%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL879^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Gcy69SHoy5 true
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:37:31 PM UTC 2026
% Result : Theorem 4.76s 1.39s
% Output : Refutation 4.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL879^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Gcy69SHoy5 true
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 20:58:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Running portfolio for 300 s
% 0.10/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Number of cores: 8
% 0.10/0.37 % Python version: Python 3.12.3
% 0.10/0.38 % Running in HO mode
% 0.44/0.67 % Total configuration time : 828
% 0.44/0.67 % Estimated wc time : 1656
% 0.44/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.49/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.49/0.80 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.49/0.80 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.49/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.49/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.49/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.49/0.87 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.49/0.87 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.49/0.88 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 4.76/1.39 % Solved by lams/35_full_unif4.sh.
% 4.76/1.39 % done 70 iterations in 0.516s
% 4.76/1.39 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.76/1.39 % SZS output start Refutation
% 4.76/1.39 thf(mbox_type, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 4.76/1.39 thf('#sk24_type', type, '#sk24': $i > ($i > $o) > $i).
% 4.76/1.39 thf('#sk18_type', type, '#sk18': $i).
% 4.76/1.39 thf('#sk77_type', type, '#sk77': $i).
% 4.76/1.39 thf(mnot_type, type, mnot: ($i > $o) > $i > $o).
% 4.76/1.39 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 4.76/1.39 thf('#form78_type', type, '#form78': $o).
% 4.76/1.39 thf('#sk5_type', type, '#sk5': $i).
% 4.76/1.39 thf('#sk4_type', type, '#sk4': $i > $o).
% 4.76/1.39 thf('#form13_type', type, '#form13': $o).
% 4.76/1.39 thf('#sk2_type', type, '#sk2': $i > $i > $o).
% 4.76/1.39 thf('#sk3_type', type, '#sk3': $i).
% 4.76/1.39 thf('#sk1_type', type, '#sk1': $i > $i > $o).
% 4.76/1.39 thf('#sk12_type', type, '#sk12': $i).
% 4.76/1.39 thf('#sk25_type', type, '#sk25': $i).
% 4.76/1.39 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 4.76/1.39 thf(mforall_prop_type, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 4.76/1.39 thf(mvalid_type, type, mvalid: ($i > $o) > $o).
% 4.76/1.39 thf(mvalid, axiom,(( mvalid ) =
% 4.76/1.39 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))).
% 4.76/1.39 thf('0', plain,
% 4.76/1.39 (( mvalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )),
% 4.76/1.39 inference('simplify_rw_rule', [status(thm)], [mvalid])).
% 4.76/1.39 thf('1', plain,
% 4.76/1.39 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )),
% 4.76/1.39 define([status(thm)])).
% 4.76/1.39 thf(mbox, axiom,(( mbox ) =
% 4.76/1.39 (^[R:( $i > $i > $o ),Phi:( $i > $o ),W:$i]:
% 4.76/1.39 ( ![V:$i]: ( ( Phi @ V ) | ( ~( R @ W @ V ) ) ) )))).
% 4.76/1.39 thf('2', plain,
% 4.76/1.39 (( mbox ) =
% 4.76/1.39 ( ^[R:( $i > $i > $o ),Phi:( $i > $o ),W:$i]:
% 4.76/1.39 ( ![V:$i]: ( ( Phi @ V ) | ( ~( R @ W @ V ) ) ) ) )),
% 4.76/1.39 inference('simplify_rw_rule', [status(thm)], [mbox])).
% 4.76/1.39 thf('3', plain,
% 4.76/1.39 (( mbox ) =
% 4.76/1.39 ( ^[V_1:( $i > $i > $o ),V_2:( $i > $o ),V_3:$i]:
% 4.76/1.39 ( ![X4:$i]: ( ( V_2 @ X4 ) | ( ~( V_1 @ V_3 @ X4 ) ) ) ) )),
% 4.76/1.39 define([status(thm)])).
% 4.76/1.39 thf(mforall_prop, axiom,(( mforall_prop ) =
% 4.76/1.39 (^[Phi:( ( $i > $o ) > $i > $o ),W:$i]:
% 4.76/1.39 ( ![P:( $i > $o )]: ( Phi @ P @ W ) )))).
% 4.76/1.39 thf('4', plain,
% 4.76/1.39 (( mforall_prop ) =
% 4.76/1.39 ( ^[Phi:( ( $i > $o ) > $i > $o ),W:$i]:
% 4.76/1.39 ( ![P:( $i > $o )]: ( Phi @ P @ W ) ) )),
% 4.76/1.39 inference('simplify_rw_rule', [status(thm)], [mforall_prop])).
% 4.76/1.39 thf('5', plain,
% 4.76/1.39 (( mforall_prop ) =
% 4.76/1.39 ( ^[V_1:( ( $i > $o ) > $i > $o ),V_2:$i]:
% 4.76/1.39 ( ![X4:( $i > $o )]: ( V_1 @ X4 @ V_2 ) ) )),
% 4.76/1.39 define([status(thm)])).
% 4.76/1.39 thf(mimplies, axiom,(( mimplies ) =
% 4.76/1.39 (^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi )))).
% 4.76/1.39 thf(mor, axiom,(( mor ) =
% 4.76/1.39 (^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) )))).
% 4.76/1.39 thf('6', plain,
% 4.76/1.39 (( mor ) =
% 4.76/1.39 ( ^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) ) )),
% 4.76/1.39 inference('simplify_rw_rule', [status(thm)], [mor])).
% 4.76/1.39 thf('7', plain,
% 4.76/1.39 (( mor ) =
% 4.76/1.39 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]:
% 4.76/1.39 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )),
% 4.76/1.39 define([status(thm)])).
% 4.76/1.39 thf(mnot, axiom,(( mnot ) = (^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) )))).
% 4.76/1.39 thf('8', plain, (( mnot ) = ( ^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) ) )),
% 4.76/1.39 inference('simplify_rw_rule', [status(thm)], [mnot])).
% 4.76/1.39 thf('9', plain,
% 4.76/1.39 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )),
% 4.76/1.39 define([status(thm)])).
% 4.76/1.39 thf('10', plain,
% 4.76/1.39 (( mimplies ) =
% 4.76/1.39 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi ) )),
% 4.76/1.39 inference('simplify_rw_rule', [status(thm)], [mimplies, '7', '9'])).
% 4.76/1.39 thf('11', plain,
% 4.76/1.39 (( mimplies ) =
% 4.76/1.39 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )),
% 4.76/1.39 define([status(thm)])).
% 4.76/1.39 thf(conj, conjecture,
% 4.76/1.39 (![I:( $i > $i > $o ),J:( $i > $i > $o )]:
% 4.76/1.39 ( ( mvalid @
% 4.76/1.39 ( mforall_prop @
% 4.76/1.39 ( ^[Phi:( $i > $o )]:
% 4.76/1.39 ( mimplies @
% 4.76/1.39 ( mbox @ I @ Phi ) @ ( mbox @ J @ ( mbox @ I @ Phi ) ) ) ) ) ) <=>
% 4.76/1.39 ( ![U:$i,V:$i,W:$i]:
% 4.76/1.39 ( ( ( J @ U @ V ) & ( I @ V @ W ) ) => ( I @ U @ W ) ) ) ))).
% 4.76/1.39 thf(zf_stmt_0, conjecture,
% 4.76/1.39 (![X4:( $i > $i > $o ),X6:( $i > $i > $o )]:
% 4.76/1.39 ( ( ![X8:$i,X10:( $i > $o )]:
% 4.76/1.39 ( ( ![X14:$i]:
% 4.76/1.39 ( ( ~( X6 @ X8 @ X14 ) ) |
% 4.76/1.39 ( ![X16:$i]: ( ( ~( X4 @ X14 @ X16 ) ) | ( X10 @ X16 ) ) ) ) ) |
% 4.76/1.39 ( ~( ![X12:$i]: ( ( ~( X4 @ X8 @ X12 ) ) | ( X10 @ X12 ) ) ) ) ) ) <=>
% 4.76/1.39 ( ![X18:$i,X20:$i,X22:$i]:
% 4.76/1.39 ( ( ( X4 @ X20 @ X22 ) & ( X6 @ X18 @ X20 ) ) => ( X4 @ X18 @ X22 ) ) ) ))).
% 4.76/1.39 thf(zf_stmt_1, negated_conjecture,
% 4.76/1.39 (~( ![X4:( $i > $i > $o ),X6:( $i > $i > $o )]:
% 4.76/1.39 ( ( ![X8:$i,X10:( $i > $o )]:
% 4.76/1.39 ( ( ![X14:$i]:
% 4.76/1.39 ( ( ~( X6 @ X8 @ X14 ) ) |
% 4.76/1.39 ( ![X16:$i]: ( ( ~( X4 @ X14 @ X16 ) ) | ( X10 @ X16 ) ) ) ) ) |
% 4.76/1.39 ( ~( ![X12:$i]: ( ( ~( X4 @ X8 @ X12 ) ) | ( X10 @ X12 ) ) ) ) ) ) <=>
% 4.76/1.39 ( ![X18:$i,X20:$i,X22:$i]:
% 4.76/1.39 ( ( ( X4 @ X20 @ X22 ) & ( X6 @ X18 @ X20 ) ) => ( X4 @ X18 @ X22 ) ) ) ) )),
% 4.76/1.39 inference('cnf.neg', [status(esa)], [zf_stmt_0])).
% 4.76/1.39 thf(zip_derived_cl0, plain,
% 4.76/1.39 (~ (((!!) @ (^[Y0 : $i > $i > $o]:
% 4.76/1.39 (((!!) @ (^[Y1 : $i > $i > $o]:
% 4.76/1.39 (((((!!) @ (^[Y2 : $i]:
% 4.76/1.39 (((!!) @ (^[Y3 : $i > $o]:
% 4.76/1.39 (((((!!) @ (
% 4.76/1.39 ^[Y4 : $i]:
% 4.76/1.39 (((((~) @ (
% 4.76/1.39 Y1 @ Y2 @
% 4.76/1.39 Y4))) |
% 4.76/1.39 (((!!) @ (
% 4.76/1.39 ^[Y5 : $i]:
% 4.76/1.39 ((
% 4.76/1.39 ((
% 4.76/1.39 (~) @ (
% 4.76/1.39 Y0 @
% 4.76/1.39 Y4 @ Y5))) |
% 4.76/1.39 (Y3 @ Y5))))))))))) |
% 4.76/1.39 (((~) @ ((
% 4.76/1.39 (!!) @ (
% 4.76/1.39 ^[Y4 : $i]:
% 4.76/1.39 ((
% 4.76/1.39 ((
% 4.76/1.39 (~) @ (
% 4.76/1.39 Y0 @
% 4.76/1.39 Y2 @ Y4))) |
% 4.76/1.39 (Y3 @ Y4)))))))))))))))) <=>
% 4.76/1.39 (((!!) @ (^[Y2 : $i]:
% 4.76/1.39 (((!!) @ (^[Y3 : $i]:
% 4.76/1.39 (((!!) @ (^[Y4 : $i]:
% 4.76/1.39 ((
% 4.76/1.39 ((
% 4.76/1.39 (Y0 @
% 4.76/1.39 Y3 @
% 4.76/1.39 Y4) &
% 4.76/1.39 (Y1 @
% 4.76/1.39 Y2 @ Y3))) =>
% 4.76/1.39 (Y0 @
% 4.76/1.39 Y2 @ Y4))))))))))))))))))))),
% 4.76/1.39 inference('cnf', [status(esa)], [zf_stmt_1])).
% 4.76/1.39 thf(zip_derived_cl1, plain,
% 4.76/1.39 (~ (((!!) @ (^[Y0 : $i > $i > $o]:
% 4.76/1.39 (((((!!) @ (^[Y1 : $i]:
% 4.76/1.39 (((!!) @ (^[Y2 : $i > $o]:
% 4.76/1.39 (((((!!) @ (^[Y3 : $i]:
% 4.76/1.39 (((((~) @ (
% 4.76/1.39 Y0 @ Y1 @ Y3))) |
% 4.76/1.39 (((!!) @ (
% 4.76/1.39 ^[Y4 : $i]:
% 4.76/1.39 ((((
% 4.76/1.39 (~) @ (
% 4.76/1.39 '#sk1' @
% 4.76/1.39 Y3 @ Y4))) |
% 4.76/1.39 (Y2 @ Y4))))))))))) |
% 4.76/1.39 (((~) @ (((!!) @ (^[Y3 : $i]:
% 4.76/1.39 ((
% 4.76/1.39 ((
% 4.76/1.39 (~) @ (
% 4.76/1.39 '#sk1' @
% 4.76/1.39 Y1 @ Y3))) |
% 4.76/1.39 (Y2 @ Y3)))))))))))))))) <=>
% 4.76/1.39 (((!!) @ (^[Y1 : $i]:
% 4.76/1.39 (((!!) @ (^[Y2 : $i]:
% 4.76/1.39 (((!!) @ (^[Y3 : $i]:
% 4.76/1.39 ((((('#sk1' @ Y2 @
% 4.76/1.39 Y3) & (Y0 @
% 4.76/1.39 Y1 @ Y2))) =>
% 4.76/1.39 ('#sk1' @ Y1 @ Y3)))))))))))))))))),
% 4.76/1.39 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])).
% 4.76/1.39 thf(zip_derived_cl2, plain,
% 4.76/1.39 (~ (((((!!) @ (^[Y0 : $i]:
% 4.76/1.39 (((!!) @ (^[Y1 : $i > $o]:
% 4.76/1.39 (((((!!) @ (^[Y2 : $i]:
% 4.76/1.39 (((((~) @ ('#sk2' @ Y0 @ Y2))) |
% 4.76/1.39 (((!!) @ (^[Y3 : $i]:
% 4.76/1.39 (((((~) @ (
% 4.76/1.39 '#sk1' @
% 4.76/1.39 Y2 @ Y3))) |
% 4.76/1.39 (Y1 @ Y3))))))))))) |
% 4.76/1.39 (((~) @ (((!!) @ (^[Y2 : $i]:
% 4.76/1.39 (((((~) @ ('#sk1' @
% 4.76/1.39 Y0 @ Y2))) |
% 4.76/1.39 (Y1 @ Y2)))))))))))))))) <=>
% 4.76/1.39 (((!!) @ (^[Y0 : $i]:
% 4.76/1.39 (((!!) @ (^[Y1 : $i]:
% 4.76/1.39 (((!!) @ (^[Y2 : $i]:
% 4.76/1.39 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.39 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.39 ('#sk1' @ Y0 @ Y2))))))))))))))),
% 4.76/1.39 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])).
% 4.76/1.39 thf(zip_derived_cl3, plain,
% 4.76/1.39 (((((!!) @ (^[Y0 : $i]:
% 4.76/1.39 (((!!) @ (^[Y1 : $i > $o]:
% 4.76/1.39 (((((!!) @ (^[Y2 : $i]:
% 4.76/1.39 (((((~) @ ('#sk2' @ Y0 @ Y2))) |
% 4.76/1.39 (((!!) @ (^[Y3 : $i]:
% 4.76/1.39 (((((~) @ (
% 4.76/1.39 '#sk1' @ Y2 @
% 4.76/1.39 Y3))) |
% 4.76/1.39 (Y1 @ Y3))))))))))) |
% 4.76/1.39 (((~) @ (((!!) @ (^[Y2 : $i]:
% 4.76/1.39 (((((~) @ ('#sk1' @ Y0 @
% 4.76/1.39 Y2))) |
% 4.76/1.39 (Y1 @ Y2))))))))))))))))
% 4.76/1.39 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.39 (((!!) @ (^[Y1 : $i]:
% 4.76/1.39 (((!!) @ (^[Y2 : $i]:
% 4.76/1.39 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.39 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.39 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.39 inference('simplify nested equalities', [status(thm)], [zip_derived_cl2])).
% 4.76/1.39 thf(zip_derived_cl5, plain,
% 4.76/1.39 ((((^[Y0 : $i]:
% 4.76/1.39 (((!!) @ (^[Y1 : $i > $o]:
% 4.76/1.39 (((((!!) @ (^[Y2 : $i]:
% 4.76/1.39 (((((~) @ ('#sk2' @ Y0 @ Y2))) |
% 4.76/1.39 (((!!) @ (^[Y3 : $i]:
% 4.76/1.39 (((((~) @ ('#sk1' @ Y2 @ Y3))) |
% 4.76/1.39 (Y1 @ Y3))))))))))) |
% 4.76/1.39 (((~) @ (((!!) @ (^[Y2 : $i]:
% 4.76/1.39 (((((~) @ ('#sk1' @ Y0 @ Y2))) |
% 4.76/1.39 (Y1 @ Y2)))))))))))))) @
% 4.76/1.39 '#sk3')
% 4.76/1.39 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.39 (((!!) @ (^[Y1 : $i]:
% 4.76/1.39 (((!!) @ (^[Y2 : $i]:
% 4.76/1.39 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.39 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.39 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.39 inference('quantifier_rw', [status(thm)], [zip_derived_cl3])).
% 4.76/1.39 thf(zip_derived_cl6, plain,
% 4.76/1.39 (((((!!) @ (^[Y0 : $i > $o]:
% 4.76/1.39 (((((!!) @ (^[Y1 : $i]:
% 4.76/1.39 (((((~) @ ('#sk2' @ '#sk3' @ Y1))) |
% 4.76/1.39 (((!!) @ (^[Y2 : $i]:
% 4.76/1.39 (((((~) @ ('#sk1' @ Y1 @ Y2))) |
% 4.76/1.39 (Y0 @ Y2))))))))))) |
% 4.76/1.39 (((~) @ (((!!) @ (^[Y1 : $i]:
% 4.76/1.39 (((((~) @ ('#sk1' @ '#sk3' @ Y1))) |
% 4.76/1.39 (Y0 @ Y1)))))))))))))
% 4.76/1.39 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.39 (((!!) @ (^[Y1 : $i]:
% 4.76/1.39 (((!!) @ (^[Y2 : $i]:
% 4.76/1.39 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.39 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('ho_norm', [status(thm)], [zip_derived_cl5])).
% 4.76/1.40 thf(zip_derived_cl9, plain,
% 4.76/1.40 ((((^[Y0 : $i > $o]:
% 4.76/1.40 (((((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y1))) |
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y1 @ Y2))) | (Y0 @
% 4.76/1.40 Y2))))))))))) |
% 4.76/1.40 (((~) @ (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ '#sk3' @ Y1))) | (Y0 @
% 4.76/1.40 Y1))))))))))) @
% 4.76/1.40 '#sk4')
% 4.76/1.40 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('quantifier_rw', [status(thm)], [zip_derived_cl6])).
% 4.76/1.40 thf(zip_derived_cl14, plain,
% 4.76/1.40 (((((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | ('#sk4' @
% 4.76/1.40 Y1))))))))))) |
% 4.76/1.40 (((~) @ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ '#sk3' @ Y0))) | ('#sk4' @
% 4.76/1.40 Y0))))))))))
% 4.76/1.40 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('ho_norm', [status(thm)], [zip_derived_cl9])).
% 4.76/1.40 thf(zip_derived_cl15, plain,
% 4.76/1.40 (![X-83 : $i]:
% 4.76/1.40 ( ((^[Y0 : $i]: (((((~) @ ('#sk1' @ '#sk3' @ Y0))) | ('#sk4' @ Y0)))) @
% 4.76/1.40 X-83)
% 4.76/1.40 | ((((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) |
% 4.76/1.40 ('#sk4' @ Y1))))))))))) |
% 4.76/1.40 (((~) @ ($false)))))
% 4.76/1.40 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2))))))))))))))),
% 4.76/1.40 inference('forall_hoist', [status(thm)], [zip_derived_cl14])).
% 4.76/1.40 thf(zip_derived_cl24, plain,
% 4.76/1.40 (![X-83 : $i]:
% 4.76/1.40 ( (((((~) @ ('#sk1' @ '#sk3' @ X-83))) | ('#sk4' @ X-83)))
% 4.76/1.40 | ((((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) |
% 4.76/1.40 ('#sk4' @ Y1))))))))))) |
% 4.76/1.40 (((~) @ ($false)))))
% 4.76/1.40 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2))))))))))))))),
% 4.76/1.40 inference('ho_norm', [status(thm)], [zip_derived_cl15])).
% 4.76/1.40 thf(zip_derived_cl25, plain,
% 4.76/1.40 (![X-83 : $i]:
% 4.76/1.40 ( (((((~) @ ('#sk1' @ '#sk3' @ X-83))) | ('#sk4' @ X-83)))
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl24])).
% 4.76/1.40 thf(zip_derived_cl26, plain,
% 4.76/1.40 (![X0 : $i]:
% 4.76/1.40 ( (((((~) @ ('#sk1' @ '#sk3' @ X0))) | ('#sk4' @ X0)))
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('cannonize vars', [status(thm)], [zip_derived_cl25])).
% 4.76/1.40 thf(zip_derived_cl27, plain,
% 4.76/1.40 (( ('#form13')
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 define([status(thm)])).
% 4.76/1.40 thf(zip_derived_cl28, plain,
% 4.76/1.40 ((~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @ '#sk12' @
% 4.76/1.40 Y0))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y1)))))))))
% 4.76/1.40 | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl27])).
% 4.76/1.40 thf(zip_derived_cl39, plain,
% 4.76/1.40 ((~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 ((((('#sk1' @ '#sk18' @ Y0) & ('#sk2' @ '#sk12' @
% 4.76/1.40 '#sk18'))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y0))))))
% 4.76/1.40 | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])).
% 4.76/1.40 thf(zip_derived_cl44, plain,
% 4.76/1.40 ((~ ((((('#sk1' @ '#sk18' @ '#sk25') & ('#sk2' @ '#sk12' @ '#sk18'))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ '#sk25')))
% 4.76/1.40 | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl39])).
% 4.76/1.40 thf(zip_derived_cl52, plain,
% 4.76/1.40 ((~ ('#sk1' @ '#sk12' @ '#sk25') | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])).
% 4.76/1.40 thf(zip_derived_cl14, plain,
% 4.76/1.40 (((((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | ('#sk4' @
% 4.76/1.40 Y1))))))))))) |
% 4.76/1.40 (((~) @ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ '#sk3' @ Y0))) | ('#sk4' @
% 4.76/1.40 Y0))))))))))
% 4.76/1.40 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('ho_norm', [status(thm)], [zip_derived_cl9])).
% 4.76/1.40 thf(zip_derived_cl16, plain,
% 4.76/1.40 (((((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | ('#sk4' @
% 4.76/1.40 Y1))))))))))) |
% 4.76/1.40 (((~) @ ((^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ '#sk3' @ Y0))) | ('#sk4' @ Y0)))) @
% 4.76/1.40 '#sk5')))))
% 4.76/1.40 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('quantifier_rw', [status(thm)], [zip_derived_cl14])).
% 4.76/1.40 thf(zip_derived_cl21, plain,
% 4.76/1.40 (((((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | ('#sk4' @
% 4.76/1.40 Y1))))))))))) |
% 4.76/1.40 (((~) @ (((((~) @ ('#sk1' @ '#sk3' @ '#sk5'))) | ('#sk4' @ '#sk5')))))))
% 4.76/1.40 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('ho_norm', [status(thm)], [zip_derived_cl16])).
% 4.76/1.40 thf(zip_derived_cl23, plain,
% 4.76/1.40 (((((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | ('#sk4' @
% 4.76/1.40 Y1))))))))))) |
% 4.76/1.40 (((~) @ (((((~) @ ('#sk1' @ '#sk3' @ '#sk5'))) | ('#sk4' @ '#sk5')))))))
% 4.76/1.40 != ((^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) & ('#sk2' @
% 4.76/1.40 Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))) @
% 4.76/1.40 '#sk12'))),
% 4.76/1.40 inference('quantifier_rw', [status(thm)], [zip_derived_cl21])).
% 4.76/1.40 thf(zip_derived_cl34, plain,
% 4.76/1.40 (((((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | ('#sk4' @
% 4.76/1.40 Y1))))))))))) |
% 4.76/1.40 (((~) @ (((((~) @ ('#sk1' @ '#sk3' @ '#sk5'))) | ('#sk4' @ '#sk5')))))))
% 4.76/1.40 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @
% 4.76/1.40 '#sk12' @ Y0))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y1))))))))))),
% 4.76/1.40 inference('ho_norm', [status(thm)], [zip_derived_cl23])).
% 4.76/1.40 thf(zip_derived_cl82, plain,
% 4.76/1.40 ((~ (((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) |
% 4.76/1.40 ('#sk4' @ Y1))))))))))) |
% 4.76/1.40 (((~) @ (((((~) @ ('#sk1' @ '#sk3' @ '#sk5'))) | ('#sk4' @ '#sk5')))))))
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @
% 4.76/1.40 '#sk12' @ Y0))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y1))))))))))),
% 4.76/1.40 inference('eq_elim', [status(thm)], [zip_derived_cl34])).
% 4.76/1.40 thf(zip_derived_cl96, plain,
% 4.76/1.40 (( (((((~) @ ('#sk1' @ '#sk3' @ '#sk5'))) | ('#sk4' @ '#sk5')))
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @
% 4.76/1.40 '#sk12' @ Y0))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y1))))))))))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl82])).
% 4.76/1.40 thf(zip_derived_cl98, plain,
% 4.76/1.40 ((~ ('#sk1' @ '#sk3' @ '#sk5')
% 4.76/1.40 | ('#sk4' @ '#sk5')
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @
% 4.76/1.40 '#sk12' @ Y0))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y1))))))))))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl96])).
% 4.76/1.40 thf(zip_derived_cl101, plain,
% 4.76/1.40 (( ('#form78')
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @
% 4.76/1.40 '#sk12' @ Y0))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y1))))))))))),
% 4.76/1.40 define([status(thm)])).
% 4.76/1.40 thf(zip_derived_cl102, plain,
% 4.76/1.40 ((~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 ((((('#sk1' @ '#sk18' @ Y0) & ('#sk2' @ '#sk12' @
% 4.76/1.40 '#sk18'))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y0))))))
% 4.76/1.40 | ('#form78'))),
% 4.76/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])).
% 4.76/1.40 thf(zip_derived_cl106, plain,
% 4.76/1.40 ((~ ((((('#sk1' @ '#sk18' @ '#sk25') & ('#sk2' @ '#sk12' @ '#sk18'))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ '#sk25')))
% 4.76/1.40 | ('#form78'))),
% 4.76/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl102])).
% 4.76/1.40 thf(zip_derived_cl108, plain,
% 4.76/1.40 (( ((('#sk1' @ '#sk18' @ '#sk25') & ('#sk2' @ '#sk12' @ '#sk18')))
% 4.76/1.40 | ('#form78'))),
% 4.76/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl106])).
% 4.76/1.40 thf(zip_derived_cl112, plain,
% 4.76/1.40 (( ('#sk1' @ '#sk18' @ '#sk25') | ('#form78'))),
% 4.76/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl108])).
% 4.76/1.40 thf(zip_derived_cl113, plain,
% 4.76/1.40 (( ('#sk2' @ '#sk12' @ '#sk18') | ('#form78'))),
% 4.76/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl108])).
% 4.76/1.40 thf(zip_derived_cl6, plain,
% 4.76/1.40 (((((!!) @ (^[Y0 : $i > $o]:
% 4.76/1.40 (((((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y1))) |
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y1 @ Y2))) |
% 4.76/1.40 (Y0 @ Y2))))))))))) |
% 4.76/1.40 (((~) @ (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ '#sk3' @ Y1))) |
% 4.76/1.40 (Y0 @ Y1)))))))))))))
% 4.76/1.40 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('ho_norm', [status(thm)], [zip_derived_cl5])).
% 4.76/1.40 thf(zip_derived_cl7, plain,
% 4.76/1.40 (![X-82 : $i > $o]:
% 4.76/1.40 ( ((^[Y0 : $i > $o]:
% 4.76/1.40 (((((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y1))) |
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y1 @ Y2))) |
% 4.76/1.40 (Y0 @ Y2))))))))))) |
% 4.76/1.40 (((~) @ (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ '#sk3' @ Y1))) |
% 4.76/1.40 (Y0 @ Y1))))))))))) @
% 4.76/1.40 X-82)
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('forall_hoist', [status(thm)], [zip_derived_cl6])).
% 4.76/1.40 thf(zip_derived_cl17, plain,
% 4.76/1.40 (![X-82 : $i > $o]:
% 4.76/1.40 ( (((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) |
% 4.76/1.40 (X-82 @ Y1))))))))))) |
% 4.76/1.40 (((~) @ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ '#sk3' @ Y0))) | (X-82 @
% 4.76/1.40 Y0))))))))))
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('ho_norm', [status(thm)], [zip_derived_cl7])).
% 4.76/1.40 thf(zip_derived_cl18, plain,
% 4.76/1.40 (![X0 : $i > $o]:
% 4.76/1.40 ( (((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | (X0 @
% 4.76/1.40 Y1))))))))))) |
% 4.76/1.40 (((~) @ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ '#sk3' @ Y0))) | (X0 @ Y0))))))))))
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('cannonize vars', [status(thm)], [zip_derived_cl17])).
% 4.76/1.40 thf(zip_derived_cl19, plain,
% 4.76/1.40 (![X0 : $i > $o]:
% 4.76/1.40 ( (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | (X0 @ Y1)))))))))))
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ '#sk3' @ Y0))) | (X0 @ Y0))))))
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl18])).
% 4.76/1.40 thf(zip_derived_cl30, plain,
% 4.76/1.40 ((~ ('#form13')
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 define([status(thm)])).
% 4.76/1.40 thf(zip_derived_cl31, plain,
% 4.76/1.40 (![X2 : $i]:
% 4.76/1.40 ( (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @ X2 @ Y0))) =>
% 4.76/1.40 ('#sk1' @ X2 @ Y1)))))))))
% 4.76/1.40 | ~ ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl30])).
% 4.76/1.40 thf(zip_derived_cl41, plain,
% 4.76/1.40 (![X2 : $i, X4 : $i]:
% 4.76/1.40 ( (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 ((((('#sk1' @ X4 @ Y0) & ('#sk2' @ X2 @ X4))) =>
% 4.76/1.40 ('#sk1' @ X2 @ Y0))))))
% 4.76/1.40 | ~ ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])).
% 4.76/1.40 thf(zip_derived_cl47, plain,
% 4.76/1.40 (![X2 : $i, X4 : $i, X6 : $i]:
% 4.76/1.40 ( ((((('#sk1' @ X4 @ X6) & ('#sk2' @ X2 @ X4))) => ('#sk1' @ X2 @ X6)))
% 4.76/1.40 | ~ ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])).
% 4.76/1.40 thf(zip_derived_cl55, plain,
% 4.76/1.40 (![X2 : $i, X4 : $i, X6 : $i]:
% 4.76/1.40 (~ ((('#sk1' @ X4 @ X6) & ('#sk2' @ X2 @ X4)))
% 4.76/1.40 | ('#sk1' @ X2 @ X6)
% 4.76/1.40 | ~ ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])).
% 4.76/1.40 thf(zip_derived_cl63, plain,
% 4.76/1.40 (![X2 : $i, X4 : $i, X6 : $i]:
% 4.76/1.40 (~ ('#sk1' @ X4 @ X6)
% 4.76/1.40 | ~ ('#sk2' @ X2 @ X4)
% 4.76/1.40 | ~ ('#form13')
% 4.76/1.40 | ('#sk1' @ X2 @ X6))),
% 4.76/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])).
% 4.76/1.40 thf(zip_derived_cl131, plain,
% 4.76/1.40 (![X0 : $i]:
% 4.76/1.40 ( ('#form78')
% 4.76/1.40 | ('#sk1' @ '#sk12' @ X0)
% 4.76/1.40 | ~ ('#form13')
% 4.76/1.40 | ~ ('#sk1' @ '#sk18' @ X0))),
% 4.76/1.40 inference('sup-', [status(thm)], [zip_derived_cl113, zip_derived_cl63])).
% 4.76/1.40 thf(zip_derived_cl26, plain,
% 4.76/1.40 (![X0 : $i]:
% 4.76/1.40 ( (((((~) @ ('#sk1' @ '#sk3' @ X0))) | ('#sk4' @ X0)))
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('cannonize vars', [status(thm)], [zip_derived_cl25])).
% 4.76/1.40 thf(zip_derived_cl27, plain,
% 4.76/1.40 (( ('#form13')
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 define([status(thm)])).
% 4.76/1.40 thf(zip_derived_cl29, plain,
% 4.76/1.40 (![X0 : $i]:
% 4.76/1.40 (~ ('#form13') | (((((~) @ ('#sk1' @ '#sk3' @ X0))) | ('#sk4' @ X0))))),
% 4.76/1.40 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl27])).
% 4.76/1.40 thf(zip_derived_cl38, plain,
% 4.76/1.40 (![X0 : $i]: (~ ('#sk1' @ '#sk3' @ X0) | ('#sk4' @ X0) | ~ ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])).
% 4.76/1.40 thf(zip_derived_cl95, plain,
% 4.76/1.40 ((~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ '#sk3' @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | ('#sk4' @
% 4.76/1.40 Y1)))))))))))
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @
% 4.76/1.40 '#sk12' @ Y0))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y1))))))))))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl82])).
% 4.76/1.40 thf(zip_derived_cl97, plain,
% 4.76/1.40 ((~ (((((~) @ ('#sk2' @ '#sk3' @ '#sk77'))) |
% 4.76/1.40 (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ '#sk77' @ Y0))) | ('#sk4' @ Y0))))))))
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @
% 4.76/1.40 '#sk12' @ Y0))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y1))))))))))),
% 4.76/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl95])).
% 4.76/1.40 thf(zip_derived_cl100, plain,
% 4.76/1.40 ((~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ '#sk77' @ Y0))) | ('#sk4' @ Y0))))))
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @
% 4.76/1.40 '#sk12' @ Y0))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y1))))))))))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl97])).
% 4.76/1.40 thf(zip_derived_cl101, plain,
% 4.76/1.40 (( ('#form78')
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @
% 4.76/1.40 '#sk12' @ Y0))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y1))))))))))),
% 4.76/1.40 define([status(thm)])).
% 4.76/1.40 thf(zip_derived_cl105, plain,
% 4.76/1.40 ((~ ('#form78')
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ '#sk77' @ Y0))) | ('#sk4' @ Y0)))))))),
% 4.76/1.40 inference('renaming', [status(thm)],
% 4.76/1.40 [zip_derived_cl100, zip_derived_cl101])).
% 4.76/1.40 thf(zip_derived_cl107, plain,
% 4.76/1.40 ((~ (((((~) @ ('#sk1' @ '#sk77' @ ('#sk24' @ '#sk77' @ '#sk4')))) |
% 4.76/1.40 ('#sk4' @ ('#sk24' @ '#sk77' @ '#sk4'))))
% 4.76/1.40 | ~ ('#form78'))),
% 4.76/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])).
% 4.76/1.40 thf(zip_derived_cl110, plain,
% 4.76/1.40 (( ('#sk1' @ '#sk77' @ ('#sk24' @ '#sk77' @ '#sk4')) | ~ ('#form78'))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl107])).
% 4.76/1.40 thf(zip_derived_cl99, plain,
% 4.76/1.40 (( ('#sk2' @ '#sk3' @ '#sk77')
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @
% 4.76/1.40 '#sk12' @ Y0))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y1))))))))))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl97])).
% 4.76/1.40 thf(zip_derived_cl101, plain,
% 4.76/1.40 (( ('#form78')
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y0 @ Y1) & ('#sk2' @
% 4.76/1.40 '#sk12' @ Y0))) =>
% 4.76/1.40 ('#sk1' @ '#sk12' @ Y1))))))))))),
% 4.76/1.40 define([status(thm)])).
% 4.76/1.40 thf(zip_derived_cl104, plain,
% 4.76/1.40 ((~ ('#form78') | ('#sk2' @ '#sk3' @ '#sk77'))),
% 4.76/1.40 inference('renaming', [status(thm)],
% 4.76/1.40 [zip_derived_cl99, zip_derived_cl101])).
% 4.76/1.40 thf(zip_derived_cl63, plain,
% 4.76/1.40 (![X2 : $i, X4 : $i, X6 : $i]:
% 4.76/1.40 (~ ('#sk1' @ X4 @ X6)
% 4.76/1.40 | ~ ('#sk2' @ X2 @ X4)
% 4.76/1.40 | ~ ('#form13')
% 4.76/1.40 | ('#sk1' @ X2 @ X6))),
% 4.76/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])).
% 4.76/1.40 thf(zip_derived_cl133, plain,
% 4.76/1.40 (![X0 : $i]:
% 4.76/1.40 (~ ('#form78')
% 4.76/1.40 | ('#sk1' @ '#sk3' @ X0)
% 4.76/1.40 | ~ ('#form13')
% 4.76/1.40 | ~ ('#sk1' @ '#sk77' @ X0))),
% 4.76/1.40 inference('sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl63])).
% 4.76/1.40 thf(zip_derived_cl137, plain,
% 4.76/1.40 ((~ ('#form78')
% 4.76/1.40 | ~ ('#form13')
% 4.76/1.40 | ('#sk1' @ '#sk3' @ ('#sk24' @ '#sk77' @ '#sk4'))
% 4.76/1.40 | ~ ('#form78'))),
% 4.76/1.40 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl133])).
% 4.76/1.40 thf(zip_derived_cl139, plain,
% 4.76/1.40 (( ('#sk1' @ '#sk3' @ ('#sk24' @ '#sk77' @ '#sk4'))
% 4.76/1.40 | ~ ('#form13')
% 4.76/1.40 | ~ ('#form78'))),
% 4.76/1.40 inference('simplify', [status(thm)], [zip_derived_cl137])).
% 4.76/1.40 thf(zip_derived_cl142, plain,
% 4.76/1.40 ((~ ('#form13')
% 4.76/1.40 | ('#sk4' @ ('#sk24' @ '#sk77' @ '#sk4'))
% 4.76/1.40 | ~ ('#form78')
% 4.76/1.40 | ~ ('#form13'))),
% 4.76/1.40 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl139])).
% 4.76/1.40 thf(zip_derived_cl145, plain,
% 4.76/1.40 ((~ ('#form78')
% 4.76/1.40 | ('#sk4' @ ('#sk24' @ '#sk77' @ '#sk4'))
% 4.76/1.40 | ~ ('#form13'))),
% 4.76/1.40 inference('simplify', [status(thm)], [zip_derived_cl142])).
% 4.76/1.40 thf(zip_derived_cl111, plain,
% 4.76/1.40 ((~ ('#sk4' @ ('#sk24' @ '#sk77' @ '#sk4')) | ~ ('#form78'))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl107])).
% 4.76/1.40 thf(zip_derived_cl149, plain, ((~ ('#form13') | ~ ('#form78'))),
% 4.76/1.40 inference('clc', [status(thm)], [zip_derived_cl145, zip_derived_cl111])).
% 4.76/1.40 thf(zip_derived_cl156, plain,
% 4.76/1.40 (![X0 : $i]:
% 4.76/1.40 (~ ('#sk1' @ '#sk18' @ X0) | ~ ('#form13') | ('#sk1' @ '#sk12' @ X0))),
% 4.76/1.40 inference('clc', [status(thm)], [zip_derived_cl131, zip_derived_cl149])).
% 4.76/1.40 thf(zip_derived_cl157, plain,
% 4.76/1.40 (( ('#form78') | ('#sk1' @ '#sk12' @ '#sk25') | ~ ('#form13'))),
% 4.76/1.40 inference('sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl156])).
% 4.76/1.40 thf(zip_derived_cl149, plain, ((~ ('#form13') | ~ ('#form78'))),
% 4.76/1.40 inference('clc', [status(thm)], [zip_derived_cl145, zip_derived_cl111])).
% 4.76/1.40 thf(zip_derived_cl178, plain,
% 4.76/1.40 ((~ ('#form13') | ('#sk1' @ '#sk12' @ '#sk25'))),
% 4.76/1.40 inference('clc', [status(thm)], [zip_derived_cl157, zip_derived_cl149])).
% 4.76/1.40 thf(zip_derived_cl109, plain,
% 4.76/1.40 ((~ ('#sk1' @ '#sk12' @ '#sk25') | ('#form78'))),
% 4.76/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl106])).
% 4.76/1.40 thf(zip_derived_cl179, plain, ((~ ('#form13') | ('#form78'))),
% 4.76/1.40 inference('sup-', [status(thm)], [zip_derived_cl178, zip_derived_cl109])).
% 4.76/1.40 thf(zip_derived_cl149, plain, ((~ ('#form13') | ~ ('#form78'))),
% 4.76/1.40 inference('clc', [status(thm)], [zip_derived_cl145, zip_derived_cl111])).
% 4.76/1.40 thf(zip_derived_cl189, plain, (~ ('#form13')),
% 4.76/1.40 inference('clc', [status(thm)], [zip_derived_cl179, zip_derived_cl149])).
% 4.76/1.40 thf(zip_derived_cl190, plain, (~ ('#sk1' @ '#sk12' @ '#sk25')),
% 4.76/1.40 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl189])).
% 4.76/1.40 thf(zip_derived_cl51, plain,
% 4.76/1.40 (( ((('#sk1' @ '#sk18' @ '#sk25') & ('#sk2' @ '#sk12' @ '#sk18')))
% 4.76/1.40 | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])).
% 4.76/1.40 thf(zip_derived_cl59, plain,
% 4.76/1.40 (( ('#sk1' @ '#sk18' @ '#sk25') | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl51])).
% 4.76/1.40 thf(zip_derived_cl189, plain, (~ ('#form13')),
% 4.76/1.40 inference('clc', [status(thm)], [zip_derived_cl179, zip_derived_cl149])).
% 4.76/1.40 thf(zip_derived_cl191, plain, ( ('#sk1' @ '#sk18' @ '#sk25')),
% 4.76/1.40 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl189])).
% 4.76/1.40 thf(zip_derived_cl60, plain,
% 4.76/1.40 (( ('#sk2' @ '#sk12' @ '#sk18') | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl51])).
% 4.76/1.40 thf(zip_derived_cl3, plain,
% 4.76/1.40 (((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i > $o]:
% 4.76/1.40 (((((!!) @ (^[Y2 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ Y0 @ Y2))) |
% 4.76/1.40 (((!!) @ (^[Y3 : $i]:
% 4.76/1.40 (((((~) @ (
% 4.76/1.40 '#sk1' @ Y2 @
% 4.76/1.40 Y3))) |
% 4.76/1.40 (Y1 @ Y3))))))))))) |
% 4.76/1.40 (((~) @ (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @
% 4.76/1.40 Y2))) |
% 4.76/1.40 (Y1 @ Y2))))))))))))))))
% 4.76/1.40 != (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl2])).
% 4.76/1.40 thf(zip_derived_cl4, plain,
% 4.76/1.40 (![X-81 : $i]:
% 4.76/1.40 ( ((^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i > $o]:
% 4.76/1.40 (((((!!) @ (^[Y2 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ Y0 @ Y2))) |
% 4.76/1.40 (((!!) @ (^[Y3 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @
% 4.76/1.40 Y2 @ Y3))) |
% 4.76/1.40 (Y1 @ Y3))))))))))) |
% 4.76/1.40 (((~) @ (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y2))) |
% 4.76/1.40 (Y1 @ Y2)))))))))))))) @
% 4.76/1.40 X-81)
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('forall_hoist', [status(thm)], [zip_derived_cl3])).
% 4.76/1.40 thf(zip_derived_cl10, plain,
% 4.76/1.40 (![X-81 : $i]:
% 4.76/1.40 ( (((!!) @ (^[Y0 : $i > $o]:
% 4.76/1.40 (((((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ X-81 @ Y1))) |
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y1 @ Y2))) |
% 4.76/1.40 (Y0 @ Y2))))))))))) |
% 4.76/1.40 (((~) @ (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ X-81 @ Y1))) |
% 4.76/1.40 (Y0 @ Y1)))))))))))))
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('ho_norm', [status(thm)], [zip_derived_cl4])).
% 4.76/1.40 thf(zip_derived_cl11, plain,
% 4.76/1.40 (![X0 : $i]:
% 4.76/1.40 ( (((!!) @ (^[Y0 : $i > $o]:
% 4.76/1.40 (((((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ X0 @ Y1))) |
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y1 @ Y2))) |
% 4.76/1.40 (Y0 @ Y2))))))))))) |
% 4.76/1.40 (((~) @ (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ X0 @ Y1))) |
% 4.76/1.40 (Y0 @ Y1)))))))))))))
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('cannonize vars', [status(thm)], [zip_derived_cl10])).
% 4.76/1.40 thf(zip_derived_cl12, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o]:
% 4.76/1.40 ( (((((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ X0 @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | (X2 @
% 4.76/1.40 Y1))))))))))) |
% 4.76/1.40 (((~) @ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ X0 @ Y0))) | (X2 @ Y0))))))))))
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])).
% 4.76/1.40 thf(zip_derived_cl20, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o]:
% 4.76/1.40 ( (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ X0 @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | (X2 @ Y1)))))))))))
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ X0 @ Y0))) | (X2 @ Y0))))))
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl12])).
% 4.76/1.40 thf(zip_derived_cl30, plain,
% 4.76/1.40 ((~ ('#form13')
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 define([status(thm)])).
% 4.76/1.40 thf(zip_derived_cl27, plain,
% 4.76/1.40 (( ('#form13')
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((!!) @ (^[Y2 : $i]:
% 4.76/1.40 ((((('#sk1' @ Y1 @ Y2) &
% 4.76/1.40 ('#sk2' @ Y0 @ Y1))) =>
% 4.76/1.40 ('#sk1' @ Y0 @ Y2)))))))))))))),
% 4.76/1.40 define([status(thm)])).
% 4.76/1.40 thf(zip_derived_cl33, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o]:
% 4.76/1.40 ( ('#form13')
% 4.76/1.40 | ~ (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ X0 @ Y0))) | (X2 @ Y0))))))
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ X0 @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | (X2 @
% 4.76/1.40 Y1))))))))))))),
% 4.76/1.40 inference('renaming', [status(thm)],
% 4.76/1.40 [zip_derived_cl20, zip_derived_cl30, zip_derived_cl27])).
% 4.76/1.40 thf(zip_derived_cl42, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o]:
% 4.76/1.40 (~ (((((~) @ ('#sk1' @ X0 @ ('#sk24' @ X0 @ X2)))) | (X2 @
% 4.76/1.40 ('#sk24' @ X0 @ X2))))
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ X0 @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | (X2 @
% 4.76/1.40 Y1)))))))))))
% 4.76/1.40 | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl33])).
% 4.76/1.40 thf(zip_derived_cl48, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o]:
% 4.76/1.40 ( ('#sk1' @ X0 @ ('#sk24' @ X0 @ X2))
% 4.76/1.40 | ('#form13')
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ X0 @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | (X2 @
% 4.76/1.40 Y1))))))))))))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])).
% 4.76/1.40 thf(zip_derived_cl56, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o, X4 : $i]:
% 4.76/1.40 ( (((((~) @ ('#sk2' @ X0 @ X4))) |
% 4.76/1.40 (((!!) @ (^[Y0 : $i]: (((((~) @ ('#sk1' @ X4 @ Y0))) | (X2 @ Y0))))))))
% 4.76/1.40 | ('#form13')
% 4.76/1.40 | ('#sk1' @ X0 @ ('#sk24' @ X0 @ X2)))),
% 4.76/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl48])).
% 4.76/1.40 thf(zip_derived_cl64, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o, X4 : $i]:
% 4.76/1.40 (~ ('#sk2' @ X0 @ X4)
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]: (((((~) @ ('#sk1' @ X4 @ Y0))) | (X2 @ Y0))))))
% 4.76/1.40 | ('#sk1' @ X0 @ ('#sk24' @ X0 @ X2))
% 4.76/1.40 | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl56])).
% 4.76/1.40 thf(zip_derived_cl69, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o, X4 : $i, X6 : $i]:
% 4.76/1.40 ( (((((~) @ ('#sk1' @ X4 @ X6))) | (X2 @ X6)))
% 4.76/1.40 | ('#form13')
% 4.76/1.40 | ('#sk1' @ X0 @ ('#sk24' @ X0 @ X2))
% 4.76/1.40 | ~ ('#sk2' @ X0 @ X4))),
% 4.76/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])).
% 4.76/1.40 thf(zip_derived_cl74, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o, X4 : $i, X6 : $i]:
% 4.76/1.40 (~ ('#sk1' @ X4 @ X6)
% 4.76/1.40 | (X2 @ X6)
% 4.76/1.40 | ~ ('#sk2' @ X0 @ X4)
% 4.76/1.40 | ('#sk1' @ X0 @ ('#sk24' @ X0 @ X2))
% 4.76/1.40 | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl69])).
% 4.76/1.40 thf(zip_derived_cl91, plain,
% 4.76/1.40 (![X0 : $i > $o, X1 : $i]:
% 4.76/1.40 ( ('#form13')
% 4.76/1.40 | ('#form13')
% 4.76/1.40 | ('#sk1' @ '#sk12' @ ('#sk24' @ '#sk12' @ X0))
% 4.76/1.40 | (X0 @ X1)
% 4.76/1.40 | ~ ('#sk1' @ '#sk18' @ X1))),
% 4.76/1.40 inference('sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl74])).
% 4.76/1.40 thf(zip_derived_cl93, plain,
% 4.76/1.40 (![X0 : $i > $o, X1 : $i]:
% 4.76/1.40 (~ ('#sk1' @ '#sk18' @ X1)
% 4.76/1.40 | (X0 @ X1)
% 4.76/1.40 | ('#sk1' @ '#sk12' @ ('#sk24' @ '#sk12' @ X0))
% 4.76/1.40 | ('#form13'))),
% 4.76/1.40 inference('simplify', [status(thm)], [zip_derived_cl91])).
% 4.76/1.40 thf(zip_derived_cl189, plain, (~ ('#form13')),
% 4.76/1.40 inference('clc', [status(thm)], [zip_derived_cl179, zip_derived_cl149])).
% 4.76/1.40 thf(zip_derived_cl197, plain,
% 4.76/1.40 (![X0 : $i > $o, X1 : $i]:
% 4.76/1.40 (~ ('#sk1' @ '#sk18' @ X1)
% 4.76/1.40 | (X0 @ X1)
% 4.76/1.40 | ('#sk1' @ '#sk12' @ ('#sk24' @ '#sk12' @ X0)))),
% 4.76/1.40 inference('demod', [status(thm)], [zip_derived_cl93, zip_derived_cl189])).
% 4.76/1.40 thf(zip_derived_cl198, plain,
% 4.76/1.40 (![X0 : $i > $o]:
% 4.76/1.40 ( ('#sk1' @ '#sk12' @ ('#sk24' @ '#sk12' @ X0)) | (X0 @ '#sk25'))),
% 4.76/1.40 inference('sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl197])).
% 4.76/1.40 thf(zip_derived_cl60, plain,
% 4.76/1.40 (( ('#sk2' @ '#sk12' @ '#sk18') | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl51])).
% 4.76/1.40 thf(zip_derived_cl189, plain, (~ ('#form13')),
% 4.76/1.40 inference('clc', [status(thm)], [zip_derived_cl179, zip_derived_cl149])).
% 4.76/1.40 thf(zip_derived_cl192, plain, ( ('#sk2' @ '#sk12' @ '#sk18')),
% 4.76/1.40 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl189])).
% 4.76/1.40 thf(zip_derived_cl191, plain, ( ('#sk1' @ '#sk18' @ '#sk25')),
% 4.76/1.40 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl189])).
% 4.76/1.40 thf(zip_derived_cl49, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o]:
% 4.76/1.40 (~ (X2 @ ('#sk24' @ X0 @ X2))
% 4.76/1.40 | ('#form13')
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]:
% 4.76/1.40 (((((~) @ ('#sk2' @ X0 @ Y0))) |
% 4.76/1.40 (((!!) @ (^[Y1 : $i]:
% 4.76/1.40 (((((~) @ ('#sk1' @ Y0 @ Y1))) | (X2 @
% 4.76/1.40 Y1))))))))))))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])).
% 4.76/1.40 thf(zip_derived_cl57, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o, X4 : $i]:
% 4.76/1.40 ( (((((~) @ ('#sk2' @ X0 @ X4))) |
% 4.76/1.40 (((!!) @ (^[Y0 : $i]: (((((~) @ ('#sk1' @ X4 @ Y0))) | (X2 @ Y0))))))))
% 4.76/1.40 | ('#form13')
% 4.76/1.40 | ~ (X2 @ ('#sk24' @ X0 @ X2)))),
% 4.76/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl49])).
% 4.76/1.40 thf(zip_derived_cl65, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o, X4 : $i]:
% 4.76/1.40 (~ ('#sk2' @ X0 @ X4)
% 4.76/1.40 | (((!!) @ (^[Y0 : $i]: (((((~) @ ('#sk1' @ X4 @ Y0))) | (X2 @ Y0))))))
% 4.76/1.40 | ~ (X2 @ ('#sk24' @ X0 @ X2))
% 4.76/1.40 | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl57])).
% 4.76/1.40 thf(zip_derived_cl70, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o, X4 : $i, X6 : $i]:
% 4.76/1.40 ( (((((~) @ ('#sk1' @ X4 @ X6))) | (X2 @ X6)))
% 4.76/1.40 | ('#form13')
% 4.76/1.40 | ~ (X2 @ ('#sk24' @ X0 @ X2))
% 4.76/1.40 | ~ ('#sk2' @ X0 @ X4))),
% 4.76/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])).
% 4.76/1.40 thf(zip_derived_cl75, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o, X4 : $i, X6 : $i]:
% 4.76/1.40 (~ ('#sk1' @ X4 @ X6)
% 4.76/1.40 | (X2 @ X6)
% 4.76/1.40 | ~ ('#sk2' @ X0 @ X4)
% 4.76/1.40 | ~ (X2 @ ('#sk24' @ X0 @ X2))
% 4.76/1.40 | ('#form13'))),
% 4.76/1.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl70])).
% 4.76/1.40 thf(zip_derived_cl189, plain, (~ ('#form13')),
% 4.76/1.40 inference('clc', [status(thm)], [zip_derived_cl179, zip_derived_cl149])).
% 4.76/1.40 thf(zip_derived_cl297, plain,
% 4.76/1.40 (![X0 : $i, X2 : $i > $o, X4 : $i, X6 : $i]:
% 4.76/1.40 (~ ('#sk1' @ X4 @ X6)
% 4.76/1.40 | (X2 @ X6)
% 4.76/1.40 | ~ ('#sk2' @ X0 @ X4)
% 4.76/1.40 | ~ (X2 @ ('#sk24' @ X0 @ X2)))),
% 4.76/1.40 inference('demod', [status(thm)], [zip_derived_cl75, zip_derived_cl189])).
% 4.76/1.40 thf(zip_derived_cl298, plain,
% 4.76/1.40 (![X0 : $i > $o, X1 : $i]:
% 4.76/1.40 (~ (X0 @ ('#sk24' @ X1 @ X0))
% 4.76/1.40 | ~ ('#sk2' @ X1 @ '#sk18')
% 4.76/1.40 | (X0 @ '#sk25'))),
% 4.76/1.40 inference('sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl297])).
% 4.76/1.40 thf(zip_derived_cl353, plain,
% 4.76/1.40 (![X0 : $i > $o]: ( (X0 @ '#sk25') | ~ (X0 @ ('#sk24' @ '#sk12' @ X0)))),
% 4.76/1.40 inference('sup-', [status(thm)], [zip_derived_cl192, zip_derived_cl298])).
% 4.76/1.40 thf(zip_derived_cl385, plain,
% 4.76/1.40 (( ('#sk1' @ '#sk12' @ '#sk25') | ('#sk1' @ '#sk12' @ '#sk25'))),
% 4.76/1.40 inference('sup-', [status(thm)], [zip_derived_cl198, zip_derived_cl353])).
% 4.76/1.40 thf(zip_derived_cl403, plain, ( ('#sk1' @ '#sk12' @ '#sk25')),
% 4.76/1.40 inference('simplify', [status(thm)], [zip_derived_cl385])).
% 4.76/1.40 thf(zip_derived_cl433, plain, ($false),
% 4.76/1.40 inference('demod', [status(thm)], [zip_derived_cl190, zip_derived_cl403])).
% 4.76/1.40
% 4.76/1.40 % SZS output end Refutation
% 4.76/1.40
% 4.76/1.40
% 4.76/1.40 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 4.76/1.40 % Terminating...
% 2.27/1.51 % Runner terminated.
% 2.27/1.56 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------