%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWV426^4 : TPTP v9.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.cY0LPIUuQz true
% Computer : n023.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 05:01:08 PM UTC 2025
% Result : Theorem 110.93s 14.69s
% Output : Refutation 110.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV426^4 : TPTP v9.2.0. Released v3.6.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.cY0LPIUuQz true
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Oct 1 12:49:23 EDT 2025
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.35 % Python version: Python 3.6.8
% 0.15/0.36 % Running in HO mode
% 0.58/0.66 % Total configuration time : 828
% 0.58/0.66 % Estimated wc time : 1656
% 0.58/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.59/0.79 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.80 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.80 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.81 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.61/0.82 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 0.61/0.96 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 110.93/14.69 % Solved by lams/30_b.l.sh.
% 110.93/14.69 % done 96 iterations in 13.823s
% 110.93/14.69 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 110.93/14.69 % SZS output start Refutation
% 110.93/14.69 thf(icl_says_type, type, icl_says: ($i > $o) > ($i > $o) > $i > $o).
% 110.93/14.69 thf('#sk19_type', type, '#sk19': $i).
% 110.93/14.69 thf(b_type, type, b: $i > $o).
% 110.93/14.69 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 110.93/14.69 thf(mnot_type, type, mnot: ($i > $o) > $i > $o).
% 110.93/14.69 thf(s_type, type, s: $i > $o).
% 110.93/14.69 thf('#sk13_type', type, '#sk13': ($i > $o) > $i > $i).
% 110.93/14.69 thf(rel_type, type, rel: $i > $i > $o).
% 110.93/14.69 thf(icl_atom_type, type, icl_atom: ($i > $o) > $i > $o).
% 110.93/14.69 thf(mimpl_type, type, mimpl: ($i > $o) > ($i > $o) > $i > $o).
% 110.93/14.69 thf(icl_impl_type, type, icl_impl: ($i > $o) > ($i > $o) > $i > $o).
% 110.93/14.69 thf(icl_princ_type, type, icl_princ: ($i > $o) > $i > $o).
% 110.93/14.69 thf(a_type, type, a: $i > $o).
% 110.93/14.69 thf(mvalid_type, type, mvalid: ($i > $o) > $o).
% 110.93/14.69 thf(iclval_type, type, iclval: ($i > $o) > $o).
% 110.93/14.69 thf(mbox_type, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 110.93/14.69 thf(cuc, conjecture,
% 110.93/14.69 (iclval @
% 110.93/14.69 ( icl_impl @
% 110.93/14.69 ( icl_says @
% 110.93/14.69 ( icl_impl @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @
% 110.93/14.69 ( icl_atom @ s ) ) @
% 110.93/14.69 ( icl_impl @
% 110.93/14.69 ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @
% 110.93/14.69 ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ))).
% 110.93/14.69 thf(zf_stmt_0, negated_conjecture,
% 110.93/14.69 (~( iclval @
% 110.93/14.69 ( icl_impl @
% 110.93/14.69 ( icl_says @
% 110.93/14.69 ( icl_impl @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @
% 110.93/14.69 ( icl_atom @ s ) ) @
% 110.93/14.69 ( icl_impl @
% 110.93/14.69 ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @
% 110.93/14.69 ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ) )),
% 110.93/14.69 inference('cnf.neg', [status(esa)], [cuc])).
% 110.93/14.69 thf(zip_derived_cl2, plain,
% 110.93/14.69 (~ (iclval @
% 110.93/14.69 (icl_impl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))))),
% 110.93/14.69 inference('cnf', [status(esa)], [zf_stmt_0])).
% 110.93/14.69 thf(icl_s4_valid, axiom,(( iclval @ (X0)) = ((mvalid @ X0)))).
% 110.93/14.69 thf('0', plain, (![X0:( $i > $o )]: ( ( iclval @ X0 ) = ( mvalid @ X0 ) )),
% 110.93/14.69 define([status(thm)])).
% 110.93/14.69 thf(zip_derived_cl14, plain,
% 110.93/14.69 (~ (mvalid @
% 110.93/14.69 (icl_impl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl2, '0'])).
% 110.93/14.69 thf(mvalid, axiom, ~ (mvalid @ X0) =>
% 110.93/14.69 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))).
% 110.93/14.69 thf('1', plain,
% 110.93/14.69 (![X0:( $i > $o )]:
% 110.93/14.69 ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )),
% 110.93/14.69 inference('rw.lit', [status(esa)], [mvalid])).
% 110.93/14.69 thf(zip_derived_cl15, plain,
% 110.93/14.69 (~ (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (icl_impl @
% 110.93/14.69 (icl_says @
% 110.93/14.69 (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @
% 110.93/14.69 (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 Y0))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl14, '1'])).
% 110.93/14.69 thf(zip_derived_cl16, plain,
% 110.93/14.69 (~ (icl_impl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 '#sk19')),
% 110.93/14.69 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])).
% 110.93/14.69 thf(icl_impl, axiom,(( icl_impl @ (X0)@ (X1)@ (X2)) =
% 110.93/14.69 ((mbox @ rel @ (mimpl @ X0 @ X1) @ X2)))).
% 110.93/14.69 thf('2', plain,
% 110.93/14.69 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 110.93/14.69 ( ( icl_impl @ X0 @ X1 @ X2 ) =
% 110.93/14.69 ( mbox @ rel @ ( mimpl @ X0 @ X1 ) @ X2 ) )),
% 110.93/14.69 define([status(thm)])).
% 110.93/14.69 thf(zip_derived_cl17, plain,
% 110.93/14.69 (~ (mbox @ rel @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl16, '2'])).
% 110.93/14.69 thf(mbox, axiom, ~ (mbox @ X0 @ X1 @ X2) =>
% 110.93/14.69 ((((!!) @ (^[Y0 : $i]: (((X0 @ X2 @ Y0) => (X1 @ Y0)))))) != ($true))).
% 110.93/14.69 thf('3', plain,
% 110.93/14.69 (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 110.93/14.69 ( ( ~( mbox @ X0 @ X1 @ X2 ) ) <=>
% 110.93/14.69 ( ~( ![X7:$i]: ( ( X0 @ X2 @ X7 ) => ( X1 @ X7 ) ) ) ) )),
% 110.93/14.69 inference('rw.lit', [status(esa)], [mbox])).
% 110.93/14.69 thf(zip_derived_cl18, plain,
% 110.93/14.69 (~ (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (((rel @ '#sk19' @ Y0) => (mimpl @
% 110.93/14.69 (icl_says @
% 110.93/14.69 (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @
% 110.93/14.69 (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 Y0))))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl17, '3'])).
% 110.93/14.69 thf(zip_derived_cl19, plain,
% 110.93/14.69 (~ (((rel @ '#sk19' @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) =>
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))))),
% 110.93/14.69 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl18])).
% 110.93/14.69 thf(mimpl, axiom,(( mimpl @ (X0)@ (X1)@ (X2)) =
% 110.93/14.69 ((mor @ (mnot @ X0) @ X1 @ X2)))).
% 110.93/14.69 thf('4', plain,
% 110.93/14.69 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 110.93/14.69 ( ( mimpl @ X0 @ X1 @ X2 ) = ( mor @ ( mnot @ X0 ) @ X1 @ X2 ) )),
% 110.93/14.69 define([status(thm)])).
% 110.93/14.69 thf(zip_derived_cl20, plain,
% 110.93/14.69 (~ (((rel @ '#sk19' @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) =>
% 110.93/14.69 (mor @
% 110.93/14.69 (mnot @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s))) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl19, '4'])).
% 110.93/14.69 thf(zip_derived_cl22, plain,
% 110.93/14.69 (~ (mor @
% 110.93/14.69 (mnot @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s))) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])).
% 110.93/14.69 thf(mor, axiom, ~ (mor @ X0 @ X1 @ X2) =>
% 110.93/14.69 ((((X1 @ X2) | (X0 @ X2))) != ($true))).
% 110.93/14.69 thf('5', plain,
% 110.93/14.69 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 110.93/14.69 ( ( ~( mor @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X1 @ X2 ) | ( X0 @ X2 ) ) ) )),
% 110.93/14.69 inference('rw.lit', [status(esa)], [mor])).
% 110.93/14.69 thf(zip_derived_cl23, plain,
% 110.93/14.69 (~ (((icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) |
% 110.93/14.69 (mnot @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl22, '5'])).
% 110.93/14.69 thf(zip_derived_cl24, plain,
% 110.93/14.69 (~ (((mbox @ rel @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) |
% 110.93/14.69 (mnot @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl23, '2'])).
% 110.93/14.69 thf(zip_derived_cl25, plain,
% 110.93/14.69 (~ (mbox @ rel @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))),
% 110.93/14.69 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])).
% 110.93/14.69 thf(zip_derived_cl27, plain,
% 110.93/14.69 (~ (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (((rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @
% 110.93/14.69 (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @
% 110.93/14.69 (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 Y0) => (mimpl @
% 110.93/14.69 (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)) @ Y0))))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl25, '3'])).
% 110.93/14.69 thf(zip_derived_cl29, plain,
% 110.93/14.69 (~ (((rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))) =>
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))))),
% 110.93/14.69 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl27])).
% 110.93/14.69 thf(zip_derived_cl32, plain,
% 110.93/14.69 (~ (((rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))) =>
% 110.93/14.69 (mor @ (mnot @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s))) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl29, '4'])).
% 110.93/14.69 thf(zip_derived_cl34, plain,
% 110.93/14.69 (~ (mor @ (mnot @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s))) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl32])).
% 110.93/14.69 thf(zip_derived_cl36, plain,
% 110.93/14.69 (~ (((icl_says @ (icl_princ @ b) @ (icl_atom @ s) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))) |
% 110.93/14.69 (mnot @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl34, '5'])).
% 110.93/14.69 thf(icl_says, axiom,(( icl_says @ (X0)@ (X1)@ (X2)) =
% 110.93/14.69 ((mbox @ rel @ (mor @ X0 @ X1) @ X2)))).
% 110.93/14.69 thf('6', plain,
% 110.93/14.69 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 110.93/14.69 ( ( icl_says @ X0 @ X1 @ X2 ) = ( mbox @ rel @ ( mor @ X0 @ X1 ) @ X2 ) )),
% 110.93/14.69 define([status(thm)])).
% 110.93/14.69 thf(zip_derived_cl38, plain,
% 110.93/14.69 (~ (((mbox @ rel @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))) |
% 110.93/14.69 (mnot @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl36, '6'])).
% 110.93/14.69 thf(zip_derived_cl39, plain,
% 110.93/14.69 (~ (mbox @ rel @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))),
% 110.93/14.69 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl38])).
% 110.93/14.69 thf(zip_derived_cl42, plain,
% 110.93/14.69 (~ (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (((rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @
% 110.93/14.69 (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @
% 110.93/14.69 (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) @
% 110.93/14.69 Y0) => (mor @ (icl_princ @ b) @ (icl_atom @ s) @ Y0))))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl39, '3'])).
% 110.93/14.69 thf(zip_derived_cl46, plain,
% 110.93/14.69 (~ (((rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))) =>
% 110.93/14.69 (mor @ (icl_princ @ b) @ (icl_atom @ s) @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))))))),
% 110.93/14.69 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl42])).
% 110.93/14.69 thf(zip_derived_cl51, plain,
% 110.93/14.69 (~ (mor @ (icl_princ @ b) @ (icl_atom @ s) @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 110.93/14.69 thf(zip_derived_cl54, plain,
% 110.93/14.69 (~ (((icl_atom @ s @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))) |
% 110.93/14.69 (icl_princ @ b @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl51, '5'])).
% 110.93/14.69 thf(icl_atom, axiom,(( icl_atom @ (X0)@ (X1)) = ((mbox @ rel @ X0 @ X1)))).
% 110.93/14.69 thf('7', plain,
% 110.93/14.69 (![X1:$i,X0:( $i > $o )]:
% 110.93/14.69 ( ( icl_atom @ X0 @ X1 ) = ( mbox @ rel @ X0 @ X1 ) )),
% 110.93/14.69 define([status(thm)])).
% 110.93/14.69 thf(icl_princ, axiom,(( icl_princ @ (X0)@ (X1)) = ((X0 @ X1)))).
% 110.93/14.69 thf('8', plain,
% 110.93/14.69 (![X0:( $i > $o ),X1:$i]: ( ( icl_princ @ X0 @ X1 ) = ( X0 @ X1 ) )),
% 110.93/14.69 define([status(thm)])).
% 110.93/14.69 thf(zip_derived_cl57, plain,
% 110.93/14.69 (~ (((mbox @ rel @ s @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))) |
% 110.93/14.69 (b @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))))))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl54, '7', '8'])).
% 110.93/14.69 thf(zip_derived_cl58, plain,
% 110.93/14.69 (~ (mbox @ rel @ s @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))))),
% 110.93/14.69 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl57])).
% 110.93/14.69 thf(zip_derived_cl63, plain,
% 110.93/14.69 (~ (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (((rel @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @
% 110.93/14.69 (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @
% 110.93/14.69 (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))) @
% 110.93/14.69 Y0) => (s @ Y0))))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl58, '3'])).
% 110.93/14.69 thf(zip_derived_cl67, plain,
% 110.93/14.69 (~ (((rel @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))) @
% 110.93/14.69 ('#sk13' @ s @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))))) =>
% 110.93/14.69 (s @
% 110.93/14.69 ('#sk13' @ s @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))))))),
% 110.93/14.69 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl63])).
% 110.93/14.69 thf(zip_derived_cl71, plain,
% 110.93/14.69 ( (rel @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))) @
% 110.93/14.69 ('#sk13' @ s @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])).
% 110.93/14.69 thf(zip_derived_cl59, plain,
% 110.93/14.69 (~ (b @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))))),
% 110.93/14.69 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl57])).
% 110.93/14.69 thf(zip_derived_cl33, plain,
% 110.93/14.69 ( (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl32])).
% 110.93/14.69 thf(zip_derived_cl72, plain,
% 110.93/14.69 (~ (s @
% 110.93/14.69 ('#sk13' @ s @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])).
% 110.93/14.69 thf(zip_derived_cl50, plain,
% 110.93/14.69 ( (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) @
% 110.93/14.69 ('#sk13' @ (mor @ (icl_princ @ b) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 110.93/14.69 thf(zip_derived_cl26, plain,
% 110.93/14.69 (~ (mnot @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))),
% 110.93/14.69 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])).
% 110.93/14.69 thf(mnot, axiom, ~ (mnot @ X0 @ X1) => ((X0 @ X1) = ($true))).
% 110.93/14.69 thf('9', plain,
% 110.93/14.69 (![X0:( $i > $o ),X1:$i]: ( ( ~( mnot @ X0 @ X1 ) ) <=> ( X0 @ X1 ) )),
% 110.93/14.69 inference('rw.lit', [status(esa)], [mnot])).
% 110.93/14.69 thf(zip_derived_cl28, plain,
% 110.93/14.69 ( (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl26, '9'])).
% 110.93/14.69 thf(zip_derived_cl30, plain,
% 110.93/14.69 ( (mbox @ rel @
% 110.93/14.69 (mor @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19'))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl28, '6'])).
% 110.93/14.69 thf(mbox, axiom, (mbox @ X0 @ X1 @ X2) =>
% 110.93/14.69 ((((!!) @ (^[Y0 : $i]: (((X0 @ X2 @ Y0) => (X1 @ Y0)))))) = ($true))).
% 110.93/14.69 thf('10', plain,
% 110.93/14.69 (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 110.93/14.69 ( ( mbox @ X0 @ X1 @ X2 ) <=>
% 110.93/14.69 ( ![X7:$i]: ( ( X0 @ X2 @ X7 ) => ( X1 @ X7 ) ) ) )),
% 110.93/14.69 inference('rw.lit', [status(esa)], [mbox])).
% 110.93/14.69 thf(zip_derived_cl31, plain,
% 110.93/14.69 ( (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (((rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @
% 110.93/14.69 (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @
% 110.93/14.69 (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 Y0) => (mor @
% 110.93/14.69 (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s) @ Y0))))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl30, '10'])).
% 110.93/14.69 thf(zip_derived_cl35, plain,
% 110.93/14.69 (![X2 : $i]:
% 110.93/14.69 (((rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X2) => (mor @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s) @ X2)))),
% 110.93/14.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])).
% 110.93/14.69 thf(zip_derived_cl37, plain,
% 110.93/14.69 (![X2 : $i]:
% 110.93/14.69 (~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X2)
% 110.93/14.69 | (mor @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s) @ X2))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])).
% 110.93/14.69 thf(mor, axiom, (mor @ X0 @ X1 @ X2) =>
% 110.93/14.69 ((((X1 @ X2) | (X0 @ X2))) = ($true))).
% 110.93/14.69 thf('11', plain,
% 110.93/14.69 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 110.93/14.69 ( ( mor @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) | ( X1 @ X2 ) ) )),
% 110.93/14.69 inference('rw.lit', [status(esa)], [mor])).
% 110.93/14.69 thf(zip_derived_cl41, plain,
% 110.93/14.69 (![X0 : $i]:
% 110.93/14.69 ( (((icl_atom @ s @ X0) | (icl_impl @ (icl_princ @ a) @
% 110.93/14.69 (icl_princ @ b) @ X0)))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl37, '11'])).
% 110.93/14.69 thf(zip_derived_cl44, plain,
% 110.93/14.69 (![X0 : $i]:
% 110.93/14.69 ( (((mbox @ rel @ s @ X0) | (mbox @ rel @
% 110.93/14.69 (mimpl @ (icl_princ @ a) @ (icl_princ @ b)) @ X0)))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl41, '7', '2'])).
% 110.93/14.69 thf(zip_derived_cl45, plain,
% 110.93/14.69 (![X0 : $i]:
% 110.93/14.69 ( (mbox @ rel @ s @ X0)
% 110.93/14.69 | (mbox @ rel @ (mimpl @ (icl_princ @ a) @ (icl_princ @ b)) @ X0)
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0))),
% 110.93/14.69 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])).
% 110.93/14.69 thf(zip_derived_cl49, plain,
% 110.93/14.69 (![X0 : $i]:
% 110.93/14.69 ( (((!!) @ (^[Y0 : $i]: (((rel @ X0 @ Y0) => (s @ Y0))))))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0)
% 110.93/14.69 | (mbox @ rel @ (mimpl @ (icl_princ @ a) @ (icl_princ @ b)) @ X0))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl45, '10'])).
% 110.93/14.69 thf(zip_derived_cl53, plain,
% 110.93/14.69 (![X0 : $i]:
% 110.93/14.69 ( (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (((rel @ X0 @ Y0) => (mimpl @ (icl_princ @ a) @
% 110.93/14.69 (icl_princ @ b) @ Y0))))))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0)
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]: (((rel @ X0 @ Y0) => (s @ Y0)))))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl49, '10'])).
% 110.93/14.69 thf(zip_derived_cl56, plain,
% 110.93/14.69 (![X0 : $i, X2 : $i]:
% 110.93/14.69 ( (((rel @ X0 @ X2) => (mimpl @ (icl_princ @ a) @ (icl_princ @ b) @
% 110.93/14.69 X2)))
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]: (((rel @ X0 @ Y0) => (s @ Y0))))))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0))),
% 110.93/14.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl53])).
% 110.93/14.69 thf(zip_derived_cl61, plain,
% 110.93/14.69 (![X0 : $i, X2 : $i]:
% 110.93/14.69 ( (((rel @ X0 @ X2) => (mor @ (mnot @ (icl_princ @ a)) @
% 110.93/14.69 (icl_princ @ b) @ X2)))
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]: (((rel @ X0 @ Y0) => (s @ Y0))))))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl56, '4'])).
% 110.93/14.69 thf(zip_derived_cl62, plain,
% 110.93/14.69 (![X0 : $i, X2 : $i]:
% 110.93/14.69 (~ (rel @ X0 @ X2)
% 110.93/14.69 | (mor @ (mnot @ (icl_princ @ a)) @ (icl_princ @ b) @ X2)
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0)
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]: (((rel @ X0 @ Y0) => (s @ Y0)))))))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])).
% 110.93/14.69 thf(zip_derived_cl66, plain,
% 110.93/14.69 (![X0 : $i, X1 : $i]:
% 110.93/14.69 ( (((icl_princ @ b @ X1) | (mnot @ (icl_princ @ a) @ X1)))
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]: (((rel @ X0 @ Y0) => (s @ Y0))))))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0)
% 110.93/14.69 | ~ (rel @ X0 @ X1))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl62, '11'])).
% 110.93/14.69 thf(zip_derived_cl69, plain,
% 110.93/14.69 (![X0 : $i, X1 : $i]:
% 110.93/14.69 ( (((b @ X1) | (mnot @ (icl_princ @ a) @ X1)))
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]: (((rel @ X0 @ Y0) => (s @ Y0))))))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0)
% 110.93/14.69 | ~ (rel @ X0 @ X1))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl66, '8'])).
% 110.93/14.69 thf(zip_derived_cl70, plain,
% 110.93/14.69 (![X0 : $i, X1 : $i]:
% 110.93/14.69 ( (b @ X1)
% 110.93/14.69 | (mnot @ (icl_princ @ a) @ X1)
% 110.93/14.69 | ~ (rel @ X0 @ X1)
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0)
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]: (((rel @ X0 @ Y0) => (s @ Y0)))))))),
% 110.93/14.69 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl69])).
% 110.93/14.69 thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))).
% 110.93/14.69 thf('12', plain,
% 110.93/14.69 (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )),
% 110.93/14.69 inference('rw.lit', [status(esa)], [mnot])).
% 110.93/14.69 thf(zip_derived_cl74, plain,
% 110.93/14.69 (![X0 : $i, X1 : $i]:
% 110.93/14.69 (~ (icl_princ @ a @ X1)
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]: (((rel @ X0 @ Y0) => (s @ Y0))))))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0)
% 110.93/14.69 | ~ (rel @ X0 @ X1)
% 110.93/14.69 | (b @ X1))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl70, '12'])).
% 110.93/14.69 thf(zip_derived_cl76, plain,
% 110.93/14.69 (![X0 : $i, X1 : $i]:
% 110.93/14.69 (~ (a @ X1)
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]: (((rel @ X0 @ Y0) => (s @ Y0))))))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0)
% 110.93/14.69 | ~ (rel @ X0 @ X1)
% 110.93/14.69 | (b @ X1))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl74, '8'])).
% 110.93/14.69 thf(zip_derived_cl77, plain,
% 110.93/14.69 (![X0 : $i, X1 : $i, X3 : $i]:
% 110.93/14.69 ( (((rel @ X0 @ X3) => (s @ X3)))
% 110.93/14.69 | (b @ X1)
% 110.93/14.69 | ~ (rel @ X0 @ X1)
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0)
% 110.93/14.69 | ~ (a @ X1))),
% 110.93/14.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl76])).
% 110.93/14.69 thf(zip_derived_cl78, plain,
% 110.93/14.69 (![X0 : $i, X1 : $i, X3 : $i]:
% 110.93/14.69 (~ (rel @ X0 @ X3)
% 110.93/14.69 | (s @ X3)
% 110.93/14.69 | ~ (a @ X1)
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19') @
% 110.93/14.69 X0)
% 110.93/14.69 | ~ (rel @ X0 @ X1)
% 110.93/14.69 | (b @ X1))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl77])).
% 110.93/14.69 thf(trans_axiom, axiom,
% 110.93/14.69 (![B:( $i > $o )]:
% 110.93/14.69 ( mvalid @
% 110.93/14.69 ( mimpl @ ( mbox @ rel @ B ) @ ( mbox @ rel @ ( mbox @ rel @ B ) ) ) ))).
% 110.93/14.69 thf(zip_derived_cl1, plain,
% 110.93/14.69 ( (((!!) @ (^[Y0 : $i > $o]:
% 110.93/14.69 (mvalid @
% 110.93/14.69 (mimpl @ (mbox @ rel @ Y0) @
% 110.93/14.69 (mbox @ rel @ (mbox @ rel @ Y0)))))))),
% 110.93/14.69 inference('cnf', [status(esa)], [trans_axiom])).
% 110.93/14.69 thf(zip_derived_cl79, plain,
% 110.93/14.69 (![X2 : $i > $o]:
% 110.93/14.69 (mvalid @
% 110.93/14.69 (mimpl @ (mbox @ rel @ X2) @ (mbox @ rel @ (mbox @ rel @ X2))))),
% 110.93/14.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])).
% 110.93/14.69 thf(mvalid, axiom, (mvalid @ X0) =>
% 110.93/14.69 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))).
% 110.93/14.69 thf('13', plain,
% 110.93/14.69 (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )),
% 110.93/14.69 inference('rw.lit', [status(esa)], [mvalid])).
% 110.93/14.69 thf(zip_derived_cl80, plain,
% 110.93/14.69 (![X0 : $i > $o]:
% 110.93/14.69 (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (mimpl @ (mbox @ rel @ X0) @
% 110.93/14.69 (mbox @ rel @ (mbox @ rel @ X0)) @ Y0))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl79, '13'])).
% 110.93/14.69 thf(zip_derived_cl81, plain,
% 110.93/14.69 (![X0 : $i > $o, X2 : $i]:
% 110.93/14.69 (mimpl @ (mbox @ rel @ X0) @ (mbox @ rel @ (mbox @ rel @ X0)) @ X2)),
% 110.93/14.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl80])).
% 110.93/14.69 thf(zip_derived_cl82, plain,
% 110.93/14.69 (![X0 : $i > $o, X2 : $i]:
% 110.93/14.69 (mor @ (mnot @ (mbox @ rel @ X0)) @
% 110.93/14.69 (mbox @ rel @ (mbox @ rel @ X0)) @ X2)),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl81, '4'])).
% 110.93/14.69 thf(zip_derived_cl83, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i]:
% 110.93/14.69 (((mbox @ rel @ (mbox @ rel @ X0) @ X1) | (mnot @
% 110.93/14.69 (mbox @ rel @ X0) @ X1)))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl82, '11'])).
% 110.93/14.69 thf(zip_derived_cl84, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i]:
% 110.93/14.69 ( (mbox @ rel @ (mbox @ rel @ X0) @ X1)
% 110.93/14.69 | (mnot @ (mbox @ rel @ X0) @ X1))),
% 110.93/14.69 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl83])).
% 110.93/14.69 thf(zip_derived_cl85, plain,
% 110.93/14.69 (![X0 : $i, X1 : $i > $o]:
% 110.93/14.69 ( (((!!) @ (^[Y0 : $i]: (((rel @ X0 @ Y0) => (mbox @ rel @ X1 @ Y0))))))
% 110.93/14.69 | (mnot @ (mbox @ rel @ X1) @ X0))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl84, '10'])).
% 110.93/14.69 thf(zip_derived_cl86, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i]:
% 110.93/14.69 (~ (mbox @ rel @ X0 @ X1)
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (((rel @ X1 @ Y0) => (mbox @ rel @ X0 @ Y0)))))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl85, '12'])).
% 110.93/14.69 thf(zip_derived_cl87, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i]:
% 110.93/14.69 (~ (((!!) @ (^[Y0 : $i]: (((rel @ X1 @ Y0) => (X0 @ Y0))))))
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (((rel @ X1 @ Y0) => (mbox @ rel @ X0 @ Y0)))))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl86, '3'])).
% 110.93/14.69 thf(zip_derived_cl88, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i]:
% 110.93/14.69 (~ (((rel @ X1 @ ('#sk13' @ X0 @ X1)) => (X0 @ ('#sk13' @ X0 @ X1))))
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (((rel @ X1 @ Y0) => (mbox @ rel @ X0 @ Y0)))))))),
% 110.93/14.69 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl87])).
% 110.93/14.69 thf(zip_derived_cl89, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i]:
% 110.93/14.69 ( (rel @ X1 @ ('#sk13' @ X0 @ X1))
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (((rel @ X1 @ Y0) => (mbox @ rel @ X0 @ Y0)))))))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])).
% 110.93/14.69 thf(zip_derived_cl91, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i, X3 : $i]:
% 110.93/14.69 ( (((rel @ X1 @ X3) => (mbox @ rel @ X0 @ X3)))
% 110.93/14.69 | (rel @ X1 @ ('#sk13' @ X0 @ X1)))),
% 110.93/14.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl89])).
% 110.93/14.69 thf(zip_derived_cl93, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i, X3 : $i]:
% 110.93/14.69 (~ (rel @ X1 @ X3)
% 110.93/14.69 | (mbox @ rel @ X0 @ X3)
% 110.93/14.69 | (rel @ X1 @ ('#sk13' @ X0 @ X1)))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl91])).
% 110.93/14.69 thf(zip_derived_cl95, plain,
% 110.93/14.69 (![X0 : $i, X1 : $i > $o, X2 : $i]:
% 110.93/14.69 ( (((!!) @ (^[Y0 : $i]: (((rel @ X2 @ Y0) => (X1 @ Y0))))))
% 110.93/14.69 | (rel @ X0 @ ('#sk13' @ X1 @ X0))
% 110.93/14.69 | ~ (rel @ X0 @ X2))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl93, '10'])).
% 110.93/14.69 thf(zip_derived_cl97, plain,
% 110.93/14.69 (![X0 : $i, X1 : $i > $o, X2 : $i, X4 : $i]:
% 110.93/14.69 ( (((rel @ X2 @ X4) => (X1 @ X4)))
% 110.93/14.69 | ~ (rel @ X0 @ X2)
% 110.93/14.69 | (rel @ X0 @ ('#sk13' @ X1 @ X0)))),
% 110.93/14.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])).
% 110.93/14.69 thf(zip_derived_cl99, plain,
% 110.93/14.69 (![X0 : $i, X1 : $i > $o, X2 : $i, X4 : $i]:
% 110.93/14.69 (~ (rel @ X2 @ X4)
% 110.93/14.69 | (X1 @ X4)
% 110.93/14.69 | (rel @ X0 @ ('#sk13' @ X1 @ X0))
% 110.93/14.69 | ~ (rel @ X0 @ X2))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])).
% 110.93/14.69 thf(zip_derived_cl90, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i]:
% 110.93/14.69 (~ (X0 @ ('#sk13' @ X0 @ X1))
% 110.93/14.69 | (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (((rel @ X1 @ Y0) => (mbox @ rel @ X0 @ Y0)))))))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])).
% 110.93/14.69 thf(zip_derived_cl92, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i, X3 : $i]:
% 110.93/14.69 ( (((rel @ X1 @ X3) => (mbox @ rel @ X0 @ X3)))
% 110.93/14.69 | ~ (X0 @ ('#sk13' @ X0 @ X1)))),
% 110.93/14.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl90])).
% 110.93/14.69 thf(zip_derived_cl94, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i, X3 : $i]:
% 110.93/14.69 (~ (rel @ X1 @ X3)
% 110.93/14.69 | (mbox @ rel @ X0 @ X3)
% 110.93/14.69 | ~ (X0 @ ('#sk13' @ X0 @ X1)))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])).
% 110.93/14.69 thf(zip_derived_cl96, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i, X2 : $i]:
% 110.93/14.69 ( (((!!) @ (^[Y0 : $i]: (((rel @ X2 @ Y0) => (X0 @ Y0))))))
% 110.93/14.69 | ~ (X0 @ ('#sk13' @ X0 @ X1))
% 110.93/14.69 | ~ (rel @ X1 @ X2))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl94, '10'])).
% 110.93/14.69 thf(zip_derived_cl98, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i, X2 : $i, X4 : $i]:
% 110.93/14.69 ( (((rel @ X2 @ X4) => (X0 @ X4)))
% 110.93/14.69 | ~ (rel @ X1 @ X2)
% 110.93/14.69 | ~ (X0 @ ('#sk13' @ X0 @ X1)))),
% 110.93/14.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl96])).
% 110.93/14.69 thf(zip_derived_cl100, plain,
% 110.93/14.69 (![X0 : $i > $o, X1 : $i, X2 : $i, X4 : $i]:
% 110.93/14.69 (~ (rel @ X2 @ X4)
% 110.93/14.69 | (X0 @ X4)
% 110.93/14.69 | ~ (X0 @ ('#sk13' @ X0 @ X1))
% 110.93/14.69 | ~ (rel @ X1 @ X2))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl98])).
% 110.93/14.69 thf(zip_derived_cl40, plain,
% 110.93/14.69 (~ (mnot @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))),
% 110.93/14.69 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl38])).
% 110.93/14.69 thf(zip_derived_cl43, plain,
% 110.93/14.69 ( (icl_says @ (icl_princ @ a) @ (icl_atom @ s) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl40, '9'])).
% 110.93/14.69 thf(zip_derived_cl47, plain,
% 110.93/14.69 ( (mbox @ rel @ (mor @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl43, '6'])).
% 110.93/14.69 thf(zip_derived_cl48, plain,
% 110.93/14.69 ( (((!!) @ (^[Y0 : $i]:
% 110.93/14.69 (((rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @
% 110.93/14.69 (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @
% 110.93/14.69 (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) @
% 110.93/14.69 Y0) => (mor @ (icl_princ @ a) @ (icl_atom @ s) @ Y0))))))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl47, '10'])).
% 110.93/14.69 thf(zip_derived_cl52, plain,
% 110.93/14.69 (![X2 : $i]:
% 110.93/14.69 (((rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) @
% 110.93/14.69 X2) => (mor @ (icl_princ @ a) @ (icl_atom @ s) @ X2)))),
% 110.93/14.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl48])).
% 110.93/14.69 thf(zip_derived_cl55, plain,
% 110.93/14.69 (![X2 : $i]:
% 110.93/14.69 (~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) @
% 110.93/14.69 X2)
% 110.93/14.69 | (mor @ (icl_princ @ a) @ (icl_atom @ s) @ X2))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 110.93/14.69 thf(zip_derived_cl60, plain,
% 110.93/14.69 (![X0 : $i]:
% 110.93/14.69 ( (((icl_atom @ s @ X0) | (icl_princ @ a @ X0)))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) @
% 110.93/14.69 X0))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl55, '11'])).
% 110.93/14.69 thf(zip_derived_cl64, plain,
% 110.93/14.69 (![X0 : $i]:
% 110.93/14.69 ( (((mbox @ rel @ s @ X0) | (a @ X0)))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) @
% 110.93/14.69 X0))),
% 110.93/14.69 inference('rw', [status(thm)], [zip_derived_cl60, '7', '8'])).
% 110.93/14.69 thf(zip_derived_cl65, plain,
% 110.93/14.69 (![X0 : $i]:
% 110.93/14.69 ( (mbox @ rel @ s @ X0)
% 110.93/14.69 | (a @ X0)
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) @
% 110.93/14.69 X0))),
% 110.93/14.69 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])).
% 110.93/14.69 thf(zip_derived_cl68, plain,
% 110.93/14.69 (![X0 : $i]:
% 110.93/14.69 ( (((!!) @ (^[Y0 : $i]: (((rel @ X0 @ Y0) => (s @ Y0))))))
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) @
% 110.93/14.69 X0)
% 110.93/14.69 | (a @ X0))),
% 110.93/14.69 inference('rw_clause', [status(thm)], [zip_derived_cl65, '10'])).
% 110.93/14.69 thf(zip_derived_cl73, plain,
% 110.93/14.69 (![X0 : $i, X2 : $i]:
% 110.93/14.69 ( (((rel @ X0 @ X2) => (s @ X2)))
% 110.93/14.69 | (a @ X0)
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) @
% 110.93/14.69 X0))),
% 110.93/14.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl68])).
% 110.93/14.69 thf(zip_derived_cl75, plain,
% 110.93/14.69 (![X0 : $i, X2 : $i]:
% 110.93/14.69 (~ (rel @ X0 @ X2)
% 110.93/14.69 | (s @ X2)
% 110.93/14.69 | ~ (rel @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s))) @
% 110.93/14.69 ('#sk13' @
% 110.93/14.69 (mimpl @
% 110.93/14.69 (icl_says @ (icl_impl @ (icl_princ @ a) @ (icl_princ @ b)) @
% 110.93/14.69 (icl_atom @ s)) @
% 110.93/14.69 (icl_impl @ (icl_says @ (icl_princ @ a) @ (icl_atom @ s)) @
% 110.93/14.69 (icl_says @ (icl_princ @ b) @ (icl_atom @ s)))) @
% 110.93/14.69 '#sk19')) @
% 110.93/14.69 X0)
% 110.93/14.69 | (a @ X0))),
% 110.93/14.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])).
% 110.93/14.69 thf(zip_derived_cl2468, plain, ($false),
% 110.93/14.69 inference('eprover', [status(thm)],
% 110.93/14.69 [zip_derived_cl71, zip_derived_cl59, zip_derived_cl33,
% 110.93/14.69 zip_derived_cl72, zip_derived_cl50, zip_derived_cl78,
% 110.93/14.69 zip_derived_cl99, zip_derived_cl100, zip_derived_cl75])).
% 110.93/14.69
% 110.93/14.69 % SZS output end Refutation
% 110.93/14.69
% 110.93/14.69
% 110.93/14.69 % Terminating...
% 111.81/14.87 % Runner terminated.
% 111.81/14.89 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------