%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV125^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.76xNkaHIZH true
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:59:41 EDT 2023
% Result : Theorem 53.37s 7.55s
% Output : Refutation 53.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV125^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.76xNkaHIZH true
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 02:39:34 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.21/0.63 % Total configuration time : 828
% 0.21/0.63 % Estimated wc time : 1656
% 0.21/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.82 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 53.37/7.55 % Solved by lams/35_full_unif4.sh.
% 53.37/7.55 % done 422 iterations in 6.768s
% 53.37/7.55 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 53.37/7.55 % SZS output start Refutation
% 53.37/7.55 thf(a_type, type, a: $tType).
% 53.37/7.55 thf('#sk2_type', type, '#sk2': (a > a > $o) > $o).
% 53.37/7.55 thf('#sk3_type', type, '#sk3': a).
% 53.37/7.55 thf('#sk12196_type', type, '#sk12196': a > a > (a > a > $o) > a > a > $o).
% 53.37/7.55 thf('#sk43_type', type, '#sk43': (a > a > $o) > a).
% 53.37/7.55 thf('#sk117_type', type, '#sk117': (a > a > $o) > a > a > $o).
% 53.37/7.55 thf('#sk73_type', type, '#sk73': (a > a > $o) > a > a > $o).
% 53.37/7.55 thf('#sk66_type', type, '#sk66': (a > a > $o) > a).
% 53.37/7.55 thf('#sk1_type', type, '#sk1': (a > a > $o) > $o).
% 53.37/7.55 thf('#sk48_type', type, '#sk48': (a > a > $o) > a).
% 53.37/7.55 thf('#sk5_type', type, '#sk5': a > a > $o).
% 53.37/7.55 thf('#sk438_type', type, '#sk438': (a > a > $o) > a).
% 53.37/7.55 thf('#sk430_type', type, '#sk430': (a > a > $o) > a).
% 53.37/7.55 thf('#sk216_type', type, '#sk216': a > a > $o).
% 53.37/7.55 thf('#sk4_type', type, '#sk4': a).
% 53.37/7.55 thf('#sk31_type', type, '#sk31': (a > a > $o) > a).
% 53.37/7.55 thf('#form18_type', type, '#form18': $o).
% 53.37/7.55 thf('#sk106_type', type, '#sk106': (a > a > $o) > a > a > $o).
% 53.37/7.55 thf(cTHM254_pme, conjecture,
% 53.37/7.55 (![PROP:( ( a > a > $o ) > $o ),S:( ( a > a > $o ) > $o )]:
% 53.37/7.55 ( ( ^[Xx:a,Xy:a]:
% 53.37/7.55 ( ![Xp:( a > a > $o )]:
% 53.37/7.55 ( ( ( PROP @ Xp ) &
% 53.37/7.55 ( ![Xx0:a,Xy0:a]:
% 53.37/7.55 ( ( ?[R:( a > a > $o )]: ( ( S @ R ) & ( R @ Xx0 @ Xy0 ) ) ) =>
% 53.37/7.55 ( Xp @ Xx0 @ Xy0 ) ) ) ) =>
% 53.37/7.55 ( Xp @ Xx @ Xy ) ) ) ) =
% 53.37/7.55 ( ^[Xx:a,Xy:a]:
% 53.37/7.55 ( ![Xp:( a > a > $o )]:
% 53.37/7.55 ( ( ( PROP @ Xp ) &
% 53.37/7.55 ( ![Xx0:a,Xy0:a]:
% 53.37/7.55 ( ( ?[R:( a > a > $o )]:
% 53.37/7.55 ( ( ?[Q:( a > a > $o )]:
% 53.37/7.55 ( ( S @ Q ) &
% 53.37/7.55 ( ( R ) =
% 53.37/7.55 ( ^[Xx1:a,Xy1:a]:
% 53.37/7.55 ( ![Xp0:( a > a > $o )]:
% 53.37/7.55 ( ( ( PROP @ Xp0 ) &
% 53.37/7.55 ( ![Xx2:a,Xy2:a]:
% 53.37/7.55 ( ( Q @ Xx2 @ Xy2 ) =>
% 53.37/7.55 ( Xp0 @ Xx2 @ Xy2 ) ) ) ) =>
% 53.37/7.55 ( Xp0 @ Xx1 @ Xy1 ) ) ) ) ) ) ) &
% 53.37/7.55 ( R @ Xx0 @ Xy0 ) ) ) =>
% 53.37/7.55 ( Xp @ Xx0 @ Xy0 ) ) ) ) =>
% 53.37/7.55 ( Xp @ Xx @ Xy ) ) ) ) ))).
% 53.37/7.55 thf(zf_stmt_0, negated_conjecture,
% 53.37/7.55 (~( ![PROP:( ( a > a > $o ) > $o ),S:( ( a > a > $o ) > $o )]:
% 53.37/7.55 ( ( ^[Xx:a,Xy:a]:
% 53.37/7.55 ( ![Xp:( a > a > $o )]:
% 53.37/7.55 ( ( ( PROP @ Xp ) &
% 53.37/7.55 ( ![Xx0:a,Xy0:a]:
% 53.37/7.55 ( ( ?[R:( a > a > $o )]: ( ( S @ R ) & ( R @ Xx0 @ Xy0 ) ) ) =>
% 53.37/7.55 ( Xp @ Xx0 @ Xy0 ) ) ) ) =>
% 53.37/7.55 ( Xp @ Xx @ Xy ) ) ) ) =
% 53.37/7.55 ( ^[Xx:a,Xy:a]:
% 53.37/7.55 ( ![Xp:( a > a > $o )]:
% 53.37/7.55 ( ( ( PROP @ Xp ) &
% 53.37/7.55 ( ![Xx0:a,Xy0:a]:
% 53.37/7.55 ( ( ?[R:( a > a > $o )]:
% 53.37/7.55 ( ( ?[Q:( a > a > $o )]:
% 53.37/7.55 ( ( S @ Q ) &
% 53.37/7.55 ( ( R ) =
% 53.37/7.55 ( ^[Xx1:a,Xy1:a]:
% 53.37/7.55 ( ![Xp0:( a > a > $o )]:
% 53.37/7.55 ( ( ( PROP @ Xp0 ) &
% 53.37/7.55 ( ![Xx2:a,Xy2:a]:
% 53.37/7.55 ( ( Q @ Xx2 @ Xy2 ) =>
% 53.37/7.55 ( Xp0 @ Xx2 @ Xy2 ) ) ) ) =>
% 53.37/7.55 ( Xp0 @ Xx1 @ Xy1 ) ) ) ) ) ) ) &
% 53.37/7.55 ( R @ Xx0 @ Xy0 ) ) ) =>
% 53.37/7.55 ( Xp @ Xx0 @ Xy0 ) ) ) ) =>
% 53.37/7.55 ( Xp @ Xx @ Xy ) ) ) ) ) )),
% 53.37/7.55 inference('cnf.neg', [status(esa)], [cTHM254_pme])).
% 53.37/7.55 thf(zip_derived_cl0, plain,
% 53.37/7.55 (~ (((!!) @ (^[Y0 : (a > a > $o) > $o]:
% 53.37/7.55 (((!!) @ (^[Y1 : (a > a > $o) > $o]:
% 53.37/7.55 ((((^[Y2 : a,Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a > a > $o]:
% 53.37/7.55 (((((Y0 @ Y4) &
% 53.37/7.55 (((!!) @ (^[Y5 : a]:
% 53.37/7.55 (((!!) @ (
% 53.37/7.55 ^[Y6 : a]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 (??) @ (
% 53.37/7.55 ^[Y7 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 (Y1 @
% 53.37/7.55 Y7) &
% 53.37/7.55 (Y7 @
% 53.37/7.55 Y5 @ Y6)))))) =>
% 53.37/7.55 (Y4 @
% 53.37/7.55 Y5 @ Y6))))))))))) =>
% 53.37/7.55 (Y4 @ Y2 @ Y3)))))))) =
% 53.37/7.55 ((^[Y2 : a,Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a > a > $o]:
% 53.37/7.55 (((((Y0 @ Y4) &
% 53.37/7.55 (((!!) @ (^[Y5 : a]:
% 53.37/7.55 (((!!) @ (
% 53.37/7.55 ^[Y6 : a]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 (??) @ (
% 53.37/7.55 ^[Y7 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 (??) @ (
% 53.37/7.55 ^[Y8 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 (Y1 @
% 53.37/7.55 Y8) &
% 53.37/7.55 ((
% 53.37/7.55 (Y7) =
% 53.37/7.55 ((
% 53.37/7.55 ^[Y9 : a,
% 53.37/7.55 Y10 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y11 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 (Y0 @
% 53.37/7.55 Y11) &
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y12 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y13 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y8 @
% 53.37/7.55 Y12 @
% 53.37/7.55 Y13) =>
% 53.37/7.55 (Y11 @
% 53.37/7.55 Y12 @
% 53.37/7.55 Y13))))))))))) =>
% 53.37/7.55 (Y11 @
% 53.37/7.55 Y9 @ Y10))))))))))))))) &
% 53.37/7.55 (Y7 @
% 53.37/7.55 Y5 @ Y6)))))) =>
% 53.37/7.55 (Y4 @
% 53.37/7.55 Y5 @ Y6))))))))))) =>
% 53.37/7.55 (Y4 @ Y2 @ Y3))))))))))))))))),
% 53.37/7.55 inference('cnf', [status(esa)], [zf_stmt_0])).
% 53.37/7.55 thf(zip_derived_cl1, plain,
% 53.37/7.55 (~ (((!!) @ (^[Y0 : (a > a > $o) > $o]:
% 53.37/7.55 ((((^[Y1 : a,Y2 : a]:
% 53.37/7.55 (((!!) @ (^[Y3 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y3) &
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 (((!!) @ (^[Y5 : a]:
% 53.37/7.55 ((((
% 53.37/7.55 (??) @ (
% 53.37/7.55 ^[Y6 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 (Y0 @
% 53.37/7.55 Y6) &
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y4 @ Y5)))))) =>
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y4 @ Y5))))))))))) =>
% 53.37/7.55 (Y3 @ Y1 @ Y2)))))))) =
% 53.37/7.55 ((^[Y1 : a,Y2 : a]:
% 53.37/7.55 (((!!) @ (^[Y3 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y3) &
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 (((!!) @ (^[Y5 : a]:
% 53.37/7.55 ((((
% 53.37/7.55 (??) @ (
% 53.37/7.55 ^[Y6 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 (??) @ (
% 53.37/7.55 ^[Y7 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 (Y0 @
% 53.37/7.55 Y7) &
% 53.37/7.55 ((
% 53.37/7.55 (Y6) =
% 53.37/7.55 ((
% 53.37/7.55 ^[Y8 : a,
% 53.37/7.55 Y9 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y10 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 ('#sk1' @
% 53.37/7.55 Y10) &
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y11 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y12 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y7 @
% 53.37/7.55 Y11 @
% 53.37/7.55 Y12) =>
% 53.37/7.55 (Y10 @
% 53.37/7.55 Y11 @
% 53.37/7.55 Y12))))))))))) =>
% 53.37/7.55 (Y10 @
% 53.37/7.55 Y8 @ Y9))))))))))))))) &
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y4 @ Y5)))))) =>
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y4 @ Y5))))))))))) =>
% 53.37/7.55 (Y3 @ Y1 @ Y2)))))))))))))),
% 53.37/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])).
% 53.37/7.55 thf(zip_derived_cl2, plain,
% 53.37/7.55 (~ ((((^[Y0 : a,Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y2) &
% 53.37/7.55 (((!!) @ (^[Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 (((((??) @ (^[Y5 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ('#sk2' @
% 53.37/7.55 Y5) &
% 53.37/7.55 (Y5 @
% 53.37/7.55 Y3 @ Y4)))))) =>
% 53.37/7.55 (Y2 @ Y3 @ Y4))))))))))) =>
% 53.37/7.55 (Y2 @ Y0 @ Y1)))))))) =
% 53.37/7.55 ((^[Y0 : a,Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y2) &
% 53.37/7.55 (((!!) @ (^[Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 (((((??) @ (^[Y5 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 (??) @ (
% 53.37/7.55 ^[Y6 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ('#sk2' @
% 53.37/7.55 Y6) &
% 53.37/7.55 ((
% 53.37/7.55 (Y5) =
% 53.37/7.55 ((
% 53.37/7.55 ^[Y7 : a,
% 53.37/7.55 Y8 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y9 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 ('#sk1' @
% 53.37/7.55 Y9) &
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y10 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y11 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y10 @
% 53.37/7.55 Y11) =>
% 53.37/7.55 (Y9 @
% 53.37/7.55 Y10 @
% 53.37/7.55 Y11))))))))))) =>
% 53.37/7.55 (Y9 @
% 53.37/7.55 Y7 @ Y8))))))))))))))) &
% 53.37/7.55 (Y5 @
% 53.37/7.55 Y3 @ Y4)))))) =>
% 53.37/7.55 (Y2 @ Y3 @ Y4))))))))))) =>
% 53.37/7.55 (Y2 @ Y0 @ Y1))))))))))),
% 53.37/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])).
% 53.37/7.55 thf(zip_derived_cl3, plain,
% 53.37/7.55 ((((^[Y0 : a,Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y2) &
% 53.37/7.55 (((!!) @ (^[Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 (((((??) @ (^[Y5 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y5) &
% 53.37/7.55 (Y5 @ Y3 @
% 53.37/7.55 Y4)))))) =>
% 53.37/7.55 (Y2 @ Y3 @ Y4))))))))))) =>
% 53.37/7.55 (Y2 @ Y0 @ Y1))))))))
% 53.37/7.55 != ((^[Y0 : a,Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y2) &
% 53.37/7.55 (((!!) @ (^[Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 (((((??) @ (^[Y5 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 (
% 53.37/7.55 (
% 53.37/7.55 ((
% 53.37/7.55 (??) @ (
% 53.37/7.55 ^[Y6 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ('#sk2' @
% 53.37/7.55 Y6) &
% 53.37/7.55 ((
% 53.37/7.55 (Y5) =
% 53.37/7.55 ((
% 53.37/7.55 ^[Y7 : a,
% 53.37/7.55 Y8 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y9 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 ('#sk1' @
% 53.37/7.55 Y9) &
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y10 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y11 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y10 @
% 53.37/7.55 Y11) =>
% 53.37/7.55 (Y9 @
% 53.37/7.55 Y10 @
% 53.37/7.55 Y11))))))))))) =>
% 53.37/7.55 (Y9 @
% 53.37/7.55 Y7 @ Y8))))))))))))))) &
% 53.37/7.55 (Y5 @
% 53.37/7.55 Y3 @ Y4)))))) =>
% 53.37/7.55 (Y2 @ Y3 @ Y4))))))))))) =>
% 53.37/7.55 (Y2 @ Y0 @ Y1)))))))))),
% 53.37/7.55 inference('simplify nested equalities', [status(thm)], [zip_derived_cl2])).
% 53.37/7.55 thf(zip_derived_cl4, plain,
% 53.37/7.55 (((((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ (^[Y1 : a,Y2 : a]: (Y0 @ Y1 @ Y2))) &
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a]:
% 53.37/7.55 (((((??) @ (^[Y3 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 (^[Y4 : a,
% 53.37/7.55 Y5 : a]:
% 53.37/7.55 (Y3 @ Y4 @
% 53.37/7.55 Y5))) &
% 53.37/7.55 (Y3 @ Y1 @ Y2)))))) =>
% 53.37/7.55 (Y0 @ Y1 @ Y2))))))))))) =>
% 53.37/7.55 (Y0 @ '#sk3' @ '#sk4'))))))
% 53.37/7.55 != (((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ (^[Y1 : a,Y2 : a]: (Y0 @ Y1 @ Y2))) &
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a]:
% 53.37/7.55 (((((??) @ (^[Y3 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 (((((??) @ (
% 53.37/7.55 ^[Y4 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
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% 53.37/7.55 ^[Y5 : a,
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% 53.37/7.55 ((
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% 53.37/7.55 ((((('#sk1' @ Y0) &
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% 53.37/7.55 (Y0 @ '#sk3' @ '#sk4'))))))
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% 53.37/7.55 Y7 @ Y8))))))))))) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y4 @ Y5))))))))))))))) &
% 53.37/7.55 (Y2 @ Y0 @ Y1)))))) =>
% 53.37/7.55 (X-81 @ Y0 @ Y1))))))))))) =>
% 53.37/7.55 (X-81 @ '#sk3' @ '#sk4')))
% 53.37/7.55 | (((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y0) &
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a]:
% 53.37/7.55 (((((??) @ (^[Y3 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) &
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y1 @ Y2)))))) =>
% 53.37/7.55 (Y0 @ Y1 @ Y2))))))))))) =>
% 53.37/7.55 (Y0 @ '#sk3' @ '#sk4')))))))),
% 53.37/7.55 inference('ho_norm', [status(thm)], [zip_derived_cl8])).
% 53.37/7.55 thf(zip_derived_cl15, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 ( ((((('#sk1' @ X0) &
% 53.37/7.55 (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 (((((??) @ (^[Y3 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) &
% 53.37/7.55 ((
% 53.37/7.55 (Y2) =
% 53.37/7.55 ((
% 53.37/7.55 ^[Y4 : a,
% 53.37/7.55 Y5 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y6 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 ('#sk1' @
% 53.37/7.55 Y6) &
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y7 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y8 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y7 @
% 53.37/7.55 Y8) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y7 @ Y8))))))))))) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y4 @ Y5))))))))))))))) &
% 53.37/7.55 (Y2 @ Y0 @ Y1)))))) =>
% 53.37/7.55 (X0 @ Y0 @ Y1))))))))))) =>
% 53.37/7.55 (X0 @ '#sk3' @ '#sk4')))
% 53.37/7.55 | (((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y0) &
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a]:
% 53.37/7.55 (((((??) @ (^[Y3 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) &
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y1 @ Y2)))))) =>
% 53.37/7.55 (Y0 @ Y1 @ Y2))))))))))) =>
% 53.37/7.55 (Y0 @ '#sk3' @ '#sk4')))))))),
% 53.37/7.55 inference('cannonize vars', [status(thm)], [zip_derived_cl14])).
% 53.37/7.55 thf(zip_derived_cl16, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 (~ ((('#sk1' @ X0) &
% 53.37/7.55 (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 (((((??) @ (^[Y3 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) &
% 53.37/7.55 (((Y2) =
% 53.37/7.55 ((
% 53.37/7.55 ^[Y4 : a,
% 53.37/7.55 Y5 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y6 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 ('#sk1' @
% 53.37/7.55 Y6) &
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y7 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y8 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y7 @
% 53.37/7.55 Y8) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y7 @ Y8))))))))))) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y4 @ Y5))))))))))))))) &
% 53.37/7.55 (Y2 @ Y0 @ Y1)))))) =>
% 53.37/7.55 (X0 @ Y0 @ Y1)))))))))))
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | (((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y0) &
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a]:
% 53.37/7.55 (((((??) @ (^[Y3 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) &
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y1 @ Y2)))))) =>
% 53.37/7.55 (Y0 @ Y1 @ Y2))))))))))) =>
% 53.37/7.55 (Y0 @ '#sk3' @ '#sk4')))))))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])).
% 53.37/7.55 thf(zip_derived_cl17, plain,
% 53.37/7.55 ((~ ('#form18')
% 53.37/7.55 | (((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y0) &
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a]:
% 53.37/7.55 (((((??) @ (^[Y3 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) & (Y3 @
% 53.37/7.55 Y1 @ Y2)))))) =>
% 53.37/7.55 (Y0 @ Y1 @ Y2))))))))))) =>
% 53.37/7.55 (Y0 @ '#sk3' @ '#sk4')))))))),
% 53.37/7.55 define([status(thm)])).
% 53.37/7.55 thf(zip_derived_cl62, plain,
% 53.37/7.55 ((~ ('#form18')
% 53.37/7.55 | ~ ((((('#sk1' @ '#sk5') &
% 53.37/7.55 (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 (((((??) @ (^[Y3 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) &
% 53.37/7.55 ((
% 53.37/7.55 (Y2) =
% 53.37/7.55 ((
% 53.37/7.55 ^[Y4 : a,
% 53.37/7.55 Y5 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y6 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 ('#sk1' @
% 53.37/7.55 Y6) &
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y7 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y8 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y7 @
% 53.37/7.55 Y8) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y7 @ Y8))))))))))) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y4 @ Y5))))))))))))))) &
% 53.37/7.55 (Y2 @ Y0 @ Y1)))))) =>
% 53.37/7.55 ('#sk5' @ Y0 @ Y1))))))))))) =>
% 53.37/7.55 ('#sk5' @ '#sk3' @ '#sk4'))))),
% 53.37/7.55 inference('renaming', [status(thm)],
% 53.37/7.55 [zip_derived_cl45, zip_derived_cl58, zip_derived_cl17])).
% 53.37/7.55 thf(zip_derived_cl63, plain,
% 53.37/7.55 (( ((('#sk1' @ '#sk5') &
% 53.37/7.55 (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 (((((??) @ (^[Y3 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) &
% 53.37/7.55 (((Y2) =
% 53.37/7.55 ((^[Y4 : a,
% 53.37/7.55 Y5 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y6 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 ('#sk1' @
% 53.37/7.55 Y6) &
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y7 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y8 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y7 @
% 53.37/7.55 Y8) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y7 @ Y8))))))))))) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y4 @ Y5))))))))))))))) &
% 53.37/7.55 (Y2 @ Y0 @ Y1)))))) =>
% 53.37/7.55 ('#sk5' @ Y0 @ Y1)))))))))))
% 53.37/7.55 | ~ ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])).
% 53.37/7.55 thf(zip_derived_cl67, plain, (( ('#sk1' @ '#sk5') | ~ ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])).
% 53.37/7.55 thf(zip_derived_cl17, plain,
% 53.37/7.55 ((~ ('#form18')
% 53.37/7.55 | (((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y0) &
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a]:
% 53.37/7.55 (((((??) @ (^[Y3 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) & (Y3 @
% 53.37/7.55 Y1 @ Y2)))))) =>
% 53.37/7.55 (Y0 @ Y1 @ Y2))))))))))) =>
% 53.37/7.55 (Y0 @ '#sk3' @ '#sk4')))))))),
% 53.37/7.55 define([status(thm)])).
% 53.37/7.55 thf(zip_derived_cl18, plain,
% 53.37/7.55 (![X2 : a > a > $o]:
% 53.37/7.55 ( ((((('#sk1' @ X2) &
% 53.37/7.55 (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y2) & (Y2 @
% 53.37/7.55 Y0 @ Y1)))))) =>
% 53.37/7.55 (X2 @ Y0 @ Y1))))))))))) =>
% 53.37/7.55 (X2 @ '#sk3' @ '#sk4')))
% 53.37/7.55 | ~ ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])).
% 53.37/7.55 thf(zip_derived_cl24, plain,
% 53.37/7.55 (![X2 : a > a > $o]:
% 53.37/7.55 (~ ((('#sk1' @ X2) &
% 53.37/7.55 (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y2) & (Y2 @
% 53.37/7.55 Y0 @ Y1)))))) =>
% 53.37/7.55 (X2 @ Y0 @ Y1)))))))))))
% 53.37/7.55 | (X2 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])).
% 53.37/7.55 thf(zip_derived_cl26, plain,
% 53.37/7.55 (![X2 : a > a > $o]:
% 53.37/7.55 (~ ('#sk1' @ X2)
% 53.37/7.55 | ~ (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y2) & (Y2 @
% 53.37/7.55 Y0 @ Y1)))))) =>
% 53.37/7.55 (X2 @ Y0 @ Y1)))))))))
% 53.37/7.55 | ~ ('#form18')
% 53.37/7.55 | (X2 @ '#sk3' @ '#sk4'))),
% 53.37/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl24])).
% 53.37/7.55 thf(zip_derived_cl28, plain,
% 53.37/7.55 (![X2 : a > a > $o]:
% 53.37/7.55 (~ (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((((??) @ (^[Y1 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y1) & (Y1 @ ('#sk48' @ X2) @
% 53.37/7.55 Y0)))))) =>
% 53.37/7.55 (X2 @ ('#sk48' @ X2) @ Y0))))))
% 53.37/7.55 | (X2 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ('#form18')
% 53.37/7.55 | ~ ('#sk1' @ X2))),
% 53.37/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl26])).
% 53.37/7.55 thf(zip_derived_cl31, plain,
% 53.37/7.55 (![X2 : a > a > $o]:
% 53.37/7.55 (~ (((((??) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y0) & (Y0 @ ('#sk48' @ X2) @
% 53.37/7.55 ('#sk66' @ X2))))))) =>
% 53.37/7.55 (X2 @ ('#sk48' @ X2) @ ('#sk66' @ X2))))
% 53.37/7.55 | ~ ('#sk1' @ X2)
% 53.37/7.55 | ~ ('#form18')
% 53.37/7.55 | (X2 @ '#sk3' @ '#sk4'))),
% 53.37/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])).
% 53.37/7.55 thf(zip_derived_cl34, plain,
% 53.37/7.55 (![X2 : a > a > $o]:
% 53.37/7.55 (~ (X2 @ ('#sk48' @ X2) @ ('#sk66' @ X2))
% 53.37/7.55 | (X2 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ('#form18')
% 53.37/7.55 | ~ ('#sk1' @ X2))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl31])).
% 53.37/7.55 thf(zip_derived_cl199, plain,
% 53.37/7.55 ((~ ('#form18')
% 53.37/7.55 | ~ ('#form18')
% 53.37/7.55 | ('#sk5' @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ('#sk5' @ ('#sk48' @ '#sk5') @ ('#sk66' @ '#sk5')))),
% 53.37/7.55 inference('sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl34])).
% 53.37/7.55 thf(zip_derived_cl202, plain,
% 53.37/7.55 ((~ ('#sk5' @ ('#sk48' @ '#sk5') @ ('#sk66' @ '#sk5'))
% 53.37/7.55 | ('#sk5' @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ('#form18'))),
% 53.37/7.55 inference('simplify', [status(thm)], [zip_derived_cl199])).
% 53.37/7.55 thf(zip_derived_cl64, plain,
% 53.37/7.55 ((~ ('#sk5' @ '#sk3' @ '#sk4') | ~ ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])).
% 53.37/7.55 thf(zip_derived_cl204, plain,
% 53.37/7.55 ((~ ('#form18') | ~ ('#sk5' @ ('#sk48' @ '#sk5') @ ('#sk66' @ '#sk5')))),
% 53.37/7.55 inference('clc', [status(thm)], [zip_derived_cl202, zip_derived_cl64])).
% 53.37/7.55 thf(zip_derived_cl58, plain,
% 53.37/7.55 (( ('#form18')
% 53.37/7.55 | ~ (((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y0) &
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a]:
% 53.37/7.55 (((((??) @ (^[Y3 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) &
% 53.37/7.55 (Y3 @ Y1 @
% 53.37/7.55 Y2)))))) =>
% 53.37/7.55 (Y0 @ Y1 @ Y2))))))))))) =>
% 53.37/7.55 (Y0 @ '#sk3' @ '#sk4')))))))),
% 53.37/7.55 define([status(thm)])).
% 53.37/7.55 thf(zip_derived_cl61, plain,
% 53.37/7.55 ((~ ((((('#sk1' @ '#sk216') &
% 53.37/7.55 (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y2) & (Y2 @
% 53.37/7.55 Y0 @ Y1)))))) =>
% 53.37/7.55 ('#sk216' @ Y0 @ Y1))))))))))) =>
% 53.37/7.55 ('#sk216' @ '#sk3' @ '#sk4')))
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])).
% 53.37/7.55 thf(zip_derived_cl65, plain,
% 53.37/7.55 (( ((('#sk1' @ '#sk216') &
% 53.37/7.55 (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y2) & (Y2 @ Y0 @
% 53.37/7.55 Y1)))))) =>
% 53.37/7.55 ('#sk216' @ Y0 @ Y1)))))))))))
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])).
% 53.37/7.55 thf(zip_derived_cl69, plain, (( ('#sk1' @ '#sk216') | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])).
% 53.37/7.55 thf(zip_derived_cl16, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 (~ ((('#sk1' @ X0) &
% 53.37/7.55 (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 (((((??) @ (^[Y3 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) &
% 53.37/7.55 (((Y2) =
% 53.37/7.55 ((
% 53.37/7.55 ^[Y4 : a,
% 53.37/7.55 Y5 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y6 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 ('#sk1' @
% 53.37/7.55 Y6) &
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y7 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y8 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y7 @
% 53.37/7.55 Y8) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y7 @ Y8))))))))))) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y4 @ Y5))))))))))))))) &
% 53.37/7.55 (Y2 @ Y0 @ Y1)))))) =>
% 53.37/7.55 (X0 @ Y0 @ Y1)))))))))))
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | (((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y0) &
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a]:
% 53.37/7.55 (((((??) @ (^[Y3 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) &
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y1 @ Y2)))))) =>
% 53.37/7.55 (Y0 @ Y1 @ Y2))))))))))) =>
% 53.37/7.55 (Y0 @ '#sk3' @ '#sk4')))))))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])).
% 53.37/7.55 thf(zip_derived_cl17, plain,
% 53.37/7.55 ((~ ('#form18')
% 53.37/7.55 | (((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y0) &
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a]:
% 53.37/7.55 (((((??) @ (^[Y3 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) & (Y3 @
% 53.37/7.55 Y1 @ Y2)))))) =>
% 53.37/7.55 (Y0 @ Y1 @ Y2))))))))))) =>
% 53.37/7.55 (Y0 @ '#sk3' @ '#sk4')))))))),
% 53.37/7.55 define([status(thm)])).
% 53.37/7.55 thf(zip_derived_cl22, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 ( ('#form18')
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ((('#sk1' @ X0) &
% 53.37/7.55 (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 (((((??) @ (^[Y3 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) &
% 53.37/7.55 ((
% 53.37/7.55 (Y2) =
% 53.37/7.55 ((
% 53.37/7.55 ^[Y4 : a,
% 53.37/7.55 Y5 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y6 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 ('#sk1' @
% 53.37/7.55 Y6) &
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y7 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y8 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y7 @
% 53.37/7.55 Y8) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y7 @ Y8))))))))))) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y4 @ Y5))))))))))))))) &
% 53.37/7.55 (Y2 @ Y0 @ Y1)))))) =>
% 53.37/7.55 (X0 @ Y0 @ Y1))))))))))))),
% 53.37/7.55 inference('renaming', [status(thm)], [zip_derived_cl16, zip_derived_cl17])).
% 53.37/7.55 thf(zip_derived_cl23, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 (~ ('#sk1' @ X0)
% 53.37/7.55 | ~ (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 (((((??) @ (^[Y3 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((('#sk2' @
% 53.37/7.55 Y3) &
% 53.37/7.55 (((Y2) =
% 53.37/7.55 ((
% 53.37/7.55 ^[Y4 : a,
% 53.37/7.55 Y5 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y6 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 ('#sk1' @
% 53.37/7.55 Y6) &
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y7 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y8 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y7 @
% 53.37/7.55 Y8) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y7 @ Y8))))))))))) =>
% 53.37/7.55 (Y6 @
% 53.37/7.55 Y4 @ Y5))))))))))))))) &
% 53.37/7.55 (Y2 @ Y0 @ Y1)))))) =>
% 53.37/7.55 (X0 @ Y0 @ Y1)))))))))
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl22])).
% 53.37/7.55 thf(zip_derived_cl25, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 (~ (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((((??) @ (^[Y1 : a > a > $o]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y2) &
% 53.37/7.55 (((Y1) =
% 53.37/7.55 ((^[Y3 : a,Y4 : a]:
% 53.37/7.55 (((!!) @ (^[Y5 :
% 53.37/7.55 a > a > $o]:
% 53.37/7.55 ((
% 53.37/7.55 ((
% 53.37/7.55 ('#sk1' @
% 53.37/7.55 Y5) &
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y6 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (!!) @ (
% 53.37/7.55 ^[Y7 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y2 @
% 53.37/7.55 Y6 @
% 53.37/7.55 Y7) =>
% 53.37/7.55 (Y5 @
% 53.37/7.55 Y6 @ Y7))))))))))) =>
% 53.37/7.55 (Y5 @
% 53.37/7.55 Y3 @ Y4))))))))))))))) &
% 53.37/7.55 (Y1 @ ('#sk31' @ X0) @ Y0)))))) =>
% 53.37/7.55 (X0 @ ('#sk31' @ X0) @ Y0))))))
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ('#sk1' @ X0))),
% 53.37/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl23])).
% 53.37/7.55 thf(zip_derived_cl27, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 (~ (((((??) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 (((((??) @ (^[Y1 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y1) &
% 53.37/7.55 (((Y0) =
% 53.37/7.55 ((^[Y2 : a,Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y4) &
% 53.37/7.55 (((!!) @ (
% 53.37/7.55 ^[Y5 : a]:
% 53.37/7.55 (((!!) @ (
% 53.37/7.55 ^[Y6 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y1 @
% 53.37/7.55 Y5 @
% 53.37/7.55 Y6) =>
% 53.37/7.55 (Y4 @
% 53.37/7.55 Y5 @ Y6))))))))))) =>
% 53.37/7.55 (Y4 @ Y2 @ Y3))))))))))))))) &
% 53.37/7.55 (Y0 @ ('#sk31' @ X0) @ ('#sk43' @ X0))))))) =>
% 53.37/7.55 (X0 @ ('#sk31' @ X0) @ ('#sk43' @ X0))))
% 53.37/7.55 | ~ ('#sk1' @ X0)
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl25])).
% 53.37/7.55 thf(zip_derived_cl29, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 ( (((??) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 (((((??) @ (^[Y1 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y1) &
% 53.37/7.55 (((Y0) =
% 53.37/7.55 ((^[Y2 : a,Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y4) &
% 53.37/7.55 (((!!) @ (
% 53.37/7.55 ^[Y5 : a]:
% 53.37/7.55 (((!!) @ (
% 53.37/7.55 ^[Y6 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y1 @
% 53.37/7.55 Y5 @
% 53.37/7.55 Y6) =>
% 53.37/7.55 (Y4 @
% 53.37/7.55 Y5 @ Y6))))))))))) =>
% 53.37/7.55 (Y4 @ Y2 @ Y3))))))))))))))) &
% 53.37/7.55 (Y0 @ ('#sk31' @ X0) @ ('#sk43' @ X0)))))))
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ('#sk1' @ X0))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])).
% 53.37/7.55 thf(zip_derived_cl32, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 ( (((((??) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y0) &
% 53.37/7.55 ((('#sk73' @ X0) =
% 53.37/7.55 ((^[Y1 : a,Y2 : a]:
% 53.37/7.55 (((!!) @ (^[Y3 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y3) &
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 (((!!) @ (
% 53.37/7.55 ^[Y5 : a]:
% 53.37/7.55 (((Y0 @ Y4 @
% 53.37/7.55 Y5) =>
% 53.37/7.55 (Y3 @ Y4 @
% 53.37/7.55 Y5))))))))))) =>
% 53.37/7.55 (Y3 @ Y1 @ Y2))))))))))))))) &
% 53.37/7.55 ('#sk73' @ X0 @ ('#sk31' @ X0) @ ('#sk43' @ X0))))
% 53.37/7.55 | ~ ('#sk1' @ X0)
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])).
% 53.37/7.55 thf(zip_derived_cl36, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 ( ('#sk73' @ X0 @ ('#sk31' @ X0) @ ('#sk43' @ X0))
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ('#sk1' @ X0))),
% 53.37/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])).
% 53.37/7.55 thf(zip_derived_cl109, plain,
% 53.37/7.55 (( ('#form18')
% 53.37/7.55 | ('#sk216' @ '#sk3' @ '#sk4')
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | ('#sk73' @ '#sk216' @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216')))),
% 53.37/7.55 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl36])).
% 53.37/7.55 thf(zip_derived_cl116, plain,
% 53.37/7.55 (( ('#sk73' @ '#sk216' @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216'))
% 53.37/7.55 | ('#sk216' @ '#sk3' @ '#sk4')
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('simplify', [status(thm)], [zip_derived_cl109])).
% 53.37/7.55 thf(zip_derived_cl66, plain,
% 53.37/7.55 ((~ ('#sk216' @ '#sk3' @ '#sk4') | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])).
% 53.37/7.55 thf(zip_derived_cl185, plain,
% 53.37/7.55 (( ('#form18')
% 53.37/7.55 | ('#sk73' @ '#sk216' @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216')))),
% 53.37/7.55 inference('clc', [status(thm)], [zip_derived_cl116, zip_derived_cl66])).
% 53.37/7.55 thf(zip_derived_cl69, plain, (( ('#sk1' @ '#sk216') | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])).
% 53.37/7.55 thf(zip_derived_cl35, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 ( (((??) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y0) &
% 53.37/7.55 ((('#sk73' @ X0) =
% 53.37/7.55 ((^[Y1 : a,Y2 : a]:
% 53.37/7.55 (((!!) @ (^[Y3 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y3) &
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 (((!!) @ (^[Y5 : a]:
% 53.37/7.55 ((
% 53.37/7.55 (Y0 @
% 53.37/7.55 Y4 @
% 53.37/7.55 Y5) =>
% 53.37/7.55 (Y3 @
% 53.37/7.55 Y4 @ Y5))))))))))) =>
% 53.37/7.55 (Y3 @ Y1 @ Y2)))))))))))))))
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ('#sk1' @ X0))),
% 53.37/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])).
% 53.37/7.55 thf(zip_derived_cl38, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 ( ((('#sk2' @ ('#sk117' @ X0)) &
% 53.37/7.55 ((('#sk73' @ X0) =
% 53.37/7.55 ((^[Y0 : a,Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y2) &
% 53.37/7.55 (((!!) @ (^[Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 ((('#sk117' @ X0 @
% 53.37/7.55 Y3 @ Y4) => (Y2 @
% 53.37/7.55 Y3 @ Y4))))))))))) =>
% 53.37/7.55 (Y2 @ Y0 @ Y1))))))))))))
% 53.37/7.55 | ~ ('#sk1' @ X0)
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl35])).
% 53.37/7.55 thf(zip_derived_cl42, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 ( ((('#sk73' @ X0) =
% 53.37/7.55 ((^[Y0 : a,Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y2) &
% 53.37/7.55 (((!!) @ (^[Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 ((('#sk117' @ X0 @
% 53.37/7.55 Y3 @ Y4) => (Y2 @
% 53.37/7.55 Y3 @ Y4))))))))))) =>
% 53.37/7.55 (Y2 @ Y0 @ Y1))))))))))
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ('#sk1' @ X0))),
% 53.37/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl38])).
% 53.37/7.55 thf(zip_derived_cl43, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 ((('#sk73' @ X0)
% 53.37/7.55 = ((^[Y0 : a,Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y2) &
% 53.37/7.55 (((!!) @ (^[Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 ((('#sk117' @ X0 @
% 53.37/7.55 Y3 @ Y4) => (Y2 @
% 53.37/7.55 Y3 @ Y4))))))))))) =>
% 53.37/7.55 (Y2 @ Y0 @ Y1)))))))))
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ('#sk1' @ X0))),
% 53.37/7.55 inference('simplify nested equalities', [status(thm)], [zip_derived_cl42])).
% 53.37/7.55 thf(zip_derived_cl295, plain,
% 53.37/7.55 (( ('#form18')
% 53.37/7.55 | ('#sk216' @ '#sk3' @ '#sk4')
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | (('#sk73' @ '#sk216')
% 53.37/7.55 = ((^[Y0 : a,Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y2) &
% 53.37/7.55 (((!!) @ (^[Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 ((('#sk117' @
% 53.37/7.55 '#sk216' @ Y3 @
% 53.37/7.55 Y4) => (Y2 @ Y3 @
% 53.37/7.55 Y4))))))))))) =>
% 53.37/7.55 (Y2 @ Y0 @ Y1))))))))))),
% 53.37/7.55 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl43])).
% 53.37/7.55 thf(zip_derived_cl299, plain,
% 53.37/7.55 (((('#sk73' @ '#sk216')
% 53.37/7.55 = ((^[Y0 : a,Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y2) &
% 53.37/7.55 (((!!) @ (^[Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 ((('#sk117' @
% 53.37/7.55 '#sk216' @ Y3 @
% 53.37/7.55 Y4) => (Y2 @ Y3 @ Y4))))))))))) =>
% 53.37/7.55 (Y2 @ Y0 @ Y1)))))))))
% 53.37/7.55 | ('#sk216' @ '#sk3' @ '#sk4')
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('simplify', [status(thm)], [zip_derived_cl295])).
% 53.37/7.55 thf(zip_derived_cl66, plain,
% 53.37/7.55 ((~ ('#sk216' @ '#sk3' @ '#sk4') | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])).
% 53.37/7.55 thf(zip_derived_cl301, plain,
% 53.37/7.55 (( ('#form18')
% 53.37/7.55 | (('#sk73' @ '#sk216')
% 53.37/7.55 = ((^[Y0 : a,Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y2) &
% 53.37/7.55 (((!!) @ (^[Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 ((('#sk117' @
% 53.37/7.55 '#sk216' @ Y3 @
% 53.37/7.55 Y4) => (Y2 @ Y3 @
% 53.37/7.55 Y4))))))))))) =>
% 53.37/7.55 (Y2 @ Y0 @ Y1))))))))))),
% 53.37/7.55 inference('clc', [status(thm)], [zip_derived_cl299, zip_derived_cl66])).
% 53.37/7.55 thf(zip_derived_cl303, plain,
% 53.37/7.55 (![X1 : a, X2 : a]:
% 53.37/7.55 ((('#sk73' @ '#sk216' @ X1 @ X2)
% 53.37/7.55 = ((^[Y0 : a,Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y2) &
% 53.37/7.55 (((!!) @ (^[Y3 : a]:
% 53.37/7.55 (((!!) @ (^[Y4 : a]:
% 53.37/7.55 ((('#sk117' @
% 53.37/7.55 '#sk216' @ Y3 @
% 53.37/7.55 Y4) => (Y2 @ Y3 @
% 53.37/7.55 Y4))))))))))) =>
% 53.37/7.55 (Y2 @ Y0 @ Y1))))))) @
% 53.37/7.55 X1 @ X2))
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('ho_complete_eq', [status(thm)], [zip_derived_cl301])).
% 53.37/7.55 thf(zip_derived_cl305, plain,
% 53.37/7.55 (![X1 : a, X2 : a]:
% 53.37/7.55 ((('#sk73' @ '#sk216' @ X1 @ X2)
% 53.37/7.55 = (((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y0) &
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a]:
% 53.37/7.55 ((('#sk117' @ '#sk216' @
% 53.37/7.55 Y1 @ Y2) => (Y0 @ Y1 @
% 53.37/7.55 Y2))))))))))) =>
% 53.37/7.55 (Y0 @ X1 @ X2)))))))
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('ho_norm', [status(thm)], [zip_derived_cl303])).
% 53.37/7.55 thf(zip_derived_cl306, plain,
% 53.37/7.55 (![X-1059 : a > a > $o, X1 : a, X2 : a]:
% 53.37/7.55 ( ((^[Y0 : a > a > $o]:
% 53.37/7.55 ((((('#sk1' @ Y0) &
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((!!) @ (^[Y2 : a]:
% 53.37/7.55 ((('#sk117' @ '#sk216' @ Y1 @ Y2) =>
% 53.37/7.55 (Y0 @ Y1 @ Y2))))))))))) =>
% 53.37/7.55 (Y0 @ X1 @ X2)))) @
% 53.37/7.55 X-1059)
% 53.37/7.55 | ~ ('#sk73' @ '#sk216' @ X1 @ X2)
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('forall_hoist', [status(thm)], [zip_derived_cl305])).
% 53.37/7.55 thf(zip_derived_cl307, plain,
% 53.37/7.55 (![X0 : a, X1 : a]:
% 53.37/7.55 ( ((((('#sk1' @ '#sk216') &
% 53.37/7.55 (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 ((('#sk117' @ '#sk216' @ Y0 @ Y1) =>
% 53.37/7.55 ('#sk216' @ Y0 @ Y1))))))))))) =>
% 53.37/7.55 ('#sk216' @ X1 @ X0)))
% 53.37/7.55 | ~ ('#sk73' @ '#sk216' @ X1 @ X0)
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('triggered_bool_instantiation', [status(thm)],
% 53.37/7.55 [zip_derived_cl306])).
% 53.37/7.55 thf(zip_derived_cl480, plain,
% 53.37/7.55 (![X0 : a, X1 : a]:
% 53.37/7.55 (~ ((('#sk1' @ '#sk216') &
% 53.37/7.55 (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 ((('#sk117' @ '#sk216' @ Y0 @ Y1) =>
% 53.37/7.55 ('#sk216' @ Y0 @ Y1)))))))))))
% 53.37/7.55 | ('#sk216' @ X1 @ X0)
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | ~ ('#sk73' @ '#sk216' @ X1 @ X0))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])).
% 53.37/7.55 thf(zip_derived_cl481, plain,
% 53.37/7.55 (![X0 : a, X1 : a]:
% 53.37/7.55 (~ ('#sk1' @ '#sk216')
% 53.37/7.55 | ~ (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 ((('#sk117' @ '#sk216' @ Y0 @ Y1) =>
% 53.37/7.55 ('#sk216' @ Y0 @ Y1)))))))))
% 53.37/7.55 | ~ ('#sk73' @ '#sk216' @ X1 @ X0)
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | ('#sk216' @ X1 @ X0))),
% 53.37/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl480])).
% 53.37/7.55 thf(zip_derived_cl69, plain, (( ('#sk1' @ '#sk216') | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])).
% 53.37/7.55 thf(zip_derived_cl482, plain,
% 53.37/7.55 (![X0 : a, X1 : a]:
% 53.37/7.55 ( ('#sk216' @ X1 @ X0)
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | ~ ('#sk73' @ '#sk216' @ X1 @ X0)
% 53.37/7.55 | ~ (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 ((('#sk117' @ '#sk216' @ Y0 @ Y1) =>
% 53.37/7.55 ('#sk216' @ Y0 @ Y1))))))))))),
% 53.37/7.55 inference('clc', [status(thm)], [zip_derived_cl481, zip_derived_cl69])).
% 53.37/7.55 thf(zip_derived_cl483, plain,
% 53.37/7.55 (![X0 : a, X1 : a]:
% 53.37/7.55 (~ (((!!) @ (^[Y0 : a]:
% 53.37/7.55 ((('#sk117' @ '#sk216' @ ('#sk430' @ '#sk216') @ Y0) =>
% 53.37/7.55 ('#sk216' @ ('#sk430' @ '#sk216') @ Y0))))))
% 53.37/7.55 | ~ ('#sk73' @ '#sk216' @ X1 @ X0)
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | ('#sk216' @ X1 @ X0))),
% 53.37/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl482])).
% 53.37/7.55 thf(zip_derived_cl484, plain,
% 53.37/7.55 (![X0 : a, X1 : a]:
% 53.37/7.55 (~ ((('#sk117' @ '#sk216' @ ('#sk430' @ '#sk216') @
% 53.37/7.55 ('#sk438' @ '#sk216')) => ('#sk216' @ ('#sk430' @ '#sk216') @
% 53.37/7.55 ('#sk438' @ '#sk216'))))
% 53.37/7.55 | ('#sk216' @ X1 @ X0)
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | ~ ('#sk73' @ '#sk216' @ X1 @ X0))),
% 53.37/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl483])).
% 53.37/7.55 thf(zip_derived_cl486, plain,
% 53.37/7.55 (![X0 : a, X1 : a]:
% 53.37/7.55 (~ ('#sk216' @ ('#sk430' @ '#sk216') @ ('#sk438' @ '#sk216'))
% 53.37/7.55 | ~ ('#sk73' @ '#sk216' @ X1 @ X0)
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | ('#sk216' @ X1 @ X0))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl484])).
% 53.37/7.55 thf(zip_derived_cl69, plain, (( ('#sk1' @ '#sk216') | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])).
% 53.37/7.55 thf(zip_derived_cl41, plain,
% 53.37/7.55 (![X0 : a > a > $o]:
% 53.37/7.55 ( ('#sk2' @ ('#sk117' @ X0))
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.55 | ~ ('#sk1' @ X0))),
% 53.37/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl38])).
% 53.37/7.55 thf(zip_derived_cl108, plain,
% 53.37/7.55 (( ('#form18')
% 53.37/7.55 | ('#sk216' @ '#sk3' @ '#sk4')
% 53.37/7.55 | ('#form18')
% 53.37/7.55 | ('#sk2' @ ('#sk117' @ '#sk216')))),
% 53.37/7.55 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl41])).
% 53.37/7.55 thf(zip_derived_cl115, plain,
% 53.37/7.55 (( ('#sk2' @ ('#sk117' @ '#sk216'))
% 53.37/7.55 | ('#sk216' @ '#sk3' @ '#sk4')
% 53.37/7.55 | ('#form18'))),
% 53.37/7.55 inference('simplify', [status(thm)], [zip_derived_cl108])).
% 53.37/7.55 thf(zip_derived_cl66, plain,
% 53.37/7.55 ((~ ('#sk216' @ '#sk3' @ '#sk4') | ('#form18'))),
% 53.37/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])).
% 53.37/7.55 thf(zip_derived_cl183, plain,
% 53.37/7.55 (( ('#form18') | ('#sk2' @ ('#sk117' @ '#sk216')))),
% 53.37/7.55 inference('clc', [status(thm)], [zip_derived_cl115, zip_derived_cl66])).
% 53.37/7.55 thf(zip_derived_cl70, plain,
% 53.37/7.55 (( (((!!) @ (^[Y0 : a]:
% 53.37/7.55 (((!!) @ (^[Y1 : a]:
% 53.37/7.55 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.55 ((('#sk2' @ Y2) & (Y2 @ Y0 @ Y1)))))) =>
% 53.37/7.55 ('#sk216' @ Y0 @ Y1)))))))))
% 53.37/7.55 | ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])).
% 53.37/7.56 thf(zip_derived_cl72, plain,
% 53.37/7.56 (![X2 : a]:
% 53.37/7.56 ( (((!!) @ (^[Y0 : a]:
% 53.37/7.56 (((((??) @ (^[Y1 : a > a > $o]:
% 53.37/7.56 ((('#sk2' @ Y1) & (Y1 @ X2 @ Y0)))))) =>
% 53.37/7.56 ('#sk216' @ X2 @ Y0))))))
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])).
% 53.37/7.56 thf(zip_derived_cl74, plain,
% 53.37/7.56 (![X2 : a, X4 : a]:
% 53.37/7.56 ( (((((??) @ (^[Y0 : a > a > $o]: ((('#sk2' @ Y0) & (Y0 @ X2 @ X4)))))) =>
% 53.37/7.56 ('#sk216' @ X2 @ X4)))
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl72])).
% 53.37/7.56 thf(zip_derived_cl76, plain,
% 53.37/7.56 (![X2 : a, X4 : a]:
% 53.37/7.56 (~ (((??) @ (^[Y0 : a > a > $o]: ((('#sk2' @ Y0) & (Y0 @ X2 @ X4))))))
% 53.37/7.56 | ('#sk216' @ X2 @ X4)
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])).
% 53.37/7.56 thf(zip_derived_cl82, plain,
% 53.37/7.56 (![X2 : a, X4 : a, X6 : a > a > $o]:
% 53.37/7.56 (~ ((('#sk2' @ X6) & (X6 @ X2 @ X4)))
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | ('#sk216' @ X2 @ X4))),
% 53.37/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl76])).
% 53.37/7.56 thf(zip_derived_cl88, plain,
% 53.37/7.56 (![X2 : a, X4 : a, X6 : a > a > $o]:
% 53.37/7.56 (~ ('#sk2' @ X6)
% 53.37/7.56 | ~ (X6 @ X2 @ X4)
% 53.37/7.56 | ('#sk216' @ X2 @ X4)
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl82])).
% 53.37/7.56 thf(zip_derived_cl239, plain,
% 53.37/7.56 (![X0 : a, X1 : a]:
% 53.37/7.56 ( ('#form18')
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | ('#sk216' @ X1 @ X0)
% 53.37/7.56 | ~ ('#sk117' @ '#sk216' @ X1 @ X0))),
% 53.37/7.56 inference('sup-', [status(thm)], [zip_derived_cl183, zip_derived_cl88])).
% 53.37/7.56 thf(zip_derived_cl250, plain,
% 53.37/7.56 (![X0 : a, X1 : a]:
% 53.37/7.56 (~ ('#sk117' @ '#sk216' @ X1 @ X0)
% 53.37/7.56 | ('#sk216' @ X1 @ X0)
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('simplify', [status(thm)], [zip_derived_cl239])).
% 53.37/7.56 thf(zip_derived_cl69, plain, (( ('#sk1' @ '#sk216') | ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])).
% 53.37/7.56 thf(zip_derived_cl185, plain,
% 53.37/7.56 (( ('#form18')
% 53.37/7.56 | ('#sk73' @ '#sk216' @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216')))),
% 53.37/7.56 inference('clc', [status(thm)], [zip_derived_cl116, zip_derived_cl66])).
% 53.37/7.56 thf(zip_derived_cl301, plain,
% 53.37/7.56 (( ('#form18')
% 53.37/7.56 | (('#sk73' @ '#sk216')
% 53.37/7.56 = ((^[Y0 : a,Y1 : a]:
% 53.37/7.56 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y2) &
% 53.37/7.56 (((!!) @ (^[Y3 : a]:
% 53.37/7.56 (((!!) @ (^[Y4 : a]:
% 53.37/7.56 ((('#sk117' @
% 53.37/7.56 '#sk216' @ Y3 @
% 53.37/7.56 Y4) => (Y2 @ Y3 @
% 53.37/7.56 Y4))))))))))) =>
% 53.37/7.56 (Y2 @ Y0 @ Y1))))))))))),
% 53.37/7.56 inference('clc', [status(thm)], [zip_derived_cl299, zip_derived_cl66])).
% 53.37/7.56 thf(zip_derived_cl302, plain,
% 53.37/7.56 (![X1 : a]:
% 53.37/7.56 ((('#sk73' @ '#sk216' @ X1)
% 53.37/7.56 = ((^[Y0 : a,Y1 : a]:
% 53.37/7.56 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y2) &
% 53.37/7.56 (((!!) @ (^[Y3 : a]:
% 53.37/7.56 (((!!) @ (^[Y4 : a]:
% 53.37/7.56 ((('#sk117' @
% 53.37/7.56 '#sk216' @ Y3 @
% 53.37/7.56 Y4) => (Y2 @ Y3 @
% 53.37/7.56 Y4))))))))))) =>
% 53.37/7.56 (Y2 @ Y0 @ Y1))))))) @
% 53.37/7.56 X1))
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('ho_complete_eq', [status(thm)], [zip_derived_cl301])).
% 53.37/7.56 thf(zip_derived_cl304, plain,
% 53.37/7.56 (![X1 : a]:
% 53.37/7.56 ((('#sk73' @ '#sk216' @ X1)
% 53.37/7.56 = ((^[Y0 : a]:
% 53.37/7.56 (((!!) @ (^[Y1 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y1) &
% 53.37/7.56 (((!!) @ (^[Y2 : a]:
% 53.37/7.56 (((!!) @ (^[Y3 : a]:
% 53.37/7.56 ((('#sk117' @
% 53.37/7.56 '#sk216' @ Y2 @
% 53.37/7.56 Y3) => (Y1 @ Y2 @
% 53.37/7.56 Y3))))))))))) =>
% 53.37/7.56 (Y1 @ X1 @ Y0)))))))))
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('ho_norm', [status(thm)], [zip_derived_cl302])).
% 53.37/7.56 thf(zip_derived_cl348, plain,
% 53.37/7.56 (![X1 : a, X2 : a]:
% 53.37/7.56 ((('#sk73' @ '#sk216' @ X1 @ X2)
% 53.37/7.56 = ((^[Y0 : a]:
% 53.37/7.56 (((!!) @ (^[Y1 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y1) &
% 53.37/7.56 (((!!) @ (^[Y2 : a]:
% 53.37/7.56 (((!!) @ (^[Y3 : a]:
% 53.37/7.56 ((('#sk117' @
% 53.37/7.56 '#sk216' @ Y2 @
% 53.37/7.56 Y3) => (Y1 @ Y2 @
% 53.37/7.56 Y3))))))))))) =>
% 53.37/7.56 (Y1 @ X1 @ Y0))))))) @
% 53.37/7.56 X2))
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('ho_complete_eq', [status(thm)], [zip_derived_cl304])).
% 53.37/7.56 thf(zip_derived_cl349, plain,
% 53.37/7.56 (![X1 : a, X2 : a]:
% 53.37/7.56 ((('#sk73' @ '#sk216' @ X1 @ X2)
% 53.37/7.56 = (((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y0) &
% 53.37/7.56 (((!!) @ (^[Y1 : a]:
% 53.37/7.56 (((!!) @ (^[Y2 : a]:
% 53.37/7.56 ((('#sk117' @ '#sk216' @
% 53.37/7.56 Y1 @ Y2) => (Y0 @ Y1 @
% 53.37/7.56 Y2))))))))))) =>
% 53.37/7.56 (Y0 @ X1 @ X2)))))))
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('ho_norm', [status(thm)], [zip_derived_cl348])).
% 53.37/7.56 thf(zip_derived_cl350, plain,
% 53.37/7.56 (![X-1253 : a > a > $o, X1 : a, X2 : a]:
% 53.37/7.56 ( ((^[Y0 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y0) &
% 53.37/7.56 (((!!) @ (^[Y1 : a]:
% 53.37/7.56 (((!!) @ (^[Y2 : a]:
% 53.37/7.56 ((('#sk117' @ '#sk216' @ Y1 @ Y2) =>
% 53.37/7.56 (Y0 @ Y1 @ Y2))))))))))) =>
% 53.37/7.56 (Y0 @ X1 @ X2)))) @
% 53.37/7.56 X-1253)
% 53.37/7.56 | ~ ('#sk73' @ '#sk216' @ X1 @ X2)
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('forall_hoist', [status(thm)], [zip_derived_cl349])).
% 53.37/7.56 thf(zip_derived_cl357, plain,
% 53.37/7.56 (![X-1253 : a > a > $o, X1 : a, X2 : a]:
% 53.37/7.56 ( ((((('#sk1' @ X-1253) &
% 53.37/7.56 (((!!) @ (^[Y0 : a]:
% 53.37/7.56 (((!!) @ (^[Y1 : a]:
% 53.37/7.56 ((('#sk117' @ '#sk216' @ Y0 @ Y1) =>
% 53.37/7.56 (X-1253 @ Y0 @ Y1))))))))))) =>
% 53.37/7.56 (X-1253 @ X1 @ X2)))
% 53.37/7.56 | ~ ('#sk73' @ '#sk216' @ X1 @ X2)
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('ho_norm', [status(thm)], [zip_derived_cl350])).
% 53.37/7.56 thf(zip_derived_cl358, plain,
% 53.37/7.56 (![X1 : a, X2 : a, X3 : a > a > $o]:
% 53.37/7.56 ( ((((('#sk1' @ X3) &
% 53.37/7.56 (((!!) @ (^[Y0 : a]:
% 53.37/7.56 (((!!) @ (^[Y1 : a]:
% 53.37/7.56 ((('#sk117' @ '#sk216' @ Y0 @ Y1) =>
% 53.37/7.56 (X3 @ Y0 @ Y1))))))))))) =>
% 53.37/7.56 (X3 @ X1 @ X2)))
% 53.37/7.56 | ~ ('#sk73' @ '#sk216' @ X1 @ X2)
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('cannonize vars', [status(thm)], [zip_derived_cl357])).
% 53.37/7.56 thf(zip_derived_cl359, plain,
% 53.37/7.56 (![X1 : a, X2 : a, X3 : a > a > $o]:
% 53.37/7.56 (~ ((('#sk1' @ X3) &
% 53.37/7.56 (((!!) @ (^[Y0 : a]:
% 53.37/7.56 (((!!) @ (^[Y1 : a]:
% 53.37/7.56 ((('#sk117' @ '#sk216' @ Y0 @ Y1) =>
% 53.37/7.56 (X3 @ Y0 @ Y1)))))))))))
% 53.37/7.56 | (X3 @ X1 @ X2)
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | ~ ('#sk73' @ '#sk216' @ X1 @ X2))),
% 53.37/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl358])).
% 53.37/7.56 thf(zip_derived_cl360, plain,
% 53.37/7.56 (![X1 : a, X2 : a, X3 : a > a > $o]:
% 53.37/7.56 (~ ('#sk1' @ X3)
% 53.37/7.56 | ~ (((!!) @ (^[Y0 : a]:
% 53.37/7.56 (((!!) @ (^[Y1 : a]:
% 53.37/7.56 ((('#sk117' @ '#sk216' @ Y0 @ Y1) =>
% 53.37/7.56 (X3 @ Y0 @ Y1)))))))))
% 53.37/7.56 | ~ ('#sk73' @ '#sk216' @ X1 @ X2)
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | (X3 @ X1 @ X2))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl359])).
% 53.37/7.56 thf(zip_derived_cl361, plain,
% 53.37/7.56 (![X1 : a, X2 : a, X3 : a > a > $o]:
% 53.37/7.56 (~ (((!!) @ (^[Y0 : a]:
% 53.37/7.56 ((('#sk117' @ '#sk216' @ ('#sk430' @ X3) @ Y0) =>
% 53.37/7.56 (X3 @ ('#sk430' @ X3) @ Y0))))))
% 53.37/7.56 | (X3 @ X1 @ X2)
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | ~ ('#sk73' @ '#sk216' @ X1 @ X2)
% 53.37/7.56 | ~ ('#sk1' @ X3))),
% 53.37/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl360])).
% 53.37/7.56 thf(zip_derived_cl362, plain,
% 53.37/7.56 (![X1 : a, X2 : a, X3 : a > a > $o]:
% 53.37/7.56 (~ ((('#sk117' @ '#sk216' @ ('#sk430' @ X3) @ ('#sk438' @ X3)) =>
% 53.37/7.56 (X3 @ ('#sk430' @ X3) @ ('#sk438' @ X3))))
% 53.37/7.56 | ~ ('#sk1' @ X3)
% 53.37/7.56 | ~ ('#sk73' @ '#sk216' @ X1 @ X2)
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | (X3 @ X1 @ X2))),
% 53.37/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl361])).
% 53.37/7.56 thf(zip_derived_cl363, plain,
% 53.37/7.56 (![X1 : a, X2 : a, X3 : a > a > $o]:
% 53.37/7.56 ( ('#sk117' @ '#sk216' @ ('#sk430' @ X3) @ ('#sk438' @ X3))
% 53.37/7.56 | (X3 @ X1 @ X2)
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | ~ ('#sk73' @ '#sk216' @ X1 @ X2)
% 53.37/7.56 | ~ ('#sk1' @ X3))),
% 53.37/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
% 53.37/7.56 thf(zip_derived_cl365, plain,
% 53.37/7.56 (![X0 : a > a > $o]:
% 53.37/7.56 ( ('#form18')
% 53.37/7.56 | ~ ('#sk1' @ X0)
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | (X0 @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216'))
% 53.37/7.56 | ('#sk117' @ '#sk216' @ ('#sk430' @ X0) @ ('#sk438' @ X0)))),
% 53.37/7.56 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl363])).
% 53.37/7.56 thf(zip_derived_cl367, plain,
% 53.37/7.56 (![X0 : a > a > $o]:
% 53.37/7.56 ( ('#sk117' @ '#sk216' @ ('#sk430' @ X0) @ ('#sk438' @ X0))
% 53.37/7.56 | (X0 @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216'))
% 53.37/7.56 | ~ ('#sk1' @ X0)
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('simplify', [status(thm)], [zip_derived_cl365])).
% 53.37/7.56 thf(zip_derived_cl369, plain,
% 53.37/7.56 (( ('#form18')
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | ('#sk216' @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216'))
% 53.37/7.56 | ('#sk117' @ '#sk216' @ ('#sk430' @ '#sk216') @ ('#sk438' @ '#sk216')))),
% 53.37/7.56 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl367])).
% 53.37/7.56 thf(zip_derived_cl373, plain,
% 53.37/7.56 (( ('#sk117' @ '#sk216' @ ('#sk430' @ '#sk216') @ ('#sk438' @ '#sk216'))
% 53.37/7.56 | ('#sk216' @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216'))
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('simplify', [status(thm)], [zip_derived_cl369])).
% 53.37/7.56 thf(zip_derived_cl69, plain, (( ('#sk1' @ '#sk216') | ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])).
% 53.37/7.56 thf(zip_derived_cl30, plain,
% 53.37/7.56 (![X0 : a > a > $o]:
% 53.37/7.56 (~ (X0 @ ('#sk31' @ X0) @ ('#sk43' @ X0))
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | (X0 @ '#sk3' @ '#sk4')
% 53.37/7.56 | ~ ('#sk1' @ X0))),
% 53.37/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])).
% 53.37/7.56 thf(zip_derived_cl110, plain,
% 53.37/7.56 (( ('#form18')
% 53.37/7.56 | ('#sk216' @ '#sk3' @ '#sk4')
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | ~ ('#sk216' @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216')))),
% 53.37/7.56 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl30])).
% 53.37/7.56 thf(zip_derived_cl117, plain,
% 53.37/7.56 ((~ ('#sk216' @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216'))
% 53.37/7.56 | ('#sk216' @ '#sk3' @ '#sk4')
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('simplify', [status(thm)], [zip_derived_cl110])).
% 53.37/7.56 thf(zip_derived_cl66, plain,
% 53.37/7.56 ((~ ('#sk216' @ '#sk3' @ '#sk4') | ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])).
% 53.37/7.56 thf(zip_derived_cl187, plain,
% 53.37/7.56 (( ('#form18')
% 53.37/7.56 | ~ ('#sk216' @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216')))),
% 53.37/7.56 inference('clc', [status(thm)], [zip_derived_cl117, zip_derived_cl66])).
% 53.37/7.56 thf(zip_derived_cl377, plain,
% 53.37/7.56 (( ('#form18')
% 53.37/7.56 | ('#sk117' @ '#sk216' @ ('#sk430' @ '#sk216') @ ('#sk438' @ '#sk216')))),
% 53.37/7.56 inference('clc', [status(thm)], [zip_derived_cl373, zip_derived_cl187])).
% 53.37/7.56 thf(zip_derived_cl379, plain,
% 53.37/7.56 (( ('#form18')
% 53.37/7.56 | ('#sk216' @ ('#sk430' @ '#sk216') @ ('#sk438' @ '#sk216'))
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('sup+', [status(thm)], [zip_derived_cl250, zip_derived_cl377])).
% 53.37/7.56 thf(zip_derived_cl382, plain,
% 53.37/7.56 (( ('#sk216' @ ('#sk430' @ '#sk216') @ ('#sk438' @ '#sk216'))
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('simplify', [status(thm)], [zip_derived_cl379])).
% 53.37/7.56 thf(zip_derived_cl489, plain,
% 53.37/7.56 (![X0 : a, X1 : a]:
% 53.37/7.56 ( ('#sk216' @ X1 @ X0)
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | ~ ('#sk73' @ '#sk216' @ X1 @ X0))),
% 53.37/7.56 inference('clc', [status(thm)], [zip_derived_cl486, zip_derived_cl382])).
% 53.37/7.56 thf(zip_derived_cl493, plain,
% 53.37/7.56 (( ('#form18')
% 53.37/7.56 | ('#form18')
% 53.37/7.56 | ('#sk216' @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216')))),
% 53.37/7.56 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl489])).
% 53.37/7.56 thf(zip_derived_cl498, plain,
% 53.37/7.56 (( ('#sk216' @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216'))
% 53.37/7.56 | ('#form18'))),
% 53.37/7.56 inference('simplify', [status(thm)], [zip_derived_cl493])).
% 53.37/7.56 thf(zip_derived_cl187, plain,
% 53.37/7.56 (( ('#form18')
% 53.37/7.56 | ~ ('#sk216' @ ('#sk31' @ '#sk216') @ ('#sk43' @ '#sk216')))),
% 53.37/7.56 inference('clc', [status(thm)], [zip_derived_cl117, zip_derived_cl66])).
% 53.37/7.56 thf(zip_derived_cl502, plain, ( ('#form18')),
% 53.37/7.56 inference('clc', [status(thm)], [zip_derived_cl498, zip_derived_cl187])).
% 53.37/7.56 thf(zip_derived_cl509, plain,
% 53.37/7.56 (~ ('#sk5' @ ('#sk48' @ '#sk5') @ ('#sk66' @ '#sk5'))),
% 53.37/7.56 inference('demod', [status(thm)], [zip_derived_cl204, zip_derived_cl502])).
% 53.37/7.56 thf(zip_derived_cl68, plain,
% 53.37/7.56 (( (((!!) @ (^[Y0 : a]:
% 53.37/7.56 (((!!) @ (^[Y1 : a]:
% 53.37/7.56 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.56 (((((??) @ (^[Y3 : a > a > $o]:
% 53.37/7.56 ((('#sk2' @ Y3) &
% 53.37/7.56 (((Y2) =
% 53.37/7.56 ((^[Y4 : a,
% 53.37/7.56 Y5 : a]:
% 53.37/7.56 ((
% 53.37/7.56 (!!) @ (
% 53.37/7.56 ^[Y6 :
% 53.37/7.56 a > a > $o]:
% 53.37/7.56 ((
% 53.37/7.56 ((
% 53.37/7.56 ('#sk1' @
% 53.37/7.56 Y6) &
% 53.37/7.56 ((
% 53.37/7.56 (!!) @ (
% 53.37/7.56 ^[Y7 : a]:
% 53.37/7.56 ((
% 53.37/7.56 (!!) @ (
% 53.37/7.56 ^[Y8 : a]:
% 53.37/7.56 ((
% 53.37/7.56 (Y3 @
% 53.37/7.56 Y7 @
% 53.37/7.56 Y8) =>
% 53.37/7.56 (Y6 @
% 53.37/7.56 Y7 @ Y8))))))))))) =>
% 53.37/7.56 (Y6 @
% 53.37/7.56 Y4 @ Y5))))))))))))))) &
% 53.37/7.56 (Y2 @ Y0 @ Y1)))))) =>
% 53.37/7.56 ('#sk5' @ Y0 @ Y1)))))))))
% 53.37/7.56 | ~ ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])).
% 53.37/7.56 thf(zip_derived_cl71, plain,
% 53.37/7.56 (![X2 : a]:
% 53.37/7.56 ( (((!!) @ (^[Y0 : a]:
% 53.37/7.56 (((((??) @ (^[Y1 : a > a > $o]:
% 53.37/7.56 (((((??) @ (^[Y2 : a > a > $o]:
% 53.37/7.56 ((('#sk2' @ Y2) &
% 53.37/7.56 (((Y1) =
% 53.37/7.56 ((^[Y3 : a,Y4 : a]:
% 53.37/7.56 (((!!) @ (^[Y5 :
% 53.37/7.56 a > a > $o]:
% 53.37/7.56 ((
% 53.37/7.56 ((
% 53.37/7.56 ('#sk1' @
% 53.37/7.56 Y5) &
% 53.37/7.56 ((
% 53.37/7.56 (!!) @ (
% 53.37/7.56 ^[Y6 : a]:
% 53.37/7.56 ((
% 53.37/7.56 (!!) @ (
% 53.37/7.56 ^[Y7 : a]:
% 53.37/7.56 ((
% 53.37/7.56 (Y2 @
% 53.37/7.56 Y6 @
% 53.37/7.56 Y7) =>
% 53.37/7.56 (Y5 @
% 53.37/7.56 Y6 @ Y7))))))))))) =>
% 53.37/7.56 (Y5 @
% 53.37/7.56 Y3 @ Y4))))))))))))))) &
% 53.37/7.56 (Y1 @ X2 @ Y0)))))) =>
% 53.37/7.56 ('#sk5' @ X2 @ Y0))))))
% 53.37/7.56 | ~ ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl68])).
% 53.37/7.56 thf(zip_derived_cl73, plain,
% 53.37/7.56 (![X2 : a, X4 : a]:
% 53.37/7.56 ( (((((??) @ (^[Y0 : a > a > $o]:
% 53.37/7.56 (((((??) @ (^[Y1 : a > a > $o]:
% 53.37/7.56 ((('#sk2' @ Y1) &
% 53.37/7.56 (((Y0) =
% 53.37/7.56 ((^[Y2 : a,Y3 : a]:
% 53.37/7.56 (((!!) @ (^[Y4 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y4) &
% 53.37/7.56 (((!!) @ (
% 53.37/7.56 ^[Y5 : a]:
% 53.37/7.56 (((!!) @ (
% 53.37/7.56 ^[Y6 : a]:
% 53.37/7.56 ((
% 53.37/7.56 (Y1 @
% 53.37/7.56 Y5 @
% 53.37/7.56 Y6) =>
% 53.37/7.56 (Y4 @
% 53.37/7.56 Y5 @ Y6))))))))))) =>
% 53.37/7.56 (Y4 @ Y2 @ Y3))))))))))))))) &
% 53.37/7.56 (Y0 @ X2 @ X4)))))) =>
% 53.37/7.56 ('#sk5' @ X2 @ X4)))
% 53.37/7.56 | ~ ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])).
% 53.37/7.56 thf(zip_derived_cl75, plain,
% 53.37/7.56 (![X2 : a, X4 : a]:
% 53.37/7.56 (~ (((??) @ (^[Y0 : a > a > $o]:
% 53.37/7.56 (((((??) @ (^[Y1 : a > a > $o]:
% 53.37/7.56 ((('#sk2' @ Y1) &
% 53.37/7.56 (((Y0) =
% 53.37/7.56 ((^[Y2 : a,Y3 : a]:
% 53.37/7.56 (((!!) @ (^[Y4 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y4) &
% 53.37/7.56 (((!!) @ (
% 53.37/7.56 ^[Y5 : a]:
% 53.37/7.56 (((!!) @ (
% 53.37/7.56 ^[Y6 : a]:
% 53.37/7.56 (
% 53.37/7.56 (
% 53.37/7.56 (Y1 @
% 53.37/7.56 Y5 @
% 53.37/7.56 Y6) =>
% 53.37/7.56 (Y4 @
% 53.37/7.56 Y5 @ Y6))))))))))) =>
% 53.37/7.56 (Y4 @ Y2 @ Y3))))))))))))))) &
% 53.37/7.56 (Y0 @ X2 @ X4))))))
% 53.37/7.56 | ('#sk5' @ X2 @ X4)
% 53.37/7.56 | ~ ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])).
% 53.37/7.56 thf(zip_derived_cl77, plain,
% 53.37/7.56 (![X2 : a, X4 : a, X6 : a > a > $o]:
% 53.37/7.56 (~ (((((??) @ (^[Y0 : a > a > $o]:
% 53.37/7.56 ((('#sk2' @ Y0) &
% 53.37/7.56 (((X6) =
% 53.37/7.56 ((^[Y1 : a,Y2 : a]:
% 53.37/7.56 (((!!) @ (^[Y3 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y3) &
% 53.37/7.56 (((!!) @ (^[Y4 : a]:
% 53.37/7.56 (((!!) @ (
% 53.37/7.56 ^[Y5 : a]:
% 53.37/7.56 (((Y0 @ Y4 @
% 53.37/7.56 Y5) =>
% 53.37/7.56 (Y3 @ Y4 @
% 53.37/7.56 Y5))))))))))) =>
% 53.37/7.56 (Y3 @ Y1 @ Y2))))))))))))))) &
% 53.37/7.56 (X6 @ X2 @ X4)))
% 53.37/7.56 | ~ ('#form18')
% 53.37/7.56 | ('#sk5' @ X2 @ X4))),
% 53.37/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl75])).
% 53.37/7.56 thf(zip_derived_cl87, plain,
% 53.37/7.56 (![X2 : a, X4 : a, X6 : a > a > $o]:
% 53.37/7.56 (~ (((??) @ (^[Y0 : a > a > $o]:
% 53.37/7.56 ((('#sk2' @ Y0) &
% 53.37/7.56 (((X6) =
% 53.37/7.56 ((^[Y1 : a,Y2 : a]:
% 53.37/7.56 (((!!) @ (^[Y3 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y3) &
% 53.37/7.56 (((!!) @ (^[Y4 : a]:
% 53.37/7.56 (((!!) @ (^[Y5 : a]:
% 53.37/7.56 ((
% 53.37/7.56 (Y0 @
% 53.37/7.56 Y4 @
% 53.37/7.56 Y5) =>
% 53.37/7.56 (Y3 @
% 53.37/7.56 Y4 @ Y5))))))))))) =>
% 53.37/7.56 (Y3 @ Y1 @ Y2)))))))))))))))
% 53.37/7.56 | ~ (X6 @ X2 @ X4)
% 53.37/7.56 | ('#sk5' @ X2 @ X4)
% 53.37/7.56 | ~ ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl77])).
% 53.37/7.56 thf(zip_derived_cl89, plain,
% 53.37/7.56 (![X2 : a, X4 : a, X6 : a > a > $o, X8 : a > a > $o]:
% 53.37/7.56 (~ ((('#sk2' @ X8) &
% 53.37/7.56 (((X6) =
% 53.37/7.56 ((^[Y0 : a,Y1 : a]:
% 53.37/7.56 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y2) &
% 53.37/7.56 (((!!) @ (^[Y3 : a]:
% 53.37/7.56 (((!!) @ (^[Y4 : a]:
% 53.37/7.56 (((X8 @ Y3 @ Y4) =>
% 53.37/7.56 (Y2 @ Y3 @ Y4))))))))))) =>
% 53.37/7.56 (Y2 @ Y0 @ Y1))))))))))))
% 53.37/7.56 | ~ ('#form18')
% 53.37/7.56 | ('#sk5' @ X2 @ X4)
% 53.37/7.56 | ~ (X6 @ X2 @ X4))),
% 53.37/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl87])).
% 53.37/7.56 thf(zip_derived_cl94, plain,
% 53.37/7.56 (![X2 : a, X4 : a, X6 : a > a > $o, X8 : a > a > $o]:
% 53.37/7.56 (~ ('#sk2' @ X8)
% 53.37/7.56 | ~ (((X6) =
% 53.37/7.56 ((^[Y0 : a,Y1 : a]:
% 53.37/7.56 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y2) &
% 53.37/7.56 (((!!) @ (^[Y3 : a]:
% 53.37/7.56 (((!!) @ (^[Y4 : a]:
% 53.37/7.56 (((X8 @ Y3 @ Y4) =>
% 53.37/7.56 (Y2 @ Y3 @ Y4))))))))))) =>
% 53.37/7.56 (Y2 @ Y0 @ Y1))))))))))
% 53.37/7.56 | ~ (X6 @ X2 @ X4)
% 53.37/7.56 | ('#sk5' @ X2 @ X4)
% 53.37/7.56 | ~ ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl89])).
% 53.37/7.56 thf(zip_derived_cl95, plain,
% 53.37/7.56 (![X2 : a, X4 : a, X6 : a > a > $o, X8 : a > a > $o]:
% 53.37/7.56 (~ ('#sk2' @ X8)
% 53.37/7.56 | ((X6)
% 53.37/7.56 != ((^[Y0 : a,Y1 : a]:
% 53.37/7.56 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y2) &
% 53.37/7.56 (((!!) @ (^[Y3 : a]:
% 53.37/7.56 (((!!) @ (^[Y4 : a]:
% 53.37/7.56 (((X8 @ Y3 @
% 53.37/7.56 Y4) => (Y2 @
% 53.37/7.56 Y3 @ Y4))))))))))) =>
% 53.37/7.56 (Y2 @ Y0 @ Y1)))))))))
% 53.37/7.56 | ~ (X6 @ X2 @ X4)
% 53.37/7.56 | ('#sk5' @ X2 @ X4)
% 53.37/7.56 | ~ ('#form18'))),
% 53.37/7.56 inference('simplify nested equalities', [status(thm)], [zip_derived_cl94])).
% 53.37/7.56 thf(zip_derived_cl502, plain, ( ('#form18')),
% 53.37/7.56 inference('clc', [status(thm)], [zip_derived_cl498, zip_derived_cl187])).
% 53.37/7.56 thf(zip_derived_cl1524, plain,
% 53.37/7.56 (![X2 : a, X4 : a, X6 : a > a > $o, X8 : a > a > $o]:
% 53.37/7.56 (~ ('#sk2' @ X8)
% 53.37/7.56 | ((X6)
% 53.37/7.56 != ((^[Y0 : a,Y1 : a]:
% 53.37/7.56 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y2) &
% 53.37/7.56 (((!!) @ (^[Y3 : a]:
% 53.37/7.56 (((!!) @ (^[Y4 : a]:
% 53.37/7.56 (((X8 @ Y3 @
% 53.37/7.56 Y4) => (Y2 @
% 53.37/7.56 Y3 @ Y4))))))))))) =>
% 53.37/7.56 (Y2 @ Y0 @ Y1)))))))))
% 53.37/7.56 | ~ (X6 @ X2 @ X4)
% 53.37/7.56 | ('#sk5' @ X2 @ X4))),
% 53.37/7.56 inference('demod', [status(thm)], [zip_derived_cl95, zip_derived_cl502])).
% 53.37/7.56 thf(zip_derived_cl1528, plain,
% 53.37/7.56 (![X0 : a, X1 : a, X2 : a > a > $o]:
% 53.37/7.56 ( ('#sk5' @ X1 @ X0)
% 53.37/7.56 | ~ ((^[Y0 : a,Y1 : a]:
% 53.37/7.56 (((!!) @ (^[Y2 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y2) &
% 53.37/7.56 (((!!) @ (^[Y3 : a]:
% 53.37/7.56 (((!!) @ (^[Y4 : a]:
% 53.37/7.56 (((X2 @ Y3 @ Y4) =>
% 53.37/7.56 (Y2 @ Y3 @ Y4))))))))))) =>
% 53.37/7.56 (Y2 @ Y0 @ Y1))))))) @
% 53.37/7.56 X1 @ X0)
% 53.37/7.56 | ~ ('#sk2' @ X2))),
% 53.37/7.56 inference('eq_res', [status(thm)], [zip_derived_cl1524])).
% 53.37/7.56 thf(zip_derived_cl1529, plain,
% 53.37/7.56 (![X0 : a, X1 : a, X2 : a > a > $o]:
% 53.37/7.56 ( ('#sk5' @ X1 @ X0)
% 53.37/7.56 | ~ (((!!) @ (^[Y0 : a > a > $o]:
% 53.37/7.56 ((((('#sk1' @ Y0) &
% 53.37/7.56 (((!!) @ (^[Y1 : a]:
% 53.37/7.56 (((!!) @ (^[Y2 : a]:
% 53.37/7.56 (((X2 @ Y1 @ Y2) =>
% 53.37/7.56 (Y0 @ Y1 @ Y2))))))))))) =>
% 53.37/7.56 (Y0 @ X1 @ X0))))))
% 53.37/7.56 | ~ ('#sk2' @ X2))),
% 53.37/7.56 inference('ho_norm', [status(thm)], [zip_derived_cl1528])).
% 53.37/7.56 thf(zip_derived_cl2568, plain,
% 53.37/7.56 (![X0 : a, X1 : a, X2 : a > a > $o]:
% 53.37/7.56 (~ ((((('#sk1' @ ('#sk12196' @ X0 @ X1 @ X2)) &
% 53.37/7.56 (((!!) @ (^[Y0 : a]:
% 53.37/7.56 (((!!) @ (^[Y1 : a]:
% 53.37/7.56 (((X2 @ Y0 @ Y1) => ('#sk12196' @ X0 @
% 53.37/7.56 X1 @ X2 @ Y0 @ Y1))))))))))) =>
% 53.37/7.56 ('#sk12196' @ X0 @ X1 @ X2 @ X1 @ X0)))
% 53.37/7.56 | ~ ('#sk2' @ X2)
% 53.37/7.56 | ('#sk5' @ X1 @ X0))),
% 53.37/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1529])).
% 53.37/7.56 thf(zip_derived_cl2570, plain,
% 53.37/7.56 (![X0 : a, X1 : a, X2 : a > a > $o]:
% 53.37/7.56 (~ ('#sk12196' @ X0 @ X1 @ X2 @ X1 @ X0)
% 53.37/7.56 | ('#sk5' @ X1 @ X0)
% 53.37/7.56 | ~ ('#sk2' @ X2))),
% 53.37/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2568])).
% 53.37/7.56 thf(zip_derived_cl67, plain, (( ('#sk1' @ '#sk5') | ~ ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])).
% 53.37/7.56 thf(zip_derived_cl33, plain,
% 53.37/7.56 (![X2 : a > a > $o]:
% 53.37/7.56 ( (((??) @ (^[Y0 : a > a > $o]:
% 53.37/7.56 ((('#sk2' @ Y0) & (Y0 @ ('#sk48' @ X2) @ ('#sk66' @ X2)))))))
% 53.37/7.56 | (X2 @ '#sk3' @ '#sk4')
% 53.37/7.56 | ~ ('#form18')
% 53.37/7.56 | ~ ('#sk1' @ X2))),
% 53.37/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl31])).
% 53.37/7.56 thf(zip_derived_cl37, plain,
% 53.37/7.56 (![X2 : a > a > $o]:
% 53.37/7.56 ( ((('#sk2' @ ('#sk106' @ X2)) & ('#sk106' @ X2 @ ('#sk48' @ X2) @
% 53.37/7.56 ('#sk66' @ X2))))
% 53.37/7.56 | ~ ('#sk1' @ X2)
% 53.37/7.56 | ~ ('#form18')
% 53.37/7.56 | (X2 @ '#sk3' @ '#sk4'))),
% 53.37/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl33])).
% 53.37/7.56 thf(zip_derived_cl39, plain,
% 53.37/7.56 (![X2 : a > a > $o]:
% 53.37/7.56 ( ('#sk2' @ ('#sk106' @ X2))
% 53.37/7.56 | (X2 @ '#sk3' @ '#sk4')
% 53.37/7.56 | ~ ('#form18')
% 53.37/7.56 | ~ ('#sk1' @ X2))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl37])).
% 53.37/7.56 thf(zip_derived_cl96, plain,
% 53.37/7.56 ((~ ('#form18')
% 53.37/7.56 | ~ ('#form18')
% 53.37/7.56 | ('#sk5' @ '#sk3' @ '#sk4')
% 53.37/7.56 | ('#sk2' @ ('#sk106' @ '#sk5')))),
% 53.37/7.56 inference('sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl39])).
% 53.37/7.56 thf(zip_derived_cl104, plain,
% 53.37/7.56 (( ('#sk2' @ ('#sk106' @ '#sk5'))
% 53.37/7.56 | ('#sk5' @ '#sk3' @ '#sk4')
% 53.37/7.56 | ~ ('#form18'))),
% 53.37/7.56 inference('simplify', [status(thm)], [zip_derived_cl96])).
% 53.37/7.56 thf(zip_derived_cl64, plain,
% 53.37/7.56 ((~ ('#sk5' @ '#sk3' @ '#sk4') | ~ ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])).
% 53.37/7.56 thf(zip_derived_cl181, plain,
% 53.37/7.56 ((~ ('#form18') | ('#sk2' @ ('#sk106' @ '#sk5')))),
% 53.37/7.56 inference('clc', [status(thm)], [zip_derived_cl104, zip_derived_cl64])).
% 53.37/7.56 thf(zip_derived_cl502, plain, ( ('#form18')),
% 53.37/7.56 inference('clc', [status(thm)], [zip_derived_cl498, zip_derived_cl187])).
% 53.37/7.56 thf(zip_derived_cl508, plain, ( ('#sk2' @ ('#sk106' @ '#sk5'))),
% 53.37/7.56 inference('demod', [status(thm)], [zip_derived_cl181, zip_derived_cl502])).
% 53.37/7.56 thf(zip_derived_cl2569, plain,
% 53.37/7.56 (![X0 : a, X1 : a, X2 : a > a > $o]:
% 53.37/7.56 ( ((('#sk1' @ ('#sk12196' @ X0 @ X1 @ X2)) &
% 53.37/7.56 (((!!) @ (^[Y0 : a]:
% 53.37/7.56 (((!!) @ (^[Y1 : a]:
% 53.37/7.56 (((X2 @ Y0 @ Y1) => ('#sk12196' @ X0 @
% 53.37/7.56 X1 @ X2 @ Y0 @ Y1)))))))))))
% 53.37/7.56 | ('#sk5' @ X1 @ X0)
% 53.37/7.56 | ~ ('#sk2' @ X2))),
% 53.37/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2568])).
% 53.37/7.56 thf(zip_derived_cl2572, plain,
% 53.37/7.56 (![X0 : a, X1 : a, X2 : a > a > $o]:
% 53.37/7.56 ( (((!!) @ (^[Y0 : a]:
% 53.37/7.56 (((!!) @ (^[Y1 : a]:
% 53.37/7.56 (((X2 @ Y0 @ Y1) => ('#sk12196' @ X0 @ X1 @
% 53.37/7.56 X2 @ Y0 @ Y1)))))))))
% 53.37/7.56 | ~ ('#sk2' @ X2)
% 53.37/7.56 | ('#sk5' @ X1 @ X0))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2569])).
% 53.37/7.56 thf(zip_derived_cl2573, plain,
% 53.37/7.56 (![X0 : a, X1 : a, X2 : a > a > $o, X4 : a]:
% 53.37/7.56 ( (((!!) @ (^[Y0 : a]:
% 53.37/7.56 (((X2 @ X4 @ Y0) => ('#sk12196' @ X0 @ X1 @ X2 @ X4 @
% 53.37/7.56 Y0))))))
% 53.37/7.56 | ('#sk5' @ X1 @ X0)
% 53.37/7.56 | ~ ('#sk2' @ X2))),
% 53.37/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2572])).
% 53.37/7.56 thf(zip_derived_cl2574, plain,
% 53.37/7.56 (![X0 : a, X1 : a, X2 : a > a > $o, X4 : a, X6 : a]:
% 53.37/7.56 ( (((X2 @ X4 @ X6) => ('#sk12196' @ X0 @ X1 @ X2 @ X4 @ X6)))
% 53.37/7.56 | ~ ('#sk2' @ X2)
% 53.37/7.56 | ('#sk5' @ X1 @ X0))),
% 53.37/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2573])).
% 53.37/7.56 thf(zip_derived_cl2575, plain,
% 53.37/7.56 (![X0 : a, X1 : a, X2 : a > a > $o, X4 : a, X6 : a]:
% 53.37/7.56 (~ (X2 @ X4 @ X6)
% 53.37/7.56 | ('#sk12196' @ X0 @ X1 @ X2 @ X4 @ X6)
% 53.37/7.56 | ('#sk5' @ X1 @ X0)
% 53.37/7.56 | ~ ('#sk2' @ X2))),
% 53.37/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2574])).
% 53.37/7.56 thf(zip_derived_cl2641, plain,
% 53.37/7.56 (![X0 : a, X1 : a, X2 : a, X3 : a]:
% 53.37/7.56 ( ('#sk5' @ X1 @ X0)
% 53.37/7.56 | ('#sk12196' @ X0 @ X1 @ ('#sk106' @ '#sk5') @ X3 @ X2)
% 53.37/7.56 | ~ ('#sk106' @ '#sk5' @ X3 @ X2))),
% 53.37/7.56 inference('sup-', [status(thm)], [zip_derived_cl508, zip_derived_cl2575])).
% 53.37/7.56 thf(zip_derived_cl2648, plain,
% 53.37/7.56 (![X0 : a, X1 : a]:
% 53.37/7.56 (~ ('#sk2' @ ('#sk106' @ '#sk5'))
% 53.37/7.56 | ('#sk5' @ X1 @ X0)
% 53.37/7.56 | ~ ('#sk106' @ '#sk5' @ X1 @ X0)
% 53.37/7.56 | ('#sk5' @ X1 @ X0))),
% 53.37/7.56 inference('sup+', [status(thm)], [zip_derived_cl2570, zip_derived_cl2641])).
% 53.37/7.56 thf(zip_derived_cl508, plain, ( ('#sk2' @ ('#sk106' @ '#sk5'))),
% 53.37/7.56 inference('demod', [status(thm)], [zip_derived_cl181, zip_derived_cl502])).
% 53.37/7.56 thf(zip_derived_cl2653, plain,
% 53.37/7.56 (![X0 : a, X1 : a]:
% 53.37/7.56 ( ('#sk5' @ X1 @ X0)
% 53.37/7.56 | ~ ('#sk106' @ '#sk5' @ X1 @ X0)
% 53.37/7.56 | ('#sk5' @ X1 @ X0))),
% 53.37/7.56 inference('demod', [status(thm)], [zip_derived_cl2648, zip_derived_cl508])).
% 53.37/7.56 thf(zip_derived_cl2654, plain,
% 53.37/7.56 (![X0 : a, X1 : a]:
% 53.37/7.56 (~ ('#sk106' @ '#sk5' @ X1 @ X0) | ('#sk5' @ X1 @ X0))),
% 53.37/7.56 inference('simplify', [status(thm)], [zip_derived_cl2653])).
% 53.37/7.56 thf(zip_derived_cl67, plain, (( ('#sk1' @ '#sk5') | ~ ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])).
% 53.37/7.56 thf(zip_derived_cl40, plain,
% 53.37/7.56 (![X2 : a > a > $o]:
% 53.37/7.56 ( ('#sk106' @ X2 @ ('#sk48' @ X2) @ ('#sk66' @ X2))
% 53.37/7.56 | (X2 @ '#sk3' @ '#sk4')
% 53.37/7.56 | ~ ('#form18')
% 53.37/7.56 | ~ ('#sk1' @ X2))),
% 53.37/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl37])).
% 53.37/7.56 thf(zip_derived_cl449, plain,
% 53.37/7.56 ((~ ('#form18')
% 53.37/7.56 | ~ ('#form18')
% 53.37/7.56 | ('#sk5' @ '#sk3' @ '#sk4')
% 53.37/7.56 | ('#sk106' @ '#sk5' @ ('#sk48' @ '#sk5') @ ('#sk66' @ '#sk5')))),
% 53.37/7.56 inference('sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl40])).
% 53.37/7.56 thf(zip_derived_cl450, plain,
% 53.37/7.56 (( ('#sk106' @ '#sk5' @ ('#sk48' @ '#sk5') @ ('#sk66' @ '#sk5'))
% 53.37/7.56 | ('#sk5' @ '#sk3' @ '#sk4')
% 53.37/7.56 | ~ ('#form18'))),
% 53.37/7.56 inference('simplify', [status(thm)], [zip_derived_cl449])).
% 53.37/7.56 thf(zip_derived_cl64, plain,
% 53.37/7.56 ((~ ('#sk5' @ '#sk3' @ '#sk4') | ~ ('#form18'))),
% 53.37/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])).
% 53.37/7.56 thf(zip_derived_cl475, plain,
% 53.37/7.56 ((~ ('#form18')
% 53.37/7.56 | ('#sk106' @ '#sk5' @ ('#sk48' @ '#sk5') @ ('#sk66' @ '#sk5')))),
% 53.37/7.56 inference('clc', [status(thm)], [zip_derived_cl450, zip_derived_cl64])).
% 53.37/7.56 thf(zip_derived_cl502, plain, ( ('#form18')),
% 53.37/7.56 inference('clc', [status(thm)], [zip_derived_cl498, zip_derived_cl187])).
% 53.37/7.56 thf(zip_derived_cl513, plain,
% 53.37/7.56 ( ('#sk106' @ '#sk5' @ ('#sk48' @ '#sk5') @ ('#sk66' @ '#sk5'))),
% 53.37/7.56 inference('demod', [status(thm)], [zip_derived_cl475, zip_derived_cl502])).
% 53.37/7.56 thf(zip_derived_cl2665, plain,
% 53.37/7.56 ( ('#sk5' @ ('#sk48' @ '#sk5') @ ('#sk66' @ '#sk5'))),
% 53.37/7.56 inference('sup+', [status(thm)], [zip_derived_cl2654, zip_derived_cl513])).
% 53.37/7.56 thf(zip_derived_cl2667, plain, ($false),
% 53.37/7.56 inference('demod', [status(thm)], [zip_derived_cl509, zip_derived_cl2665])).
% 53.37/7.56
% 53.37/7.56 % SZS output end Refutation
% 53.37/7.56
% 53.37/7.56
% 53.37/7.56 % Terminating...
% 54.00/7.66 % Runner terminated.
% 54.00/7.67 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------