%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV303^5 : TPTP v9.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WbLxnK2PIJ true
% Computer : n006.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 04:57:32 PM UTC 2025
% Result : Theorem 34.60s 6.70s
% Output : Refutation 34.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV303^5 : TPTP v9.2.0. Bugfixed v6.2.0.
% 0.09/0.10 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WbLxnK2PIJ true
% 0.09/0.32 % Computer : n006.cluster.edu
% 0.09/0.32 % Model : x86_64 x86_64
% 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32 % Memory : 8042.1875MB
% 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 300
% 0.09/0.32 % DateTime : Wed Oct 1 15:39:23 EDT 2025
% 0.09/0.32 % CPUTime :
% 0.09/0.32 % Running portfolio for 300 s
% 0.09/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.32 % Number of cores: 8
% 0.09/0.32 % Python version: Python 3.6.8
% 0.09/0.33 % Running in HO mode
% 0.44/0.62 % Total configuration time : 828
% 0.44/0.62 % Estimated wc time : 1656
% 0.44/0.62 % Estimated cpu time (8 cpus) : 207.0
% 0.44/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.44/0.80 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.44/0.80 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.44/0.82 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.44/0.83 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.44/0.83 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.44/0.85 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.44/0.85 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 34.60/6.70 % Solved by lams/40_b.comb.sh.
% 34.60/6.70 % done 210 iterations in 5.727s
% 34.60/6.70 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 34.60/6.70 % SZS output start Refutation
% 34.60/6.70 thf('#sk1_type', type, '#sk1': (($i > $o) > $o) > $o).
% 34.60/6.70 thf(cNAT_type, type, cNAT: (($i > $o) > $o) > $o).
% 34.60/6.70 thf('#sk2_type', type, '#sk2': ($i > $o) > $o).
% 34.60/6.70 thf(cZERO_type, type, cZERO: ($i > $o) > $o).
% 34.60/6.70 thf('#sk5_type', type, '#sk5': ((($i > $o) > $o) > $o) > ($i > $o) > $o).
% 34.60/6.70 thf(cSUCC_type, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 34.60/6.70 thf('#sk3_type', type, '#sk3': (($i > $o) > $o) > (($i > $o) > $o) > $o).
% 34.60/6.70 thf('#sk4_type', type, '#sk4': ($i > $o) > $o).
% 34.60/6.70 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 34.60/6.70 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 34.60/6.70 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 34.60/6.70 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 34.60/6.70 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 34.60/6.70 thf(cX6102_C, conjecture,
% 34.60/6.70 (![Xp:( ( ( $i > $o ) > $o ) > $o )]:
% 34.60/6.70 ( ( ( ![Xx:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( cNAT @ Xx ) => ( ( Xp @ Xx ) => ( Xp @ ( cSUCC @ Xx ) ) ) ) ) &
% 34.60/6.70 ( Xp @ cZERO ) ) =>
% 34.60/6.70 ( ![Xm:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( ( ( ![Xx:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( ( Xp @ Xx ) &
% 34.60/6.70 ( ![Xp0:( ( ( $i > $o ) > $o ) > $o )]:
% 34.60/6.70 ( ( ( ![Xx0:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( Xp0 @ Xx0 ) => ( Xp0 @ ( cSUCC @ Xx0 ) ) ) ) &
% 34.60/6.70 ( Xp0 @ cZERO ) ) =>
% 34.60/6.70 ( Xp0 @ Xx ) ) ) ) =>
% 34.60/6.70 ( ( Xp @ ( cSUCC @ Xx ) ) &
% 34.60/6.70 ( ![Xp0:( ( ( $i > $o ) > $o ) > $o )]:
% 34.60/6.70 ( ( ( ![Xx0:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( Xp0 @ Xx0 ) => ( Xp0 @ ( cSUCC @ Xx0 ) ) ) ) &
% 34.60/6.70 ( Xp0 @ cZERO ) ) =>
% 34.60/6.70 ( Xp0 @ ( cSUCC @ Xx ) ) ) ) ) ) ) &
% 34.60/6.70 ( Xp @ cZERO ) &
% 34.60/6.70 ( ![Xp0:( ( ( $i > $o ) > $o ) > $o )]:
% 34.60/6.70 ( ( ( ![Xx:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( Xp0 @ Xx ) => ( Xp0 @ ( cSUCC @ Xx ) ) ) ) &
% 34.60/6.70 ( Xp0 @ cZERO ) ) =>
% 34.60/6.70 ( Xp0 @ cZERO ) ) ) ) =>
% 34.60/6.70 ( ( Xp @ Xm ) & ( cNAT @ Xm ) ) ) =>
% 34.60/6.70 ( Xp @ Xm ) ) ) ))).
% 34.60/6.70 thf(zf_stmt_0, negated_conjecture,
% 34.60/6.70 (~( ![Xp:( ( ( $i > $o ) > $o ) > $o )]:
% 34.60/6.70 ( ( ( ![Xx:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( cNAT @ Xx ) => ( ( Xp @ Xx ) => ( Xp @ ( cSUCC @ Xx ) ) ) ) ) &
% 34.60/6.70 ( Xp @ cZERO ) ) =>
% 34.60/6.70 ( ![Xm:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( ( ( ![Xx:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( ( Xp @ Xx ) &
% 34.60/6.70 ( ![Xp0:( ( ( $i > $o ) > $o ) > $o )]:
% 34.60/6.70 ( ( ( ![Xx0:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( Xp0 @ Xx0 ) => ( Xp0 @ ( cSUCC @ Xx0 ) ) ) ) &
% 34.60/6.70 ( Xp0 @ cZERO ) ) =>
% 34.60/6.70 ( Xp0 @ Xx ) ) ) ) =>
% 34.60/6.70 ( ( Xp @ ( cSUCC @ Xx ) ) &
% 34.60/6.70 ( ![Xp0:( ( ( $i > $o ) > $o ) > $o )]:
% 34.60/6.70 ( ( ( ![Xx0:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( Xp0 @ Xx0 ) => ( Xp0 @ ( cSUCC @ Xx0 ) ) ) ) &
% 34.60/6.70 ( Xp0 @ cZERO ) ) =>
% 34.60/6.70 ( Xp0 @ ( cSUCC @ Xx ) ) ) ) ) ) ) &
% 34.60/6.70 ( Xp @ cZERO ) &
% 34.60/6.70 ( ![Xp0:( ( ( $i > $o ) > $o ) > $o )]:
% 34.60/6.70 ( ( ( ![Xx:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( Xp0 @ Xx ) => ( Xp0 @ ( cSUCC @ Xx ) ) ) ) &
% 34.60/6.70 ( Xp0 @ cZERO ) ) =>
% 34.60/6.70 ( Xp0 @ cZERO ) ) ) ) =>
% 34.60/6.70 ( ( Xp @ Xm ) & ( cNAT @ Xm ) ) ) =>
% 34.60/6.70 ( Xp @ Xm ) ) ) ) )),
% 34.60/6.70 inference('cnf.neg', [status(esa)], [cX6102_C])).
% 34.60/6.70 thf(zip_derived_cl0, plain,
% 34.60/6.70 (~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]:
% 34.60/6.70 (((((((!!) @ (^[Y1 : ($i > $o) > $o]:
% 34.60/6.70 (((cNAT @ Y1) =>
% 34.60/6.70 (((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))))) &
% 34.60/6.70 (Y0 @ cZERO))) =>
% 34.60/6.70 (((!!) @ (^[Y1 : ($i > $o) > $o]:
% 34.60/6.70 (((((((((!!) @ (^[Y2 : ($i > $o) > $o]:
% 34.60/6.70 (((((Y0 @ Y2) &
% 34.60/6.70 (((!!) @ (^[Y3 : (
% 34.60/6.70 ($i > $o) > $o) > $o]:
% 34.60/6.70 ((
% 34.60/6.70 ((
% 34.60/6.70 ((
% 34.60/6.70 (!!) @ (
% 34.60/6.70 ^[Y4 : (
% 34.60/6.70 $i > $o) > $o]:
% 34.60/6.70 ((
% 34.60/6.70 (Y3 @
% 34.60/6.70 Y4) =>
% 34.60/6.70 (Y3 @
% 34.60/6.70 (
% 34.60/6.70 cSUCC @
% 34.60/6.70 Y4))))))) &
% 34.60/6.70 (Y3 @
% 34.60/6.70 cZERO))) =>
% 34.60/6.70 (Y3 @ Y2)))))))) =>
% 34.60/6.70 (((Y0 @ (cSUCC @ Y2)) &
% 34.60/6.70 (((!!) @ (^[Y3 : (
% 34.60/6.70 ($i > $o) > $o) > $o]:
% 34.60/6.70 ((
% 34.60/6.70 ((
% 34.60/6.70 ((
% 34.60/6.70 (!!) @ (
% 34.60/6.70 ^[Y4 : (
% 34.60/6.70 $i > $o) > $o]:
% 34.60/6.70 ((
% 34.60/6.70 (Y3 @
% 34.60/6.70 Y4) =>
% 34.60/6.70 (Y3 @
% 34.60/6.70 (
% 34.60/6.70 cSUCC @
% 34.60/6.70 Y4))))))) &
% 34.60/6.70 (Y3 @
% 34.60/6.70 cZERO))) =>
% 34.60/6.70 (Y3 @
% 34.60/6.70 (
% 34.60/6.70 cSUCC @
% 34.60/6.70 Y2)))))))))))))) &
% 34.60/6.70 (Y0 @ cZERO) &
% 34.60/6.70 (((!!) @ (^[Y2 : (($i > $o) > $o) > $o]:
% 34.60/6.70 (((((((!!) @ (^[Y3 : (
% 34.60/6.70 $i > $o) > $o]:
% 34.60/6.70 ((
% 34.60/6.70 (Y2 @
% 34.60/6.70 Y3) =>
% 34.60/6.70 (Y2 @
% 34.60/6.70 (
% 34.60/6.70 cSUCC @
% 34.60/6.70 Y3))))))) &
% 34.60/6.70 (Y2 @ cZERO))) =>
% 34.60/6.70 (Y2 @ cZERO)))))))) =>
% 34.60/6.70 (((Y0 @ Y1) & (cNAT @ Y1))))) =>
% 34.60/6.70 (Y0 @ Y1)))))))))))),
% 34.60/6.70 inference('cnf', [status(esa)], [zf_stmt_0])).
% 34.60/6.70 thf(zip_derived_cl1, plain,
% 34.60/6.70 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#B') @ ((('#S') @ ((('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 cNAT)))) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ ('#S') @
% 34.60/6.70 ((('#B') @ ((('#B') @ (=>))) @
% 34.60/6.70 ((('#S') @ ((('#B') @ ('#B') @
% 34.60/6.70 ((('#B') @ (=>) @
% 34.60/6.70 ((('#C') @ ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 &))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I'))))))))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 &))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I'))) @
% 34.60/6.70 cSUCC)))))))))))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))) @
% 34.60/6.70 (((!!) @ ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))))))))))) @
% 34.60/6.70 ((('#C') @ ((('#B') @ ('#S') @
% 34.60/6.70 ((('#B') @ (&))))) @
% 34.60/6.70 cNAT)))))))) @
% 34.60/6.70 ('#I')))))))))),
% 34.60/6.70 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 34.60/6.70 thf(zip_derived_cl2, plain,
% 34.60/6.70 (~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ cNAT)) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (=>) @ '#sk1')) @
% 34.60/6.70 ((('#B') @ '#sk1' @ cSUCC)))))))) &
% 34.60/6.70 ('#sk1' @ cZERO))) =>
% 34.60/6.70 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#B') @ (((=>) @ (((((!!) @ ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 '#sk1')) @
% 34.60/6.70 ((
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I'))))))))))) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((
% 34.60/6.70 ('#B') @ '#sk1' @
% 34.60/6.70 cSUCC)))) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I'))) @
% 34.60/6.70 cSUCC)))))))))))) &
% 34.60/6.70 ('#sk1' @ cZERO) &
% 34.60/6.70 (((!!) @ ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 ((
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))))))))) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @ cNAT)))))) @
% 34.60/6.70 '#sk1'))))))),
% 34.60/6.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])).
% 34.60/6.70 thf(zip_derived_cl4, plain,
% 34.60/6.70 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#B') @ (((=>) @ (((((!!) @ ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 &) @ '#sk1')) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 ((
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I'))))))))))) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((('#B') @ '#sk1' @
% 34.60/6.70 cSUCC)))) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#I'))) @
% 34.60/6.70 cSUCC)))))))))))) &
% 34.60/6.70 ('#sk1' @ cZERO) &
% 34.60/6.70 (((!!) @ ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#I') @ cZERO)))))))))) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @ cNAT)))))) @
% 34.60/6.70 '#sk1'))))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])).
% 34.60/6.70 thf(zip_derived_cl7, plain,
% 34.60/6.70 (~ (((((((((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#B') @ ((('#S') @ ((('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#I') @
% 34.60/6.70 cZERO)))))))) @
% 34.60/6.70 ((('#C') @ ('#I'))))))))))) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ '#sk1' @ cSUCC)))) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 ((
% 34.60/6.70 ('#S') @ (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @
% 34.60/6.70 cZERO)))))))) @
% 34.60/6.70 ((('#B') @ ((('#C') @ ('#I'))) @ cSUCC)))))))))))) &
% 34.60/6.70 ('#sk1' @ cZERO) &
% 34.60/6.70 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))))) =>
% 34.60/6.70 ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))) =>
% 34.60/6.70 ('#sk1' @ '#sk2')))),
% 34.60/6.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])).
% 34.60/6.70 thf(zip_derived_cl9, plain,
% 34.60/6.70 ( (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#B') @ ((('#S') @ ((('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 ((
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#I') @ cZERO)))))))) @
% 34.60/6.70 ((('#C') @ ('#I'))))))))))) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @ ((('#B') @ '#sk1' @ cSUCC)))) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))))) @
% 34.60/6.70 ((('#B') @ ((('#C') @ ('#I'))) @ cSUCC)))))))))))) &
% 34.60/6.70 ('#sk1' @ cZERO) &
% 34.60/6.70 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))))) =>
% 34.60/6.70 ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 34.60/6.70 thf(zip_derived_cl12, plain,
% 34.60/6.70 ((~ (((((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#B') @ ((('#S') @ ((('#B') @ (
% 34.60/6.70 =>) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 (
% 34.60/6.70 (
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 ((
% 34.60/6.70 ('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#I') @ cZERO)))))))) @
% 34.60/6.70 ((('#C') @ ('#I'))))))))))) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @ ((('#B') @ '#sk1' @ cSUCC)))) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((
% 34.60/6.70 ('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))))) @
% 34.60/6.70 ((('#B') @ ((('#C') @ ('#I'))) @ cSUCC)))))))))))) &
% 34.60/6.70 ('#sk1' @ cZERO) &
% 34.60/6.70 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))))
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])).
% 34.60/6.70 thf(zip_derived_cl14, plain,
% 34.60/6.70 ((~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#I') @ cZERO)))))))) @
% 34.60/6.70 ((('#C') @ ('#I'))))))))))) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @ ((('#B') @ '#sk1' @ cSUCC)))) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 &) @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 !!) @
% 34.60/6.70 ((('#S') @ (
% 34.60/6.70 (('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (
% 34.60/6.70 =>))))) @
% 34.60/6.70 ((('#C') @ (
% 34.60/6.70 '#B') @
% 34.60/6.70 cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))))) @
% 34.60/6.70 ((('#B') @ ((('#C') @ ('#I'))) @ cSUCC))))))))))))
% 34.60/6.70 | ~ ('#sk1' @ cZERO)
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 34.60/6.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])).
% 34.60/6.70 thf(zip_derived_cl17, plain,
% 34.60/6.70 ((~ ((((('#sk1' @ '#sk4') &
% 34.60/6.70 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ '#sk4')))))))) =>
% 34.60/6.70 ((('#sk1' @ (cSUCC @ '#sk4')) &
% 34.60/6.70 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ (cSUCC @ '#sk4')))))))))))
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.70 | ~ ('#sk1' @ cZERO))),
% 34.60/6.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])).
% 34.60/6.70 thf(zip_derived_cl20, plain,
% 34.60/6.70 (( ((('#sk1' @ '#sk4') &
% 34.60/6.70 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ '#sk4'))))))))
% 34.60/6.70 | ~ ('#sk1' @ cZERO)
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])).
% 34.60/6.70 thf(zip_derived_cl26, plain,
% 34.60/6.70 (( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ ('#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ '#sk4'))))))
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.70 | ~ ('#sk1' @ cZERO))),
% 34.60/6.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl20])).
% 34.60/6.70 thf(zip_derived_cl32, plain,
% 34.60/6.70 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.70 ( (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ X2)) @
% 34.60/6.70 ((('#B') @ X2 @ cSUCC)))))) &
% 34.60/6.70 (X2 @ cZERO))) =>
% 34.60/6.70 (X2 @ '#sk4')))
% 34.60/6.70 | ~ ('#sk1' @ cZERO)
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 34.60/6.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])).
% 34.60/6.70 thf(zip_derived_cl37, plain,
% 34.60/6.70 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.70 (~ (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ X2)) @
% 34.60/6.70 ((('#B') @ X2 @ cSUCC)))))) &
% 34.60/6.70 (X2 @ cZERO)))
% 34.60/6.70 | (X2 @ '#sk4')
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.70 | ~ ('#sk1' @ cZERO))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl32])).
% 34.60/6.70 thf(zip_derived_cl44, plain,
% 34.60/6.70 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.70 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ X2)) @
% 34.60/6.70 ((('#B') @ X2 @ cSUCC))))))
% 34.60/6.70 | ~ (X2 @ cZERO)
% 34.60/6.70 | ~ ('#sk1' @ cZERO)
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.70 | (X2 @ '#sk4'))),
% 34.60/6.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl37])).
% 34.60/6.70 thf(zip_derived_cl50, plain,
% 34.60/6.70 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.70 (~ (((X2 @ ('#sk5' @ X2)) => (X2 @ (cSUCC @ ('#sk5' @ X2)))))
% 34.60/6.70 | (X2 @ '#sk4')
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.70 | ~ ('#sk1' @ cZERO)
% 34.60/6.70 | ~ (X2 @ cZERO))),
% 34.60/6.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl44])).
% 34.60/6.70 thf(zip_derived_cl56, plain,
% 34.60/6.70 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.70 ( (X2 @ ('#sk5' @ X2))
% 34.60/6.70 | ~ (X2 @ cZERO)
% 34.60/6.70 | ~ ('#sk1' @ cZERO)
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.70 | (X2 @ '#sk4'))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])).
% 34.60/6.70 thf(zip_derived_cl66, plain,
% 34.60/6.70 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.70 (~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ cZERO))) @
% 34.60/6.70 ((('#B') @ ('#sk3' @ cZERO) @ cSUCC)))))) &
% 34.60/6.70 ('#sk3' @ cZERO @ cZERO))) =>
% 34.60/6.70 ('#sk3' @ cZERO @ cZERO)))
% 34.60/6.70 | (X2 @ '#sk4')
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.70 | ~ ('#sk1' @ cZERO)
% 34.60/6.70 | ~ (X2 @ cZERO)
% 34.60/6.70 | (X2 @ ('#sk5' @ X2)))),
% 34.60/6.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl56])).
% 34.60/6.70 thf(zip_derived_cl73, plain,
% 34.60/6.70 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.70 ( (X2 @ '#sk4')
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.70 | ~ ('#sk1' @ cZERO)
% 34.60/6.70 | ~ (X2 @ cZERO)
% 34.60/6.70 | (X2 @ ('#sk5' @ X2)))),
% 34.60/6.70 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl66])).
% 34.60/6.70 thf(zip_derived_cl74, plain,
% 34.60/6.70 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.70 ( ('#sk1' @ '#sk2')
% 34.60/6.70 | (X2 @ ('#sk5' @ X2))
% 34.60/6.70 | ~ (X2 @ cZERO)
% 34.60/6.70 | ~ ('#sk1' @ cZERO)
% 34.60/6.70 | (X2 @ '#sk4'))),
% 34.60/6.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl73])).
% 34.60/6.70 thf(zip_derived_cl10, plain, (~ ('#sk1' @ '#sk2')),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 34.60/6.70 thf(zip_derived_cl3, plain,
% 34.60/6.70 ( (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ cNAT)) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (=>) @ '#sk1')) @
% 34.60/6.70 ((('#B') @ '#sk1' @ cSUCC)))))))) &
% 34.60/6.70 ('#sk1' @ cZERO)))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])).
% 34.60/6.70 thf(zip_derived_cl6, plain, ( ('#sk1' @ cZERO)),
% 34.60/6.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 34.60/6.70 thf(zip_derived_cl128, plain,
% 34.60/6.70 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.70 ( (X2 @ ('#sk5' @ X2)) | ~ (X2 @ cZERO) | (X2 @ '#sk4'))),
% 34.60/6.70 inference('demod', [status(thm)],
% 34.60/6.70 [zip_derived_cl74, zip_derived_cl10, zip_derived_cl6])).
% 34.60/6.70 thf(zip_derived_cl5, plain,
% 34.60/6.70 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ cNAT)) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (=>) @ '#sk1')) @
% 34.60/6.70 ((('#B') @ '#sk1' @ cSUCC))))))))),
% 34.60/6.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 34.60/6.70 thf(zip_derived_cl8, plain,
% 34.60/6.70 (![X2 : ($i > $o) > $o]:
% 34.60/6.70 (((cNAT @ X2) => ((('#sk1' @ X2) => ('#sk1' @ (cSUCC @ X2))))))),
% 34.60/6.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])).
% 34.60/6.70 thf(zip_derived_cl11, plain,
% 34.60/6.70 (![X2 : ($i > $o) > $o]:
% 34.60/6.70 (~ (cNAT @ X2) | ((('#sk1' @ X2) => ('#sk1' @ (cSUCC @ X2)))))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])).
% 34.60/6.70 thf(cNAT_def, axiom, ~ (cNAT @ X0) =>
% 34.60/6.70 ((((!!) @ (^[Y0 : (($i > $o) > $o) > $o]:
% 34.60/6.70 (((((((!!) @ (^[Y1 : ($i > $o) > $o]:
% 34.60/6.70 (((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) &
% 34.60/6.70 (Y0 @ cZERO))) =>
% 34.60/6.70 (Y0 @ X0))))))
% 34.60/6.70 != ($true))).
% 34.60/6.70 thf('0', plain,
% 34.60/6.70 (![X0:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( ~( cNAT @ X0 ) ) <=>
% 34.60/6.70 ( ~( ![X5:( ( ( $i > $o ) > $o ) > $o )]:
% 34.60/6.70 ( ( ( ![X7:( ( $i > $o ) > $o )]:
% 34.60/6.70 ( ( X5 @ X7 ) => ( X5 @ ( cSUCC @ X7 ) ) ) ) &
% 34.60/6.70 ( X5 @ cZERO ) ) =>
% 34.60/6.70 ( X5 @ X0 ) ) ) ) )),
% 34.60/6.70 inference('rw.lit', [status(esa)], [cNAT_def])).
% 34.60/6.70 thf(zip_derived_cl13, plain,
% 34.60/6.70 (![X0 : ($i > $o) > $o]:
% 34.60/6.70 (~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]:
% 34.60/6.70 (((((((!!) @ (^[Y1 : ($i > $o) > $o]:
% 34.60/6.70 (((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) &
% 34.60/6.70 (Y0 @ cZERO))) =>
% 34.60/6.70 (Y0 @ X0))))))
% 34.60/6.70 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 34.60/6.70 inference('rw_clause', [status(thm)], [zip_derived_cl11, '0'])).
% 34.60/6.70 thf(zip_derived_cl15, plain,
% 34.60/6.70 (![X0 : ($i > $o) > $o]:
% 34.60/6.70 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ X0))))))
% 34.60/6.70 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 34.60/6.70 inference('comb-normalize', [status(thm)], [zip_derived_cl13])).
% 34.60/6.70 thf(zip_derived_cl16, plain,
% 34.60/6.70 (![X0 : ($i > $o) > $o]:
% 34.60/6.70 (~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ X0))) @
% 34.60/6.70 ((('#B') @ ('#sk3' @ X0) @ cSUCC)))))) &
% 34.60/6.70 ('#sk3' @ X0 @ cZERO))) =>
% 34.60/6.70 ('#sk3' @ X0 @ X0)))
% 34.60/6.70 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 34.60/6.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])).
% 34.60/6.70 thf(zip_derived_cl18, plain,
% 34.60/6.70 (![X0 : ($i > $o) > $o]:
% 34.60/6.70 ( (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ X0))) @
% 34.60/6.70 ((('#B') @ ('#sk3' @ X0) @ cSUCC)))))) &
% 34.60/6.70 ('#sk3' @ X0 @ cZERO)))
% 34.60/6.70 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])).
% 34.60/6.70 thf(zip_derived_cl22, plain,
% 34.60/6.70 (![X0 : ($i > $o) > $o]:
% 34.60/6.70 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ X0))) @
% 34.60/6.70 ((('#B') @ ('#sk3' @ X0) @ cSUCC))))))
% 34.60/6.70 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 34.60/6.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])).
% 34.60/6.70 thf(zip_derived_cl28, plain,
% 34.60/6.70 (![X0 : ($i > $o) > $o, X2 : ($i > $o) > $o]:
% 34.60/6.70 ( ((('#sk3' @ X0 @ X2) => ('#sk3' @ X0 @ (cSUCC @ X2))))
% 34.60/6.70 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 34.60/6.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])).
% 34.60/6.70 thf(zip_derived_cl34, plain,
% 34.60/6.70 (![X0 : ($i > $o) > $o, X2 : ($i > $o) > $o]:
% 34.60/6.70 (~ ('#sk3' @ X0 @ X2)
% 34.60/6.70 | ('#sk3' @ X0 @ (cSUCC @ X2))
% 34.60/6.70 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl28])).
% 34.60/6.70 thf(zip_derived_cl40, plain,
% 34.60/6.70 (![X0 : ($i > $o) > $o, X2 : ($i > $o) > $o]:
% 34.60/6.70 (~ ('#sk1' @ X0)
% 34.60/6.70 | ('#sk1' @ (cSUCC @ X0))
% 34.60/6.70 | ('#sk3' @ X0 @ (cSUCC @ X2))
% 34.60/6.70 | ~ ('#sk3' @ X0 @ X2))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 34.60/6.70 thf(zip_derived_cl19, plain,
% 34.60/6.70 (![X0 : ($i > $o) > $o]:
% 34.60/6.70 (~ ('#sk3' @ X0 @ X0) | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])).
% 34.60/6.70 thf(zip_derived_cl24, plain,
% 34.60/6.70 (![X0 : ($i > $o) > $o]:
% 34.60/6.70 (~ ('#sk1' @ X0) | ('#sk1' @ (cSUCC @ X0)) | ~ ('#sk3' @ X0 @ X0))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])).
% 34.60/6.70 thf(zip_derived_cl21, plain,
% 34.60/6.70 ((~ ((('#sk1' @ (cSUCC @ '#sk4')) &
% 34.60/6.70 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ (cSUCC @ '#sk4')))))))))
% 34.60/6.70 | ~ ('#sk1' @ cZERO)
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 34.60/6.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])).
% 34.60/6.70 thf(zip_derived_cl27, plain,
% 34.60/6.70 ((~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ (cSUCC @ '#sk4')))))))
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.70 | ~ ('#sk1' @ cZERO))),
% 34.60/6.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])).
% 34.60/6.70 thf(zip_derived_cl33, plain,
% 34.60/6.70 ((~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ (cSUCC @ '#sk4')))) @
% 34.60/6.70 ((('#B') @ ('#sk3' @ (cSUCC @ '#sk4')) @ cSUCC)))))) &
% 34.60/6.70 ('#sk3' @ (cSUCC @ '#sk4') @ cZERO))) =>
% 34.60/6.70 ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ '#sk4'))))
% 34.60/6.70 | ~ ('#sk1' @ cZERO)
% 34.60/6.70 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.70 ((('#B') @ (!!) @
% 34.60/6.70 ((('#S') @ ((('#B') @ (
% 34.60/6.70 '#S') @
% 34.60/6.70 ((('#B') @ (=>))))) @
% 34.60/6.70 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.70 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.70 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.70 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl27])).
% 34.60/6.71 thf(zip_derived_cl38, plain,
% 34.60/6.71 (( (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ (cSUCC @ '#sk4')))) @
% 34.60/6.71 ((('#B') @ ('#sk3' @ (cSUCC @ '#sk4')) @ cSUCC)))))) &
% 34.60/6.71 ('#sk3' @ (cSUCC @ '#sk4') @ cZERO)))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.71 ((('#B') @ (!!) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (
% 34.60/6.71 '#S') @
% 34.60/6.71 ((('#B') @ (=>))))) @
% 34.60/6.71 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.71 | ~ ('#sk1' @ cZERO))),
% 34.60/6.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 34.60/6.71 thf(zip_derived_cl45, plain,
% 34.60/6.71 (( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ (cSUCC @ '#sk4')))) @
% 34.60/6.71 ((('#B') @ ('#sk3' @ (cSUCC @ '#sk4')) @ cSUCC))))))
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.71 ((('#B') @ (!!) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (
% 34.60/6.71 '#S') @
% 34.60/6.71 ((('#B') @ (=>))))) @
% 34.60/6.71 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl38])).
% 34.60/6.71 thf(zip_derived_cl51, plain,
% 34.60/6.71 (![X2 : ($i > $o) > $o]:
% 34.60/6.71 ( ((('#sk3' @ (cSUCC @ '#sk4') @ X2) => ('#sk3' @ (cSUCC @ '#sk4') @
% 34.60/6.71 (cSUCC @ X2))))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.71 ((('#B') @ (!!) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (
% 34.60/6.71 '#S') @
% 34.60/6.71 ((('#B') @ (=>))))) @
% 34.60/6.71 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.71 | ~ ('#sk1' @ cZERO))),
% 34.60/6.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl45])).
% 34.60/6.71 thf(zip_derived_cl58, plain,
% 34.60/6.71 (![X2 : ($i > $o) > $o]:
% 34.60/6.71 (~ ('#sk3' @ (cSUCC @ '#sk4') @ X2)
% 34.60/6.71 | ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ X2))
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.71 ((('#B') @ (!!) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (
% 34.60/6.71 '#S') @
% 34.60/6.71 ((('#B') @ (=>))))) @
% 34.60/6.71 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])).
% 34.60/6.71 thf(zip_derived_cl68, plain,
% 34.60/6.71 (![X2 : ($i > $o) > $o]:
% 34.60/6.71 (~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ cZERO))) @
% 34.60/6.71 ((('#B') @ ('#sk3' @ cZERO) @ cSUCC)))))) &
% 34.60/6.71 ('#sk3' @ cZERO @ cZERO))) =>
% 34.60/6.71 ('#sk3' @ cZERO @ cZERO)))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ X2))
% 34.60/6.71 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ X2))),
% 34.60/6.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])).
% 34.60/6.71 thf(zip_derived_cl79, plain,
% 34.60/6.71 (![X2 : ($i > $o) > $o]:
% 34.60/6.71 (~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ X2))
% 34.60/6.71 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ X2))),
% 34.60/6.71 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl68])).
% 34.60/6.71 thf(zip_derived_cl80, plain,
% 34.60/6.71 (![X2 : ($i > $o) > $o]:
% 34.60/6.71 ( ('#sk1' @ '#sk2')
% 34.60/6.71 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ X2)
% 34.60/6.71 | ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ X2))
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])).
% 34.60/6.71 thf(zip_derived_cl10, plain, (~ ('#sk1' @ '#sk2')),
% 34.60/6.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 34.60/6.71 thf(zip_derived_cl6, plain, ( ('#sk1' @ cZERO)),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 34.60/6.71 thf(zip_derived_cl131, plain,
% 34.60/6.71 (![X2 : ($i > $o) > $o]:
% 34.60/6.71 (~ ('#sk3' @ (cSUCC @ '#sk4') @ X2)
% 34.60/6.71 | ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ X2))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl80, zip_derived_cl10, zip_derived_cl6])).
% 34.60/6.71 thf(zip_derived_cl57, plain,
% 34.60/6.71 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.71 (~ (X2 @ (cSUCC @ ('#sk5' @ X2)))
% 34.60/6.71 | ~ (X2 @ cZERO)
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.71 ((('#B') @ (!!) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (
% 34.60/6.71 '#S') @
% 34.60/6.71 ((('#B') @ (=>))))) @
% 34.60/6.71 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | (X2 @ '#sk4'))),
% 34.60/6.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])).
% 34.60/6.71 thf(zip_derived_cl67, plain,
% 34.60/6.71 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.71 (~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ cZERO))) @
% 34.60/6.71 ((('#B') @ ('#sk3' @ cZERO) @ cSUCC)))))) &
% 34.60/6.71 ('#sk3' @ cZERO @ cZERO))) =>
% 34.60/6.71 ('#sk3' @ cZERO @ cZERO)))
% 34.60/6.71 | (X2 @ '#sk4')
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ~ (X2 @ cZERO)
% 34.60/6.71 | ~ (X2 @ (cSUCC @ ('#sk5' @ X2))))),
% 34.60/6.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl57])).
% 34.60/6.71 thf(zip_derived_cl76, plain,
% 34.60/6.71 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.71 ( (X2 @ '#sk4')
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ~ (X2 @ cZERO)
% 34.60/6.71 | ~ (X2 @ (cSUCC @ ('#sk5' @ X2))))),
% 34.60/6.71 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl67])).
% 34.60/6.71 thf(zip_derived_cl77, plain,
% 34.60/6.71 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.71 ( ('#sk1' @ '#sk2')
% 34.60/6.71 | ~ (X2 @ (cSUCC @ ('#sk5' @ X2)))
% 34.60/6.71 | ~ (X2 @ cZERO)
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | (X2 @ '#sk4'))),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl76])).
% 34.60/6.71 thf(zip_derived_cl10, plain, (~ ('#sk1' @ '#sk2')),
% 34.60/6.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 34.60/6.71 thf(zip_derived_cl6, plain, ( ('#sk1' @ cZERO)),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 34.60/6.71 thf(zip_derived_cl130, plain,
% 34.60/6.71 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.71 (~ (X2 @ (cSUCC @ ('#sk5' @ X2))) | ~ (X2 @ cZERO) | (X2 @ '#sk4'))),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl77, zip_derived_cl10, zip_derived_cl6])).
% 34.60/6.71 thf(zip_derived_cl281, plain,
% 34.60/6.71 ((~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ ('#sk5' @ ('#sk3' @ (cSUCC @ '#sk4'))))
% 34.60/6.71 | ('#sk3' @ (cSUCC @ '#sk4') @ '#sk4')
% 34.60/6.71 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ cZERO))),
% 34.60/6.71 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl130])).
% 34.60/6.71 thf(zip_derived_cl128, plain,
% 34.60/6.71 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.71 ( (X2 @ ('#sk5' @ X2)) | ~ (X2 @ cZERO) | (X2 @ '#sk4'))),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl74, zip_derived_cl10, zip_derived_cl6])).
% 34.60/6.71 thf(zip_derived_cl3469, plain,
% 34.60/6.71 ((~ ('#sk3' @ (cSUCC @ '#sk4') @ cZERO)
% 34.60/6.71 | ('#sk3' @ (cSUCC @ '#sk4') @ '#sk4')
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('clc', [status(thm)], [zip_derived_cl281, zip_derived_cl128])).
% 34.60/6.71 thf(zip_derived_cl46, plain,
% 34.60/6.71 (( ('#sk3' @ (cSUCC @ '#sk4') @ cZERO)
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.71 ((('#B') @ (!!) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (
% 34.60/6.71 '#S') @
% 34.60/6.71 ((('#B') @ (=>))))) @
% 34.60/6.71 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl38])).
% 34.60/6.71 thf(zip_derived_cl52, plain,
% 34.60/6.71 ((~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ cZERO))) @
% 34.60/6.71 ((('#B') @ ('#sk3' @ cZERO) @ cSUCC)))))) &
% 34.60/6.71 ('#sk3' @ cZERO @ cZERO))) =>
% 34.60/6.71 ('#sk3' @ cZERO @ cZERO)))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ('#sk3' @ (cSUCC @ '#sk4') @ cZERO))),
% 34.60/6.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl46])).
% 34.60/6.71 thf(zip_derived_cl59, plain,
% 34.60/6.71 ((~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ('#sk3' @ (cSUCC @ '#sk4') @ cZERO))),
% 34.60/6.71 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl52])).
% 34.60/6.71 thf(zip_derived_cl60, plain,
% 34.60/6.71 (( ('#sk1' @ '#sk2')
% 34.60/6.71 | ('#sk3' @ (cSUCC @ '#sk4') @ cZERO)
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl59])).
% 34.60/6.71 thf(zip_derived_cl10, plain, (~ ('#sk1' @ '#sk2')),
% 34.60/6.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 34.60/6.71 thf(zip_derived_cl6, plain, ( ('#sk1' @ cZERO)),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 34.60/6.71 thf(zip_derived_cl127, plain,
% 34.60/6.71 (( ('#sk3' @ (cSUCC @ '#sk4') @ cZERO) | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl60, zip_derived_cl10, zip_derived_cl6])).
% 34.60/6.71 thf(zip_derived_cl3470, plain,
% 34.60/6.71 ((~ ('#sk1' @ (cSUCC @ '#sk4')) | ('#sk3' @ (cSUCC @ '#sk4') @ '#sk4'))),
% 34.60/6.71 inference('clc', [status(thm)], [zip_derived_cl3469, zip_derived_cl127])).
% 34.60/6.71 thf(zip_derived_cl39, plain,
% 34.60/6.71 ((~ ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.71 ((('#B') @ (!!) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (
% 34.60/6.71 '#S') @
% 34.60/6.71 ((('#B') @ (=>))))) @
% 34.60/6.71 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.71 | ~ ('#sk1' @ cZERO))),
% 34.60/6.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 34.60/6.71 thf(zip_derived_cl47, plain,
% 34.60/6.71 (( ('#sk1' @ '#sk2')
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.71 ((('#B') @ (!!) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (
% 34.60/6.71 '#S') @
% 34.60/6.71 ((('#B') @ (=>))))) @
% 34.60/6.71 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl39])).
% 34.60/6.71 thf(zip_derived_cl53, plain,
% 34.60/6.71 ((~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ cZERO))) @
% 34.60/6.71 ((('#B') @ ('#sk3' @ cZERO) @ cSUCC)))))) &
% 34.60/6.71 ('#sk3' @ cZERO @ cZERO))) =>
% 34.60/6.71 ('#sk3' @ cZERO @ cZERO)))
% 34.60/6.71 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ('#sk1' @ '#sk2'))),
% 34.60/6.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])).
% 34.60/6.71 thf(zip_derived_cl62, plain,
% 34.60/6.71 ((~ ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ('#sk1' @ '#sk2'))),
% 34.60/6.71 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl53])).
% 34.60/6.71 thf(zip_derived_cl6, plain, ( ('#sk1' @ cZERO)),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 34.60/6.71 thf(zip_derived_cl10, plain, (~ ('#sk1' @ '#sk2')),
% 34.60/6.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 34.60/6.71 thf(zip_derived_cl126, plain,
% 34.60/6.71 ((~ ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl62, zip_derived_cl6, zip_derived_cl10])).
% 34.60/6.71 thf(zip_derived_cl131, plain,
% 34.60/6.71 (![X2 : ($i > $o) > $o]:
% 34.60/6.71 (~ ('#sk3' @ (cSUCC @ '#sk4') @ X2)
% 34.60/6.71 | ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ X2))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl80, zip_derived_cl10, zip_derived_cl6])).
% 34.60/6.71 thf(zip_derived_cl286, plain,
% 34.60/6.71 ((~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ '#sk4'))),
% 34.60/6.71 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl131])).
% 34.60/6.71 thf(zip_derived_cl288, plain,
% 34.60/6.71 ((~ ('#sk3' @ (cSUCC @ '#sk4') @ '#sk4') | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('simplify', [status(thm)], [zip_derived_cl286])).
% 34.60/6.71 thf(zip_derived_cl3471, plain, (~ ('#sk1' @ (cSUCC @ '#sk4'))),
% 34.60/6.71 inference('clc', [status(thm)], [zip_derived_cl3470, zip_derived_cl288])).
% 34.60/6.71 thf(zip_derived_cl3475, plain,
% 34.60/6.71 ((~ ('#sk3' @ '#sk4' @ '#sk4') | ~ ('#sk1' @ '#sk4'))),
% 34.60/6.71 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl3471])).
% 34.60/6.71 thf(zip_derived_cl25, plain,
% 34.60/6.71 (( ('#sk1' @ '#sk4')
% 34.60/6.71 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 34.60/6.71 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.71 ((('#B') @ (!!) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (
% 34.60/6.71 '#S') @
% 34.60/6.71 ((('#B') @ (=>))))) @
% 34.60/6.71 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.71 | ~ ('#sk1' @ cZERO))),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl20])).
% 34.60/6.71 thf(zip_derived_cl30, plain,
% 34.60/6.71 (( ('#sk1' @ '#sk2')
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (&) @
% 34.60/6.71 ((('#B') @ (!!) @
% 34.60/6.71 ((('#S') @ ((('#B') @ (
% 34.60/6.71 '#S') @
% 34.60/6.71 ((('#B') @ (=>))))) @
% 34.60/6.71 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO)))))) @
% 34.60/6.71 ((('#C') @ ('#I') @ cZERO))))))
% 34.60/6.71 | ('#sk1' @ '#sk4'))),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])).
% 34.60/6.71 thf(zip_derived_cl35, plain,
% 34.60/6.71 ((~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ cZERO))) @
% 34.60/6.71 ((('#B') @ ('#sk3' @ cZERO) @ cSUCC)))))) &
% 34.60/6.71 ('#sk3' @ cZERO @ cZERO))) =>
% 34.60/6.71 ('#sk3' @ cZERO @ cZERO)))
% 34.60/6.71 | ('#sk1' @ '#sk4')
% 34.60/6.71 | ~ ('#sk1' @ cZERO)
% 34.60/6.71 | ('#sk1' @ '#sk2'))),
% 34.60/6.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])).
% 34.60/6.71 thf(zip_derived_cl41, plain,
% 34.60/6.71 (( ('#sk1' @ '#sk4') | ~ ('#sk1' @ cZERO) | ('#sk1' @ '#sk2'))),
% 34.60/6.71 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl35])).
% 34.60/6.71 thf(zip_derived_cl6, plain, ( ('#sk1' @ cZERO)),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 34.60/6.71 thf(zip_derived_cl10, plain, (~ ('#sk1' @ '#sk2')),
% 34.60/6.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 34.60/6.71 thf(zip_derived_cl125, plain, ( ('#sk1' @ '#sk4')),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl41, zip_derived_cl6, zip_derived_cl10])).
% 34.60/6.71 thf(zip_derived_cl3477, plain, (~ ('#sk3' @ '#sk4' @ '#sk4')),
% 34.60/6.71 inference('demod', [status(thm)], [zip_derived_cl3475, zip_derived_cl125])).
% 34.60/6.71 thf(zip_derived_cl130, plain,
% 34.60/6.71 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.71 (~ (X2 @ (cSUCC @ ('#sk5' @ X2))) | ~ (X2 @ cZERO) | (X2 @ '#sk4'))),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl77, zip_derived_cl10, zip_derived_cl6])).
% 34.60/6.71 thf(zip_derived_cl130, plain,
% 34.60/6.71 (![X2 : (($i > $o) > $o) > $o]:
% 34.60/6.71 (~ (X2 @ (cSUCC @ ('#sk5' @ X2))) | ~ (X2 @ cZERO) | (X2 @ '#sk4'))),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl77, zip_derived_cl10, zip_derived_cl6])).
% 34.60/6.71 thf(zip_derived_cl173, plain,
% 34.60/6.71 (![X0 : (($i > $o) > $o) > $o, X1 : (($i > $o) > $o) > $o]:
% 34.60/6.71 (((X1 @ '#sk4') = (X0 @ '#sk4'))
% 34.60/6.71 | ~ (X0 @ cZERO)
% 34.60/6.71 | ~ (X0 @ (cSUCC @ ('#sk5' @ X0)))
% 34.60/6.71 | ~ (X1 @ cZERO)
% 34.60/6.71 | ~ (X1 @ (cSUCC @ ('#sk5' @ X1))))),
% 34.60/6.71 inference('sup+', [status(thm)], [zip_derived_cl130, zip_derived_cl130])).
% 34.60/6.71 thf(zip_derived_cl517, plain,
% 34.60/6.71 (![X0 : $o, X1 : (($i > $o) > $o) > $o]:
% 34.60/6.71 ((((('#K') @ X0 @ '#sk4')) = (X1 @ '#sk4'))
% 34.60/6.71 | ~ (X1 @ cZERO)
% 34.60/6.71 | ~ (X1 @ (cSUCC @ ('#sk5' @ X1)))
% 34.60/6.71 | ~ ((('#K') @ X0 @ cZERO))
% 34.60/6.71 | ~ ((('#K') @ X0 @ (cSUCC @ ('#sk5' @ ((('#K') @ X0)))))))),
% 34.60/6.71 inference('narrow_applied_variable', [status(thm)], [zip_derived_cl173])).
% 34.60/6.71 thf(zip_derived_cl518, plain,
% 34.60/6.71 (![X0 : $o, X1 : (($i > $o) > $o) > $o]:
% 34.60/6.71 (((X0) = (X1 @ '#sk4'))
% 34.60/6.71 | ~ (X1 @ cZERO)
% 34.60/6.71 | ~ (X1 @ (cSUCC @ ('#sk5' @ X1)))
% 34.60/6.71 | ~ (X0)
% 34.60/6.71 | ~ (X0))),
% 34.60/6.71 inference('comb-normalize', [status(thm)], [zip_derived_cl517])).
% 34.60/6.71 thf(zip_derived_cl519, plain,
% 34.60/6.71 (![X0 : $o, X1 : (($i > $o) > $o) > $o]:
% 34.60/6.71 (~ (X0)
% 34.60/6.71 | ~ (X1 @ (cSUCC @ ('#sk5' @ X1)))
% 34.60/6.71 | ~ (X1 @ cZERO)
% 34.60/6.71 | ((X0) = (X1 @ '#sk4')))),
% 34.60/6.71 inference('simplify', [status(thm)], [zip_derived_cl518])).
% 34.60/6.71 thf(zip_derived_cl3489, plain,
% 34.60/6.71 (![X0 : $o]:
% 34.60/6.71 (~ (X0)
% 34.60/6.71 | ~ ('#sk3' @ '#sk4' @ cZERO)
% 34.60/6.71 | ~ ('#sk3' @ '#sk4' @ (cSUCC @ ('#sk5' @ ('#sk3' @ '#sk4'))))
% 34.60/6.71 | ~ (X0))),
% 34.60/6.71 inference('sup+', [status(thm)], [zip_derived_cl3477, zip_derived_cl519])).
% 34.60/6.71 thf(zip_derived_cl3501, plain,
% 34.60/6.71 (![X0 : $o]:
% 34.60/6.71 (~ ('#sk3' @ '#sk4' @ (cSUCC @ ('#sk5' @ ('#sk3' @ '#sk4'))))
% 34.60/6.71 | ~ ('#sk3' @ '#sk4' @ cZERO)
% 34.60/6.71 | ~ (X0))),
% 34.60/6.71 inference('simplify', [status(thm)], [zip_derived_cl3489])).
% 34.60/6.71 thf(zip_derived_cl23, plain,
% 34.60/6.71 (![X0 : ($i > $o) > $o]:
% 34.60/6.71 ( ('#sk3' @ X0 @ cZERO)
% 34.60/6.71 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 34.60/6.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])).
% 34.60/6.71 thf(zip_derived_cl29, plain,
% 34.60/6.71 (![X0 : ($i > $o) > $o]:
% 34.60/6.71 (~ ('#sk1' @ X0) | ('#sk1' @ (cSUCC @ X0)) | ('#sk3' @ X0 @ cZERO))),
% 34.60/6.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])).
% 34.60/6.71 thf(zip_derived_cl3471, plain, (~ ('#sk1' @ (cSUCC @ '#sk4'))),
% 34.60/6.71 inference('clc', [status(thm)], [zip_derived_cl3470, zip_derived_cl288])).
% 34.60/6.71 thf(zip_derived_cl3476, plain,
% 34.60/6.71 (( ('#sk3' @ '#sk4' @ cZERO) | ~ ('#sk1' @ '#sk4'))),
% 34.60/6.71 inference('sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl3471])).
% 34.60/6.71 thf(zip_derived_cl125, plain, ( ('#sk1' @ '#sk4')),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl41, zip_derived_cl6, zip_derived_cl10])).
% 34.60/6.71 thf(zip_derived_cl3478, plain, ( ('#sk3' @ '#sk4' @ cZERO)),
% 34.60/6.71 inference('demod', [status(thm)], [zip_derived_cl3476, zip_derived_cl125])).
% 34.60/6.71 thf(zip_derived_cl3513, plain,
% 34.60/6.71 (![X0 : $o]:
% 34.60/6.71 (~ ('#sk3' @ '#sk4' @ (cSUCC @ ('#sk5' @ ('#sk3' @ '#sk4')))) | ~ (X0))),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl3501, zip_derived_cl3478])).
% 34.60/6.71 thf(zip_derived_cl3514, plain,
% 34.60/6.71 (~ ('#sk3' @ '#sk4' @ (cSUCC @ ('#sk5' @ ('#sk3' @ '#sk4'))))),
% 34.60/6.71 inference('condensation', [status(thm)], [zip_derived_cl3513])).
% 34.60/6.71 thf(zip_derived_cl3517, plain,
% 34.60/6.71 ((~ ('#sk3' @ '#sk4' @ ('#sk5' @ ('#sk3' @ '#sk4')))
% 34.60/6.71 | ('#sk1' @ (cSUCC @ '#sk4'))
% 34.60/6.71 | ~ ('#sk1' @ '#sk4'))),
% 34.60/6.71 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl3514])).
% 34.60/6.71 thf(zip_derived_cl125, plain, ( ('#sk1' @ '#sk4')),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl41, zip_derived_cl6, zip_derived_cl10])).
% 34.60/6.71 thf(zip_derived_cl3518, plain,
% 34.60/6.71 ((~ ('#sk3' @ '#sk4' @ ('#sk5' @ ('#sk3' @ '#sk4')))
% 34.60/6.71 | ('#sk1' @ (cSUCC @ '#sk4')))),
% 34.60/6.71 inference('demod', [status(thm)], [zip_derived_cl3517, zip_derived_cl125])).
% 34.60/6.71 thf(zip_derived_cl3471, plain, (~ ('#sk1' @ (cSUCC @ '#sk4'))),
% 34.60/6.71 inference('clc', [status(thm)], [zip_derived_cl3470, zip_derived_cl288])).
% 34.60/6.71 thf(zip_derived_cl3520, plain,
% 34.60/6.71 (~ ('#sk3' @ '#sk4' @ ('#sk5' @ ('#sk3' @ '#sk4')))),
% 34.60/6.71 inference('clc', [status(thm)], [zip_derived_cl3518, zip_derived_cl3471])).
% 34.60/6.71 thf(zip_derived_cl3530, plain,
% 34.60/6.71 (( ('#sk3' @ '#sk4' @ '#sk4') | ~ ('#sk3' @ '#sk4' @ cZERO))),
% 34.60/6.71 inference('sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl3520])).
% 34.60/6.71 thf(zip_derived_cl3477, plain, (~ ('#sk3' @ '#sk4' @ '#sk4')),
% 34.60/6.71 inference('demod', [status(thm)], [zip_derived_cl3475, zip_derived_cl125])).
% 34.60/6.71 thf(zip_derived_cl3478, plain, ( ('#sk3' @ '#sk4' @ cZERO)),
% 34.60/6.71 inference('demod', [status(thm)], [zip_derived_cl3476, zip_derived_cl125])).
% 34.60/6.71 thf(zip_derived_cl3540, plain, ($false),
% 34.60/6.71 inference('demod', [status(thm)],
% 34.60/6.71 [zip_derived_cl3530, zip_derived_cl3477, zip_derived_cl3478])).
% 34.60/6.71
% 34.60/6.71 % SZS output end Refutation
% 34.60/6.71
% 34.60/6.71
% 34.60/6.71 % Terminating...
% 35.08/6.87 % Runner terminated.
% 35.08/6.91 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------