%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV119^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.g3gk41ceW6 true
% Computer : n028.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 Oct 2 04:57:12 PM UTC 2025
% Result : Theorem 43.41s 6.15s
% Output : Refutation 43.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEV119^5 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.g3gk41ceW6 true
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Oct 1 15:41:23 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % Running portfolio for 300 s
% 0.13/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in HO mode
% 0.53/0.64 % Total configuration time : 828
% 0.53/0.64 % Estimated wc time : 1656
% 0.53/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.53/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.53/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.53/0.75 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 43.41/6.15 % Solved by lams/35_full_unif4.sh.
% 43.41/6.15 % done 205 iterations in 5.332s
% 43.41/6.15 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 43.41/6.15 % SZS output start Refutation
% 43.41/6.15 thf(a_type, type, a: $tType).
% 43.41/6.15 thf('#sk3_type', type, '#sk3': a > a > $o).
% 43.41/6.15 thf('#sk627_type', type, '#sk627': a > a > $o).
% 43.41/6.15 thf('#sk41_type', type, '#sk41': (a > a > $o) > a).
% 43.41/6.15 thf('#sk61_type', type, '#sk61': (a > a > $o) > a).
% 43.41/6.15 thf('#sk628_type', type, '#sk628': a > a > a > a > $o).
% 43.41/6.15 thf('#sk4_type', type, '#sk4': a).
% 43.41/6.15 thf('#sk36_type', type, '#sk36': (a > a > $o) > a).
% 43.41/6.15 thf('#sk254_type', type, '#sk254': (a > a > $o) > a).
% 43.41/6.15 thf('#sk1_type', type, '#sk1': (a > a > $o) > $o).
% 43.41/6.15 thf('#sk213_type', type, '#sk213': (a > a > $o) > a).
% 43.41/6.15 thf('#sk224_type', type, '#sk224': (a > a > $o) > a).
% 43.41/6.15 thf('#sk629_type', type, '#sk629': a > a > a > a > $o).
% 43.41/6.15 thf('#sk2_type', type, '#sk2': a > a > $o).
% 43.41/6.15 thf('#sk6_type', type, '#sk6': a > a > $o).
% 43.41/6.15 thf('#sk51_type', type, '#sk51': (a > a > $o) > a).
% 43.41/6.15 thf('#sk240_type', type, '#sk240': (a > a > $o) > a).
% 43.41/6.15 thf('#sk5_type', type, '#sk5': a).
% 43.41/6.15 thf('#form15_type', type, '#form15': $o).
% 43.41/6.15 thf('#form156_type', type, '#form156': (a > a > $o) > $o).
% 43.41/6.15 thf(cTHM252_pme, conjecture,
% 43.41/6.15 (![PROP:( ( a > a > $o ) > $o ),R:( a > a > $o ),S:( a > a > $o )]:
% 43.41/6.15 ( ( ^[Xx:a,Xy:a]:
% 43.41/6.15 ( ![Xp:( a > a > $o )]:
% 43.41/6.15 ( ( ( PROP @ Xp ) &
% 43.41/6.15 ( ![Xx0:a,Xy0:a]:
% 43.41/6.15 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) =>
% 43.41/6.15 ( Xp @ Xx0 @ Xy0 ) ) ) ) =>
% 43.41/6.15 ( Xp @ Xx @ Xy ) ) ) ) =
% 43.41/6.15 ( ^[Xx:a,Xy:a]:
% 43.41/6.15 ( ![Xp:( a > a > $o )]:
% 43.41/6.15 ( ( ( PROP @ Xp ) &
% 43.41/6.15 ( ![Xx0:a,Xy0:a]:
% 43.41/6.15 ( ( ( ![Xp0:( a > a > $o )]:
% 43.41/6.15 ( ( ( PROP @ Xp0 ) &
% 43.41/6.15 ( ![Xx1:a,Xy1:a]:
% 43.41/6.15 ( ( S @ Xx1 @ Xy1 ) => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) =>
% 43.41/6.15 ( Xp0 @ Xx0 @ Xy0 ) ) ) |
% 43.41/6.15 ( ![Xp0:( a > a > $o )]:
% 43.41/6.15 ( ( ( PROP @ Xp0 ) &
% 43.41/6.15 ( ![Xx1:a,Xy1:a]:
% 43.41/6.15 ( ( R @ Xx1 @ Xy1 ) => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) =>
% 43.41/6.15 ( Xp0 @ Xx0 @ Xy0 ) ) ) ) =>
% 43.41/6.15 ( Xp @ Xx0 @ Xy0 ) ) ) ) =>
% 43.41/6.15 ( Xp @ Xx @ Xy ) ) ) ) ))).
% 43.41/6.15 thf(zf_stmt_0, negated_conjecture,
% 43.41/6.15 (~( ![PROP:( ( a > a > $o ) > $o ),R:( a > a > $o ),S:( a > a > $o )]:
% 43.41/6.15 ( ( ^[Xx:a,Xy:a]:
% 43.41/6.15 ( ![Xp:( a > a > $o )]:
% 43.41/6.15 ( ( ( PROP @ Xp ) &
% 43.41/6.15 ( ![Xx0:a,Xy0:a]:
% 43.41/6.15 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) =>
% 43.41/6.15 ( Xp @ Xx0 @ Xy0 ) ) ) ) =>
% 43.41/6.15 ( Xp @ Xx @ Xy ) ) ) ) =
% 43.41/6.15 ( ^[Xx:a,Xy:a]:
% 43.41/6.15 ( ![Xp:( a > a > $o )]:
% 43.41/6.15 ( ( ( PROP @ Xp ) &
% 43.41/6.15 ( ![Xx0:a,Xy0:a]:
% 43.41/6.15 ( ( ( ![Xp0:( a > a > $o )]:
% 43.41/6.15 ( ( ( PROP @ Xp0 ) &
% 43.41/6.15 ( ![Xx1:a,Xy1:a]:
% 43.41/6.15 ( ( S @ Xx1 @ Xy1 ) => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) =>
% 43.41/6.15 ( Xp0 @ Xx0 @ Xy0 ) ) ) |
% 43.41/6.15 ( ![Xp0:( a > a > $o )]:
% 43.41/6.15 ( ( ( PROP @ Xp0 ) &
% 43.41/6.15 ( ![Xx1:a,Xy1:a]:
% 43.41/6.15 ( ( R @ Xx1 @ Xy1 ) => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) =>
% 43.41/6.15 ( Xp0 @ Xx0 @ Xy0 ) ) ) ) =>
% 43.41/6.15 ( Xp @ Xx0 @ Xy0 ) ) ) ) =>
% 43.41/6.15 ( Xp @ Xx @ Xy ) ) ) ) ) )),
% 43.41/6.15 inference('cnf.neg', [status(esa)], [cTHM252_pme])).
% 43.41/6.15 thf(zip_derived_cl0, plain,
% 43.41/6.15 (~ (((!!) @ (^[Y0 : (a > a > $o) > $o]:
% 43.41/6.15 (((!!) @ (^[Y1 : a > a > $o]:
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((^[Y3 : a,Y4 : a]:
% 43.41/6.15 (((!!) @ (^[Y5 : a > a > $o]:
% 43.41/6.15 (((((Y0 @ Y5) &
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y6 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y7 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y6 @
% 43.41/6.15 Y7) |
% 43.41/6.15 (Y1 @
% 43.41/6.15 Y6 @ Y7))) =>
% 43.41/6.15 (Y5 @
% 43.41/6.15 Y6 @ Y7))))))))))) =>
% 43.41/6.15 (Y5 @ Y3 @ Y4)))))))) =
% 43.41/6.15 ((^[Y3 : a,Y4 : a]:
% 43.41/6.15 (((!!) @ (^[Y5 : a > a > $o]:
% 43.41/6.15 (((((Y0 @ Y5) &
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y6 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y7 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y8 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 (Y0 @
% 43.41/6.15 Y8) &
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y9 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y10 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y9 @
% 43.41/6.15 Y10) =>
% 43.41/6.15 (Y8 @
% 43.41/6.15 Y9 @ Y10))))))))))) =>
% 43.41/6.15 (Y8 @
% 43.41/6.15 Y6 @ Y7)))))) |
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y8 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 (Y0 @
% 43.41/6.15 Y8) &
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y9 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y10 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (Y1 @
% 43.41/6.15 Y9 @
% 43.41/6.15 Y10) =>
% 43.41/6.15 (Y8 @
% 43.41/6.15 Y9 @ Y10))))))))))) =>
% 43.41/6.15 (Y8 @
% 43.41/6.15 Y6 @ Y7)))))))) =>
% 43.41/6.15 (Y5 @
% 43.41/6.15 Y6 @ Y7))))))))))) =>
% 43.41/6.15 (Y5 @ Y3 @ Y4)))))))))))))))))))),
% 43.41/6.15 inference('cnf', [status(esa)], [zf_stmt_0])).
% 43.41/6.15 thf(zip_derived_cl1, plain,
% 43.41/6.15 (~ (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 (((!!) @ (^[Y1 : a > a > $o]:
% 43.41/6.15 ((((^[Y2 : a,Y3 : a]:
% 43.41/6.15 (((!!) @ (^[Y4 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y4) &
% 43.41/6.15 (((!!) @ (^[Y5 : a]:
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y6 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 (Y1 @
% 43.41/6.15 Y5 @
% 43.41/6.15 Y6) |
% 43.41/6.15 (Y0 @
% 43.41/6.15 Y5 @ Y6))) =>
% 43.41/6.15 (Y4 @
% 43.41/6.15 Y5 @ Y6))))))))))) =>
% 43.41/6.15 (Y4 @ Y2 @ Y3)))))))) =
% 43.41/6.15 ((^[Y2 : a,Y3 : a]:
% 43.41/6.15 (((!!) @ (^[Y4 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y4) &
% 43.41/6.15 (((!!) @ (^[Y5 : a]:
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y6 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y7 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 ('#sk1' @
% 43.41/6.15 Y7) &
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y8 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y9 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (Y1 @
% 43.41/6.15 Y8 @
% 43.41/6.15 Y9) =>
% 43.41/6.15 (Y7 @
% 43.41/6.15 Y8 @ Y9))))))))))) =>
% 43.41/6.15 (Y7 @
% 43.41/6.15 Y5 @ Y6)))))) |
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y7 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 ('#sk1' @
% 43.41/6.15 Y7) &
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y8 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y9 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (Y0 @
% 43.41/6.15 Y8 @
% 43.41/6.15 Y9) =>
% 43.41/6.15 (Y7 @
% 43.41/6.15 Y8 @ Y9))))))))))) =>
% 43.41/6.15 (Y7 @
% 43.41/6.15 Y5 @ Y6)))))))) =>
% 43.41/6.15 (Y4 @
% 43.41/6.15 Y5 @ Y6))))))))))) =>
% 43.41/6.15 (Y4 @ Y2 @ Y3))))))))))))))))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])).
% 43.41/6.15 thf(zip_derived_cl2, plain,
% 43.41/6.15 (~ (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((^[Y1 : a,Y2 : a]:
% 43.41/6.15 (((!!) @ (^[Y3 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y3) &
% 43.41/6.15 (((!!) @ (^[Y4 : a]:
% 43.41/6.15 (((!!) @ (^[Y5 : a]:
% 43.41/6.15 ((((
% 43.41/6.15 (Y0 @
% 43.41/6.15 Y4 @ Y5) |
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y4 @ Y5))) =>
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y4 @ Y5))))))))))) =>
% 43.41/6.15 (Y3 @ Y1 @ Y2)))))))) =
% 43.41/6.15 ((^[Y1 : a,Y2 : a]:
% 43.41/6.15 (((!!) @ (^[Y3 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y3) &
% 43.41/6.15 (((!!) @ (^[Y4 : a]:
% 43.41/6.15 (((!!) @ (^[Y5 : a]:
% 43.41/6.15 ((((
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y6 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 ('#sk1' @
% 43.41/6.15 Y6) &
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y7 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y8 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (Y0 @
% 43.41/6.15 Y7 @
% 43.41/6.15 Y8) =>
% 43.41/6.15 (Y6 @
% 43.41/6.15 Y7 @ Y8))))))))))) =>
% 43.41/6.15 (Y6 @
% 43.41/6.15 Y4 @ Y5)))))) |
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y6 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 ('#sk1' @
% 43.41/6.15 Y6) &
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y7 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y8 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y7 @
% 43.41/6.15 Y8) =>
% 43.41/6.15 (Y6 @
% 43.41/6.15 Y7 @ Y8))))))))))) =>
% 43.41/6.15 (Y6 @
% 43.41/6.15 Y4 @ Y5)))))))) =>
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y4 @ Y5))))))))))) =>
% 43.41/6.15 (Y3 @ Y1 @ Y2)))))))))))))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])).
% 43.41/6.15 thf(zip_derived_cl3, plain,
% 43.41/6.15 (~ ((((^[Y0 : a,Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 (((!!) @ (^[Y4 : a]:
% 43.41/6.15 ((((('#sk3' @ Y3 @ Y4) |
% 43.41/6.15 ('#sk2' @ Y3 @ Y4))) =>
% 43.41/6.15 (Y2 @ Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =
% 43.41/6.15 ((^[Y0 : a,Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 (((!!) @ (^[Y4 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y5 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 ('#sk1' @
% 43.41/6.15 Y5) &
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y6 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y7 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk3' @
% 43.41/6.15 Y6 @
% 43.41/6.15 Y7) =>
% 43.41/6.15 (Y5 @
% 43.41/6.15 Y6 @ Y7))))))))))) =>
% 43.41/6.15 (Y5 @
% 43.41/6.15 Y3 @ Y4)))))) |
% 43.41/6.15 (((!!) @ (^[Y5 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 ('#sk1' @
% 43.41/6.15 Y5) &
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y6 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y7 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y6 @
% 43.41/6.15 Y7) =>
% 43.41/6.15 (Y5 @
% 43.41/6.15 Y6 @ Y7))))))))))) =>
% 43.41/6.15 (Y5 @
% 43.41/6.15 Y3 @ Y4)))))))) =>
% 43.41/6.15 (Y2 @ Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1))))))))))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])).
% 43.41/6.15 thf(zip_derived_cl4, plain,
% 43.41/6.15 ((((^[Y0 : a,Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 (((!!) @ (^[Y4 : a]:
% 43.41/6.15 ((((('#sk3' @ Y3 @ Y4) |
% 43.41/6.15 ('#sk2' @ Y3 @ Y4))) =>
% 43.41/6.15 (Y2 @ Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1))))))))
% 43.41/6.15 != ((^[Y0 : a,Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 (((!!) @ (^[Y4 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y5 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((
% 43.41/6.15 ((
% 43.41/6.15 ('#sk1' @
% 43.41/6.15 Y5) &
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y6 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y7 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk3' @
% 43.41/6.15 Y6 @
% 43.41/6.15 Y7) =>
% 43.41/6.15 (Y5 @
% 43.41/6.15 Y6 @ Y7))))))))))) =>
% 43.41/6.15 (Y5 @
% 43.41/6.15 Y3 @ Y4)))))) |
% 43.41/6.15 (((!!) @ (^[Y5 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((
% 43.41/6.15 ((
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% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y6 : a]:
% 43.41/6.15 ((
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% 43.41/6.15 ((
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% 43.41/6.15 Y6 @
% 43.41/6.15 Y7) =>
% 43.41/6.15 (Y5 @
% 43.41/6.15 Y6 @ Y7))))))))))) =>
% 43.41/6.15 (Y5 @
% 43.41/6.15 Y3 @ Y4)))))))) =>
% 43.41/6.15 (Y2 @ Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))))),
% 43.41/6.15 inference('simplify nested equalities', [status(thm)], [zip_derived_cl3])).
% 43.41/6.15 thf(zip_derived_cl5, plain,
% 43.41/6.15 (((((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ (^[Y1 : a,Y2 : a]: (Y0 @ Y1 @ Y2))) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5'))))))
% 43.41/6.15 != (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ (^[Y1 : a,Y2 : a]: (Y0 @ Y1 @ Y2))) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y3 :
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% 43.41/6.15 ((((
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% 43.41/6.15 (
% 43.41/6.15 ^[Y4 : a,
% 43.41/6.15 Y5 : a]:
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y4 @ Y5))) &
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
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% 43.41/6.15 ((
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% 43.41/6.15 Y4 @
% 43.41/6.15 Y5) =>
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y4 @ Y5))))))))))) =>
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y1 @ Y2)))))) |
% 43.41/6.15 (((!!) @ (^[Y3 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((((
% 43.41/6.15 ('#sk1' @
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% 43.41/6.15 Y5 : a]:
% 43.41/6.15 (Y3 @
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% 43.41/6.15 ((
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% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
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% 43.41/6.15 ((
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% 43.41/6.15 Y4 @
% 43.41/6.15 Y5) =>
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y4 @ Y5))))))))))) =>
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y1 @ Y2)))))))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5')))))))),
% 43.41/6.15 inference('neg_ext', [status(thm)], [zip_derived_cl4])).
% 43.41/6.15 thf(zip_derived_cl8, plain,
% 43.41/6.15 (((((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5'))))))
% 43.41/6.15 != (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y3 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((((
% 43.41/6.15 ('#sk1' @
% 43.41/6.15 Y3) &
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
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% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
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% 43.41/6.15 ((
% 43.41/6.15 ('#sk3' @
% 43.41/6.15 Y4 @
% 43.41/6.15 Y5) =>
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y4 @ Y5))))))))))) =>
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y1 @ Y2)))))) |
% 43.41/6.15 (((!!) @ (^[Y3 :
% 43.41/6.15 a > a > $o]:
% 43.41/6.15 ((((
% 43.41/6.15 ('#sk1' @
% 43.41/6.15 Y3) &
% 43.41/6.15 ((
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% 43.41/6.15 ((
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% 43.41/6.15 ((
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% 43.41/6.15 Y4 @
% 43.41/6.15 Y5) =>
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y4 @ Y5))))))))))) =>
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y1 @ Y2)))))))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5')))))))),
% 43.41/6.15 inference('ho_norm', [status(thm)], [zip_derived_cl5])).
% 43.41/6.15 thf(zip_derived_cl15, plain,
% 43.41/6.15 (((((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5'))))))
% 43.41/6.15 != ((^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ (^[Y1 : a,Y2 : a]: (Y0 @ Y1 @ Y2))) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y3 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @
% 43.41/6.15 (^[Y4 : a,
% 43.41/6.15 Y5 : a]:
% 43.41/6.15 (Y3 @ Y4 @
% 43.41/6.15 Y5))) &
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y5 : a]:
% 43.41/6.15 ((
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% 43.41/6.15 Y4 @
% 43.41/6.15 Y5) =>
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y4 @ Y5))))))))))) =>
% 43.41/6.15 (Y3 @ Y1 @ Y2)))))) |
% 43.41/6.15 (((!!) @ (^[Y3 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @
% 43.41/6.15 (^[Y4 : a,
% 43.41/6.15 Y5 : a]:
% 43.41/6.15 (Y3 @ Y4 @
% 43.41/6.15 Y5))) &
% 43.41/6.15 (((!!) @ (
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% 43.41/6.15 (((!!) @ (
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% 43.41/6.15 ((
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% 43.41/6.15 Y4 @
% 43.41/6.15 Y5) =>
% 43.41/6.15 (Y3 @
% 43.41/6.15 Y4 @ Y5))))))))))) =>
% 43.41/6.15 (Y3 @ Y1 @ Y2)))))))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5')))) @
% 43.41/6.15 '#sk6'))),
% 43.41/6.15 inference('quantifier_rw', [status(thm)], [zip_derived_cl8])).
% 43.41/6.15 thf(zip_derived_cl16, plain,
% 43.41/6.15 (((((!!) @ (^[Y0 : a > a > $o]:
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% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5'))))))
% 43.41/6.15 != ((((('#sk1' @ '#sk6') &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
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% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
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% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))) |
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((
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% 43.41/6.15 ((
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% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
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% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =>
% 43.41/6.15 ('#sk6' @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 ('#sk6' @ '#sk4' @ '#sk5'))))),
% 43.41/6.15 inference('ho_norm', [status(thm)], [zip_derived_cl15])).
% 43.41/6.15 thf(zip_derived_cl68, plain,
% 43.41/6.15 ((~ (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
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% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5'))))))
% 43.41/6.15 | ~ ((((('#sk1' @ '#sk6') &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y2 : a > a > $o]:
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% 43.41/6.15 ((
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% 43.41/6.15 ((
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% 43.41/6.15 (Y2 @ Y0 @ Y1)))))) |
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
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% 43.41/6.15 ((
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% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =>
% 43.41/6.15 ('#sk6' @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 ('#sk6' @ '#sk4' @ '#sk5'))))),
% 43.41/6.15 inference('eq_elim', [status(thm)], [zip_derived_cl16])).
% 43.41/6.15 thf(zip_derived_cl97, plain,
% 43.41/6.15 (( ('#form15')
% 43.41/6.15 | ~ (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
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% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
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% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5')))))))),
% 43.41/6.15 define([status(thm)])).
% 43.41/6.15 thf(zip_derived_cl102, plain,
% 43.41/6.15 ((~ ((((('#sk1' @ '#sk627') &
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% 43.41/6.15 Y1))) =>
% 43.41/6.15 ('#sk627' @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 ('#sk627' @ '#sk4' @ '#sk5')))
% 43.41/6.15 | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl97])).
% 43.41/6.15 thf(zip_derived_cl106, plain,
% 43.41/6.15 (( ((('#sk1' @ '#sk627') &
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% 43.41/6.15 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) =>
% 43.41/6.15 ('#sk627' @ Y0 @ Y1)))))))))))
% 43.41/6.15 | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])).
% 43.41/6.15 thf(zip_derived_cl110, plain, (( ('#sk1' @ '#sk627') | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])).
% 43.41/6.15 thf(zip_derived_cl8, plain,
% 43.41/6.15 (((((!!) @ (^[Y0 : a > a > $o]:
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% 43.41/6.15 != (((!!) @ (^[Y0 : a > a > $o]:
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% 43.41/6.15 (Y3 @
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% 43.41/6.15 (((!!) @ (^[Y3 :
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% 43.41/6.15 X-81)
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% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))) |
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =>
% 43.41/6.15 (X-81 @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 (X-81 @ '#sk4' @ '#sk5')))
% 43.41/6.15 | (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5')))))))),
% 43.41/6.15 inference('ho_norm', [status(thm)], [zip_derived_cl9])).
% 43.41/6.15 thf(zip_derived_cl18, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 ( ((((('#sk1' @ X0) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk3' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))) |
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =>
% 43.41/6.15 (X0 @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 (X0 @ '#sk4' @ '#sk5')))
% 43.41/6.15 | (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5')))))))),
% 43.41/6.15 inference('cannonize vars', [status(thm)], [zip_derived_cl17])).
% 43.41/6.15 thf(zip_derived_cl18, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 ( ((((('#sk1' @ X0) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk3' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))) |
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =>
% 43.41/6.15 (X0 @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 (X0 @ '#sk4' @ '#sk5')))
% 43.41/6.15 | (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5')))))))),
% 43.41/6.15 inference('cannonize vars', [status(thm)], [zip_derived_cl17])).
% 43.41/6.15 thf(zip_derived_cl19, plain,
% 43.41/6.15 ((~ ('#form15')
% 43.41/6.15 | (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5')))))))),
% 43.41/6.15 define([status(thm)])).
% 43.41/6.15 thf(zip_derived_cl26, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 ( ('#form15')
% 43.41/6.15 | ((((('#sk1' @ X0) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y3 : a]:
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk3' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))) |
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y3 : a]:
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =>
% 43.41/6.15 (X0 @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 (X0 @ '#sk4' @ '#sk5'))))),
% 43.41/6.15 inference('renaming', [status(thm)], [zip_derived_cl18, zip_derived_cl19])).
% 43.41/6.15 thf(zip_derived_cl27, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ ((('#sk1' @ X0) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 (
% 43.41/6.15 (
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk3' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))) |
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 (
% 43.41/6.15 (
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =>
% 43.41/6.15 (X0 @ Y0 @ Y1)))))))))))
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])).
% 43.41/6.15 thf(zip_derived_cl29, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ ('#sk1' @ X0)
% 43.41/6.15 | ~ (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 (
% 43.41/6.15 (
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk3' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))) |
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 (
% 43.41/6.15 (
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =>
% 43.41/6.15 (X0 @ Y0 @ Y1)))))))))
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5'))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])).
% 43.41/6.15 thf(zip_derived_cl31, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y1 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y1) &
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((('#sk3' @
% 43.41/6.15 Y2 @
% 43.41/6.15 Y3) =>
% 43.41/6.15 (Y1 @
% 43.41/6.15 Y2 @ Y3))))))))))) =>
% 43.41/6.15 (Y1 @ ('#sk36' @ X0) @ Y0)))))) |
% 43.41/6.15 (((!!) @ (^[Y1 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y1) &
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((('#sk2' @
% 43.41/6.15 Y2 @
% 43.41/6.15 Y3) =>
% 43.41/6.15 (Y1 @
% 43.41/6.15 Y2 @ Y3))))))))))) =>
% 43.41/6.15 (Y1 @ ('#sk36' @ X0) @ Y0)))))))) =>
% 43.41/6.15 (X0 @ ('#sk36' @ X0) @ Y0))))))
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X0))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])).
% 43.41/6.15 thf(zip_derived_cl33, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ (((((((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk3' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))) |
% 43.41/6.15 (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk2' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))))) =>
% 43.41/6.15 (X0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5'))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])).
% 43.41/6.15 thf(zip_derived_cl36, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ (X0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X0))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 43.41/6.15 thf(zip_derived_cl245, plain,
% 43.41/6.15 (( ('#form15')
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | ('#sk627' @ '#sk4' @ '#sk5')
% 43.41/6.15 | ~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl36])).
% 43.41/6.15 thf(zip_derived_cl252, plain,
% 43.41/6.15 ((~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))
% 43.41/6.15 | ('#sk627' @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form15'))),
% 43.41/6.15 inference('simplify', [status(thm)], [zip_derived_cl245])).
% 43.41/6.15 thf(zip_derived_cl107, plain,
% 43.41/6.15 ((~ ('#sk627' @ '#sk4' @ '#sk5') | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])).
% 43.41/6.15 thf(zip_derived_cl278, plain,
% 43.41/6.15 (( ('#form15')
% 43.41/6.15 | ~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')))),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl252, zip_derived_cl107])).
% 43.41/6.15 thf(zip_derived_cl68, plain,
% 43.41/6.15 ((~ (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5'))))))
% 43.41/6.15 | ~ ((((('#sk1' @ '#sk6') &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk3' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))) |
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =>
% 43.41/6.15 ('#sk6' @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 ('#sk6' @ '#sk4' @ '#sk5'))))),
% 43.41/6.15 inference('eq_elim', [status(thm)], [zip_derived_cl16])).
% 43.41/6.15 thf(zip_derived_cl97, plain,
% 43.41/6.15 (( ('#form15')
% 43.41/6.15 | ~ (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5')))))))),
% 43.41/6.15 define([status(thm)])).
% 43.41/6.15 thf(zip_derived_cl19, plain,
% 43.41/6.15 ((~ ('#form15')
% 43.41/6.15 | (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5')))))))),
% 43.41/6.15 define([status(thm)])).
% 43.41/6.15 thf(zip_derived_cl103, plain,
% 43.41/6.15 ((~ ('#form15')
% 43.41/6.15 | ~ ((((('#sk1' @ '#sk6') &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk3' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))) |
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((
% 43.41/6.15 (!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =>
% 43.41/6.15 ('#sk6' @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 ('#sk6' @ '#sk4' @ '#sk5'))))),
% 43.41/6.15 inference('renaming', [status(thm)],
% 43.41/6.15 [zip_derived_cl68, zip_derived_cl97, zip_derived_cl19])).
% 43.41/6.15 thf(zip_derived_cl104, plain,
% 43.41/6.15 (( ((('#sk1' @ '#sk6') &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk3' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))) |
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =>
% 43.41/6.15 ('#sk6' @ Y0 @ Y1)))))))))))
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])).
% 43.41/6.15 thf(zip_derived_cl108, plain, (( ('#sk1' @ '#sk6') | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl104])).
% 43.41/6.15 thf(zip_derived_cl19, plain,
% 43.41/6.15 ((~ ('#form15')
% 43.41/6.15 | (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((((('#sk3' @ Y1 @ Y2) |
% 43.41/6.15 ('#sk2' @ Y1 @ Y2))) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ '#sk4' @ '#sk5')))))))),
% 43.41/6.15 define([status(thm)])).
% 43.41/6.15 thf(zip_derived_cl20, plain,
% 43.41/6.15 (![X2 : a > a > $o]:
% 43.41/6.15 ( ((((('#sk1' @ X2) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @
% 43.41/6.15 Y1))) =>
% 43.41/6.15 (X2 @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 (X2 @ '#sk4' @ '#sk5')))
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])).
% 43.41/6.15 thf(zip_derived_cl28, plain,
% 43.41/6.15 (![X2 : a > a > $o]:
% 43.41/6.15 (~ ((('#sk1' @ X2) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @
% 43.41/6.15 Y1))) =>
% 43.41/6.15 (X2 @ Y0 @ Y1)))))))))))
% 43.41/6.15 | (X2 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])).
% 43.41/6.15 thf(zip_derived_cl30, plain,
% 43.41/6.15 (![X2 : a > a > $o]:
% 43.41/6.15 (~ ('#sk1' @ X2)
% 43.41/6.15 | ~ (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @
% 43.41/6.15 Y1))) =>
% 43.41/6.15 (X2 @ Y0 @ Y1)))))))))
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | (X2 @ '#sk4' @ '#sk5'))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl28])).
% 43.41/6.15 thf(zip_derived_cl32, plain,
% 43.41/6.15 (![X2 : a > a > $o]:
% 43.41/6.15 (~ (((!!) @ (^[Y0 : a]:
% 43.41/6.15 ((((('#sk3' @ ('#sk41' @ X2) @ Y0) | ('#sk2' @
% 43.41/6.15 ('#sk41' @ X2) @ Y0))) =>
% 43.41/6.15 (X2 @ ('#sk41' @ X2) @ Y0))))))
% 43.41/6.15 | (X2 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X2))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])).
% 43.41/6.15 thf(zip_derived_cl34, plain,
% 43.41/6.15 (![X2 : a > a > $o]:
% 43.41/6.15 (~ ((((('#sk3' @ ('#sk41' @ X2) @ ('#sk61' @ X2)) | ('#sk2' @
% 43.41/6.15 ('#sk41' @ X2) @ ('#sk61' @ X2)))) =>
% 43.41/6.15 (X2 @ ('#sk41' @ X2) @ ('#sk61' @ X2))))
% 43.41/6.15 | ~ ('#sk1' @ X2)
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | (X2 @ '#sk4' @ '#sk5'))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])).
% 43.41/6.15 thf(zip_derived_cl37, plain,
% 43.41/6.15 (![X2 : a > a > $o]:
% 43.41/6.15 ( ((('#sk3' @ ('#sk41' @ X2) @ ('#sk61' @ X2)) | ('#sk2' @
% 43.41/6.15 ('#sk41' @ X2) @ ('#sk61' @ X2))))
% 43.41/6.15 | (X2 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X2))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 43.41/6.15 thf(zip_derived_cl40, plain,
% 43.41/6.15 (![X2 : a > a > $o]:
% 43.41/6.15 ( ('#sk3' @ ('#sk41' @ X2) @ ('#sk61' @ X2))
% 43.41/6.15 | ('#sk2' @ ('#sk41' @ X2) @ ('#sk61' @ X2))
% 43.41/6.15 | ~ ('#sk1' @ X2)
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | (X2 @ '#sk4' @ '#sk5'))),
% 43.41/6.15 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl37])).
% 43.41/6.15 thf(zip_derived_cl138, plain,
% 43.41/6.15 ((~ ('#form15')
% 43.41/6.15 | ('#sk6' @ '#sk4' @ '#sk5')
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk2' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6'))
% 43.41/6.15 | ('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl108, zip_derived_cl40])).
% 43.41/6.15 thf(zip_derived_cl146, plain,
% 43.41/6.15 (( ('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6'))
% 43.41/6.15 | ('#sk2' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6'))
% 43.41/6.15 | ('#sk6' @ '#sk4' @ '#sk5')
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('simplify', [status(thm)], [zip_derived_cl138])).
% 43.41/6.15 thf(zip_derived_cl105, plain,
% 43.41/6.15 ((~ ('#sk6' @ '#sk4' @ '#sk5') | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])).
% 43.41/6.15 thf(zip_derived_cl384, plain,
% 43.41/6.15 ((~ ('#form15')
% 43.41/6.15 | ('#sk2' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6'))
% 43.41/6.15 | ('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')))),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl146, zip_derived_cl105])).
% 43.41/6.15 thf(zip_derived_cl109, plain,
% 43.41/6.15 (( (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk3' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))) |
% 43.41/6.15 (((!!) @ (^[Y2 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y2) &
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 (((!!) @ (
% 43.41/6.15 ^[Y4 : a]:
% 43.41/6.15 ((
% 43.41/6.15 ('#sk2' @
% 43.41/6.15 Y3 @
% 43.41/6.15 Y4) =>
% 43.41/6.15 (Y2 @
% 43.41/6.15 Y3 @ Y4))))))))))) =>
% 43.41/6.15 (Y2 @ Y0 @ Y1)))))))) =>
% 43.41/6.15 ('#sk6' @ Y0 @ Y1)))))))))
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl104])).
% 43.41/6.15 thf(zip_derived_cl112, plain,
% 43.41/6.15 (![X2 : a]:
% 43.41/6.15 ( (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((((((!!) @ (^[Y1 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y1) &
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((('#sk3' @
% 43.41/6.15 Y2 @
% 43.41/6.15 Y3) =>
% 43.41/6.15 (Y1 @
% 43.41/6.15 Y2 @ Y3))))))))))) =>
% 43.41/6.15 (Y1 @ X2 @ Y0)))))) |
% 43.41/6.15 (((!!) @ (^[Y1 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y1) &
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 (((!!) @ (^[Y3 : a]:
% 43.41/6.15 ((('#sk2' @
% 43.41/6.15 Y2 @
% 43.41/6.15 Y3) =>
% 43.41/6.15 (Y1 @
% 43.41/6.15 Y2 @ Y3))))))))))) =>
% 43.41/6.15 (Y1 @ X2 @ Y0)))))))) =>
% 43.41/6.15 ('#sk6' @ X2 @ Y0))))))
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl109])).
% 43.41/6.15 thf(zip_derived_cl114, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 ( (((((((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk3' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ X2 @ X4)))))) |
% 43.41/6.15 (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk2' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ X2 @ X4)))))))) =>
% 43.41/6.15 ('#sk6' @ X2 @ X4)))
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl112])).
% 43.41/6.15 thf(zip_derived_cl116, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 (~ (((((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk3' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ X2 @ X4)))))) |
% 43.41/6.15 (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk2' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ X2 @ X4))))))))
% 43.41/6.15 | ('#sk6' @ X2 @ X4)
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])).
% 43.41/6.15 thf(zip_derived_cl118, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 (~ (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk3' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ X2 @ X4))))))
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ X2 @ X4))),
% 43.41/6.15 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl116])).
% 43.41/6.15 thf(zip_derived_cl122, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 (~ ((((('#sk1' @ ('#sk628' @ X2 @ X4)) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk3' @ Y0 @ Y1) => ('#sk628' @
% 43.41/6.15 X2 @ X4 @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 ('#sk628' @ X2 @ X4 @ X2 @ X4)))
% 43.41/6.15 | ('#sk6' @ X2 @ X4)
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl118])).
% 43.41/6.15 thf(zip_derived_cl125, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 (~ ('#sk628' @ X2 @ X4 @ X2 @ X4)
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ X2 @ X4))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl122])).
% 43.41/6.15 thf(zip_derived_cl124, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 ( ((('#sk1' @ ('#sk628' @ X2 @ X4)) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk3' @ Y0 @ Y1) => ('#sk628' @ X2 @
% 43.41/6.15 X4 @ Y0 @ Y1)))))))))))
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ X2 @ X4))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl122])).
% 43.41/6.15 thf(zip_derived_cl129, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 ( (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk3' @ Y0 @ Y1) => ('#sk628' @ X2 @
% 43.41/6.15 X4 @ Y0 @ Y1)))))))))
% 43.41/6.15 | ('#sk6' @ X2 @ X4)
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl124])).
% 43.41/6.15 thf(zip_derived_cl132, plain,
% 43.41/6.15 (![X2 : a, X4 : a, X6 : a]:
% 43.41/6.15 ( (((!!) @ (^[Y0 : a]:
% 43.41/6.15 ((('#sk3' @ X6 @ Y0) => ('#sk628' @ X2 @ X4 @ X6 @ Y0))))))
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ X2 @ X4))),
% 43.41/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl129])).
% 43.41/6.15 thf(zip_derived_cl134, plain,
% 43.41/6.15 (![X2 : a, X4 : a, X6 : a, X8 : a]:
% 43.41/6.15 ( ((('#sk3' @ X6 @ X8) => ('#sk628' @ X2 @ X4 @ X6 @ X8)))
% 43.41/6.15 | ('#sk6' @ X2 @ X4)
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl132])).
% 43.41/6.15 thf(zip_derived_cl136, plain,
% 43.41/6.15 (![X2 : a, X4 : a, X6 : a, X8 : a]:
% 43.41/6.15 (~ ('#sk3' @ X6 @ X8)
% 43.41/6.15 | ('#sk628' @ X2 @ X4 @ X6 @ X8)
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ X2 @ X4))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl134])).
% 43.41/6.15 thf(zip_derived_cl369, plain,
% 43.41/6.15 (![X0 : a, X1 : a]:
% 43.41/6.15 ( ('#sk6' @ X1 @ X0)
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ X1 @ X0)
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ~ ('#sk3' @ X1 @ X0))),
% 43.41/6.15 inference('sup+', [status(thm)], [zip_derived_cl125, zip_derived_cl136])).
% 43.41/6.15 thf(zip_derived_cl372, plain,
% 43.41/6.15 (![X0 : a, X1 : a]:
% 43.41/6.15 (~ ('#sk3' @ X1 @ X0) | ~ ('#form15') | ('#sk6' @ X1 @ X0))),
% 43.41/6.15 inference('simplify', [status(thm)], [zip_derived_cl369])).
% 43.41/6.15 thf(zip_derived_cl401, plain,
% 43.41/6.15 (( ('#sk2' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6'))
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6'))
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl384, zip_derived_cl372])).
% 43.41/6.15 thf(zip_derived_cl403, plain,
% 43.41/6.15 (( ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6'))
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk2' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')))),
% 43.41/6.15 inference('simplify', [status(thm)], [zip_derived_cl401])).
% 43.41/6.15 thf(zip_derived_cl108, plain, (( ('#sk1' @ '#sk6') | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl104])).
% 43.41/6.15 thf(zip_derived_cl38, plain,
% 43.41/6.15 (![X2 : a > a > $o]:
% 43.41/6.15 (~ (X2 @ ('#sk41' @ X2) @ ('#sk61' @ X2))
% 43.41/6.15 | (X2 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X2))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 43.41/6.15 thf(zip_derived_cl307, plain,
% 43.41/6.15 ((~ ('#form15')
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ '#sk4' @ '#sk5')
% 43.41/6.15 | ~ ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl108, zip_derived_cl38])).
% 43.41/6.15 thf(zip_derived_cl314, plain,
% 43.41/6.15 ((~ ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6'))
% 43.41/6.15 | ('#sk6' @ '#sk4' @ '#sk5')
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('simplify', [status(thm)], [zip_derived_cl307])).
% 43.41/6.15 thf(zip_derived_cl105, plain,
% 43.41/6.15 ((~ ('#sk6' @ '#sk4' @ '#sk5') | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])).
% 43.41/6.15 thf(zip_derived_cl318, plain,
% 43.41/6.15 ((~ ('#form15') | ~ ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')))),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl314, zip_derived_cl105])).
% 43.41/6.15 thf(zip_derived_cl441, plain,
% 43.41/6.15 (( ('#sk2' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) | ~ ('#form15'))),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl403, zip_derived_cl318])).
% 43.41/6.15 thf(zip_derived_cl119, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 (~ (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk2' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ X2 @ X4))))))
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ X2 @ X4))),
% 43.41/6.15 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl116])).
% 43.41/6.15 thf(zip_derived_cl123, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 (~ ((((('#sk1' @ ('#sk629' @ X2 @ X4)) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk2' @ Y0 @ Y1) => ('#sk629' @
% 43.41/6.15 X2 @ X4 @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 ('#sk629' @ X2 @ X4 @ X2 @ X4)))
% 43.41/6.15 | ('#sk6' @ X2 @ X4)
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])).
% 43.41/6.15 thf(zip_derived_cl127, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 (~ ('#sk629' @ X2 @ X4 @ X2 @ X4)
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ X2 @ X4))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 43.41/6.15 thf(zip_derived_cl126, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 ( ((('#sk1' @ ('#sk629' @ X2 @ X4)) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk2' @ Y0 @ Y1) => ('#sk629' @ X2 @
% 43.41/6.15 X4 @ Y0 @ Y1)))))))))))
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ X2 @ X4))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 43.41/6.15 thf(zip_derived_cl131, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 ( (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk2' @ Y0 @ Y1) => ('#sk629' @ X2 @
% 43.41/6.15 X4 @ Y0 @ Y1)))))))))
% 43.41/6.15 | ('#sk6' @ X2 @ X4)
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])).
% 43.41/6.15 thf(zip_derived_cl133, plain,
% 43.41/6.15 (![X2 : a, X4 : a, X6 : a]:
% 43.41/6.15 ( (((!!) @ (^[Y0 : a]:
% 43.41/6.15 ((('#sk2' @ X6 @ Y0) => ('#sk629' @ X2 @ X4 @ X6 @ Y0))))))
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ X2 @ X4))),
% 43.41/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl131])).
% 43.41/6.15 thf(zip_derived_cl135, plain,
% 43.41/6.15 (![X2 : a, X4 : a, X6 : a, X8 : a]:
% 43.41/6.15 ( ((('#sk2' @ X6 @ X8) => ('#sk629' @ X2 @ X4 @ X6 @ X8)))
% 43.41/6.15 | ('#sk6' @ X2 @ X4)
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl133])).
% 43.41/6.15 thf(zip_derived_cl137, plain,
% 43.41/6.15 (![X2 : a, X4 : a, X6 : a, X8 : a]:
% 43.41/6.15 (~ ('#sk2' @ X6 @ X8)
% 43.41/6.15 | ('#sk629' @ X2 @ X4 @ X6 @ X8)
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ X2 @ X4))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl135])).
% 43.41/6.15 thf(zip_derived_cl377, plain,
% 43.41/6.15 (![X0 : a, X1 : a]:
% 43.41/6.15 ( ('#sk6' @ X1 @ X0)
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ('#sk6' @ X1 @ X0)
% 43.41/6.15 | ~ ('#form15')
% 43.41/6.15 | ~ ('#sk2' @ X1 @ X0))),
% 43.41/6.15 inference('sup+', [status(thm)], [zip_derived_cl127, zip_derived_cl137])).
% 43.41/6.15 thf(zip_derived_cl380, plain,
% 43.41/6.15 (![X0 : a, X1 : a]:
% 43.41/6.15 (~ ('#sk2' @ X1 @ X0) | ~ ('#form15') | ('#sk6' @ X1 @ X0))),
% 43.41/6.15 inference('simplify', [status(thm)], [zip_derived_cl377])).
% 43.41/6.15 thf(zip_derived_cl442, plain,
% 43.41/6.15 ((~ ('#form15')
% 43.41/6.15 | ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6'))
% 43.41/6.15 | ~ ('#form15'))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl441, zip_derived_cl380])).
% 43.41/6.15 thf(zip_derived_cl446, plain,
% 43.41/6.15 (( ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) | ~ ('#form15'))),
% 43.41/6.15 inference('simplify', [status(thm)], [zip_derived_cl442])).
% 43.41/6.15 thf(zip_derived_cl318, plain,
% 43.41/6.15 ((~ ('#form15') | ~ ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')))),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl314, zip_derived_cl105])).
% 43.41/6.15 thf(zip_derived_cl448, plain, (~ ('#form15')),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl446, zip_derived_cl318])).
% 43.41/6.15 thf(zip_derived_cl457, plain,
% 43.41/6.15 (~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl278, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl110, plain, (( ('#sk1' @ '#sk627') | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])).
% 43.41/6.15 thf(zip_derived_cl448, plain, (~ ('#form15')),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl446, zip_derived_cl318])).
% 43.41/6.15 thf(zip_derived_cl453, plain, ( ('#sk1' @ '#sk627')),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl110, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl35, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 ( (((((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk3' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))) |
% 43.41/6.15 (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk2' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))))))))
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X0))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 43.41/6.15 thf(zip_derived_cl39, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 ( (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk3' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))))))
% 43.41/6.15 | (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk2' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))))))
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5'))),
% 43.41/6.15 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl35])).
% 43.41/6.15 thf(zip_derived_cl41, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 ( ((((('#sk1' @ X2) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk3' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk2' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))))),
% 43.41/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl39])).
% 43.41/6.15 thf(zip_derived_cl47, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ ('#form156' @ X0)
% 43.41/6.15 | (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk2' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))))),
% 43.41/6.15 define([status(thm)])).
% 43.41/6.15 thf(zip_derived_cl48, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 ( ((((('#sk1' @ X2) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))
% 43.41/6.15 | ~ ('#form156' @ X0))),
% 43.41/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])).
% 43.41/6.15 thf(zip_derived_cl56, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 (~ ((('#sk1' @ X2) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1)))))))))))
% 43.41/6.15 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0))
% 43.41/6.15 | ~ ('#form156' @ X0))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])).
% 43.41/6.15 thf(zip_derived_cl58, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 (~ ('#sk1' @ X2)
% 43.41/6.15 | ~ (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1)))))))))
% 43.41/6.15 | ~ ('#form156' @ X0)
% 43.41/6.15 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl56])).
% 43.41/6.15 thf(zip_derived_cl60, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 (~ (((!!) @ (^[Y0 : a]:
% 43.41/6.15 ((('#sk2' @ ('#sk224' @ X2) @ Y0) => (X2 @
% 43.41/6.15 ('#sk224' @ X2) @ Y0))))))
% 43.41/6.15 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0))
% 43.41/6.15 | ~ ('#form156' @ X0)
% 43.41/6.15 | ~ ('#sk1' @ X2))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])).
% 43.41/6.15 thf(zip_derived_cl62, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 (~ ((('#sk2' @ ('#sk224' @ X2) @ ('#sk254' @ X2)) => (X2 @
% 43.41/6.15 ('#sk224' @ X2) @ ('#sk254' @ X2))))
% 43.41/6.15 | ~ ('#sk1' @ X2)
% 43.41/6.15 | ~ ('#form156' @ X0)
% 43.41/6.15 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])).
% 43.41/6.15 thf(zip_derived_cl66, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 (~ (X2 @ ('#sk224' @ X2) @ ('#sk254' @ X2))
% 43.41/6.15 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0))
% 43.41/6.15 | ~ ('#form156' @ X0)
% 43.41/6.15 | ~ ('#sk1' @ X2))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])).
% 43.41/6.15 thf(zip_derived_cl887, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ ('#form156' @ X0)
% 43.41/6.15 | ('#sk627' @ ('#sk36' @ X0) @ ('#sk51' @ X0))
% 43.41/6.15 | ~ ('#sk627' @ ('#sk224' @ '#sk627') @ ('#sk254' @ '#sk627')))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl453, zip_derived_cl66])).
% 43.41/6.15 thf(zip_derived_cl457, plain,
% 43.41/6.15 (~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl278, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl453, plain, ( ('#sk1' @ '#sk627')),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl110, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl65, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 ( ('#sk2' @ ('#sk224' @ X2) @ ('#sk254' @ X2))
% 43.41/6.15 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0))
% 43.41/6.15 | ~ ('#form156' @ X0)
% 43.41/6.15 | ~ ('#sk1' @ X2))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])).
% 43.41/6.15 thf(zip_derived_cl1031, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ ('#form156' @ X0)
% 43.41/6.15 | ('#sk627' @ ('#sk36' @ X0) @ ('#sk51' @ X0))
% 43.41/6.15 | ('#sk2' @ ('#sk224' @ '#sk627') @ ('#sk254' @ '#sk627')))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl453, zip_derived_cl65])).
% 43.41/6.15 thf(zip_derived_cl1070, plain,
% 43.41/6.15 (( ('#sk2' @ ('#sk224' @ '#sk627') @ ('#sk254' @ '#sk627'))
% 43.41/6.15 | ~ ('#form156' @ '#sk627'))),
% 43.41/6.15 inference('sup+', [status(thm)], [zip_derived_cl457, zip_derived_cl1031])).
% 43.41/6.15 thf(zip_derived_cl453, plain, ( ('#sk1' @ '#sk627')),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl110, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl110, plain, (( ('#sk1' @ '#sk627') | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])).
% 43.41/6.15 thf(zip_derived_cl41, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 ( ((((('#sk1' @ X2) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk3' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk2' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))))),
% 43.41/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl39])).
% 43.41/6.15 thf(zip_derived_cl47, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ ('#form156' @ X0)
% 43.41/6.15 | (((!!) @ (^[Y0 : a > a > $o]:
% 43.41/6.15 ((((('#sk1' @ Y0) &
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 (((!!) @ (^[Y2 : a]:
% 43.41/6.15 ((('#sk2' @ Y1 @ Y2) =>
% 43.41/6.15 (Y0 @ Y1 @ Y2))))))))))) =>
% 43.41/6.15 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))))),
% 43.41/6.15 define([status(thm)])).
% 43.41/6.15 thf(zip_derived_cl54, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 ( ('#form156' @ X0)
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ((((('#sk1' @ X2) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk3' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) =>
% 43.41/6.15 (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))))),
% 43.41/6.15 inference('renaming', [status(thm)], [zip_derived_cl41, zip_derived_cl47])).
% 43.41/6.15 thf(zip_derived_cl55, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 (~ ((('#sk1' @ X2) &
% 43.41/6.15 (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk3' @ Y0 @ Y1) => (X2 @ Y0 @ Y1)))))))))))
% 43.41/6.15 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0))
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form156' @ X0))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])).
% 43.41/6.15 thf(zip_derived_cl57, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 (~ ('#sk1' @ X2)
% 43.41/6.15 | ~ (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((('#sk3' @ Y0 @ Y1) => (X2 @ Y0 @ Y1)))))))))
% 43.41/6.15 | ('#form156' @ X0)
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])).
% 43.41/6.15 thf(zip_derived_cl59, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 (~ (((!!) @ (^[Y0 : a]:
% 43.41/6.15 ((('#sk3' @ ('#sk213' @ X2) @ Y0) => (X2 @
% 43.41/6.15 ('#sk213' @ X2) @ Y0))))))
% 43.41/6.15 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0))
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form156' @ X0)
% 43.41/6.15 | ~ ('#sk1' @ X2))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl57])).
% 43.41/6.15 thf(zip_derived_cl61, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 (~ ((('#sk3' @ ('#sk213' @ X2) @ ('#sk240' @ X2)) => (X2 @
% 43.41/6.15 ('#sk213' @ X2) @ ('#sk240' @ X2))))
% 43.41/6.15 | ~ ('#sk1' @ X2)
% 43.41/6.15 | ('#form156' @ X0)
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))),
% 43.41/6.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl59])).
% 43.41/6.15 thf(zip_derived_cl64, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 (~ (X2 @ ('#sk213' @ X2) @ ('#sk240' @ X2))
% 43.41/6.15 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0))
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form156' @ X0)
% 43.41/6.15 | ~ ('#sk1' @ X2))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])).
% 43.41/6.15 thf(zip_derived_cl243, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 ( ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form156' @ '#sk627')
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | ('#sk627' @ '#sk4' @ '#sk5')
% 43.41/6.15 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))
% 43.41/6.15 | ~ (X0 @ ('#sk213' @ X0) @ ('#sk240' @ X0)))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl64])).
% 43.41/6.15 thf(zip_derived_cl250, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ (X0 @ ('#sk213' @ X0) @ ('#sk240' @ X0))
% 43.41/6.15 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))
% 43.41/6.15 | ('#sk627' @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form156' @ '#sk627')
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form15'))),
% 43.41/6.15 inference('simplify', [status(thm)], [zip_derived_cl243])).
% 43.41/6.15 thf(zip_derived_cl448, plain, (~ ('#form15')),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl446, zip_derived_cl318])).
% 43.41/6.15 thf(zip_derived_cl606, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ (X0 @ ('#sk213' @ X0) @ ('#sk240' @ X0))
% 43.41/6.15 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))
% 43.41/6.15 | ('#sk627' @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form156' @ '#sk627')
% 43.41/6.15 | ~ ('#sk1' @ X0))),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl250, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl107, plain,
% 43.41/6.15 ((~ ('#sk627' @ '#sk4' @ '#sk5') | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])).
% 43.41/6.15 thf(zip_derived_cl448, plain, (~ ('#form15')),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl446, zip_derived_cl318])).
% 43.41/6.15 thf(zip_derived_cl452, plain, (~ ('#sk627' @ '#sk4' @ '#sk5')),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl607, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form156' @ '#sk627')
% 43.41/6.15 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))
% 43.41/6.15 | ~ (X0 @ ('#sk213' @ X0) @ ('#sk240' @ X0)))),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl606, zip_derived_cl452])).
% 43.41/6.15 thf(zip_derived_cl608, plain,
% 43.41/6.15 ((~ ('#sk627' @ ('#sk213' @ '#sk627') @ ('#sk240' @ '#sk627'))
% 43.41/6.15 | ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))
% 43.41/6.15 | ('#form156' @ '#sk627'))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl453, zip_derived_cl607])).
% 43.41/6.15 thf(zip_derived_cl453, plain, ( ('#sk1' @ '#sk627')),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl110, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl110, plain, (( ('#sk1' @ '#sk627') | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])).
% 43.41/6.15 thf(zip_derived_cl63, plain,
% 43.41/6.15 (![X0 : a > a > $o, X2 : a > a > $o]:
% 43.41/6.15 ( ('#sk3' @ ('#sk213' @ X2) @ ('#sk240' @ X2))
% 43.41/6.15 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0))
% 43.41/6.15 | (X0 @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form156' @ X0)
% 43.41/6.15 | ~ ('#sk1' @ X2))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])).
% 43.41/6.15 thf(zip_derived_cl244, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 ( ('#form15')
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form156' @ '#sk627')
% 43.41/6.15 | ('#form15')
% 43.41/6.15 | ('#sk627' @ '#sk4' @ '#sk5')
% 43.41/6.15 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))
% 43.41/6.15 | ('#sk3' @ ('#sk213' @ X0) @ ('#sk240' @ X0)))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl63])).
% 43.41/6.15 thf(zip_derived_cl251, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 ( ('#sk3' @ ('#sk213' @ X0) @ ('#sk240' @ X0))
% 43.41/6.15 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))
% 43.41/6.15 | ('#sk627' @ '#sk4' @ '#sk5')
% 43.41/6.15 | ('#form156' @ '#sk627')
% 43.41/6.15 | ~ ('#sk1' @ X0)
% 43.41/6.15 | ('#form15'))),
% 43.41/6.15 inference('simplify', [status(thm)], [zip_derived_cl244])).
% 43.41/6.15 thf(zip_derived_cl452, plain, (~ ('#sk627' @ '#sk4' @ '#sk5')),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl448, plain, (~ ('#form15')),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl446, zip_derived_cl318])).
% 43.41/6.15 thf(zip_derived_cl535, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 ( ('#sk3' @ ('#sk213' @ X0) @ ('#sk240' @ X0))
% 43.41/6.15 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))
% 43.41/6.15 | ('#form156' @ '#sk627')
% 43.41/6.15 | ~ ('#sk1' @ X0))),
% 43.41/6.15 inference('demod', [status(thm)],
% 43.41/6.15 [zip_derived_cl251, zip_derived_cl452, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl536, plain,
% 43.41/6.15 (( ('#form156' @ '#sk627')
% 43.41/6.15 | ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))
% 43.41/6.15 | ('#sk3' @ ('#sk213' @ '#sk627') @ ('#sk240' @ '#sk627')))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl453, zip_derived_cl535])).
% 43.41/6.15 thf(zip_derived_cl457, plain,
% 43.41/6.15 (~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl278, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl538, plain,
% 43.41/6.15 (( ('#sk3' @ ('#sk213' @ '#sk627') @ ('#sk240' @ '#sk627'))
% 43.41/6.15 | ('#form156' @ '#sk627'))),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl536, zip_derived_cl457])).
% 43.41/6.15 thf(zip_derived_cl111, plain,
% 43.41/6.15 (( (((!!) @ (^[Y0 : a]:
% 43.41/6.15 (((!!) @ (^[Y1 : a]:
% 43.41/6.15 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) =>
% 43.41/6.15 ('#sk627' @ Y0 @ Y1)))))))))
% 43.41/6.15 | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])).
% 43.41/6.15 thf(zip_derived_cl113, plain,
% 43.41/6.15 (![X2 : a]:
% 43.41/6.15 ( (((!!) @ (^[Y0 : a]:
% 43.41/6.15 ((((('#sk3' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) =>
% 43.41/6.15 ('#sk627' @ X2 @ Y0))))))
% 43.41/6.15 | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl111])).
% 43.41/6.15 thf(zip_derived_cl115, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 ( ((((('#sk3' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk627' @ X2 @
% 43.41/6.15 X4)))
% 43.41/6.15 | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl113])).
% 43.41/6.15 thf(zip_derived_cl117, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 (~ ((('#sk3' @ X2 @ X4) | ('#sk2' @ X2 @ X4)))
% 43.41/6.15 | ('#sk627' @ X2 @ X4)
% 43.41/6.15 | ('#form15'))),
% 43.41/6.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl115])).
% 43.41/6.15 thf(zip_derived_cl120, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 (~ ('#sk3' @ X2 @ X4) | ('#form15') | ('#sk627' @ X2 @ X4))),
% 43.41/6.15 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl117])).
% 43.41/6.15 thf(zip_derived_cl448, plain, (~ ('#form15')),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl446, zip_derived_cl318])).
% 43.41/6.15 thf(zip_derived_cl454, plain,
% 43.41/6.15 (![X2 : a, X4 : a]: (~ ('#sk3' @ X2 @ X4) | ('#sk627' @ X2 @ X4))),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl120, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl539, plain,
% 43.41/6.15 (( ('#form156' @ '#sk627')
% 43.41/6.15 | ('#sk627' @ ('#sk213' @ '#sk627') @ ('#sk240' @ '#sk627')))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl538, zip_derived_cl454])).
% 43.41/6.15 thf(zip_derived_cl610, plain,
% 43.41/6.15 (( ('#form156' @ '#sk627')
% 43.41/6.15 | ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')))),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl608, zip_derived_cl539])).
% 43.41/6.15 thf(zip_derived_cl457, plain,
% 43.41/6.15 (~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl278, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl611, plain, ( ('#form156' @ '#sk627')),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl610, zip_derived_cl457])).
% 43.41/6.15 thf(zip_derived_cl1074, plain,
% 43.41/6.15 ( ('#sk2' @ ('#sk224' @ '#sk627') @ ('#sk254' @ '#sk627'))),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl1070, zip_derived_cl611])).
% 43.41/6.15 thf(zip_derived_cl121, plain,
% 43.41/6.15 (![X2 : a, X4 : a]:
% 43.41/6.15 (~ ('#sk2' @ X2 @ X4) | ('#form15') | ('#sk627' @ X2 @ X4))),
% 43.41/6.15 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl117])).
% 43.41/6.15 thf(zip_derived_cl448, plain, (~ ('#form15')),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl446, zip_derived_cl318])).
% 43.41/6.15 thf(zip_derived_cl455, plain,
% 43.41/6.15 (![X2 : a, X4 : a]: (~ ('#sk2' @ X2 @ X4) | ('#sk627' @ X2 @ X4))),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl121, zip_derived_cl448])).
% 43.41/6.15 thf(zip_derived_cl1078, plain,
% 43.41/6.15 ( ('#sk627' @ ('#sk224' @ '#sk627') @ ('#sk254' @ '#sk627'))),
% 43.41/6.15 inference('sup-', [status(thm)], [zip_derived_cl1074, zip_derived_cl455])).
% 43.41/6.15 thf(zip_derived_cl1080, plain,
% 43.41/6.15 (![X0 : a > a > $o]:
% 43.41/6.15 (~ ('#form156' @ X0) | ('#sk627' @ ('#sk36' @ X0) @ ('#sk51' @ X0)))),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl887, zip_derived_cl1078])).
% 43.41/6.15 thf(zip_derived_cl1113, plain, (~ ('#form156' @ '#sk627')),
% 43.41/6.15 inference('sup+', [status(thm)], [zip_derived_cl457, zip_derived_cl1080])).
% 43.41/6.15 thf(zip_derived_cl611, plain, ( ('#form156' @ '#sk627')),
% 43.41/6.15 inference('clc', [status(thm)], [zip_derived_cl610, zip_derived_cl457])).
% 43.41/6.15 thf(zip_derived_cl1116, plain, ($false),
% 43.41/6.15 inference('demod', [status(thm)], [zip_derived_cl1113, zip_derived_cl611])).
% 43.41/6.15
% 43.41/6.15 % SZS output end Refutation
% 43.41/6.15
% 43.41/6.15
% 43.41/6.15 % Terminating...
% 44.91/6.27 % Runner terminated.
% 44.91/6.30 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------