84/6.12 ( iimplies @ ( iatom @ b2 ) @ ( iatom @ b0 ) ) @ 40.84/6.12 ( iatom @ a2 ) ) @ 40.84/6.12 ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) @ 40.84/6.12 ( iatom @ f ) ) ))). 40.84/6.12 thf(zf_stmt_0, conjecture, 40.84/6.12 (![X4:$i]: 40.84/6.12 ( ( ( ![X68:$i]: ( ( irel @ X4 @ X68 ) => ( f @ X68 ) ) ) | 40.84/6.12 ( ~( ![X38:$i]: 40.84/6.12 ( ( irel @ X4 @ X38 ) => 40.84/6.12 ( ( ( ![X66:$i]: ( ( irel @ X38 @ X66 ) => ( f @ X66 ) ) ) | 40.84/6.12 ( ~( ![X64:$i]: ( ( irel @ X38 @ X64 ) => ( a0 @ X64 ) ) ) ) ) & 40.84/6.12 ( ( ![X62:$i]: ( ( irel @ X38 @ X62 ) => ( a2 @ X62 ) ) ) | 40.84/6.12 ( ~( ![X56:$i]: 40.84/6.12 ( ( irel @ X38 @ X56 ) => 40.84/6.12 ( ( ![X60:$i]: 40.84/6.12 ( ( irel @ X56 @ X60 ) => ( b0 @ X60 ) ) ) | 40.84/6.12 ( ~( ![X58:$i]: 40.84/6.12 ( ( irel @ X56 @ X58 ) => ( b2 @ X58 ) ) ) ) ) ) ) ) ) & 40.84/6.12 ( ( ![X54:$i]: ( ( irel @ X38 @ X54 ) => ( a0 @ X54 ) ) ) | 40.84/6.12 ( ~( ![X48:$i]: 40.84/6.12 ( ( irel @ X38 @ X48 ) => 40.84/6.12 ( ( ![X52:$i]: 40.84/6.12 ( ( irel @ X48 @ X52 ) => ( a1 @ X52 ) ) ) | 40.84/6.12 ( ~( ![X50:$i]: 40.84/6.12 ( ( irel @ X48 @ X50 ) => ( b0 @ X50 ) ) ) ) ) ) ) ) ) & 40.84/6.12 ( ( ![X46:$i]: ( ( irel @ X38 @ X46 ) => ( a1 @ X46 ) ) ) | 40.84/6.12 ( ~( ![X40:$i]: 40.84/6.12 ( ( irel @ X38 @ X40 ) => 40.84/6.12 ( ( ![X44:$i]: 40.84/6.12 ( ( irel @ X40 @ X44 ) => ( a2 @ X44 ) ) ) | 40.84/6.12 ( ~( ![X42:$i]: 40.84/6.12 ( ( irel @ X40 @ X42 ) => ( b1 @ X42 ) ) ) ) ) ) ) ) ) ) ) ) ) ) & 40.84/6.12 ( ( ![X36:$i]: ( ( irel @ X4 @ X36 ) => ( f @ X36 ) ) ) | 40.84/6.12 ( ~( ![X6:$i]: 40.84/6.12 ( ( irel @ X4 @ X6 ) => 40.84/6.12 ( ( ( ![X34:$i]: ( ( irel @ X6 @ X34 ) => ( a1 @ X34 ) ) ) | 40.84/6.12 ( ~( ![X28:$i]: 40.84/6.12 ( ( irel @ X6 @ X28 ) => 40.84/6.12 ( ( ![X32:$i]: 40.84/6.12 ( ( irel @ X28 @ X32 ) => ( a2 @ X32 ) ) ) | 40.84/6.12 ( ~( ![X30:$i]: 40.84/6.12 ( ( irel @ X28 @ X30 ) => ( b1 @ X30 ) ) ) ) ) ) ) ) ) & 40.84/6.12 ( ( ![X26:$i]: ( ( irel @ X6 @ X26 ) => ( a0 @ X26 ) ) ) | 40.84/6.12 ( ~( ![X20:$i]: 40.84/6.12 ( ( irel @ X6 @ X20 ) => 40.84/6.12 ( ( ![X24:$i]: 40.84/6.12 ( ( irel @ X20 @ X24 ) => ( a1 @ X24 ) ) ) | 40.84/6.12 ( ~( ![X22:$i]: 40.84/6.12 ( ( irel @ X20 @ X22 ) => ( b0 @ X22 ) ) ) ) ) ) ) ) ) & 40.84/6.12 ( ( ![X18:$i]: ( ( irel @ X6 @ X18 ) => ( a2 @ X18 ) ) ) | 40.84/6.12 ( ~( ![X12:$i]: 40.84/6.12 ( ( irel @ X6 @ X12 ) => 40.84/6.12 ( ( ![X16:$i]: 40.84/6.12 ( ( irel @ X12 @ X16 ) => ( b0 @ X16 ) ) ) | 40.84/6.12 ( ~( ![X14:$i]: 40.84/6.12 ( ( irel @ X12 @ X14 ) => ( b2 @ X14 ) ) ) ) ) ) ) ) ) & 40.84/6.12 ( ( ![X10:$i]: ( ( irel @ X6 @ X10 ) => ( f @ X10 ) ) ) | 40.84/6.12 ( ~( ![X8:$i]: ( ( irel @ X6 @ X8 ) => ( a0 @ X8 ) ) ) ) ) ) ) ) ) ) ))). 40.84/6.12 thf(zf_stmt_1, negated_conjecture, 40.84/6.12 (~( ![X4:$i]: 40.84/6.12 ( ( ( ![X68:$i]: ( ( irel @ X4 @ X68 ) => ( f @ X68 ) ) ) | 40.84/6.12 ( ~( ![X38:$i]: 40.84/6.12 ( ( irel @ X4 @ X38 ) => 40.84/6.12 ( ( ( ![X66:$i]: ( ( irel @ X38 @ X66 ) => ( f @ X66 ) ) ) | 40.84/6.12 ( ~( ![X64:$i]: ( ( irel @ X38 @ X64 ) => ( a0 @ X64 ) ) ) ) ) & 40.84/6.12 ( ( ![X62:$i]: ( ( irel @ X38 @ X62 ) => ( a2 @ X62 ) ) ) | 40.84/6.12 ( ~( ![X56:$i]: 40.84/6.12 ( ( irel @ X38 @ X56 ) => 40.84/6.12 ( ( ![X60:$i]: 40.84/6.12 ( ( irel @ X56 @ X60 ) => ( b0 @ X60 ) ) ) | 40.84/6.12 ( ~( ![X58:$i]: 40.84/6.12 ( ( irel @ X56 @ X58 ) => ( b2 @ X58 ) ) ) ) ) ) ) ) ) & 40.84/6.12 ( ( ![X54:$i]: ( ( irel @ X38 @ X54 ) => ( a0 @ X54 ) ) ) | 40.84/6.12 ( ~( ![X48:$i]: 40.84/6.12 ( ( irel @ X38 @ X48 ) => 40.84/6.12 ( ( ![X52:$i]: 40.84/6.12 ( ( irel @ X48 @ X52 ) => ( a1 @ X52 ) ) ) | 40.84/6.12 ( ~( ![X50:$i]: 40.84/6.12 ( ( irel @ X48 @ X50 ) => ( b0 @ X50 ) ) ) ) ) ) ) ) ) & 40.84/6.12 ( ( ![X46:$i]: ( ( irel @ X38 @ X46 ) => ( a1 @ X46 ) ) ) | 40.84/6.12 ( ~( ![X40:$i]: 40.84/6.12 ( ( irel @ X38 @ X40 ) => 40.84/6.12 ( ( ![X44:$i]: 40.84/6.12 ( ( irel @ X40 @ X44 ) => ( a2 @ X44 ) ) ) | 40.84/6.12 ( ~( ![X42:$i]: 40.84/6.12 ( ( irel @ X40 @ X42 ) => ( b1 @ X42 ) ) ) ) ) ) ) ) ) ) ) ) ) ) & 40.84/6.12 ( ( ![X36:$i]: ( ( irel @ X4 @ X36 ) => ( f @ X36 ) ) ) | 40.84/6.12 ( ~( ![X6:$i]: 40.84/6.12 ( ( irel @ X4 @ X6 ) => 40.84/6.12 ( ( ( ![X34:$i]: ( ( irel @ X6 @ X34 ) => ( a1 @ X34 ) ) ) | 40.84/6.12 ( ~( ![X28:$i]: 40.84/6.12 ( ( irel @ X6 @ X28 ) => 40.84/6.12 ( ( ![X32:$i]: 40.84/6.12 ( ( irel @ X28 @ X32 ) => ( a2 @ X32 ) ) ) | 40.84/6.12 ( ~( ![X30:$i]: 40.84/6.12 ( ( irel @ X28 @ X30 ) => ( b1 @ X30 ) ) ) ) ) ) ) ) ) & 40.84/6.12 ( ( ![X26:$i]: ( ( irel @ X6 @ X26 ) => ( a0 @ X26 ) ) ) | 40.84/6.12 ( ~( ![X20:$i]: 40.84/6.12 ( ( irel @ X6 @ X20 ) => 40.84/6.12 ( ( ![X24:$i]: 40.84/6.12 ( ( irel @ X20 @ X24 ) => ( a1 @ X24 ) ) ) | 40.84/6.12 ( ~( ![X22:$i]: 40.84/6.12 ( ( irel @ X20 @ X22 ) => ( b0 @ X22 ) ) ) ) ) ) ) ) ) & 40.84/6.12 ( ( ![X18:$i]: ( ( irel @ X6 @ X18 ) => ( a2 @ X18 ) ) ) | 40.84/6.12 ( ~( ![X12:$i]: 40.84/6.12 ( ( irel @ X6 @ X12 ) => 40.84/6.12 ( ( ![X16:$i]: 40.84/6.12 ( ( irel @ X12 @ X16 ) => ( b0 @ X16 ) ) ) | 40.84/6.12 ( ~( ![X14:$i]: 40.84/6.12 ( ( irel @ X12 @ X14 ) => ( b2 @ X14 ) ) ) ) ) ) ) ) ) & 40.84/6.12 ( ( ![X10:$i]: ( ( irel @ X6 @ X10 ) => ( f @ X10 ) ) ) | 40.84/6.12 ( ~( ![X8:$i]: ( ( irel @ X6 @ X8 ) => ( a0 @ X8 ) ) ) ) ) ) ) ) ) ) ) )), 40.84/6.12 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 40.84/6.12 thf(zip_derived_cl2, plain, 40.84/6.12 (~ (((!!) @ (^[Y0 : $i]: 40.84/6.12 (((((((!!) @ (^[Y1 : $i]: (((irel @ Y0 @ Y1) => (f @ Y1)))))) | 40.84/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 40.84/6.12 (((irel @ Y0 @ Y1) => 40.84/6.12 (((((((!!) @ (^[Y2 : $i]: 40.84/6.12 (((irel @ Y1 @ 40.84/6.12 Y2) => (f @ 40.84/6.12 Y2)))))) | 40.84/6.12 (((~) @ (((!!) @ (^[Y2 : $i]: 40.84/6.12 (( 40.84/6.12 (irel @ 40.84/6.12 Y1 @ 40.84/6.12 Y2) => 40.84/6.12 (a0 @ Y2)))))))))) & 40.84/6.12 (((((!!) @ (^[Y2 : $i]: 40.84/6.12 (((irel @ Y1 @ 40.84/6.12 Y2) => (a2 @ 40.84/6.12 Y2)))))) | 40.84/6.12 (((~) @ (((!!) @ (^[Y2 : $i]: 40.84/6.12 (( 40.84/6.12 (irel @ 40.84/6.12 Y1 @ 40.84/6.12 Y2) => 40.84/6.12 (( 40.84/6.12 (( 40.84/6.12 (!!) @ ( 40.84/6.12 ^[Y3 : $i]: 40.84/6.12 (( 40.84/6.12 (irel @ 40.84/6.12 Y2 @ 40.84/6.12 Y3) => 40.84/6.12 (b0 @ Y3)))))) | 40.84/6.12 (( 40.84/6.12 (~) @ ( 40.84/6.12 ( 40.84/6.12 (!!) @ ( 40.84/6.12 ^[Y3 : $i]: 40.84/6.12 (( 40.84/6.12 (irel @ 40.84/6.12 Y2 @ 40.84/6.12 Y3) => 40.84/6.12 (b2 @ Y3))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y2 : $i]: 41.59/6.12 (((irel @ Y1 @ 41.59/6.12 Y2) => (a0 @ 41.59/6.12 Y2)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (( 41.59/6.12 (( 41.59/6.12 (!!) @ ( 41.59/6.12 ^[Y3 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y2 @ 41.59/6.12 Y3) => 41.59/6.12 (a1 @ Y3)))))) | 41.59/6.12 (( 41.59/6.12 (~) @ ( 41.59/6.12 ( 41.59/6.12 (!!) @ ( 41.59/6.12 ^[Y3 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y2 @ 41.59/6.12 Y3) => 41.59/6.12 (b0 @ Y3))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y2 : $i]: 41.59/6.12 (((irel @ Y1 @ 41.59/6.12 Y2) => (a1 @ 41.59/6.12 Y2)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (( 41.59/6.12 (( 41.59/6.12 (!!) @ ( 41.59/6.12 ^[Y3 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y2 @ 41.59/6.12 Y3) => 41.59/6.12 (a2 @ Y3)))))) | 41.59/6.12 (( 41.59/6.12 (~) @ ( 41.59/6.12 ( 41.59/6.12 (!!) @ ( 41.59/6.12 ^[Y3 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y2 @ 41.59/6.12 Y3) => 41.59/6.12 (b1 @ Y3)))))))))))))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: (((irel @ Y0 @ Y1) => (f @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (((((((!!) @ (^[Y2 : $i]: 41.59/6.12 (((irel @ Y1 @ 41.59/6.12 Y2) => (a1 @ 41.59/6.12 Y2)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (( 41.59/6.12 (( 41.59/6.12 (!!) @ ( 41.59/6.12 ^[Y3 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y2 @ 41.59/6.12 Y3) => 41.59/6.12 (a2 @ Y3)))))) | 41.59/6.12 (( 41.59/6.12 (~) @ ( 41.59/6.12 ( 41.59/6.12 (!!) @ ( 41.59/6.12 ^[Y3 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y2 @ 41.59/6.12 Y3) => 41.59/6.12 (b1 @ Y3))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y2 : $i]: 41.59/6.12 (((irel @ Y1 @ 41.59/6.12 Y2) => (a0 @ 41.59/6.12 Y2)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (( 41.59/6.12 (( 41.59/6.12 (!!) @ ( 41.59/6.12 ^[Y3 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y2 @ 41.59/6.12 Y3) => 41.59/6.12 (a1 @ Y3)))))) | 41.59/6.12 (( 41.59/6.12 (~) @ ( 41.59/6.12 ( 41.59/6.12 (!!) @ ( 41.59/6.12 ^[Y3 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y2 @ 41.59/6.12 Y3) => 41.59/6.12 (b0 @ Y3))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y2 : $i]: 41.59/6.12 (((irel @ Y1 @ 41.59/6.12 Y2) => (a2 @ 41.59/6.12 Y2)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (( 41.59/6.12 (( 41.59/6.12 (!!) @ ( 41.59/6.12 ^[Y3 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y2 @ 41.59/6.12 Y3) => 41.59/6.12 (b0 @ Y3)))))) | 41.59/6.12 (( 41.59/6.12 (~) @ ( 41.59/6.12 ( 41.59/6.12 (!!) @ ( 41.59/6.12 ^[Y3 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y2 @ 41.59/6.12 Y3) => 41.59/6.12 (b2 @ Y3))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y2 : $i]: 41.59/6.12 (((irel @ Y1 @ 41.59/6.12 Y2) => (f @ 41.59/6.12 Y2)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a0 @ Y2))))))))))))))))))))))))))), 41.59/6.12 inference('cnf', [status(esa)], [zf_stmt_1])). 41.59/6.12 thf(zip_derived_cl17, plain, 41.59/6.12 (~ (((((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ '#sk1' @ Y0) => 41.59/6.12 (((((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (f @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => (a0 @ Y1)))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a2 @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b2 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a0 @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a1 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a1 @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a2 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b1 @ Y2)))))))))))))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ '#sk1' @ Y0) => 41.59/6.12 (((((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a1 @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a2 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b1 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a0 @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a1 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a2 @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b2 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (f @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => (a0 @ Y1)))))))))))))))))))))))), 41.59/6.12 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 41.59/6.12 thf(zip_derived_cl18, plain, 41.59/6.12 ((~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ '#sk1' @ Y0) => 41.59/6.12 (((((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (f @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a0 @ Y1)))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a2 @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ Y2) => 41.59/6.12 (b0 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b2 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a0 @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ Y2) => 41.59/6.12 (a1 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a1 @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ Y2) => 41.59/6.12 (a2 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b1 @ Y2)))))))))))))))))))))))))))))) 41.59/6.12 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ '#sk1' @ Y0) => 41.59/6.12 (((((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a1 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a2 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b1 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a0 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a1 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a2 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b2 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (f @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => (a0 @ Y1))))))))))))))))))))))), 41.59/6.12 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl17])). 41.59/6.12 thf(zip_derived_cl19, plain, 41.59/6.12 ((~ (((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) 41.59/6.12 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ '#sk1' @ Y0) => 41.59/6.12 (((((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a1 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a2 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b1 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a0 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a1 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a2 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b2 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (f @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => (a0 @ Y1))))))))))))))))))))))), 41.59/6.12 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl18])). 41.59/6.12 thf(zip_derived_cl21, plain, 41.59/6.12 ((~ (((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) 41.59/6.12 | ~ ((($true) | 41.59/6.12 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ '#sk1' @ Y0) => 41.59/6.12 (((((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a1 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a2 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b1 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a0 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a1 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a2 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b2 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (f @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => (a0 @ Y1))))))))))))))))))))))), 41.59/6.12 inference('local_rewriting', [status(thm)], [zip_derived_cl19])). 41.59/6.12 thf(zip_derived_cl22, plain, 41.59/6.12 (~ (((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0))))))), 41.59/6.12 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl21])). 41.59/6.12 thf(zip_derived_cl23, plain, 41.59/6.12 (~ (((irel @ '#sk1' @ '#sk2') => (f @ '#sk2')))), 41.59/6.12 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl22])). 41.59/6.12 thf(zip_derived_cl25, plain, ( (irel @ '#sk1' @ '#sk2')), 41.59/6.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 41.59/6.12 thf(zip_derived_cl20, plain, 41.59/6.12 (( (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ '#sk1' @ Y0) => 41.59/6.12 (((((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (f @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a0 @ Y1)))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (((((!!) @ (^[Y2 : $i]: 41.59/6.12 (((irel @ Y1 @ 41.59/6.12 Y2) => (b0 @ 41.59/6.12 Y2)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b2 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a0 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (((((!!) @ (^[Y2 : $i]: 41.59/6.12 (((irel @ Y1 @ 41.59/6.12 Y2) => (a1 @ 41.59/6.12 Y2)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (((((!!) @ (^[Y2 : $i]: 41.59/6.12 (((irel @ Y1 @ 41.59/6.12 Y2) => (a2 @ 41.59/6.12 Y2)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b1 @ Y2)))))))))))))))))))))))))) 41.59/6.12 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ '#sk1' @ Y0) => 41.59/6.12 (((((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a1 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a2 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b1 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a0 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a1 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a2 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (((irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b0 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b2 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => (f @ 41.59/6.12 Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => (a0 @ Y1))))))))))))))))))))))), 41.59/6.12 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl18])). 41.59/6.12 thf(zip_derived_cl24, plain, 41.59/6.12 (![X2 : $i]: 41.59/6.12 ( (((irel @ '#sk1' @ X2) => 41.59/6.12 (((((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))) & 41.59/6.12 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ X2 @ Y0) => 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (b0 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => (b2 @ Y1))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ X2 @ Y0) => 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a1 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => (b0 @ Y1))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ X2 @ Y0) => 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a2 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => (b1 @ Y1))))))))))))))))))))))) 41.59/6.12 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.12 (((irel @ '#sk1' @ Y0) => 41.59/6.12 (((((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a1 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 ( 41.59/6.12 ( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (a2 @ Y2)))))) | 41.59/6.12 (((~) @ ( 41.59/6.12 ((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 (( 41.59/6.12 (irel @ 41.59/6.12 Y1 @ 41.59/6.12 Y2) => 41.59/6.12 (b1 @ Y2))))))))))))))))))) & 41.59/6.12 (((((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ Y1) => 41.59/6.12 (a0 @ Y1)))))) | 41.59/6.12 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.12 (((irel @ Y0 @ 41.59/6.12 Y1) => 41.59/6.12 (((((!!) @ ( 41.59/6.12 ^[Y2 : $i]: 41.59/6.12 ( 41.59/6.12 ( 41.59/6.12 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a1 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a2 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b2 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (f @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (a0 @ 41.59/6.13 Y1))))))))))))))))))))))), 41.59/6.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 41.59/6.13 thf(zip_derived_cl27, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 (~ (irel @ '#sk1' @ X2) 41.59/6.13 | (((((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))) & 41.59/6.13 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (b0 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (b2 @ Y1))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (b0 @ Y1))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a2 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (b1 @ Y1))))))))))))))))))))) 41.59/6.13 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ '#sk1' @ Y0) => 41.59/6.13 (((((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a2 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b1 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a0 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a1 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a2 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b2 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (f @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (a0 @ 41.59/6.13 Y1))))))))))))))))))))))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 41.59/6.13 thf(zip_derived_cl28, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))) 41.59/6.13 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ '#sk1' @ Y0) => 41.59/6.13 (((((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a2 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b1 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a0 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a1 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a2 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b2 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (f @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (a0 @ 41.59/6.13 Y1))))))))))))))))))))) 41.59/6.13 | ~ (irel @ '#sk1' @ X2))), 41.59/6.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 41.59/6.13 thf(zip_derived_cl32, plain, 41.59/6.13 (( ('#form3') 41.59/6.13 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ '#sk1' @ Y0) => 41.59/6.13 (((((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (((irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a2 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b1 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a0 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (((irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a1 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a2 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (((irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b2 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (f @ 41.59/6.13 Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (a0 @ Y1))))))))))))))))))))))), 41.59/6.13 define([status(thm)])). 41.59/6.13 thf(zip_derived_cl34, plain, 41.59/6.13 (( (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ '#sk1' @ Y0) => 41.59/6.13 (((((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (((((!!) @ (^[Y2 : $i]: 41.59/6.13 (((irel @ Y1 @ 41.59/6.13 Y2) => (a2 @ 41.59/6.13 Y2)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b1 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a0 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (((((!!) @ (^[Y2 : $i]: 41.59/6.13 (((irel @ Y1 @ 41.59/6.13 Y2) => (a1 @ 41.59/6.13 Y2)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (((((!!) @ (^[Y2 : $i]: 41.59/6.13 (((irel @ Y1 @ 41.59/6.13 Y2) => (b0 @ 41.59/6.13 Y2)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b2 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (f @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a0 @ Y1))))))))))))))))) 41.59/6.13 | ('#form3'))), 41.59/6.13 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl32])). 41.59/6.13 thf(zip_derived_cl41, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 ( (((irel @ '#sk1' @ X2) => 41.59/6.13 (((((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a2 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (b1 @ Y1))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (b0 @ Y1))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (b0 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (b2 @ Y1))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))))))) 41.59/6.13 | ('#form3'))), 41.59/6.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 41.59/6.13 thf(zip_derived_cl48, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 (~ (irel @ '#sk1' @ X2) 41.59/6.13 | (((((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a2 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (b1 @ Y1))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (b0 @ Y1))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (b0 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (b2 @ Y1))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))))) 41.59/6.13 | ('#form3'))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 41.59/6.13 thf(zip_derived_cl56, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))) 41.59/6.13 | ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2))), 41.59/6.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl48])). 41.59/6.13 thf(zip_derived_cl64, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) 41.59/6.13 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ('#form3'))), 41.59/6.13 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl56])). 41.59/6.13 thf(zip_derived_cl73, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 ( (((irel @ X2 @ X4) => (f @ X4))) 41.59/6.13 | ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))))), 41.59/6.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 41.59/6.13 thf(zip_derived_cl83, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (irel @ X2 @ X4) 41.59/6.13 | (f @ X4) 41.59/6.13 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ('#form3'))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 41.59/6.13 thf(zip_derived_cl93, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (((irel @ X2 @ ('#sk4' @ X2)) => (a0 @ ('#sk4' @ X2)))) 41.59/6.13 | ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | (f @ X4) 41.59/6.13 | ~ (irel @ X2 @ X4))), 41.59/6.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl83])). 41.59/6.13 thf(zip_derived_cl107, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (a0 @ ('#sk4' @ X2)) 41.59/6.13 | ~ (irel @ X2 @ X4) 41.59/6.13 | (f @ X4) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ('#form3'))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl93])). 41.59/6.13 thf(zip_derived_cl28, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))) 41.59/6.13 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ '#sk1' @ Y0) => 41.59/6.13 (((((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a2 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b1 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a0 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a1 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a2 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b2 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (f @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (a0 @ 41.59/6.13 Y1))))))))))))))))))))) 41.59/6.13 | ~ (irel @ '#sk1' @ X2))), 41.59/6.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 41.59/6.13 thf(zip_derived_cl32, plain, 41.59/6.13 (( ('#form3') 41.59/6.13 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ '#sk1' @ Y0) => 41.59/6.13 (((((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (((irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a2 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b1 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a0 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (((irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a1 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a2 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (((irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b2 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (f @ 41.59/6.13 Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (a0 @ Y1))))))))))))))))))))))), 41.59/6.13 define([status(thm)])). 41.59/6.13 thf(zip_derived_cl35, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 (~ ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))))), 41.59/6.13 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl32])). 41.59/6.13 thf(zip_derived_cl39, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) 41.59/6.13 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ~ ('#form3'))), 41.59/6.13 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl35])). 41.59/6.13 thf(zip_derived_cl45, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 ( (((irel @ X2 @ X4) => (f @ X4))) 41.59/6.13 | ~ ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))))), 41.59/6.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl39])). 41.59/6.13 thf(zip_derived_cl52, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (irel @ X2 @ X4) 41.59/6.13 | (f @ X4) 41.59/6.13 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ~ ('#form3'))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 41.59/6.13 thf(zip_derived_cl60, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (((irel @ X2 @ ('#sk4' @ X2)) => (a0 @ ('#sk4' @ X2)))) 41.59/6.13 | ~ ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | (f @ X4) 41.59/6.13 | ~ (irel @ X2 @ X4))), 41.59/6.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl52])). 41.59/6.13 thf(zip_derived_cl69, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (a0 @ ('#sk4' @ X2)) 41.59/6.13 | ~ (irel @ X2 @ X4) 41.59/6.13 | (f @ X4) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ~ ('#form3'))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl60])). 41.59/6.13 thf(zip_derived_cl471, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (irel @ '#sk1' @ X2) 41.59/6.13 | (f @ X4) 41.59/6.13 | ~ (irel @ X2 @ X4) 41.59/6.13 | ~ (a0 @ ('#sk4' @ X2)))), 41.59/6.13 inference('clc', [status(thm)], [zip_derived_cl107, zip_derived_cl69])). 41.59/6.13 thf(zip_derived_cl477, plain, 41.59/6.13 ((~ (a0 @ ('#sk4' @ '#sk1')) | (f @ '#sk2') | ~ (irel @ '#sk1' @ '#sk1'))), 41.59/6.13 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl471])). 41.59/6.13 thf(zip_derived_cl26, plain, (~ (f @ '#sk2')), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 41.59/6.13 thf(refl_axiom, axiom, (![X:$i]: ( irel @ X @ X ))). 41.59/6.13 thf(zip_derived_cl1, plain, ( (((!!) @ (^[Y0 : $i]: (irel @ Y0 @ Y0))))), 41.59/6.13 inference('cnf', [status(esa)], [refl_axiom])). 41.59/6.13 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 41.59/6.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 41.59/6.13 thf(zip_derived_cl491, plain, (~ (a0 @ ('#sk4' @ '#sk1'))), 41.59/6.13 inference('demod', [status(thm)], 41.59/6.13 [zip_derived_cl477, zip_derived_cl26, zip_derived_cl3])). 41.59/6.13 thf(zip_derived_cl25, plain, ( (irel @ '#sk1' @ '#sk2')), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 41.59/6.13 thf(zip_derived_cl106, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 ( (irel @ X2 @ ('#sk4' @ X2)) 41.59/6.13 | ~ (irel @ X2 @ X4) 41.59/6.13 | (f @ X4) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ('#form3'))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl93])). 41.59/6.13 thf(zip_derived_cl68, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 ( (irel @ X2 @ ('#sk4' @ X2)) 41.59/6.13 | ~ (irel @ X2 @ X4) 41.59/6.13 | (f @ X4) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ~ ('#form3'))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl60])). 41.59/6.13 thf(zip_derived_cl381, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (irel @ '#sk1' @ X2) 41.59/6.13 | (f @ X4) 41.59/6.13 | ~ (irel @ X2 @ X4) 41.59/6.13 | (irel @ X2 @ ('#sk4' @ X2)))), 41.59/6.13 inference('clc', [status(thm)], [zip_derived_cl106, zip_derived_cl68])). 41.59/6.13 thf(zip_derived_cl385, plain, 41.59/6.13 (( (irel @ '#sk1' @ ('#sk4' @ '#sk1')) 41.59/6.13 | (f @ '#sk2') 41.59/6.13 | ~ (irel @ '#sk1' @ '#sk1'))), 41.59/6.13 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl381])). 41.59/6.13 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 41.59/6.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 41.59/6.13 thf(zip_derived_cl397, plain, 41.59/6.13 (( (irel @ '#sk1' @ ('#sk4' @ '#sk1')) | (f @ '#sk2'))), 41.59/6.13 inference('demod', [status(thm)], [zip_derived_cl385, zip_derived_cl3])). 41.59/6.13 thf(zip_derived_cl26, plain, (~ (f @ '#sk2')), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 41.59/6.13 thf(zip_derived_cl402, plain, ( (irel @ '#sk1' @ ('#sk4' @ '#sk1'))), 41.59/6.13 inference('clc', [status(thm)], [zip_derived_cl397, zip_derived_cl26])). 41.59/6.13 thf(zip_derived_cl54, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a1 @ 41.59/6.13 Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (b0 @ Y1))))))))))))))))))) 41.59/6.13 | ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2))), 41.59/6.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl48])). 41.59/6.13 thf(zip_derived_cl62, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) 41.59/6.13 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (b0 @ 41.59/6.13 Y1))))))))))))))) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ('#form3'))), 41.59/6.13 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 41.59/6.13 thf(zip_derived_cl71, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 ( (((irel @ X2 @ X4) => (a0 @ X4))) 41.59/6.13 | ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (b0 @ 41.59/6.13 Y1))))))))))))))))), 41.59/6.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 41.59/6.13 thf(zip_derived_cl81, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (irel @ X2 @ X4) 41.59/6.13 | (a0 @ X4) 41.59/6.13 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (b0 @ 41.59/6.13 Y1))))))))))))))) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ('#form3'))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 41.59/6.13 thf(zip_derived_cl91, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (((irel @ X2 @ ('#sk6' @ X2)) => 41.59/6.13 (((((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ ('#sk6' @ X2) @ Y0) => (a1 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ ('#sk6' @ X2) @ Y0) => (b0 @ Y0)))))))))))) 41.59/6.13 | ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | (a0 @ X4) 41.59/6.13 | ~ (irel @ X2 @ X4))), 41.59/6.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 41.59/6.13 thf(zip_derived_cl103, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (((((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ ('#sk6' @ X2) @ Y0) => (a1 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ ('#sk6' @ X2) @ Y0) => (b0 @ Y0)))))))))) 41.59/6.13 | ~ (irel @ X2 @ X4) 41.59/6.13 | (a0 @ X4) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ('#form3'))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl91])). 41.59/6.13 thf(zip_derived_cl119, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk6' @ X2) @ Y0) => (a1 @ Y0)))))) 41.59/6.13 | ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | (a0 @ X4) 41.59/6.13 | ~ (irel @ X2 @ X4))), 41.59/6.13 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl103])). 41.59/6.13 thf(zip_derived_cl125, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (((irel @ ('#sk6' @ X2) @ ('#sk9' @ X2)) => (a1 @ ('#sk9' @ X2)))) 41.59/6.13 | ~ (irel @ X2 @ X4) 41.59/6.13 | (a0 @ X4) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ('#form3'))), 41.59/6.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 41.59/6.13 thf(zip_derived_cl132, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 ( (irel @ ('#sk6' @ X2) @ ('#sk9' @ X2)) 41.59/6.13 | ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | (a0 @ X4) 41.59/6.13 | ~ (irel @ X2 @ X4))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])). 41.59/6.13 thf(zip_derived_cl30, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a1 @ 41.59/6.13 Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (b0 @ Y1))))))))))))))))))) 41.59/6.13 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ '#sk1' @ Y0) => 41.59/6.13 (((((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a2 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b1 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a0 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a1 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a2 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 ( 41.59/6.13 ( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b2 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (f @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (a0 @ 41.59/6.13 Y1))))))))))))))))))))) 41.59/6.13 | ~ (irel @ '#sk1' @ X2))), 41.59/6.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 41.59/6.13 thf(zip_derived_cl32, plain, 41.59/6.13 (( ('#form3') 41.59/6.13 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ '#sk1' @ Y0) => 41.59/6.13 (((((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (((irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a2 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b1 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a0 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (((irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (a1 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => 41.59/6.13 (a2 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => 41.59/6.13 (((((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (((irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b0 @ Y2)))))) | 41.59/6.13 (((~) @ ( 41.59/6.13 ((!!) @ ( 41.59/6.13 ^[Y2 : $i]: 41.59/6.13 (( 41.59/6.13 (irel @ 41.59/6.13 Y1 @ 41.59/6.13 Y2) => 41.59/6.13 (b2 @ Y2))))))))))))))))))) & 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (f @ 41.59/6.13 Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (a0 @ Y1))))))))))))))))))))))), 41.59/6.13 define([status(thm)])). 41.59/6.13 thf(zip_derived_cl37, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 (~ ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a1 @ 41.59/6.13 Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ 41.59/6.13 Y1) => (b0 @ Y1))))))))))))))))))))), 41.59/6.13 inference('renaming', [status(thm)], [zip_derived_cl30, zip_derived_cl32])). 41.59/6.13 thf(zip_derived_cl43, plain, 41.59/6.13 (![X2 : $i]: 41.59/6.13 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) 41.59/6.13 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (b0 @ 41.59/6.13 Y1))))))))))))))) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ~ ('#form3'))), 41.59/6.13 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl37])). 41.59/6.13 thf(zip_derived_cl50, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 ( (((irel @ X2 @ X4) => (a0 @ X4))) 41.59/6.13 | ~ ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (b0 @ 41.59/6.13 Y1))))))))))))))))), 41.59/6.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 41.59/6.13 thf(zip_derived_cl58, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (irel @ X2 @ X4) 41.59/6.13 | (a0 @ X4) 41.59/6.13 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ X2 @ Y0) => 41.59/6.13 (((((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.13 (((irel @ Y0 @ Y1) => (b0 @ 41.59/6.13 Y1))))))))))))))) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ~ ('#form3'))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])). 41.59/6.13 thf(zip_derived_cl66, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (((irel @ X2 @ ('#sk6' @ X2)) => 41.59/6.13 (((((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ ('#sk6' @ X2) @ Y0) => (a1 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ ('#sk6' @ X2) @ Y0) => (b0 @ Y0)))))))))))) 41.59/6.13 | ~ ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | (a0 @ X4) 41.59/6.13 | ~ (irel @ X2 @ X4))), 41.59/6.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 41.59/6.13 thf(zip_derived_cl77, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (((((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ ('#sk6' @ X2) @ Y0) => (a1 @ Y0)))))) | 41.59/6.13 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.13 (((irel @ ('#sk6' @ X2) @ Y0) => (b0 @ Y0)))))))))) 41.59/6.13 | ~ (irel @ X2 @ X4) 41.59/6.13 | (a0 @ X4) 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | ~ ('#form3'))), 41.59/6.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 41.59/6.13 thf(zip_derived_cl86, plain, 41.59/6.13 (![X2 : $i, X4 : $i]: 41.59/6.13 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk6' @ X2) @ Y0) => (a1 @ Y0)))))) 41.59/6.13 | ~ ('#form3') 41.59/6.13 | ~ (irel @ '#sk1' @ X2) 41.59/6.13 | (a0 @ X4) 41.59/6.14 | ~ (irel @ X2 @ X4))), 41.59/6.14 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl77])). 41.59/6.14 thf(zip_derived_cl96, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (((irel @ ('#sk6' @ X2) @ ('#sk9' @ X2)) => (a1 @ ('#sk9' @ X2)))) 41.59/6.14 | ~ (irel @ X2 @ X4) 41.59/6.14 | (a0 @ X4) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ~ ('#form3'))), 41.59/6.14 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])). 41.59/6.14 thf(zip_derived_cl111, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 ( (irel @ ('#sk6' @ X2) @ ('#sk9' @ X2)) 41.59/6.14 | ~ ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | (a0 @ X4) 41.59/6.14 | ~ (irel @ X2 @ X4))), 41.59/6.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 41.59/6.14 thf(zip_derived_cl954, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (irel @ X2 @ X4) 41.59/6.14 | (a0 @ X4) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | (irel @ ('#sk6' @ X2) @ ('#sk9' @ X2)))), 41.59/6.14 inference('clc', [status(thm)], [zip_derived_cl132, zip_derived_cl111])). 41.59/6.14 thf(zip_derived_cl965, plain, 41.59/6.14 (( (irel @ ('#sk6' @ '#sk1') @ ('#sk9' @ '#sk1')) 41.59/6.14 | ~ (irel @ '#sk1' @ '#sk1') 41.59/6.14 | (a0 @ ('#sk4' @ '#sk1')))), 41.59/6.14 inference('sup-', [status(thm)], [zip_derived_cl402, zip_derived_cl954])). 41.59/6.14 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 41.59/6.14 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 41.59/6.14 thf(zip_derived_cl989, plain, 41.59/6.14 (( (irel @ ('#sk6' @ '#sk1') @ ('#sk9' @ '#sk1')) 41.59/6.14 | (a0 @ ('#sk4' @ '#sk1')))), 41.59/6.14 inference('demod', [status(thm)], [zip_derived_cl965, zip_derived_cl3])). 41.59/6.14 thf(zip_derived_cl491, plain, (~ (a0 @ ('#sk4' @ '#sk1'))), 41.59/6.14 inference('demod', [status(thm)], 41.59/6.14 [zip_derived_cl477, zip_derived_cl26, zip_derived_cl3])). 41.59/6.14 thf(zip_derived_cl1087, plain, 41.59/6.14 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk9' @ '#sk1'))), 41.59/6.14 inference('clc', [status(thm)], [zip_derived_cl989, zip_derived_cl491])). 41.59/6.14 thf(zip_derived_cl53, plain, 41.59/6.14 (![X2 : $i]: 41.59/6.14 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ X2 @ Y0) => 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (a2 @ 41.59/6.14 Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => 41.59/6.14 (b1 @ Y1))))))))))))))))))) 41.59/6.14 | ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2))), 41.59/6.14 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl48])). 41.59/6.14 thf(zip_derived_cl61, plain, 41.59/6.14 (![X2 : $i]: 41.59/6.14 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) 41.59/6.14 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ X2 @ Y0) => 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (b1 @ 41.59/6.14 Y1))))))))))))))) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ('#form3'))), 41.59/6.14 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl53])). 41.59/6.14 thf(zip_derived_cl70, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 ( (((irel @ X2 @ X4) => (a1 @ X4))) 41.59/6.14 | ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ X2 @ Y0) => 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (b1 @ 41.59/6.14 Y1))))))))))))))))), 41.59/6.14 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 41.59/6.14 thf(zip_derived_cl80, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (irel @ X2 @ X4) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ X2 @ Y0) => 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (b1 @ 41.59/6.14 Y1))))))))))))))) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ('#form3'))), 41.59/6.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])). 41.59/6.14 thf(zip_derived_cl90, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (((irel @ X2 @ ('#sk7' @ X2)) => 41.59/6.14 (((((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ ('#sk7' @ X2) @ Y0) => (a2 @ Y0)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ ('#sk7' @ X2) @ Y0) => (b1 @ Y0)))))))))))) 41.59/6.14 | ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (irel @ X2 @ X4))), 41.59/6.14 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl80])). 41.59/6.14 thf(zip_derived_cl101, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (((((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ ('#sk7' @ X2) @ Y0) => (a2 @ Y0)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ ('#sk7' @ X2) @ Y0) => (b1 @ Y0)))))))))) 41.59/6.14 | ~ (irel @ X2 @ X4) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ('#form3'))), 41.59/6.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl90])). 41.59/6.14 thf(zip_derived_cl117, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk7' @ X2) @ Y0) => (a2 @ Y0)))))) 41.59/6.14 | ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (irel @ X2 @ X4))), 41.59/6.14 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl101])). 41.59/6.14 thf(zip_derived_cl123, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (((irel @ ('#sk7' @ X2) @ ('#sk10' @ X2)) => (a2 @ ('#sk10' @ X2)))) 41.59/6.14 | ~ (irel @ X2 @ X4) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ('#form3'))), 41.59/6.14 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl117])). 41.59/6.14 thf(zip_derived_cl129, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 ( (irel @ ('#sk7' @ X2) @ ('#sk10' @ X2)) 41.59/6.14 | ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (irel @ X2 @ X4))), 41.59/6.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])). 41.59/6.14 thf(zip_derived_cl31, plain, 41.59/6.14 (![X2 : $i]: 41.59/6.14 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ X2 @ Y0) => 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (a2 @ 41.59/6.14 Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => 41.59/6.14 (b1 @ Y1))))))))))))))))))) 41.59/6.14 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ '#sk1' @ Y0) => 41.59/6.14 (((((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => 41.59/6.14 (a1 @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ 41.59/6.14 Y1) => 41.59/6.14 (((((!!) @ ( 41.59/6.14 ^[Y2 : $i]: 41.59/6.14 ( 41.59/6.14 ( 41.59/6.14 (irel @ 41.59/6.14 Y1 @ 41.59/6.14 Y2) => 41.59/6.14 (a2 @ Y2)))))) | 41.59/6.14 (((~) @ ( 41.59/6.14 ((!!) @ ( 41.59/6.14 ^[Y2 : $i]: 41.59/6.14 (( 41.59/6.14 (irel @ 41.59/6.14 Y1 @ 41.59/6.14 Y2) => 41.59/6.14 (b1 @ Y2))))))))))))))))))) & 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => 41.59/6.14 (a0 @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ 41.59/6.14 Y1) => 41.59/6.14 (((((!!) @ ( 41.59/6.14 ^[Y2 : $i]: 41.59/6.14 ( 41.59/6.14 ( 41.59/6.14 (irel @ 41.59/6.14 Y1 @ 41.59/6.14 Y2) => 41.59/6.14 (a1 @ Y2)))))) | 41.59/6.14 (((~) @ ( 41.59/6.14 ((!!) @ ( 41.59/6.14 ^[Y2 : $i]: 41.59/6.14 (( 41.59/6.14 (irel @ 41.59/6.14 Y1 @ 41.59/6.14 Y2) => 41.59/6.14 (b0 @ Y2))))))))))))))))))) & 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => 41.59/6.14 (a2 @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ 41.59/6.14 Y1) => 41.59/6.14 (((((!!) @ ( 41.59/6.14 ^[Y2 : $i]: 41.59/6.14 ( 41.59/6.14 ( 41.59/6.14 (irel @ 41.59/6.14 Y1 @ 41.59/6.14 Y2) => 41.59/6.14 (b0 @ Y2)))))) | 41.59/6.14 (((~) @ ( 41.59/6.14 ((!!) @ ( 41.59/6.14 ^[Y2 : $i]: 41.59/6.14 (( 41.59/6.14 (irel @ 41.59/6.14 Y1 @ 41.59/6.14 Y2) => 41.59/6.14 (b2 @ Y2))))))))))))))))))) & 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => 41.59/6.14 (f @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ 41.59/6.14 Y1) => (a0 @ 41.59/6.14 Y1))))))))))))))))))))) 41.59/6.14 | ~ (irel @ '#sk1' @ X2))), 41.59/6.14 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 41.59/6.14 thf(zip_derived_cl32, plain, 41.59/6.14 (( ('#form3') 41.59/6.14 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ '#sk1' @ Y0) => 41.59/6.14 (((((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => 41.59/6.14 (a1 @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ 41.59/6.14 Y1) => 41.59/6.14 (((((!!) @ ( 41.59/6.14 ^[Y2 : $i]: 41.59/6.14 (((irel @ 41.59/6.14 Y1 @ 41.59/6.14 Y2) => 41.59/6.14 (a2 @ Y2)))))) | 41.59/6.14 (((~) @ ( 41.59/6.14 ((!!) @ ( 41.59/6.14 ^[Y2 : $i]: 41.59/6.14 (( 41.59/6.14 (irel @ 41.59/6.14 Y1 @ 41.59/6.14 Y2) => 41.59/6.14 (b1 @ Y2))))))))))))))))))) & 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => 41.59/6.14 (a0 @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ 41.59/6.14 Y1) => 41.59/6.14 (((((!!) @ ( 41.59/6.14 ^[Y2 : $i]: 41.59/6.14 (((irel @ 41.59/6.14 Y1 @ 41.59/6.14 Y2) => 41.59/6.14 (a1 @ Y2)))))) | 41.59/6.14 (((~) @ ( 41.59/6.14 ((!!) @ ( 41.59/6.14 ^[Y2 : $i]: 41.59/6.14 (( 41.59/6.14 (irel @ 41.59/6.14 Y1 @ 41.59/6.14 Y2) => 41.59/6.14 (b0 @ Y2))))))))))))))))))) & 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => 41.59/6.14 (a2 @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ 41.59/6.14 Y1) => 41.59/6.14 (((((!!) @ ( 41.59/6.14 ^[Y2 : $i]: 41.59/6.14 (((irel @ 41.59/6.14 Y1 @ 41.59/6.14 Y2) => 41.59/6.14 (b0 @ Y2)))))) | 41.59/6.14 (((~) @ ( 41.59/6.14 ((!!) @ ( 41.59/6.14 ^[Y2 : $i]: 41.59/6.14 (( 41.59/6.14 (irel @ 41.59/6.14 Y1 @ 41.59/6.14 Y2) => 41.59/6.14 (b2 @ Y2))))))))))))))))))) & 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (f @ 41.59/6.14 Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ 41.59/6.14 Y1) => (a0 @ Y1))))))))))))))))))))))), 41.59/6.14 define([status(thm)])). 41.59/6.14 thf(zip_derived_cl38, plain, 41.59/6.14 (![X2 : $i]: 41.59/6.14 (~ ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ X2 @ Y0) => 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (a2 @ 41.59/6.14 Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ 41.59/6.14 Y1) => (b1 @ Y1))))))))))))))))))))), 41.59/6.14 inference('renaming', [status(thm)], [zip_derived_cl31, zip_derived_cl32])). 41.59/6.14 thf(zip_derived_cl44, plain, 41.59/6.14 (![X2 : $i]: 41.59/6.14 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) 41.59/6.14 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ X2 @ Y0) => 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (b1 @ 41.59/6.14 Y1))))))))))))))) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ~ ('#form3'))), 41.59/6.14 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl38])). 41.59/6.14 thf(zip_derived_cl51, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 ( (((irel @ X2 @ X4) => (a1 @ X4))) 41.59/6.14 | ~ ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ X2 @ Y0) => 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (b1 @ 41.59/6.14 Y1))))))))))))))))), 41.59/6.14 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl44])). 41.59/6.14 thf(zip_derived_cl59, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (irel @ X2 @ X4) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ X2 @ Y0) => 41.59/6.14 (((((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.14 (((irel @ Y0 @ Y1) => (b1 @ 41.59/6.14 Y1))))))))))))))) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ~ ('#form3'))), 41.59/6.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 41.59/6.14 thf(zip_derived_cl67, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (((irel @ X2 @ ('#sk7' @ X2)) => 41.59/6.14 (((((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ ('#sk7' @ X2) @ Y0) => (a2 @ Y0)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ ('#sk7' @ X2) @ Y0) => (b1 @ Y0)))))))))))) 41.59/6.14 | ~ ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (irel @ X2 @ X4))), 41.59/6.14 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl59])). 41.59/6.14 thf(zip_derived_cl79, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (((((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ ('#sk7' @ X2) @ Y0) => (a2 @ Y0)))))) | 41.59/6.14 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.14 (((irel @ ('#sk7' @ X2) @ Y0) => (b1 @ Y0)))))))))) 41.59/6.14 | ~ (irel @ X2 @ X4) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ~ ('#form3'))), 41.59/6.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 41.59/6.14 thf(zip_derived_cl88, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk7' @ X2) @ Y0) => (a2 @ Y0)))))) 41.59/6.14 | ~ ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (irel @ X2 @ X4))), 41.59/6.14 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl79])). 41.59/6.14 thf(zip_derived_cl98, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (((irel @ ('#sk7' @ X2) @ ('#sk10' @ X2)) => (a2 @ ('#sk10' @ X2)))) 41.59/6.14 | ~ (irel @ X2 @ X4) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ~ ('#form3'))), 41.59/6.14 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl88])). 41.59/6.14 thf(zip_derived_cl114, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 ( (irel @ ('#sk7' @ X2) @ ('#sk10' @ X2)) 41.59/6.14 | ~ ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (irel @ X2 @ X4))), 41.59/6.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl98])). 41.59/6.14 thf(zip_derived_cl769, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (irel @ X2 @ X4) 41.59/6.14 | (a1 @ X4) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | (irel @ ('#sk7' @ X2) @ ('#sk10' @ X2)))), 41.59/6.14 inference('clc', [status(thm)], [zip_derived_cl129, zip_derived_cl114])). 41.59/6.14 thf(zip_derived_cl1093, plain, 41.59/6.14 (( (irel @ ('#sk7' @ ('#sk6' @ '#sk1')) @ ('#sk10' @ ('#sk6' @ '#sk1'))) 41.59/6.14 | ~ (irel @ '#sk1' @ ('#sk6' @ '#sk1')) 41.59/6.14 | (a1 @ ('#sk9' @ '#sk1')))), 41.59/6.14 inference('sup-', [status(thm)], [zip_derived_cl1087, zip_derived_cl769])). 41.59/6.14 thf(zip_derived_cl491, plain, (~ (a0 @ ('#sk4' @ '#sk1'))), 41.59/6.14 inference('demod', [status(thm)], 41.59/6.14 [zip_derived_cl477, zip_derived_cl26, zip_derived_cl3])). 41.59/6.14 thf(zip_derived_cl402, plain, ( (irel @ '#sk1' @ ('#sk4' @ '#sk1'))), 41.59/6.14 inference('clc', [status(thm)], [zip_derived_cl397, zip_derived_cl26])). 41.59/6.14 thf(zip_derived_cl102, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 ( (irel @ X2 @ ('#sk6' @ X2)) 41.59/6.14 | ~ (irel @ X2 @ X4) 41.59/6.14 | (a0 @ X4) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ('#form3'))), 41.59/6.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl91])). 41.59/6.14 thf(zip_derived_cl76, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 ( (irel @ X2 @ ('#sk6' @ X2)) 41.59/6.14 | ~ (irel @ X2 @ X4) 41.59/6.14 | (a0 @ X4) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ~ ('#form3'))), 41.59/6.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 41.59/6.14 thf(zip_derived_cl331, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (irel @ '#sk1' @ X2) 41.59/6.14 | (a0 @ X4) 41.59/6.14 | ~ (irel @ X2 @ X4) 41.59/6.14 | (irel @ X2 @ ('#sk6' @ X2)))), 41.59/6.14 inference('clc', [status(thm)], [zip_derived_cl102, zip_derived_cl76])). 41.59/6.14 thf(zip_derived_cl406, plain, 41.59/6.14 (( (irel @ '#sk1' @ ('#sk6' @ '#sk1')) 41.59/6.14 | (a0 @ ('#sk4' @ '#sk1')) 41.59/6.14 | ~ (irel @ '#sk1' @ '#sk1'))), 41.59/6.14 inference('sup-', [status(thm)], [zip_derived_cl402, zip_derived_cl331])). 41.59/6.14 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 41.59/6.14 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 41.59/6.14 thf(zip_derived_cl417, plain, 41.59/6.14 (( (irel @ '#sk1' @ ('#sk6' @ '#sk1')) | (a0 @ ('#sk4' @ '#sk1')))), 41.59/6.14 inference('demod', [status(thm)], [zip_derived_cl406, zip_derived_cl3])). 41.59/6.14 thf(zip_derived_cl498, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 41.59/6.14 inference('sup+', [status(thm)], [zip_derived_cl491, zip_derived_cl417])). 41.59/6.14 thf(zip_derived_cl402, plain, ( (irel @ '#sk1' @ ('#sk4' @ '#sk1'))), 41.59/6.14 inference('clc', [status(thm)], [zip_derived_cl397, zip_derived_cl26])). 41.59/6.14 thf(zip_derived_cl133, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (a1 @ ('#sk9' @ X2)) 41.59/6.14 | ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | (a0 @ X4) 41.59/6.14 | ~ (irel @ X2 @ X4))), 41.59/6.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])). 41.59/6.14 thf(zip_derived_cl112, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (a1 @ ('#sk9' @ X2)) 41.59/6.14 | ~ ('#form3') 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | (a0 @ X4) 41.59/6.14 | ~ (irel @ X2 @ X4))), 41.59/6.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 41.59/6.14 thf(zip_derived_cl1038, plain, 41.59/6.14 (![X2 : $i, X4 : $i]: 41.59/6.14 (~ (irel @ X2 @ X4) 41.59/6.14 | (a0 @ X4) 41.59/6.14 | ~ (irel @ '#sk1' @ X2) 41.59/6.14 | ~ (a1 @ ('#sk9' @ X2)))), 41.59/6.14 inference('clc', [status(thm)], [zip_derived_cl133, zip_derived_cl112])). 41.59/6.14 thf(zip_derived_cl1049, plain, 41.59/6.14 ((~ (a1 @ ('#sk9' @ '#sk1')) 41.59/6.14 | ~ (irel @ '#sk1' @ '#sk1') 41.59/6.14 | (a0 @ ('#sk4' @ '#sk1')))), 41.59/6.14 inference('sup-', [status(thm)], [zip_derived_cl402, zip_derived_cl1038])). 41.59/6.14 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 41.59/6.14 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 41.59/6.14 thf(zip_derived_cl491, plain, (~ (a0 @ ('#sk4' @ '#sk1'))), 41.59/6.14 inference('demod', [status(thm)], 41.59/6.14 [zip_derived_cl477, zip_derived_cl26, zip_derived_cl3])). 41.59/6.14 thf(zip_derived_cl1073, plain, (~ (a1 @ ('#sk9' @ '#sk1'))), 41.59/6.14 inference('demod', [status(thm)], 41.59/6.14 [zip_derived_cl1049, zip_derived_cl3, zip_derived_cl491])). 41.59/6.14 thf(zip_derived_cl1114, plain, 41.59/6.14 ( (irel @ ('#sk7' @ ('#sk6' @ '#sk1')) @ ('#sk10' @ ('#sk6' @ '#sk1')))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1093, zip_derived_cl498, zip_derived_cl1073])). 41.59/6.15 thf(zip_derived_cl55, plain, 41.59/6.15 (![X2 : $i]: 41.59/6.15 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ X2 @ Y0) => 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b0 @ 41.59/6.15 Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => 41.59/6.15 (b2 @ Y1))))))))))))))))))) 41.59/6.15 | ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2))), 41.59/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl48])). 41.59/6.15 thf(zip_derived_cl63, plain, 41.59/6.15 (![X2 : $i]: 41.59/6.15 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) 41.59/6.15 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ X2 @ Y0) => 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b0 @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b2 @ 41.59/6.15 Y1))))))))))))))) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ('#form3'))), 41.59/6.15 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl55])). 41.59/6.15 thf(zip_derived_cl72, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 ( (((irel @ X2 @ X4) => (a2 @ X4))) 41.59/6.15 | ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ X2 @ Y0) => 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b0 @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b2 @ 41.59/6.15 Y1))))))))))))))))), 41.59/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 41.59/6.15 thf(zip_derived_cl82, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (irel @ X2 @ X4) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ X2 @ Y0) => 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b0 @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b2 @ 41.59/6.15 Y1))))))))))))))) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ('#form3'))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 41.59/6.15 thf(zip_derived_cl92, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (((irel @ X2 @ ('#sk5' @ X2)) => 41.59/6.15 (((((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ ('#sk5' @ X2) @ Y0) => (b0 @ Y0)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ ('#sk5' @ X2) @ Y0) => (b2 @ Y0)))))))))))) 41.59/6.15 | ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl82])). 41.59/6.15 thf(zip_derived_cl104, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 ( (irel @ X2 @ ('#sk5' @ X2)) 41.59/6.15 | ~ (irel @ X2 @ X4) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ('#form3'))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 41.59/6.15 thf(zip_derived_cl29, plain, 41.59/6.15 (![X2 : $i]: 41.59/6.15 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ X2 @ Y0) => 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b0 @ 41.59/6.15 Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => 41.59/6.15 (b2 @ Y1))))))))))))))))))) 41.59/6.15 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ '#sk1' @ Y0) => 41.59/6.15 (((((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => 41.59/6.15 (a1 @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ 41.59/6.15 Y1) => 41.59/6.15 (((((!!) @ ( 41.59/6.15 ^[Y2 : $i]: 41.59/6.15 ( 41.59/6.15 ( 41.59/6.15 (irel @ 41.59/6.15 Y1 @ 41.59/6.15 Y2) => 41.59/6.15 (a2 @ Y2)))))) | 41.59/6.15 (((~) @ ( 41.59/6.15 ((!!) @ ( 41.59/6.15 ^[Y2 : $i]: 41.59/6.15 (( 41.59/6.15 (irel @ 41.59/6.15 Y1 @ 41.59/6.15 Y2) => 41.59/6.15 (b1 @ Y2))))))))))))))))))) & 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => 41.59/6.15 (a0 @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ 41.59/6.15 Y1) => 41.59/6.15 (((((!!) @ ( 41.59/6.15 ^[Y2 : $i]: 41.59/6.15 ( 41.59/6.15 ( 41.59/6.15 (irel @ 41.59/6.15 Y1 @ 41.59/6.15 Y2) => 41.59/6.15 (a1 @ Y2)))))) | 41.59/6.15 (((~) @ ( 41.59/6.15 ((!!) @ ( 41.59/6.15 ^[Y2 : $i]: 41.59/6.15 (( 41.59/6.15 (irel @ 41.59/6.15 Y1 @ 41.59/6.15 Y2) => 41.59/6.15 (b0 @ Y2))))))))))))))))))) & 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => 41.59/6.15 (a2 @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ 41.59/6.15 Y1) => 41.59/6.15 (((((!!) @ ( 41.59/6.15 ^[Y2 : $i]: 41.59/6.15 ( 41.59/6.15 ( 41.59/6.15 (irel @ 41.59/6.15 Y1 @ 41.59/6.15 Y2) => 41.59/6.15 (b0 @ Y2)))))) | 41.59/6.15 (((~) @ ( 41.59/6.15 ((!!) @ ( 41.59/6.15 ^[Y2 : $i]: 41.59/6.15 (( 41.59/6.15 (irel @ 41.59/6.15 Y1 @ 41.59/6.15 Y2) => 41.59/6.15 (b2 @ Y2))))))))))))))))))) & 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => 41.59/6.15 (f @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ 41.59/6.15 Y1) => (a0 @ 41.59/6.15 Y1))))))))))))))))))))) 41.59/6.15 | ~ (irel @ '#sk1' @ X2))), 41.59/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 41.59/6.15 thf(zip_derived_cl32, plain, 41.59/6.15 (( ('#form3') 41.59/6.15 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ '#sk1' @ Y0) => 41.59/6.15 (((((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => 41.59/6.15 (a1 @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ 41.59/6.15 Y1) => 41.59/6.15 (((((!!) @ ( 41.59/6.15 ^[Y2 : $i]: 41.59/6.15 (((irel @ 41.59/6.15 Y1 @ 41.59/6.15 Y2) => 41.59/6.15 (a2 @ Y2)))))) | 41.59/6.15 (((~) @ ( 41.59/6.15 ((!!) @ ( 41.59/6.15 ^[Y2 : $i]: 41.59/6.15 (( 41.59/6.15 (irel @ 41.59/6.15 Y1 @ 41.59/6.15 Y2) => 41.59/6.15 (b1 @ Y2))))))))))))))))))) & 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => 41.59/6.15 (a0 @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ 41.59/6.15 Y1) => 41.59/6.15 (((((!!) @ ( 41.59/6.15 ^[Y2 : $i]: 41.59/6.15 (((irel @ 41.59/6.15 Y1 @ 41.59/6.15 Y2) => 41.59/6.15 (a1 @ Y2)))))) | 41.59/6.15 (((~) @ ( 41.59/6.15 ((!!) @ ( 41.59/6.15 ^[Y2 : $i]: 41.59/6.15 (( 41.59/6.15 (irel @ 41.59/6.15 Y1 @ 41.59/6.15 Y2) => 41.59/6.15 (b0 @ Y2))))))))))))))))))) & 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => 41.59/6.15 (a2 @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ 41.59/6.15 Y1) => 41.59/6.15 (((((!!) @ ( 41.59/6.15 ^[Y2 : $i]: 41.59/6.15 (((irel @ 41.59/6.15 Y1 @ 41.59/6.15 Y2) => 41.59/6.15 (b0 @ Y2)))))) | 41.59/6.15 (((~) @ ( 41.59/6.15 ((!!) @ ( 41.59/6.15 ^[Y2 : $i]: 41.59/6.15 (( 41.59/6.15 (irel @ 41.59/6.15 Y1 @ 41.59/6.15 Y2) => 41.59/6.15 (b2 @ Y2))))))))))))))))))) & 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (f @ 41.59/6.15 Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ 41.59/6.15 Y1) => (a0 @ Y1))))))))))))))))))))))), 41.59/6.15 define([status(thm)])). 41.59/6.15 thf(zip_derived_cl36, plain, 41.59/6.15 (![X2 : $i]: 41.59/6.15 (~ ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ X2 @ Y0) => 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b0 @ 41.59/6.15 Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ 41.59/6.15 Y1) => (b2 @ Y1))))))))))))))))))))), 41.59/6.15 inference('renaming', [status(thm)], [zip_derived_cl29, zip_derived_cl32])). 41.59/6.15 thf(zip_derived_cl42, plain, 41.59/6.15 (![X2 : $i]: 41.59/6.15 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) 41.59/6.15 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ X2 @ Y0) => 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b0 @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b2 @ 41.59/6.15 Y1))))))))))))))) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ~ ('#form3'))), 41.59/6.15 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl36])). 41.59/6.15 thf(zip_derived_cl49, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 ( (((irel @ X2 @ X4) => (a2 @ X4))) 41.59/6.15 | ~ ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ X2 @ Y0) => 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b0 @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b2 @ 41.59/6.15 Y1))))))))))))))))), 41.59/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 41.59/6.15 thf(zip_derived_cl57, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (irel @ X2 @ X4) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ X2 @ Y0) => 41.59/6.15 (((((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b0 @ Y1)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((irel @ Y0 @ Y1) => (b2 @ 41.59/6.15 Y1))))))))))))))) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ~ ('#form3'))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 41.59/6.15 thf(zip_derived_cl65, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (((irel @ X2 @ ('#sk5' @ X2)) => 41.59/6.15 (((((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ ('#sk5' @ X2) @ Y0) => (b0 @ Y0)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ ('#sk5' @ X2) @ Y0) => (b2 @ Y0)))))))))))) 41.59/6.15 | ~ ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl57])). 41.59/6.15 thf(zip_derived_cl74, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 ( (irel @ X2 @ ('#sk5' @ X2)) 41.59/6.15 | ~ (irel @ X2 @ X4) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ~ ('#form3'))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])). 41.59/6.15 thf(zip_derived_cl352, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4) 41.59/6.15 | (irel @ X2 @ ('#sk5' @ X2)))), 41.59/6.15 inference('clc', [status(thm)], [zip_derived_cl104, zip_derived_cl74])). 41.59/6.15 thf(zip_derived_cl1389, plain, 41.59/6.15 (( (irel @ ('#sk7' @ ('#sk6' @ '#sk1')) @ 41.59/6.15 ('#sk5' @ ('#sk7' @ ('#sk6' @ '#sk1')))) 41.59/6.15 | (a2 @ ('#sk10' @ ('#sk6' @ '#sk1'))) 41.59/6.15 | ~ (irel @ '#sk1' @ ('#sk7' @ ('#sk6' @ '#sk1'))))), 41.59/6.15 inference('sup-', [status(thm)], [zip_derived_cl1114, zip_derived_cl352])). 41.59/6.15 thf(zip_derived_cl1087, plain, 41.59/6.15 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk9' @ '#sk1'))), 41.59/6.15 inference('clc', [status(thm)], [zip_derived_cl989, zip_derived_cl491])). 41.59/6.15 thf(zip_derived_cl130, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (a2 @ ('#sk10' @ X2)) 41.59/6.15 | ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a1 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])). 41.59/6.15 thf(zip_derived_cl115, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (a2 @ ('#sk10' @ X2)) 41.59/6.15 | ~ ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a1 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl98])). 41.59/6.15 thf(zip_derived_cl838, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (irel @ X2 @ X4) 41.59/6.15 | (a1 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ~ (a2 @ ('#sk10' @ X2)))), 41.59/6.15 inference('clc', [status(thm)], [zip_derived_cl130, zip_derived_cl115])). 41.59/6.15 thf(zip_derived_cl1092, plain, 41.59/6.15 ((~ (a2 @ ('#sk10' @ ('#sk6' @ '#sk1'))) 41.59/6.15 | ~ (irel @ '#sk1' @ ('#sk6' @ '#sk1')) 41.59/6.15 | (a1 @ ('#sk9' @ '#sk1')))), 41.59/6.15 inference('sup-', [status(thm)], [zip_derived_cl1087, zip_derived_cl838])). 41.59/6.15 thf(zip_derived_cl498, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 41.59/6.15 inference('sup+', [status(thm)], [zip_derived_cl491, zip_derived_cl417])). 41.59/6.15 thf(zip_derived_cl1073, plain, (~ (a1 @ ('#sk9' @ '#sk1'))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1049, zip_derived_cl3, zip_derived_cl491])). 41.59/6.15 thf(zip_derived_cl1113, plain, (~ (a2 @ ('#sk10' @ ('#sk6' @ '#sk1')))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1092, zip_derived_cl498, zip_derived_cl1073])). 41.59/6.15 thf(zip_derived_cl1087, plain, 41.59/6.15 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk9' @ '#sk1'))), 41.59/6.15 inference('clc', [status(thm)], [zip_derived_cl989, zip_derived_cl491])). 41.59/6.15 thf(zip_derived_cl100, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 ( (irel @ X2 @ ('#sk7' @ X2)) 41.59/6.15 | ~ (irel @ X2 @ X4) 41.59/6.15 | (a1 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ('#form3'))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl90])). 41.59/6.15 thf(zip_derived_cl78, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 ( (irel @ X2 @ ('#sk7' @ X2)) 41.59/6.15 | ~ (irel @ X2 @ X4) 41.59/6.15 | (a1 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ~ ('#form3'))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 41.59/6.15 thf(zip_derived_cl306, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a1 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4) 41.59/6.15 | (irel @ X2 @ ('#sk7' @ X2)))), 41.59/6.15 inference('clc', [status(thm)], [zip_derived_cl100, zip_derived_cl78])). 41.59/6.15 thf(zip_derived_cl1098, plain, 41.59/6.15 (( (irel @ ('#sk6' @ '#sk1') @ ('#sk7' @ ('#sk6' @ '#sk1'))) 41.59/6.15 | (a1 @ ('#sk9' @ '#sk1')) 41.59/6.15 | ~ (irel @ '#sk1' @ ('#sk6' @ '#sk1')))), 41.59/6.15 inference('sup-', [status(thm)], [zip_derived_cl1087, zip_derived_cl306])). 41.59/6.15 thf(zip_derived_cl1073, plain, (~ (a1 @ ('#sk9' @ '#sk1'))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1049, zip_derived_cl3, zip_derived_cl491])). 41.59/6.15 thf(zip_derived_cl498, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 41.59/6.15 inference('sup+', [status(thm)], [zip_derived_cl491, zip_derived_cl417])). 41.59/6.15 thf(zip_derived_cl1119, plain, 41.59/6.15 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk7' @ ('#sk6' @ '#sk1')))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1098, zip_derived_cl1073, zip_derived_cl498])). 41.59/6.15 thf(zip_derived_cl498, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 41.59/6.15 inference('sup+', [status(thm)], [zip_derived_cl491, zip_derived_cl417])). 41.59/6.15 thf(trans_axiom, axiom, 41.59/6.15 (![X:$i,Y:$i,Z:$i]: 41.59/6.15 ( ( ( irel @ X @ Y ) & ( irel @ Y @ Z ) ) => ( irel @ X @ Z ) ))). 41.59/6.15 thf(zip_derived_cl0, plain, 41.59/6.15 ( (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((!!) @ (^[Y2 : $i]: 41.59/6.15 (((((irel @ Y0 @ Y1) & (irel @ 41.59/6.15 Y1 @ Y2))) => 41.59/6.15 (irel @ Y0 @ Y2))))))))))))), 41.59/6.15 inference('cnf', [status(esa)], [trans_axiom])). 41.59/6.15 thf(zip_derived_cl4, plain, 41.59/6.15 (![X2 : $i]: 41.59/6.15 (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((!!) @ (^[Y1 : $i]: 41.59/6.15 (((((irel @ X2 @ Y0) & (irel @ Y0 @ Y1))) => 41.59/6.15 (irel @ X2 @ Y1)))))))))), 41.59/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 41.59/6.15 thf(zip_derived_cl5, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((((irel @ X2 @ X4) & (irel @ X4 @ Y0))) => (irel @ 41.59/6.15 X2 @ Y0))))))), 41.59/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 41.59/6.15 thf(zip_derived_cl6, plain, 41.59/6.15 (![X2 : $i, X4 : $i, X6 : $i]: 41.59/6.15 (((((irel @ X2 @ X4) & (irel @ X4 @ X6))) => (irel @ X2 @ X6)))), 41.59/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 41.59/6.15 thf(zip_derived_cl7, plain, 41.59/6.15 (![X2 : $i, X4 : $i, X6 : $i]: 41.59/6.15 (~ (((irel @ X2 @ X4) & (irel @ X4 @ X6))) | (irel @ X2 @ X6))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 41.59/6.15 thf(zip_derived_cl8, plain, 41.59/6.15 (![X2 : $i, X4 : $i, X6 : $i]: 41.59/6.15 (~ (irel @ X2 @ X4) | ~ (irel @ X4 @ X6) | (irel @ X2 @ X6))), 41.59/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 41.59/6.15 thf(zip_derived_cl509, plain, 41.59/6.15 (![X0 : $i]: ( (irel @ '#sk1' @ X0) | ~ (irel @ ('#sk6' @ '#sk1') @ X0))), 41.59/6.15 inference('sup-', [status(thm)], [zip_derived_cl498, zip_derived_cl8])). 41.59/6.15 thf(zip_derived_cl1180, plain, 41.59/6.15 ( (irel @ '#sk1' @ ('#sk7' @ ('#sk6' @ '#sk1')))), 41.59/6.15 inference('sup-', [status(thm)], [zip_derived_cl1119, zip_derived_cl509])). 41.59/6.15 thf(zip_derived_cl1407, plain, 41.59/6.15 ( (irel @ ('#sk7' @ ('#sk6' @ '#sk1')) @ 41.59/6.15 ('#sk5' @ ('#sk7' @ ('#sk6' @ '#sk1'))))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1389, zip_derived_cl1113, zip_derived_cl1180])). 41.59/6.15 thf(zip_derived_cl8, plain, 41.59/6.15 (![X2 : $i, X4 : $i, X6 : $i]: 41.59/6.15 (~ (irel @ X2 @ X4) | ~ (irel @ X4 @ X6) | (irel @ X2 @ X6))), 41.59/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 41.59/6.15 thf(zip_derived_cl1502, plain, 41.59/6.15 (![X0 : $i]: 41.59/6.15 ( (irel @ ('#sk7' @ ('#sk6' @ '#sk1')) @ X0) 41.59/6.15 | ~ (irel @ ('#sk5' @ ('#sk7' @ ('#sk6' @ '#sk1'))) @ X0))), 41.59/6.15 inference('sup-', [status(thm)], [zip_derived_cl1407, zip_derived_cl8])). 41.59/6.15 thf(zip_derived_cl1114, plain, 41.59/6.15 ( (irel @ ('#sk7' @ ('#sk6' @ '#sk1')) @ ('#sk10' @ ('#sk6' @ '#sk1')))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1093, zip_derived_cl498, zip_derived_cl1073])). 41.59/6.15 thf(zip_derived_cl105, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (((((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ ('#sk5' @ X2) @ Y0) => (b0 @ Y0)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ ('#sk5' @ X2) @ Y0) => (b2 @ Y0)))))))))) 41.59/6.15 | ~ (irel @ X2 @ X4) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ('#form3'))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 41.59/6.15 thf(zip_derived_cl121, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk5' @ X2) @ Y0) => (b0 @ Y0)))))) 41.59/6.15 | ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl105])). 41.59/6.15 thf(zip_derived_cl127, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (((irel @ ('#sk5' @ X2) @ ('#sk8' @ X2)) => (b0 @ ('#sk8' @ X2)))) 41.59/6.15 | ~ (irel @ X2 @ X4) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ('#form3'))), 41.59/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl121])). 41.59/6.15 thf(zip_derived_cl135, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 ( (irel @ ('#sk5' @ X2) @ ('#sk8' @ X2)) 41.59/6.15 | ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 41.59/6.15 thf(zip_derived_cl75, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (((((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ ('#sk5' @ X2) @ Y0) => (b0 @ Y0)))))) | 41.59/6.15 (((~) @ (((!!) @ (^[Y0 : $i]: 41.59/6.15 (((irel @ ('#sk5' @ X2) @ Y0) => (b2 @ Y0)))))))))) 41.59/6.15 | ~ (irel @ X2 @ X4) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ~ ('#form3'))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])). 41.59/6.15 thf(zip_derived_cl84, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk5' @ X2) @ Y0) => (b0 @ Y0)))))) 41.59/6.15 | ~ ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl75])). 41.59/6.15 thf(zip_derived_cl94, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (((irel @ ('#sk5' @ X2) @ ('#sk8' @ X2)) => (b0 @ ('#sk8' @ X2)))) 41.59/6.15 | ~ (irel @ X2 @ X4) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ~ ('#form3'))), 41.59/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl84])). 41.59/6.15 thf(zip_derived_cl108, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 ( (irel @ ('#sk5' @ X2) @ ('#sk8' @ X2)) 41.59/6.15 | ~ ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl94])). 41.59/6.15 thf(zip_derived_cl1255, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (irel @ X2 @ X4) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (irel @ ('#sk5' @ X2) @ ('#sk8' @ X2)))), 41.59/6.15 inference('clc', [status(thm)], [zip_derived_cl135, zip_derived_cl108])). 41.59/6.15 thf(zip_derived_cl1382, plain, 41.59/6.15 (( (irel @ ('#sk5' @ ('#sk7' @ ('#sk6' @ '#sk1'))) @ 41.59/6.15 ('#sk8' @ ('#sk7' @ ('#sk6' @ '#sk1')))) 41.59/6.15 | ~ (irel @ '#sk1' @ ('#sk7' @ ('#sk6' @ '#sk1'))) 41.59/6.15 | (a2 @ ('#sk10' @ ('#sk6' @ '#sk1'))))), 41.59/6.15 inference('sup-', [status(thm)], [zip_derived_cl1114, zip_derived_cl1255])). 41.59/6.15 thf(zip_derived_cl1180, plain, 41.59/6.15 ( (irel @ '#sk1' @ ('#sk7' @ ('#sk6' @ '#sk1')))), 41.59/6.15 inference('sup-', [status(thm)], [zip_derived_cl1119, zip_derived_cl509])). 41.59/6.15 thf(zip_derived_cl1113, plain, (~ (a2 @ ('#sk10' @ ('#sk6' @ '#sk1')))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1092, zip_derived_cl498, zip_derived_cl1073])). 41.59/6.15 thf(zip_derived_cl1400, plain, 41.59/6.15 ( (irel @ ('#sk5' @ ('#sk7' @ ('#sk6' @ '#sk1'))) @ 41.59/6.15 ('#sk8' @ ('#sk7' @ ('#sk6' @ '#sk1'))))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1382, zip_derived_cl1180, zip_derived_cl1113])). 41.59/6.15 thf(zip_derived_cl10326, plain, 41.59/6.15 ( (irel @ ('#sk7' @ ('#sk6' @ '#sk1')) @ 41.59/6.15 ('#sk8' @ ('#sk7' @ ('#sk6' @ '#sk1'))))), 41.59/6.15 inference('sup+', [status(thm)], [zip_derived_cl1502, zip_derived_cl1400])). 41.59/6.15 thf(zip_derived_cl1119, plain, 41.59/6.15 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk7' @ ('#sk6' @ '#sk1')))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1098, zip_derived_cl1073, zip_derived_cl498])). 41.59/6.15 thf(zip_derived_cl8, plain, 41.59/6.15 (![X2 : $i, X4 : $i, X6 : $i]: 41.59/6.15 (~ (irel @ X2 @ X4) | ~ (irel @ X4 @ X6) | (irel @ X2 @ X6))), 41.59/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 41.59/6.15 thf(zip_derived_cl1192, plain, 41.59/6.15 (![X0 : $i]: 41.59/6.15 ( (irel @ ('#sk6' @ '#sk1') @ X0) 41.59/6.15 | ~ (irel @ ('#sk7' @ ('#sk6' @ '#sk1')) @ X0))), 41.59/6.15 inference('sup-', [status(thm)], [zip_derived_cl1119, zip_derived_cl8])). 41.59/6.15 thf(zip_derived_cl10347, plain, 41.59/6.15 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk8' @ ('#sk7' @ ('#sk6' @ '#sk1'))))), 41.59/6.15 inference('sup-', [status(thm)], 41.59/6.15 [zip_derived_cl10326, zip_derived_cl1192])). 41.59/6.15 thf(zip_derived_cl120, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 ( (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk6' @ X2) @ Y0) => (b0 @ Y0)))))) 41.59/6.15 | ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a0 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl103])). 41.59/6.15 thf(zip_derived_cl126, plain, 41.59/6.15 (![X2 : $i, X4 : $i, X6 : $i]: 41.59/6.15 ( (((irel @ ('#sk6' @ X2) @ X6) => (b0 @ X6))) 41.59/6.15 | ~ (irel @ X2 @ X4) 41.59/6.15 | (a0 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ('#form3'))), 41.59/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl120])). 41.59/6.15 thf(zip_derived_cl134, plain, 41.59/6.15 (![X2 : $i, X4 : $i, X6 : $i]: 41.59/6.15 (~ (irel @ ('#sk6' @ X2) @ X6) 41.59/6.15 | (b0 @ X6) 41.59/6.15 | ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a0 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl126])). 41.59/6.15 thf(zip_derived_cl87, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 ( (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk6' @ X2) @ Y0) => (b0 @ Y0)))))) 41.59/6.15 | ~ ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a0 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl77])). 41.59/6.15 thf(zip_derived_cl97, plain, 41.59/6.15 (![X2 : $i, X4 : $i, X6 : $i]: 41.59/6.15 ( (((irel @ ('#sk6' @ X2) @ X6) => (b0 @ X6))) 41.59/6.15 | ~ (irel @ X2 @ X4) 41.59/6.15 | (a0 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ~ ('#form3'))), 41.59/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl87])). 41.59/6.15 thf(zip_derived_cl113, plain, 41.59/6.15 (![X2 : $i, X4 : $i, X6 : $i]: 41.59/6.15 (~ (irel @ ('#sk6' @ X2) @ X6) 41.59/6.15 | (b0 @ X6) 41.59/6.15 | ~ ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a0 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 41.59/6.15 thf(zip_derived_cl1166, plain, 41.59/6.15 (![X2 : $i, X4 : $i, X6 : $i]: 41.59/6.15 (~ (irel @ X2 @ X4) 41.59/6.15 | (a0 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (b0 @ X6) 41.59/6.15 | ~ (irel @ ('#sk6' @ X2) @ X6))), 41.59/6.15 inference('clc', [status(thm)], [zip_derived_cl134, zip_derived_cl113])). 41.59/6.15 thf(zip_derived_cl10438, plain, 41.59/6.15 (![X0 : $i]: 41.59/6.15 ( (b0 @ ('#sk8' @ ('#sk7' @ ('#sk6' @ '#sk1')))) 41.59/6.15 | ~ (irel @ '#sk1' @ '#sk1') 41.59/6.15 | (a0 @ X0) 41.59/6.15 | ~ (irel @ '#sk1' @ X0))), 41.59/6.15 inference('sup-', [status(thm)], 41.59/6.15 [zip_derived_cl10347, zip_derived_cl1166])). 41.59/6.15 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 41.59/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 41.59/6.15 thf(zip_derived_cl10464, plain, 41.59/6.15 (![X0 : $i]: 41.59/6.15 ( (b0 @ ('#sk8' @ ('#sk7' @ ('#sk6' @ '#sk1')))) 41.59/6.15 | (a0 @ X0) 41.59/6.15 | ~ (irel @ '#sk1' @ X0))), 41.59/6.15 inference('demod', [status(thm)], [zip_derived_cl10438, zip_derived_cl3])). 41.59/6.15 thf(zip_derived_cl1114, plain, 41.59/6.15 ( (irel @ ('#sk7' @ ('#sk6' @ '#sk1')) @ ('#sk10' @ ('#sk6' @ '#sk1')))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1093, zip_derived_cl498, zip_derived_cl1073])). 41.59/6.15 thf(zip_derived_cl136, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (b0 @ ('#sk8' @ X2)) 41.59/6.15 | ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 41.59/6.15 thf(zip_derived_cl109, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (b0 @ ('#sk8' @ X2)) 41.59/6.15 | ~ ('#form3') 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ X2 @ X4))), 41.59/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl94])). 41.59/6.15 thf(zip_derived_cl1418, plain, 41.59/6.15 (![X2 : $i, X4 : $i]: 41.59/6.15 (~ (irel @ X2 @ X4) 41.59/6.15 | (a2 @ X4) 41.59/6.15 | ~ (irel @ '#sk1' @ X2) 41.59/6.15 | ~ (b0 @ ('#sk8' @ X2)))), 41.59/6.15 inference('clc', [status(thm)], [zip_derived_cl136, zip_derived_cl109])). 41.59/6.15 thf(zip_derived_cl1420, plain, 41.59/6.15 ((~ (b0 @ ('#sk8' @ ('#sk7' @ ('#sk6' @ '#sk1')))) 41.59/6.15 | ~ (irel @ '#sk1' @ ('#sk7' @ ('#sk6' @ '#sk1'))) 41.59/6.15 | (a2 @ ('#sk10' @ ('#sk6' @ '#sk1'))))), 41.59/6.15 inference('sup-', [status(thm)], [zip_derived_cl1114, zip_derived_cl1418])). 41.59/6.15 thf(zip_derived_cl1180, plain, 41.59/6.15 ( (irel @ '#sk1' @ ('#sk7' @ ('#sk6' @ '#sk1')))), 41.59/6.15 inference('sup-', [status(thm)], [zip_derived_cl1119, zip_derived_cl509])). 41.59/6.15 thf(zip_derived_cl1113, plain, (~ (a2 @ ('#sk10' @ ('#sk6' @ '#sk1')))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1092, zip_derived_cl498, zip_derived_cl1073])). 41.59/6.15 thf(zip_derived_cl1456, plain, 41.59/6.15 (~ (b0 @ ('#sk8' @ ('#sk7' @ ('#sk6' @ '#sk1'))))), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl1420, zip_derived_cl1180, zip_derived_cl1113])). 41.59/6.15 thf(zip_derived_cl11325, plain, 41.59/6.15 (![X0 : $i]: (~ (irel @ '#sk1' @ X0) | (a0 @ X0))), 41.59/6.15 inference('clc', [status(thm)], [zip_derived_cl10464, zip_derived_cl1456])). 41.59/6.15 thf(zip_derived_cl11342, plain, (~ (irel @ '#sk1' @ ('#sk4' @ '#sk1'))), 41.59/6.15 inference('sup+', [status(thm)], [zip_derived_cl491, zip_derived_cl11325])). 41.59/6.15 thf(zip_derived_cl402, plain, ( (irel @ '#sk1' @ ('#sk4' @ '#sk1'))), 41.59/6.15 inference('clc', [status(thm)], [zip_derived_cl397, zip_derived_cl26])). 41.59/6.15 thf(zip_derived_cl11362, plain, ($false), 41.59/6.15 inference('demod', [status(thm)], 41.59/6.15 [zip_derived_cl11342, zip_derived_cl402])). 41.59/6.15 41.59/6.15 % SZS output end Refutation 41.59/6.15 41.59/6.15 41.59/6.15 % Terminating... 41.59/6.15 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 7.91/6.26 % Runner terminated. 0.25/6.30 % Zipperpin 1.5 exiting 0.25/6.34 EOF