TSTP Solution File: SEV302^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV302^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.wKvBhsIwLR true
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:00:22 EDT 2023
% Result : Theorem 25.80s 3.95s
% Output : Refutation 25.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEV302^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% 0.13/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.wKvBhsIwLR true
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 03:27:37 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running portfolio for 300 s
% 0.15/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.15/0.37 % Running in HO mode
% 0.23/0.69 % Total configuration time : 828
% 0.23/0.69 % Estimated wc time : 1656
% 0.23/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.23/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 1.08/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.30/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.30/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.30/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.30/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.30/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.30/0.82 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 25.80/3.95 % Solved by lams/40_b.comb.sh.
% 25.80/3.95 % done 287 iterations in 3.105s
% 25.80/3.95 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 25.80/3.95 % SZS output start Refutation
% 25.80/3.95 thf('#sk4_type', type, '#sk4': ($i > $o) > $o).
% 25.80/3.95 thf(cNAT_type, type, cNAT: (($i > $o) > $o) > $o).
% 25.80/3.95 thf(cZERO_type, type, cZERO: ($i > $o) > $o).
% 25.80/3.95 thf('#form5_type', type, '#form5': $o).
% 25.80/3.95 thf('#sk3_type', type, '#sk3': (($i > $o) > $o) > (($i > $o) > $o) > $o).
% 25.80/3.95 thf('#sk1_type', type, '#sk1': (($i > $o) > $o) > $o).
% 25.80/3.95 thf(cSUCC_type, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 25.80/3.95 thf('#sk2_type', type, '#sk2': ($i > $o) > $o).
% 25.80/3.95 thf('#sk6_type', type, '#sk6': ((($i > $o) > $o) > $o) > ($i > $o) > $o).
% 25.80/3.95 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 25.80/3.95 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 25.80/3.95 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 25.80/3.95 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 25.80/3.95 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 25.80/3.95 thf(cX6102_B, conjecture,
% 25.80/3.95 (![Xp:( ( ( $i > $o ) > $o ) > $o )]:
% 25.80/3.95 ( ( ( ![Xx:( ( $i > $o ) > $o )]:
% 25.80/3.95 ( ( cNAT @ Xx ) => ( ( Xp @ Xx ) => ( Xp @ ( cSUCC @ Xx ) ) ) ) ) &
% 25.80/3.95 ( Xp @ cZERO ) ) =>
% 25.80/3.95 ( ![Xm:( ( $i > $o ) > $o )]:
% 25.80/3.95 ( ( ( ( ![Xx:( ( $i > $o ) > $o )]:
% 25.80/3.95 ( ( ( Xp @ Xx ) & ( cNAT @ Xx ) ) =>
% 25.80/3.95 ( ( Xp @ ( cSUCC @ Xx ) ) & ( cNAT @ ( cSUCC @ Xx ) ) ) ) ) &
% 25.80/3.95 ( Xp @ cZERO ) & ( cNAT @ cZERO ) ) =>
% 25.80/3.95 ( ( Xp @ Xm ) & ( cNAT @ Xm ) ) ) =>
% 25.80/3.95 ( Xp @ Xm ) ) ) ))).
% 25.80/3.95 thf(zf_stmt_0, negated_conjecture,
% 25.80/3.95 (~( ![Xp:( ( ( $i > $o ) > $o ) > $o )]:
% 25.80/3.95 ( ( ( ![Xx:( ( $i > $o ) > $o )]:
% 25.80/3.95 ( ( cNAT @ Xx ) => ( ( Xp @ Xx ) => ( Xp @ ( cSUCC @ Xx ) ) ) ) ) &
% 25.80/3.95 ( Xp @ cZERO ) ) =>
% 25.80/3.95 ( ![Xm:( ( $i > $o ) > $o )]:
% 25.80/3.95 ( ( ( ( ![Xx:( ( $i > $o ) > $o )]:
% 25.80/3.95 ( ( ( Xp @ Xx ) & ( cNAT @ Xx ) ) =>
% 25.80/3.95 ( ( Xp @ ( cSUCC @ Xx ) ) & ( cNAT @ ( cSUCC @ Xx ) ) ) ) ) &
% 25.80/3.95 ( Xp @ cZERO ) & ( cNAT @ cZERO ) ) =>
% 25.80/3.95 ( ( Xp @ Xm ) & ( cNAT @ Xm ) ) ) =>
% 25.80/3.95 ( Xp @ Xm ) ) ) ) )),
% 25.80/3.95 inference('cnf.neg', [status(esa)], [cX6102_B])).
% 25.80/3.95 thf(zip_derived_cl0, plain,
% 25.80/3.95 (~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (((((((!!) @ (^[Y1 : ($i > $o) > $o]:
% 25.80/3.95 (((cNAT @ Y1) =>
% 25.80/3.95 (((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))))) &
% 25.80/3.95 (Y0 @ cZERO))) =>
% 25.80/3.95 (((!!) @ (^[Y1 : ($i > $o) > $o]:
% 25.80/3.95 (((((((((!!) @ (^[Y2 : ($i > $o) > $o]:
% 25.80/3.95 (((((Y0 @ Y2) & (cNAT @
% 25.80/3.95 Y2))) =>
% 25.80/3.95 (((Y0 @ (cSUCC @ Y2)) &
% 25.80/3.95 (cNAT @ (cSUCC @ Y2))))))))) &
% 25.80/3.95 (Y0 @ cZERO) & (cNAT @ cZERO))) =>
% 25.80/3.95 (((Y0 @ Y1) & (cNAT @ Y1))))) =>
% 25.80/3.95 (Y0 @ Y1)))))))))))),
% 25.80/3.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 25.80/3.95 thf(zip_derived_cl1, plain,
% 25.80/3.95 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @
% 25.80/3.95 ((('#B') @ (!!) @
% 25.80/3.95 ((('#B') @ ((('#S') @ ((('#B') @ (
% 25.80/3.95 =>) @
% 25.80/3.95 cNAT)))) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (
% 25.80/3.95 '#S') @
% 25.80/3.95 ((('#B') @ (=>))))) @
% 25.80/3.95 ((('#C') @ ('#B') @ cSUCC)))))))))) @
% 25.80/3.95 ((('#C') @ ('#I') @ cZERO)))))) @
% 25.80/3.95 ((('#B') @ (!!) @
% 25.80/3.95 ((('#S') @ ((('#B') @ ('#S') @
% 25.80/3.95 ((('#B') @ ((('#B') @ (=>))) @
% 25.80/3.95 ((('#S') @ ((('#B') @ ('#B') @
% 25.80/3.95 ((('#B') @ (=>) @
% 25.80/3.95 ((('#C') @ ((('#S') @ (
% 25.80/3.95 (('#B') @ (
% 25.80/3.95 &) @
% 25.80/3.95 ((('#B') @ (
% 25.80/3.95 !!) @
% 25.80/3.95 ((('#S') @ (
% 25.80/3.95 (
% 25.80/3.95 ('#B') @ (
% 25.80/3.95 '#S') @
% 25.80/3.95 (
% 25.80/3.95 (
% 25.80/3.95 ('#B') @ (
% 25.80/3.95 (
% 25.80/3.95 ('#B') @ (
% 25.80/3.95 =>))) @
% 25.80/3.95 (
% 25.80/3.95 (
% 25.80/3.95 ('#C') @ (
% 25.80/3.95 (
% 25.80/3.95 ('#B') @ (
% 25.80/3.95 '#S') @
% 25.80/3.95 (
% 25.80/3.95 (
% 25.80/3.95 ('#B') @ (
% 25.80/3.95 &))))) @
% 25.80/3.95 cNAT)))))) @
% 25.80/3.95 (
% 25.80/3.95 (
% 25.80/3.95 ('#C') @ (
% 25.80/3.95 (
% 25.80/3.95 ('#B') @ (
% 25.80/3.95 '#S') @
% 25.80/3.95 (
% 25.80/3.95 (
% 25.80/3.95 ('#B') @ (
% 25.80/3.95 (
% 25.80/3.95 ('#B') @ (
% 25.80/3.95 &))) @
% 25.80/3.95 (
% 25.80/3.95 (
% 25.80/3.95 ('#C') @ (
% 25.80/3.95 '#B') @
% 25.80/3.95 cSUCC)))))) @
% 25.80/3.95 (
% 25.80/3.95 (
% 25.80/3.95 ('#B') @ cNAT @
% 25.80/3.95 cSUCC)))))))))) @
% 25.80/3.95 ((('#C') @ (
% 25.80/3.95 '#I') @
% 25.80/3.95 cZERO)))) @
% 25.80/3.95 (cNAT @ cZERO))))))) @
% 25.80/3.95 ((('#C') @ ((('#B') @ ('#S') @
% 25.80/3.95 ((('#B') @ (&))))) @
% 25.80/3.95 cNAT)))))))) @
% 25.80/3.95 ('#I')))))))))),
% 25.80/3.95 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 25.80/3.95 thf(zip_derived_cl2, plain,
% 25.80/3.95 (~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ cNAT)) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (=>) @ '#sk1')) @
% 25.80/3.95 ((('#B') @ '#sk1' @ cSUCC)))))))) &
% 25.80/3.95 ('#sk1' @ cZERO))) =>
% 25.80/3.95 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#B') @ (((=>) @ (((((!!) @ ((('#S') @ (
% 25.80/3.95 (('#B') @ (
% 25.80/3.95 =>) @
% 25.80/3.95 ((('#S') @ (
% 25.80/3.95 (('#B') @ (
% 25.80/3.95 &) @
% 25.80/3.95 '#sk1')) @
% 25.80/3.95 cNAT)))) @
% 25.80/3.95 ((('#S') @ (
% 25.80/3.95 (('#B') @ (
% 25.80/3.95 &) @
% 25.80/3.95 ((
% 25.80/3.95 ('#B') @ '#sk1' @
% 25.80/3.95 cSUCC)))) @
% 25.80/3.95 ((('#B') @ cNAT @
% 25.80/3.95 cSUCC)))))))) &
% 25.80/3.95 ('#sk1' @ cZERO) &
% 25.80/3.95 (cNAT @ cZERO))))) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @ cNAT)))))) @
% 25.80/3.95 '#sk1'))))))),
% 25.80/3.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])).
% 25.80/3.95 thf(zip_derived_cl3, plain,
% 25.80/3.95 ( (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ cNAT)) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (=>) @ '#sk1')) @
% 25.80/3.95 ((('#B') @ '#sk1' @ cSUCC)))))))) &
% 25.80/3.95 ('#sk1' @ cZERO)))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])).
% 25.80/3.95 thf(zip_derived_cl5, plain,
% 25.80/3.95 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ cNAT)) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (=>) @ '#sk1')) @
% 25.80/3.95 ((('#B') @ '#sk1' @ cSUCC))))))))),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 25.80/3.95 thf(zip_derived_cl8, plain,
% 25.80/3.95 (![X2 : ($i > $o) > $o]:
% 25.80/3.95 (((cNAT @ X2) => ((('#sk1' @ X2) => ('#sk1' @ (cSUCC @ X2))))))),
% 25.80/3.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])).
% 25.80/3.95 thf(zip_derived_cl11, plain,
% 25.80/3.95 (![X2 : ($i > $o) > $o]:
% 25.80/3.95 (~ (cNAT @ X2) | ((('#sk1' @ X2) => ('#sk1' @ (cSUCC @ X2)))))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])).
% 25.80/3.95 thf(cNAT_def, axiom, ~ (cNAT @ X0) =>
% 25.80/3.95 ((((!!) @ (^[Y0 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (((((((!!) @ (^[Y1 : ($i > $o) > $o]:
% 25.80/3.95 (((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) &
% 25.80/3.95 (Y0 @ cZERO))) =>
% 25.80/3.95 (Y0 @ X0))))))
% 25.80/3.95 != ($true))).
% 25.80/3.95 thf('0', plain,
% 25.80/3.95 (![X0:( ( $i > $o ) > $o )]:
% 25.80/3.95 ( ( ~( cNAT @ X0 ) ) <=>
% 25.80/3.95 ( ~( ![X5:( ( ( $i > $o ) > $o ) > $o )]:
% 25.80/3.95 ( ( ( ![X7:( ( $i > $o ) > $o )]:
% 25.80/3.95 ( ( X5 @ X7 ) => ( X5 @ ( cSUCC @ X7 ) ) ) ) &
% 25.80/3.95 ( X5 @ cZERO ) ) =>
% 25.80/3.95 ( X5 @ X0 ) ) ) ) )),
% 25.80/3.95 inference('rw.lit', [status(esa)], [cNAT_def])).
% 25.80/3.95 thf(zip_derived_cl13, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o]:
% 25.80/3.95 (~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (((((((!!) @ (^[Y1 : ($i > $o) > $o]:
% 25.80/3.95 (((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) &
% 25.80/3.95 (Y0 @ cZERO))) =>
% 25.80/3.95 (Y0 @ X0))))))
% 25.80/3.95 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 25.80/3.95 inference('rw_clause', [status(thm)], [zip_derived_cl11, '0'])).
% 25.80/3.95 thf(zip_derived_cl15, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o]:
% 25.80/3.95 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @
% 25.80/3.95 ((('#B') @ (!!) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (
% 25.80/3.95 '#S') @
% 25.80/3.95 ((('#B') @ (=>))))) @
% 25.80/3.95 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 25.80/3.95 ((('#C') @ ('#I') @ cZERO)))))) @
% 25.80/3.95 ((('#C') @ ('#I') @ X0))))))
% 25.80/3.95 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 25.80/3.95 inference('comb-normalize', [status(thm)], [zip_derived_cl13])).
% 25.80/3.95 thf(zip_derived_cl16, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o]:
% 25.80/3.95 (~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ X0))) @
% 25.80/3.95 ((('#B') @ ('#sk3' @ X0) @ cSUCC)))))) &
% 25.80/3.95 ('#sk3' @ X0 @ cZERO))) =>
% 25.80/3.95 ('#sk3' @ X0 @ X0)))
% 25.80/3.95 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 25.80/3.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])).
% 25.80/3.95 thf(zip_derived_cl19, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o]:
% 25.80/3.95 (~ ('#sk3' @ X0 @ X0) | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])).
% 25.80/3.95 thf(zip_derived_cl24, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o]:
% 25.80/3.95 (~ ('#sk1' @ X0) | ('#sk1' @ (cSUCC @ X0)) | ~ ('#sk3' @ X0 @ X0))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])).
% 25.80/3.95 thf(zip_derived_cl4, plain,
% 25.80/3.95 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#B') @ (((=>) @ (((((!!) @ ((('#S') @ (
% 25.80/3.95 (('#B') @ (
% 25.80/3.95 =>) @
% 25.80/3.95 ((('#S') @ (
% 25.80/3.95 (('#B') @ (
% 25.80/3.95 &) @ '#sk1')) @
% 25.80/3.95 cNAT)))) @
% 25.80/3.95 ((('#S') @ (
% 25.80/3.95 (('#B') @ (
% 25.80/3.95 &) @
% 25.80/3.95 ((('#B') @ '#sk1' @
% 25.80/3.95 cSUCC)))) @
% 25.80/3.95 ((('#B') @ cNAT @
% 25.80/3.95 cSUCC)))))))) &
% 25.80/3.95 ('#sk1' @ cZERO) &
% 25.80/3.95 (cNAT @ cZERO))))) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @ cNAT)))))) @
% 25.80/3.95 '#sk1'))))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])).
% 25.80/3.95 thf(zip_derived_cl7, plain,
% 25.80/3.95 (~ (((((((((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @
% 25.80/3.95 cNAT)))) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @
% 25.80/3.95 ((('#B') @ '#sk1' @ cSUCC)))) @
% 25.80/3.95 ((('#B') @ cNAT @ cSUCC)))))))) &
% 25.80/3.95 ('#sk1' @ cZERO) & (cNAT @ cZERO))) =>
% 25.80/3.95 ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))) =>
% 25.80/3.95 ('#sk1' @ '#sk2')))),
% 25.80/3.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])).
% 25.80/3.95 thf(zip_derived_cl9, plain,
% 25.80/3.95 ( (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @ cNAT)))) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ ((('#B') @ '#sk1' @ cSUCC)))) @
% 25.80/3.95 ((('#B') @ cNAT @ cSUCC)))))))) &
% 25.80/3.95 ('#sk1' @ cZERO) & (cNAT @ cZERO))) =>
% 25.80/3.95 ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 25.80/3.95 thf(zip_derived_cl12, plain,
% 25.80/3.95 ((~ (((((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @ cNAT)))) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ ((('#B') @ '#sk1' @ cSUCC)))) @
% 25.80/3.95 ((('#B') @ cNAT @ cSUCC)))))))) &
% 25.80/3.95 ('#sk1' @ cZERO) & (cNAT @ cZERO)))
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])).
% 25.80/3.95 thf(zip_derived_cl14, plain,
% 25.80/3.95 ((~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @ cNAT)))) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ ((('#B') @ '#sk1' @ cSUCC)))) @
% 25.80/3.95 ((('#B') @ cNAT @ cSUCC))))))))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ~ (cNAT @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])).
% 25.80/3.95 thf(zip_derived_cl17, plain,
% 25.80/3.95 ((~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (((((((!!) @ (^[Y1 : ($i > $o) > $o]:
% 25.80/3.95 (((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) &
% 25.80/3.95 (Y0 @ cZERO))) =>
% 25.80/3.95 (Y0 @ cZERO))))))
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @ cNAT)))) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ ((('#B') @ '#sk1' @ cSUCC)))) @
% 25.80/3.95 ((('#B') @ cNAT @ cSUCC)))))))))),
% 25.80/3.95 inference('rw_clause', [status(thm)], [zip_derived_cl14, '0'])).
% 25.80/3.95 thf(zip_derived_cl20, plain,
% 25.80/3.95 ((~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @
% 25.80/3.95 ((('#B') @ (!!) @
% 25.80/3.95 ((('#S') @ ((('#B') @ ('#S') @
% 25.80/3.95 ((('#B') @ (=>))))) @
% 25.80/3.95 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 25.80/3.95 ((('#C') @ ('#I') @ cZERO)))))) @
% 25.80/3.95 ((('#C') @ ('#I') @ cZERO))))))
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @ cNAT)))) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ ((('#B') @ '#sk1' @ cSUCC)))) @
% 25.80/3.95 ((('#B') @ cNAT @ cSUCC)))))))))),
% 25.80/3.95 inference('comb-normalize', [status(thm)], [zip_derived_cl17])).
% 25.80/3.95 thf(zip_derived_cl21, plain,
% 25.80/3.95 ((~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ cZERO))) @
% 25.80/3.95 ((('#B') @ ('#sk3' @ cZERO) @ cSUCC)))))) &
% 25.80/3.95 ('#sk3' @ cZERO @ cZERO))) =>
% 25.80/3.95 ('#sk3' @ cZERO @ cZERO)))
% 25.80/3.95 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @ cNAT)))) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ ((('#B') @ '#sk1' @ cSUCC)))) @
% 25.80/3.95 ((('#B') @ cNAT @ cSUCC))))))))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl20])).
% 25.80/3.95 thf(zip_derived_cl25, plain,
% 25.80/3.95 ((~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ '#sk1')) @ cNAT)))) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @ ((('#B') @ '#sk1' @ cSUCC)))) @
% 25.80/3.95 ((('#B') @ cNAT @ cSUCC))))))))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl21])).
% 25.80/3.95 thf(zip_derived_cl26, plain,
% 25.80/3.95 ((~ ((((('#sk1' @ '#sk4') & (cNAT @ '#sk4'))) =>
% 25.80/3.95 ((('#sk1' @ (cSUCC @ '#sk4')) & (cNAT @ (cSUCC @ '#sk4'))))))
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ cZERO))),
% 25.80/3.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl25])).
% 25.80/3.95 thf(zip_derived_cl30, plain,
% 25.80/3.95 ((~ ((('#sk1' @ (cSUCC @ '#sk4')) & (cNAT @ (cSUCC @ '#sk4'))))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])).
% 25.80/3.95 thf(zip_derived_cl34, plain,
% 25.80/3.95 ((~ ('#sk1' @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ~ (cNAT @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ cZERO))),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl30])).
% 25.80/3.95 thf(zip_derived_cl39, plain,
% 25.80/3.95 ((~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (((((((!!) @ (^[Y1 : ($i > $o) > $o]:
% 25.80/3.95 (((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) &
% 25.80/3.95 (Y0 @ cZERO))) =>
% 25.80/3.95 (Y0 @ (cSUCC @ '#sk4')))))))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 25.80/3.95 inference('rw_clause', [status(thm)], [zip_derived_cl34, '0'])).
% 25.80/3.95 thf(zip_derived_cl43, plain,
% 25.80/3.95 ((~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @
% 25.80/3.95 ((('#B') @ (!!) @
% 25.80/3.95 ((('#S') @ ((('#B') @ ('#S') @
% 25.80/3.95 ((('#B') @ (=>))))) @
% 25.80/3.95 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 25.80/3.95 ((('#C') @ ('#I') @ cZERO)))))) @
% 25.80/3.95 ((('#C') @ ('#I') @ (cSUCC @ '#sk4')))))))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 25.80/3.95 inference('comb-normalize', [status(thm)], [zip_derived_cl39])).
% 25.80/3.95 thf(zip_derived_cl44, plain,
% 25.80/3.95 ((~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ (cSUCC @ '#sk4')))) @
% 25.80/3.95 ((('#B') @ ('#sk3' @ (cSUCC @ '#sk4')) @ cSUCC)))))) &
% 25.80/3.95 ('#sk3' @ (cSUCC @ '#sk4') @ cZERO))) =>
% 25.80/3.95 ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ '#sk4'))))
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ cZERO))),
% 25.80/3.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl43])).
% 25.80/3.95 thf(zip_derived_cl48, plain,
% 25.80/3.95 (( (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ (cSUCC @ '#sk4')))) @
% 25.80/3.95 ((('#B') @ ('#sk3' @ (cSUCC @ '#sk4')) @ cSUCC)))))) &
% 25.80/3.95 ('#sk3' @ (cSUCC @ '#sk4') @ cZERO)))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])).
% 25.80/3.95 thf(zip_derived_cl52, plain,
% 25.80/3.95 (( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ (cSUCC @ '#sk4')))) @
% 25.80/3.95 ((('#B') @ ('#sk3' @ (cSUCC @ '#sk4')) @ cSUCC))))))
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ cZERO))),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl48])).
% 25.80/3.95 thf(zip_derived_cl49, plain,
% 25.80/3.95 ((~ ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])).
% 25.80/3.95 thf(zip_derived_cl54, plain,
% 25.80/3.95 ((~ ('#form5') | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 define([status(thm)])).
% 25.80/3.95 thf(zip_derived_cl60, plain,
% 25.80/3.95 (( ('#form5')
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 25.80/3.95 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ (cSUCC @ '#sk4')))) @
% 25.80/3.95 ((('#B') @ ('#sk3' @ (cSUCC @ '#sk4')) @ cSUCC)))))))),
% 25.80/3.95 inference('renaming', [status(thm)], [zip_derived_cl52, zip_derived_cl54])).
% 25.80/3.95 thf(zip_derived_cl65, plain,
% 25.80/3.95 (![X2 : ($i > $o) > $o]:
% 25.80/3.95 ( ((('#sk3' @ (cSUCC @ '#sk4') @ X2) => ('#sk3' @ (cSUCC @ '#sk4') @
% 25.80/3.95 (cSUCC @ X2))))
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ('#form5'))),
% 25.80/3.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl60])).
% 25.80/3.95 thf(zip_derived_cl72, plain,
% 25.80/3.95 (![X2 : ($i > $o) > $o]:
% 25.80/3.95 (~ ('#sk3' @ (cSUCC @ '#sk4') @ X2)
% 25.80/3.95 | ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ X2))
% 25.80/3.95 | ('#form5')
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])).
% 25.80/3.95 thf(zip_derived_cl54, plain,
% 25.80/3.95 ((~ ('#form5') | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 define([status(thm)])).
% 25.80/3.95 thf(zip_derived_cl55, plain, (( ('#sk1' @ '#sk2') | ~ ('#form5'))),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl54])).
% 25.80/3.95 thf(zip_derived_cl10, plain, (~ ('#sk1' @ '#sk2')),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 25.80/3.95 thf(zip_derived_cl78, plain, (~ ('#form5')),
% 25.80/3.95 inference('clc', [status(thm)], [zip_derived_cl55, zip_derived_cl10])).
% 25.80/3.95 thf(zip_derived_cl6, plain, ( ('#sk1' @ cZERO)),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 25.80/3.95 thf(zip_derived_cl92, plain,
% 25.80/3.95 (![X2 : ($i > $o) > $o]:
% 25.80/3.95 (~ ('#sk3' @ (cSUCC @ '#sk4') @ X2)
% 25.80/3.95 | ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ X2))
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 25.80/3.95 inference('demod', [status(thm)],
% 25.80/3.95 [zip_derived_cl72, zip_derived_cl78, zip_derived_cl6])).
% 25.80/3.95 thf(zip_derived_cl29, plain,
% 25.80/3.95 (( ((('#sk1' @ '#sk4') & (cNAT @ '#sk4')))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])).
% 25.80/3.95 thf(zip_derived_cl33, plain,
% 25.80/3.95 (( (cNAT @ '#sk4')
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ cZERO))),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl29])).
% 25.80/3.95 thf(cNAT_def, axiom, (cNAT @ X0) =>
% 25.80/3.95 ((((!!) @ (^[Y0 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (((((((!!) @ (^[Y1 : ($i > $o) > $o]:
% 25.80/3.95 (((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) &
% 25.80/3.95 (Y0 @ cZERO))) =>
% 25.80/3.95 (Y0 @ X0))))))
% 25.80/3.95 = ($true))).
% 25.80/3.95 thf('1', plain,
% 25.80/3.95 (![X0:( ( $i > $o ) > $o )]:
% 25.80/3.95 ( ( cNAT @ X0 ) <=>
% 25.80/3.95 ( ![X5:( ( ( $i > $o ) > $o ) > $o )]:
% 25.80/3.95 ( ( ( ![X7:( ( $i > $o ) > $o )]:
% 25.80/3.95 ( ( X5 @ X7 ) => ( X5 @ ( cSUCC @ X7 ) ) ) ) &
% 25.80/3.95 ( X5 @ cZERO ) ) =>
% 25.80/3.95 ( X5 @ X0 ) ) ) )),
% 25.80/3.95 inference('rw.lit', [status(esa)], [cNAT_def])).
% 25.80/3.95 thf(zip_derived_cl38, plain,
% 25.80/3.95 (( (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (((((((!!) @ (^[Y1 : ($i > $o) > $o]:
% 25.80/3.95 (((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) &
% 25.80/3.95 (Y0 @ cZERO))) =>
% 25.80/3.95 (Y0 @ '#sk4'))))))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 inference('rw_clause', [status(thm)], [zip_derived_cl33, '1'])).
% 25.80/3.95 thf(zip_derived_cl41, plain,
% 25.80/3.95 (( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 25.80/3.95 ((('#S') @ ((('#B') @ (&) @
% 25.80/3.95 ((('#B') @ (!!) @
% 25.80/3.95 ((('#S') @ ((('#B') @ ('#S') @
% 25.80/3.95 ((('#B') @ (=>))))) @
% 25.80/3.95 ((('#C') @ ('#B') @ cSUCC)))))))) @
% 25.80/3.95 ((('#C') @ ('#I') @ cZERO)))))) @
% 25.80/3.95 ((('#C') @ ('#I') @ '#sk4'))))))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 inference('comb-normalize', [status(thm)], [zip_derived_cl38])).
% 25.80/3.95 thf(zip_derived_cl42, plain,
% 25.80/3.95 (![X2 : (($i > $o) > $o) > $o]:
% 25.80/3.95 ( (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ X2)) @
% 25.80/3.95 ((('#B') @ X2 @ cSUCC)))))) &
% 25.80/3.95 (X2 @ cZERO))) =>
% 25.80/3.95 (X2 @ '#sk4')))
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ cZERO))),
% 25.80/3.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])).
% 25.80/3.95 thf(zip_derived_cl47, plain,
% 25.80/3.95 (![X2 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (~ (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ X2)) @
% 25.80/3.95 ((('#B') @ X2 @ cSUCC)))))) &
% 25.80/3.95 (X2 @ cZERO)))
% 25.80/3.95 | (X2 @ '#sk4')
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])).
% 25.80/3.95 thf(zip_derived_cl51, plain,
% 25.80/3.95 (![X2 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ X2)) @
% 25.80/3.95 ((('#B') @ X2 @ cSUCC))))))
% 25.80/3.95 | ~ (X2 @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | (X2 @ '#sk4'))),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl47])).
% 25.80/3.95 thf(zip_derived_cl54, plain,
% 25.80/3.95 ((~ ('#form5') | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 define([status(thm)])).
% 25.80/3.95 thf(zip_derived_cl59, plain,
% 25.80/3.95 (![X2 : (($i > $o) > $o) > $o]:
% 25.80/3.95 ( ('#form5')
% 25.80/3.95 | (X2 @ '#sk4')
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ~ (X2 @ cZERO)
% 25.80/3.95 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ X2)) @
% 25.80/3.95 ((('#B') @ X2 @ cSUCC)))))))),
% 25.80/3.95 inference('renaming', [status(thm)], [zip_derived_cl51, zip_derived_cl54])).
% 25.80/3.95 thf(zip_derived_cl64, plain,
% 25.80/3.95 (![X2 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (~ (((X2 @ ('#sk6' @ X2)) => (X2 @ (cSUCC @ ('#sk6' @ X2)))))
% 25.80/3.95 | ~ (X2 @ cZERO)
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | (X2 @ '#sk4')
% 25.80/3.95 | ('#form5'))),
% 25.80/3.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl59])).
% 25.80/3.95 thf(zip_derived_cl71, plain,
% 25.80/3.95 (![X2 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (~ (X2 @ (cSUCC @ ('#sk6' @ X2)))
% 25.80/3.95 | ('#form5')
% 25.80/3.95 | (X2 @ '#sk4')
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ~ (X2 @ cZERO))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 25.80/3.95 thf(zip_derived_cl78, plain, (~ ('#form5')),
% 25.80/3.95 inference('clc', [status(thm)], [zip_derived_cl55, zip_derived_cl10])).
% 25.80/3.95 thf(zip_derived_cl6, plain, ( ('#sk1' @ cZERO)),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 25.80/3.95 thf(zip_derived_cl89, plain,
% 25.80/3.95 (![X2 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (~ (X2 @ (cSUCC @ ('#sk6' @ X2))) | (X2 @ '#sk4') | ~ (X2 @ cZERO))),
% 25.80/3.95 inference('demod', [status(thm)],
% 25.80/3.95 [zip_derived_cl71, zip_derived_cl78, zip_derived_cl6])).
% 25.80/3.95 thf(zip_derived_cl300, plain,
% 25.80/3.95 ((~ ('#sk1' @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ ('#sk6' @ ('#sk3' @ (cSUCC @ '#sk4'))))
% 25.80/3.95 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ cZERO)
% 25.80/3.95 | ('#sk3' @ (cSUCC @ '#sk4') @ '#sk4'))),
% 25.80/3.95 inference('sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl89])).
% 25.80/3.95 thf(zip_derived_cl70, plain,
% 25.80/3.95 (![X2 : (($i > $o) > $o) > $o]:
% 25.80/3.95 ( (X2 @ ('#sk6' @ X2))
% 25.80/3.95 | ('#form5')
% 25.80/3.95 | (X2 @ '#sk4')
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ~ (X2 @ cZERO))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 25.80/3.95 thf(zip_derived_cl78, plain, (~ ('#form5')),
% 25.80/3.95 inference('clc', [status(thm)], [zip_derived_cl55, zip_derived_cl10])).
% 25.80/3.95 thf(zip_derived_cl6, plain, ( ('#sk1' @ cZERO)),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 25.80/3.95 thf(zip_derived_cl91, plain,
% 25.80/3.95 (![X2 : (($i > $o) > $o) > $o]:
% 25.80/3.95 ( (X2 @ ('#sk6' @ X2)) | (X2 @ '#sk4') | ~ (X2 @ cZERO))),
% 25.80/3.95 inference('demod', [status(thm)],
% 25.80/3.95 [zip_derived_cl70, zip_derived_cl78, zip_derived_cl6])).
% 25.80/3.95 thf(zip_derived_cl4937, plain,
% 25.80/3.95 (( ('#sk3' @ (cSUCC @ '#sk4') @ '#sk4')
% 25.80/3.95 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ cZERO)
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 25.80/3.95 inference('clc', [status(thm)], [zip_derived_cl300, zip_derived_cl91])).
% 25.80/3.95 thf(zip_derived_cl49, plain,
% 25.80/3.95 ((~ ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])).
% 25.80/3.95 thf(zip_derived_cl54, plain,
% 25.80/3.95 ((~ ('#form5') | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 define([status(thm)])).
% 25.80/3.95 thf(zip_derived_cl57, plain,
% 25.80/3.95 (( ('#form5')
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ '#sk4')))),
% 25.80/3.95 inference('renaming', [status(thm)], [zip_derived_cl49, zip_derived_cl54])).
% 25.80/3.95 thf(zip_derived_cl78, plain, (~ ('#form5')),
% 25.80/3.95 inference('clc', [status(thm)], [zip_derived_cl55, zip_derived_cl10])).
% 25.80/3.95 thf(zip_derived_cl6, plain, ( ('#sk1' @ cZERO)),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 25.80/3.95 thf(zip_derived_cl80, plain,
% 25.80/3.95 ((~ ('#sk1' @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ '#sk4')))),
% 25.80/3.95 inference('demod', [status(thm)],
% 25.80/3.95 [zip_derived_cl57, zip_derived_cl78, zip_derived_cl6])).
% 25.80/3.95 thf(zip_derived_cl92, plain,
% 25.80/3.95 (![X2 : ($i > $o) > $o]:
% 25.80/3.95 (~ ('#sk3' @ (cSUCC @ '#sk4') @ X2)
% 25.80/3.95 | ('#sk3' @ (cSUCC @ '#sk4') @ (cSUCC @ X2))
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 25.80/3.95 inference('demod', [status(thm)],
% 25.80/3.95 [zip_derived_cl72, zip_derived_cl78, zip_derived_cl6])).
% 25.80/3.95 thf(zip_derived_cl305, plain,
% 25.80/3.95 ((~ ('#sk1' @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ~ ('#sk3' @ (cSUCC @ '#sk4') @ '#sk4'))),
% 25.80/3.95 inference('sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl92])).
% 25.80/3.95 thf(zip_derived_cl307, plain,
% 25.80/3.95 ((~ ('#sk3' @ (cSUCC @ '#sk4') @ '#sk4') | ~ ('#sk1' @ (cSUCC @ '#sk4')))),
% 25.80/3.95 inference('simplify', [status(thm)], [zip_derived_cl305])).
% 25.80/3.95 thf(zip_derived_cl4938, plain,
% 25.80/3.95 ((~ ('#sk1' @ (cSUCC @ '#sk4')) | ~ ('#sk3' @ (cSUCC @ '#sk4') @ cZERO))),
% 25.80/3.95 inference('clc', [status(thm)], [zip_derived_cl4937, zip_derived_cl307])).
% 25.80/3.95 thf(zip_derived_cl53, plain,
% 25.80/3.95 (( ('#sk3' @ (cSUCC @ '#sk4') @ cZERO)
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ cZERO))),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl48])).
% 25.80/3.95 thf(zip_derived_cl54, plain,
% 25.80/3.95 ((~ ('#form5') | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2'))))),
% 25.80/3.95 define([status(thm)])).
% 25.80/3.95 thf(zip_derived_cl61, plain,
% 25.80/3.95 (( ('#form5')
% 25.80/3.95 | ~ ('#sk1' @ cZERO)
% 25.80/3.95 | ~ ('#sk1' @ (cSUCC @ '#sk4'))
% 25.80/3.95 | ('#sk3' @ (cSUCC @ '#sk4') @ cZERO))),
% 25.80/3.95 inference('renaming', [status(thm)], [zip_derived_cl53, zip_derived_cl54])).
% 25.80/3.95 thf(zip_derived_cl78, plain, (~ ('#form5')),
% 25.80/3.95 inference('clc', [status(thm)], [zip_derived_cl55, zip_derived_cl10])).
% 25.80/3.95 thf(zip_derived_cl6, plain, ( ('#sk1' @ cZERO)),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 25.80/3.95 thf(zip_derived_cl87, plain,
% 25.80/3.95 ((~ ('#sk1' @ (cSUCC @ '#sk4')) | ('#sk3' @ (cSUCC @ '#sk4') @ cZERO))),
% 25.80/3.95 inference('demod', [status(thm)],
% 25.80/3.95 [zip_derived_cl61, zip_derived_cl78, zip_derived_cl6])).
% 25.80/3.95 thf(zip_derived_cl4939, plain, (~ ('#sk1' @ (cSUCC @ '#sk4'))),
% 25.80/3.95 inference('clc', [status(thm)], [zip_derived_cl4938, zip_derived_cl87])).
% 25.80/3.95 thf(zip_derived_cl4944, plain,
% 25.80/3.95 ((~ ('#sk3' @ '#sk4' @ '#sk4') | ~ ('#sk1' @ '#sk4'))),
% 25.80/3.95 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl4939])).
% 25.80/3.95 thf(zip_derived_cl32, plain,
% 25.80/3.95 (( ('#sk1' @ '#sk4')
% 25.80/3.95 | ((('#sk1' @ '#sk2') & (cNAT @ '#sk2')))
% 25.80/3.95 | ~ ('#sk1' @ cZERO))),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl29])).
% 25.80/3.95 thf(zip_derived_cl36, plain,
% 25.80/3.95 (( ('#sk1' @ '#sk2') | ~ ('#sk1' @ cZERO) | ('#sk1' @ '#sk4'))),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])).
% 25.80/3.95 thf(zip_derived_cl10, plain, (~ ('#sk1' @ '#sk2')),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 25.80/3.95 thf(zip_derived_cl6, plain, ( ('#sk1' @ cZERO)),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])).
% 25.80/3.95 thf(zip_derived_cl79, plain, ( ('#sk1' @ '#sk4')),
% 25.80/3.95 inference('demod', [status(thm)],
% 25.80/3.95 [zip_derived_cl36, zip_derived_cl10, zip_derived_cl6])).
% 25.80/3.95 thf(zip_derived_cl4947, plain, (~ ('#sk3' @ '#sk4' @ '#sk4')),
% 25.80/3.95 inference('demod', [status(thm)], [zip_derived_cl4944, zip_derived_cl79])).
% 25.80/3.95 thf(zip_derived_cl18, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o]:
% 25.80/3.95 ( (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ X0))) @
% 25.80/3.95 ((('#B') @ ('#sk3' @ X0) @ cSUCC)))))) &
% 25.80/3.95 ('#sk3' @ X0 @ cZERO)))
% 25.80/3.95 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])).
% 25.80/3.95 thf(zip_derived_cl22, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o]:
% 25.80/3.95 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ('#sk3' @ X0))) @
% 25.80/3.95 ((('#B') @ ('#sk3' @ X0) @ cSUCC))))))
% 25.80/3.95 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])).
% 25.80/3.95 thf(zip_derived_cl27, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o, X2 : ($i > $o) > $o]:
% 25.80/3.95 ( ((('#sk3' @ X0 @ X2) => ('#sk3' @ X0 @ (cSUCC @ X2))))
% 25.80/3.95 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 25.80/3.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])).
% 25.80/3.95 thf(zip_derived_cl31, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o, X2 : ($i > $o) > $o]:
% 25.80/3.95 (~ ('#sk3' @ X0 @ X2)
% 25.80/3.95 | ('#sk3' @ X0 @ (cSUCC @ X2))
% 25.80/3.95 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])).
% 25.80/3.95 thf(zip_derived_cl35, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o, X2 : ($i > $o) > $o]:
% 25.80/3.95 (~ ('#sk1' @ X0)
% 25.80/3.95 | ('#sk1' @ (cSUCC @ X0))
% 25.80/3.95 | ('#sk3' @ X0 @ (cSUCC @ X2))
% 25.80/3.95 | ~ ('#sk3' @ X0 @ X2))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl31])).
% 25.80/3.95 thf(zip_derived_cl89, plain,
% 25.80/3.95 (![X2 : (($i > $o) > $o) > $o]:
% 25.80/3.95 (~ (X2 @ (cSUCC @ ('#sk6' @ X2))) | (X2 @ '#sk4') | ~ (X2 @ cZERO))),
% 25.80/3.95 inference('demod', [status(thm)],
% 25.80/3.95 [zip_derived_cl71, zip_derived_cl78, zip_derived_cl6])).
% 25.80/3.95 thf(zip_derived_cl224, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o]:
% 25.80/3.95 (~ ('#sk3' @ X0 @ ('#sk6' @ ('#sk3' @ X0)))
% 25.80/3.95 | ('#sk1' @ (cSUCC @ X0))
% 25.80/3.95 | ~ ('#sk1' @ X0)
% 25.80/3.95 | ~ ('#sk3' @ X0 @ cZERO)
% 25.80/3.95 | ('#sk3' @ X0 @ '#sk4'))),
% 25.80/3.95 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl89])).
% 25.80/3.95 thf(zip_derived_cl91, plain,
% 25.80/3.95 (![X2 : (($i > $o) > $o) > $o]:
% 25.80/3.95 ( (X2 @ ('#sk6' @ X2)) | (X2 @ '#sk4') | ~ (X2 @ cZERO))),
% 25.80/3.95 inference('demod', [status(thm)],
% 25.80/3.95 [zip_derived_cl70, zip_derived_cl78, zip_derived_cl6])).
% 25.80/3.95 thf(zip_derived_cl3493, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o]:
% 25.80/3.95 ( ('#sk3' @ X0 @ '#sk4')
% 25.80/3.95 | ~ ('#sk3' @ X0 @ cZERO)
% 25.80/3.95 | ~ ('#sk1' @ X0)
% 25.80/3.95 | ('#sk1' @ (cSUCC @ X0)))),
% 25.80/3.95 inference('clc', [status(thm)], [zip_derived_cl224, zip_derived_cl91])).
% 25.80/3.95 thf(zip_derived_cl23, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o]:
% 25.80/3.95 ( ('#sk3' @ X0 @ cZERO)
% 25.80/3.95 | ((('#sk1' @ X0) => ('#sk1' @ (cSUCC @ X0)))))),
% 25.80/3.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])).
% 25.80/3.95 thf(zip_derived_cl28, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o]:
% 25.80/3.95 (~ ('#sk1' @ X0) | ('#sk1' @ (cSUCC @ X0)) | ('#sk3' @ X0 @ cZERO))),
% 25.80/3.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])).
% 25.80/3.95 thf(zip_derived_cl3494, plain,
% 25.80/3.95 (![X0 : ($i > $o) > $o]:
% 25.80/3.95 ( ('#sk1' @ (cSUCC @ X0)) | ~ ('#sk1' @ X0) | ('#sk3' @ X0 @ '#sk4'))),
% 25.80/3.95 inference('clc', [status(thm)], [zip_derived_cl3493, zip_derived_cl28])).
% 25.80/3.95 thf(zip_derived_cl4939, plain, (~ ('#sk1' @ (cSUCC @ '#sk4'))),
% 25.80/3.95 inference('clc', [status(thm)], [zip_derived_cl4938, zip_derived_cl87])).
% 25.80/3.95 thf(zip_derived_cl4946, plain,
% 25.80/3.95 (( ('#sk3' @ '#sk4' @ '#sk4') | ~ ('#sk1' @ '#sk4'))),
% 25.80/3.95 inference('sup-', [status(thm)], [zip_derived_cl3494, zip_derived_cl4939])).
% 25.80/3.95 thf(zip_derived_cl79, plain, ( ('#sk1' @ '#sk4')),
% 25.80/3.95 inference('demod', [status(thm)],
% 25.80/3.95 [zip_derived_cl36, zip_derived_cl10, zip_derived_cl6])).
% 25.80/3.95 thf(zip_derived_cl4949, plain, ( ('#sk3' @ '#sk4' @ '#sk4')),
% 25.80/3.95 inference('demod', [status(thm)], [zip_derived_cl4946, zip_derived_cl79])).
% 25.80/3.95 thf(zip_derived_cl4986, plain, ($false),
% 25.80/3.95 inference('demod', [status(thm)],
% 25.80/3.95 [zip_derived_cl4947, zip_derived_cl4949])).
% 25.80/3.95
% 25.80/3.95 % SZS output end Refutation
% 25.80/3.95
% 25.80/3.95
% 25.80/3.95 % Terminating...
% 25.94/4.01 % Runner terminated.
% 25.94/4.01 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------