TSTP Solution File: SYO064^4.004 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO064^4.004 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8n6EYUMcIL true
% Computer : n025.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 : Fri Sep 1 05:49:30 EDT 2023
% Result : Theorem 243.05s 31.88s
% Output : Refutation 243.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO064^4.004 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8n6EYUMcIL true
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 03:31:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.21/0.67 % Total configuration time : 828
% 0.21/0.67 % Estimated wc time : 1656
% 0.21/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.06/0.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.06/0.81 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 15.83/2.68 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 235.07/30.69 % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 30s
% 243.05/31.88 % Solved by lams/40_b.comb.sh.
% 243.05/31.88 % done 1081 iterations in 30.959s
% 243.05/31.88 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 243.05/31.88 % SZS output start Refutation
% 243.05/31.88 thf(iatom_type, type, iatom: ($i > $o) > $i > $o).
% 243.05/31.88 thf(a2_type, type, a2: $i > $o).
% 243.05/31.88 thf(ivalid_type, type, ivalid: ($i > $o) > $o).
% 243.05/31.88 thf('#sk11_type', type, '#sk11': $i > $i).
% 243.05/31.88 thf(a1_type, type, a1: $i > $o).
% 243.05/31.88 thf('#sk9_type', type, '#sk9': $i).
% 243.05/31.88 thf(irel_type, type, irel: $i > $i > $o).
% 243.05/31.88 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 243.05/31.88 thf('#sk1_type', type, '#sk1': $i > $i).
% 243.05/31.88 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 243.05/31.88 thf('#sk5_type', type, '#sk5': $i).
% 243.05/31.88 thf(ior_type, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 243.05/31.88 thf('#sk7_type', type, '#sk7': $i).
% 243.05/31.88 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o).
% 243.05/31.88 thf(a4_type, type, a4: $i > $o).
% 243.05/31.88 thf(iimplies_type, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 243.05/31.88 thf(a_type, type, a: $i > $o).
% 243.05/31.88 thf('#sk8_type', type, '#sk8': $i).
% 243.05/31.88 thf(iand_type, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 243.05/31.88 thf(b1_type, type, b1: $i > $o).
% 243.05/31.88 thf(b3_type, type, b3: $i > $o).
% 243.05/31.88 thf(b_type, type, b: $i > $o).
% 243.05/31.88 thf('#sk6_type', type, '#sk6': $i).
% 243.05/31.88 thf(mnot_type, type, mnot: ($i > $o) > $i > $o).
% 243.05/31.88 thf(b2_type, type, b2: $i > $o).
% 243.05/31.88 thf('#sk2_type', type, '#sk2': $i).
% 243.05/31.88 thf('#sk3_type', type, '#sk3': $i).
% 243.05/31.88 thf(a3_type, type, a3: $i > $o).
% 243.05/31.88 thf('#sk4_type', type, '#sk4': $i).
% 243.05/31.88 thf('#sk10_type', type, '#sk10': $i).
% 243.05/31.88 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 243.05/31.88 thf('#sk12_type', type, '#sk12': $i > $i).
% 243.05/31.88 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 243.05/31.88 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 243.05/31.88 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 243.05/31.88 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 243.05/31.88 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 243.05/31.88 thf(con, conjecture,
% 243.05/31.88 (ivalid @
% 243.05/31.88 ( ior @
% 243.05/31.88 ( iatom @ a ) @
% 243.05/31.88 ( ior @
% 243.05/31.88 ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @
% 243.05/31.88 ( ior @
% 243.05/31.88 ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @
% 243.05/31.88 ( ior @
% 243.05/31.88 ( iand @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @
% 243.05/31.88 ( iand @ ( iatom @ b3 ) @ ( iatom @ a4 ) ) ) ) ) ))).
% 243.05/31.88 thf(zf_stmt_0, negated_conjecture,
% 243.05/31.88 (~( ivalid @
% 243.05/31.88 ( ior @
% 243.05/31.88 ( iatom @ a ) @
% 243.05/31.88 ( ior @
% 243.05/31.88 ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @
% 243.05/31.88 ( ior @
% 243.05/31.88 ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @
% 243.05/31.88 ( ior @
% 243.05/31.88 ( iand @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @
% 243.05/31.88 ( iand @ ( iatom @ b3 ) @ ( iatom @ a4 ) ) ) ) ) ) )),
% 243.05/31.88 inference('cnf.neg', [status(esa)], [con])).
% 243.05/31.88 thf(zip_derived_cl9, plain,
% 243.05/31.88 (~ (ivalid @
% 243.05/31.88 (ior @ (iatom @ a) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b) @ (iatom @ a1)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4)))))))),
% 243.05/31.88 inference('cnf', [status(esa)], [zf_stmt_0])).
% 243.05/31.88 thf(ivalid, axiom, ~ (ivalid @ X0) =>
% 243.05/31.88 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))).
% 243.05/31.88 thf('0', plain,
% 243.05/31.88 (![X0:( $i > $o )]:
% 243.05/31.88 ( ( ~( ivalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )),
% 243.05/31.88 inference('rw.lit', [status(esa)], [ivalid])).
% 243.05/31.88 thf(zip_derived_cl112, plain,
% 243.05/31.88 (~ (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (ior @ (iatom @ a) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b) @ (iatom @ a1)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))))) @
% 243.05/31.88 Y0))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl9, '0'])).
% 243.05/31.88 thf(zip_derived_cl113, plain,
% 243.05/31.88 (~ (((!!) @ (ior @ (iatom @ a) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b) @ (iatom @ a1)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl112])).
% 243.05/31.88 thf(zip_derived_cl114, plain,
% 243.05/31.88 (~ (ior @ (iatom @ a) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b) @ (iatom @ a1)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))))) @
% 243.05/31.88 '#sk2')),
% 243.05/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl113])).
% 243.05/31.88 thf(ior, axiom,(( ior @ (X0)@ (X1)@ (X2)) =
% 243.05/31.88 ((mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1) @ X2)))).
% 243.05/31.88 thf('1', plain,
% 243.05/31.88 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 243.05/31.88 ( ( ior @ X0 @ X1 @ X2 ) =
% 243.05/31.88 ( mor @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) @ X2 ) )),
% 243.05/31.88 define([status(thm)])).
% 243.05/31.88 thf(zip_derived_cl115, plain,
% 243.05/31.88 (~ (mor @ (mbox_s4 @ (iatom @ a)) @
% 243.05/31.88 (mbox_s4 @
% 243.05/31.88 (ior @ (iand @ (iatom @ b) @ (iatom @ a1)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4)))))) @
% 243.05/31.88 '#sk2')),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl114, '1'])).
% 243.05/31.88 thf(mor, axiom, ~ (mor @ X0 @ X1 @ X2) =>
% 243.05/31.88 ((((X1 @ X2) | (X0 @ X2))) != ($true))).
% 243.05/31.88 thf('2', plain,
% 243.05/31.88 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 243.05/31.88 ( ( ~( mor @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X1 @ X2 ) | ( X0 @ X2 ) ) ) )),
% 243.05/31.88 inference('rw.lit', [status(esa)], [mor])).
% 243.05/31.88 thf(zip_derived_cl116, plain,
% 243.05/31.88 (~ (((mbox_s4 @
% 243.05/31.88 (ior @ (iand @ (iatom @ b) @ (iatom @ a1)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))))) @
% 243.05/31.88 '#sk2') | (mbox_s4 @ (iatom @ a) @ '#sk2')))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl115, '2'])).
% 243.05/31.88 thf(zip_derived_cl117, plain,
% 243.05/31.88 (~ (mbox_s4 @
% 243.05/31.88 (ior @ (iand @ (iatom @ b) @ (iatom @ a1)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))))) @
% 243.05/31.88 '#sk2')),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl116])).
% 243.05/31.88 thf(mbox_s4, axiom, ~ (mbox_s4 @ X0 @ X1) =>
% 243.05/31.88 ((((!!) @ (^[Y0 : $i]: (((irel @ X1 @ Y0) => (X0 @ Y0)))))) != ($true))).
% 243.05/31.88 thf('3', plain,
% 243.05/31.88 (![X0:( $i > $o ),X1:$i]:
% 243.05/31.88 ( ( ~( mbox_s4 @ X0 @ X1 ) ) <=>
% 243.05/31.88 ( ~( ![X6:$i]: ( ( irel @ X1 @ X6 ) => ( X0 @ X6 ) ) ) ) )),
% 243.05/31.88 inference('rw.lit', [status(esa)], [mbox_s4])).
% 243.05/31.88 thf(zip_derived_cl119, plain,
% 243.05/31.88 (~ (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ '#sk2' @ Y0) => (ior @
% 243.05/31.88 (iand @ (iatom @ b) @ (iatom @ a1)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4)))) @
% 243.05/31.88 Y0))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl117, '3'])).
% 243.05/31.88 thf(zip_derived_cl121, plain,
% 243.05/31.88 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ '#sk2'))) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b) @ (iatom @ a1)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4)))))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl119])).
% 243.05/31.88 thf(zip_derived_cl122, plain,
% 243.05/31.88 (~ (((irel @ '#sk2' @ '#sk3') => (ior @
% 243.05/31.88 (iand @ (iatom @ b) @ (iatom @ a1)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4)))) @
% 243.05/31.88 '#sk3')))),
% 243.05/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl121])).
% 243.05/31.88 thf(zip_derived_cl125, plain,
% 243.05/31.88 (~ (((irel @ '#sk2' @ '#sk3') => (mor @
% 243.05/31.88 (mbox_s4 @ (iand @ (iatom @ b) @ (iatom @ a1))) @
% 243.05/31.88 (mbox_s4 @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))))) @
% 243.05/31.88 '#sk3')))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl122, '1'])).
% 243.05/31.88 thf(zip_derived_cl127, plain,
% 243.05/31.88 (~ (mor @ (mbox_s4 @ (iand @ (iatom @ b) @ (iatom @ a1))) @
% 243.05/31.88 (mbox_s4 @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))))) @
% 243.05/31.88 '#sk3')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])).
% 243.05/31.88 thf(zip_derived_cl131, plain,
% 243.05/31.88 (~ (((mbox_s4 @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4)))) @
% 243.05/31.88 '#sk3') | (mbox_s4 @ (iand @ (iatom @ b) @ (iatom @ a1)) @ '#sk3')))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl127, '2'])).
% 243.05/31.88 thf(zip_derived_cl132, plain,
% 243.05/31.88 (~ (mbox_s4 @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4)))) @
% 243.05/31.88 '#sk3')),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl131])).
% 243.05/31.88 thf(zip_derived_cl134, plain,
% 243.05/31.88 (~ (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ '#sk3' @ Y0) => (ior @
% 243.05/31.88 (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))) @
% 243.05/31.88 Y0))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl132, '3'])).
% 243.05/31.88 thf(zip_derived_cl136, plain,
% 243.05/31.88 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ '#sk3'))) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl134])).
% 243.05/31.88 thf(zip_derived_cl137, plain,
% 243.05/31.88 (~ (((irel @ '#sk3' @ '#sk5') => (ior @
% 243.05/31.88 (iand @ (iatom @ b1) @ (iatom @ a2)) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))) @
% 243.05/31.88 '#sk5')))),
% 243.05/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl136])).
% 243.05/31.88 thf(zip_derived_cl140, plain,
% 243.05/31.88 (~ (((irel @ '#sk3' @ '#sk5') => (mor @
% 243.05/31.88 (mbox_s4 @ (iand @ (iatom @ b1) @ (iatom @ a2))) @
% 243.05/31.88 (mbox_s4 @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4)))) @
% 243.05/31.88 '#sk5')))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl137, '1'])).
% 243.05/31.88 thf(zip_derived_cl141, plain, ( (irel @ '#sk3' @ '#sk5')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl140])).
% 243.05/31.88 thf(axiom4, axiom,
% 243.05/31.88 (ivalid @
% 243.05/31.88 ( iimplies @
% 243.05/31.88 ( iatom @ b ) @
% 243.05/31.88 ( ior @ ( ior @ ( iatom @ b1 ) @ ( iatom @ a1 ) ) @ ( iatom @ b1 ) ) ))).
% 243.05/31.88 thf(zip_derived_cl7, plain,
% 243.05/31.88 ( (ivalid @
% 243.05/31.88 (iimplies @ (iatom @ b) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ (iatom @ b1))))),
% 243.05/31.88 inference('cnf', [status(esa)], [axiom4])).
% 243.05/31.88 thf(ivalid, axiom, (ivalid @ X0) =>
% 243.05/31.88 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))).
% 243.05/31.88 thf('4', plain,
% 243.05/31.88 (![X0:( $i > $o )]: ( ( ivalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )),
% 243.05/31.88 inference('rw.lit', [status(esa)], [ivalid])).
% 243.05/31.88 thf(zip_derived_cl263, plain,
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (iimplies @ (iatom @ b) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ (iatom @ b1)) @
% 243.05/31.88 Y0))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl7, '4'])).
% 243.05/31.88 thf(zip_derived_cl264, plain,
% 243.05/31.88 ( (((!!) @ (iimplies @ (iatom @ b) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ (iatom @ b1)))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl263])).
% 243.05/31.88 thf(zip_derived_cl265, plain,
% 243.05/31.88 (![X2 : $i]:
% 243.05/31.88 (iimplies @ (iatom @ b) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ (iatom @ b1)) @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl264])).
% 243.05/31.88 thf(mimplies, axiom,(( mimplies @ (X0)@ (X1)@ (X2)) =
% 243.05/31.88 ((mor @ (mnot @ X0) @ X1 @ X2)))).
% 243.05/31.88 thf('5', plain,
% 243.05/31.88 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 243.05/31.88 ( ( mimplies @ X0 @ X1 @ X2 ) = ( mor @ ( mnot @ X0 ) @ X1 @ X2 ) )),
% 243.05/31.88 define([status(thm)])).
% 243.05/31.88 thf(iimplies, axiom,(( iimplies @ (X0)@ (X1)@ (X2)) =
% 243.05/31.88 ((mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1) @ X2)))).
% 243.05/31.88 thf('6', plain,
% 243.05/31.88 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 243.05/31.88 ( ( iimplies @ X0 @ X1 @ X2 ) =
% 243.05/31.88 ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) @ X2 ) )),
% 243.05/31.88 define([status(thm)])).
% 243.05/31.88 thf(zip_derived_cl266, plain,
% 243.05/31.88 (![X2 : $i]:
% 243.05/31.88 (mor @ (mnot @ (mbox_s4 @ (iatom @ b))) @
% 243.05/31.88 (mbox_s4 @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ (iatom @ b1))) @
% 243.05/31.88 X2)),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl265, '5', '6'])).
% 243.05/31.88 thf(mor, axiom, (mor @ X0 @ X1 @ X2) =>
% 243.05/31.88 ((((X1 @ X2) | (X0 @ X2))) = ($true))).
% 243.05/31.88 thf('7', plain,
% 243.05/31.88 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 243.05/31.88 ( ( mor @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) | ( X1 @ X2 ) ) )),
% 243.05/31.88 inference('rw.lit', [status(esa)], [mor])).
% 243.05/31.88 thf(zip_derived_cl267, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (((mbox_s4 @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ (iatom @ b1)) @ X0) |
% 243.05/31.88 (mnot @ (mbox_s4 @ (iatom @ b)) @ X0)))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl266, '7'])).
% 243.05/31.88 thf(zip_derived_cl268, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (mbox_s4 @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ (iatom @ b1)) @ X0)
% 243.05/31.88 | (mnot @ (mbox_s4 @ (iatom @ b)) @ X0))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl267])).
% 243.05/31.88 thf(mbox_s4, axiom, (mbox_s4 @ X0 @ X1) =>
% 243.05/31.88 ((((!!) @ (^[Y0 : $i]: (((irel @ X1 @ Y0) => (X0 @ Y0)))))) = ($true))).
% 243.05/31.88 thf('8', plain,
% 243.05/31.88 (![X0:( $i > $o ),X1:$i]:
% 243.05/31.88 ( ( mbox_s4 @ X0 @ X1 ) <=>
% 243.05/31.88 ( ![X6:$i]: ( ( irel @ X1 @ X6 ) => ( X0 @ X6 ) ) ) )),
% 243.05/31.88 inference('rw.lit', [status(esa)], [mbox_s4])).
% 243.05/31.88 thf(zip_derived_cl269, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ X0 @ Y0) => (ior @
% 243.05/31.88 (ior @ (iatom @ b1) @ (iatom @ a1)) @ (iatom @ b1) @
% 243.05/31.88 Y0))))))
% 243.05/31.88 | (mnot @ (mbox_s4 @ (iatom @ b)) @ X0))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl268, '8'])).
% 243.05/31.88 thf(zip_derived_cl270, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ (iatom @ b1))))))
% 243.05/31.88 | (mnot @ (mbox_s4 @ (iatom @ b)) @ X0))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl269])).
% 243.05/31.88 thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))).
% 243.05/31.88 thf('9', plain,
% 243.05/31.88 (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )),
% 243.05/31.88 inference('rw.lit', [status(esa)], [mnot])).
% 243.05/31.88 thf(zip_derived_cl271, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (mbox_s4 @ (iatom @ b) @ X0)
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @
% 243.05/31.88 (iatom @ b1)))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl270, '9'])).
% 243.05/31.88 thf(zip_derived_cl272, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (((!!) @ (^[Y0 : $i]: (((irel @ X0 @ Y0) => (iatom @ b @ Y0))))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @
% 243.05/31.88 (iatom @ b1)))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl271, '3'])).
% 243.05/31.88 thf(zip_derived_cl273, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @
% 243.05/31.88 (iatom @ b1)))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl272])).
% 243.05/31.88 thf(zip_derived_cl274, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (((irel @ X0 @ ('#sk12' @ X0)) => (iatom @ b @ ('#sk12' @ X0))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @
% 243.05/31.88 (iatom @ b1)))))))),
% 243.05/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl273])).
% 243.05/31.88 thf(iatom, axiom,(( iatom @ (X0)@ (X1)) = ((X0 @ X1)))).
% 243.05/31.88 thf('10', plain,
% 243.05/31.88 (![X0:( $i > $o ),X1:$i]: ( ( iatom @ X0 @ X1 ) = ( X0 @ X1 ) )),
% 243.05/31.88 define([status(thm)])).
% 243.05/31.88 thf(zip_derived_cl275, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (((irel @ X0 @ ('#sk12' @ X0)) => (b @ ('#sk12' @ X0))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @
% 243.05/31.88 (iatom @ b1)))))))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl274, '10'])).
% 243.05/31.88 thf(zip_derived_cl277, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (b @ ('#sk12' @ X0))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @
% 243.05/31.88 (iatom @ b1)))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl275])).
% 243.05/31.88 thf(zip_derived_cl279, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @
% 243.05/31.88 (iatom @ b1) @ X2)))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl277])).
% 243.05/31.88 thf(zip_derived_cl282, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (mor @
% 243.05/31.88 (mbox_s4 @ (ior @ (iatom @ b1) @ (iatom @ a1))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b1)) @ X2)))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X0)))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl279, '1'])).
% 243.05/31.88 thf(zip_derived_cl283, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X2)
% 243.05/31.88 | (mor @ (mbox_s4 @ (ior @ (iatom @ b1) @ (iatom @ a1))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b1)) @ X2)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl282])).
% 243.05/31.88 thf(zip_derived_cl285, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ b1) @ X1) | (mbox_s4 @
% 243.05/31.88 (ior @ (iatom @ b1) @ (iatom @ a1)) @ X1)))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl283, '7'])).
% 243.05/31.88 thf(zip_derived_cl287, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ b1) @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ X1)
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl285])).
% 243.05/31.88 thf(zip_derived_cl289, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X1 @ Y0) => (iatom @ b1 @ Y0))))))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl287, '8'])).
% 243.05/31.88 thf(zip_derived_cl292, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b1)))))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ X1))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl289])).
% 243.05/31.88 thf(zip_derived_cl293, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ X0 @ Y0) => (ior @ (iatom @ b1) @
% 243.05/31.88 (iatom @ a1) @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl292, '8'])).
% 243.05/31.88 thf(zip_derived_cl296, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (iatom @ b1) @ (iatom @ a1))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl293])).
% 243.05/31.88 thf(zip_derived_cl297, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (ior @ (iatom @ b1) @ (iatom @ a1) @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl296])).
% 243.05/31.88 thf(zip_derived_cl300, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (mor @ (mbox_s4 @ (iatom @ b1)) @
% 243.05/31.88 (mbox_s4 @ (iatom @ a1)) @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl297, '1'])).
% 243.05/31.88 thf(zip_derived_cl301, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X3)
% 243.05/31.88 | (mor @ (mbox_s4 @ (iatom @ b1)) @ (mbox_s4 @ (iatom @ a1)) @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl300])).
% 243.05/31.88 thf(zip_derived_cl303, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ a1) @ X2) | (mbox_s4 @ (iatom @ b1) @ X2)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl301, '7'])).
% 243.05/31.88 thf(zip_derived_cl305, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ a1) @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b1) @ X2)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1))))))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl303])).
% 243.05/31.88 thf(zip_derived_cl307, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (iatom @ a1 @ Y0))))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b1) @ X2))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl305, '8'])).
% 243.05/31.88 thf(zip_derived_cl310, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X2))) @ (iatom @ a1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b1) @ X2))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl307])).
% 243.05/31.88 thf(zip_derived_cl311, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X0 @ Y0) => (iatom @ b1 @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl310, '8'])).
% 243.05/31.88 thf(zip_derived_cl314, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl311])).
% 243.05/31.88 thf(zip_derived_cl315, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X4) => (iatom @ b1 @ X4)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b1)))))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl314])).
% 243.05/31.88 thf(zip_derived_cl318, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X4) => (b1 @ X4)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b1)))))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl315, '10'])).
% 243.05/31.88 thf(zip_derived_cl319, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X4)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl318])).
% 243.05/31.88 thf(zip_derived_cl321, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X6) => (iatom @ b1 @ X6)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1)))))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl319])).
% 243.05/31.88 thf(zip_derived_cl324, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X6) => (b1 @ X6)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1)))))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl321, '10'])).
% 243.05/31.88 thf(zip_derived_cl325, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X6)
% 243.05/31.88 | (b1 @ X6)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl324])).
% 243.05/31.88 thf(zip_derived_cl327, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X8) => (iatom @ a1 @ X8)))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b1 @ X6)
% 243.05/31.88 | ~ (irel @ X1 @ X6))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl325])).
% 243.05/31.88 thf(zip_derived_cl330, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X8) => (a1 @ X8)))
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b1 @ X6)
% 243.05/31.88 | ~ (irel @ X1 @ X6))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl327, '10'])).
% 243.05/31.88 thf(zip_derived_cl331, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X8)
% 243.05/31.88 | (a1 @ X8)
% 243.05/31.88 | ~ (irel @ X1 @ X6)
% 243.05/31.88 | (b1 @ X6)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2)))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl330])).
% 243.05/31.88 thf(zip_derived_cl1484, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (b @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X1)
% 243.05/31.88 | (b1 @ X0)
% 243.05/31.88 | (b1 @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (a1 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X3))),
% 243.05/31.88 inference('eq_fact', [status(thm)], [zip_derived_cl331])).
% 243.05/31.88 thf(zip_derived_cl1496, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X3)
% 243.05/31.88 | (a1 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b1 @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X1)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2)))),
% 243.05/31.88 inference('simplify', [status(thm)], [zip_derived_cl1484])).
% 243.05/31.88 thf(refl_axiom, axiom, (![X:$i]: ( irel @ X @ X ))).
% 243.05/31.88 thf(zip_derived_cl0, plain, ( (((!!) @ (^[Y0 : $i]: (irel @ Y0 @ Y0))))),
% 243.05/31.88 inference('cnf', [status(esa)], [refl_axiom])).
% 243.05/31.88 thf(zip_derived_cl1, plain, ( (((!!) @ ((('#S') @ irel @ ('#I')))))),
% 243.05/31.88 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 243.05/31.88 thf(zip_derived_cl14, plain, (![X2 : $i]: (irel @ X2 @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])).
% 243.05/31.88 thf(zip_derived_cl1503, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X3)
% 243.05/31.88 | (a1 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b @ ('#sk12' @ X2)))),
% 243.05/31.88 inference('demod', [status(thm)], [zip_derived_cl1496, zip_derived_cl14])).
% 243.05/31.88 thf(trans_axiom, axiom,
% 243.05/31.88 (![X:$i,Y:$i,Z:$i]:
% 243.05/31.88 ( ( ( irel @ Y @ Z ) & ( irel @ X @ Y ) ) => ( irel @ X @ Z ) ))).
% 243.05/31.88 thf(zip_derived_cl2, plain,
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((!!) @ (^[Y1 : $i]:
% 243.05/31.88 (((!!) @ (^[Y2 : $i]:
% 243.05/31.88 (((((irel @ Y1 @ Y2) & (irel @
% 243.05/31.88 Y0 @ Y1))) =>
% 243.05/31.88 (irel @ Y0 @ Y2))))))))))))),
% 243.05/31.88 inference('cnf', [status(esa)], [trans_axiom])).
% 243.05/31.88 thf(zip_derived_cl3, plain,
% 243.05/31.88 ( (((!!) @ ((('#B') @ (!!) @
% 243.05/31.88 ((('#B') @ ((('#B') @ (!!))) @
% 243.05/31.88 ((('#S') @ ((('#B') @ ('#C') @
% 243.05/31.88 ((('#B') @ ((('#B') @ ('#S'))) @
% 243.05/31.88 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 243.05/31.88 ((('#B') @ ((('#S') @ ((('#B') @ (
% 243.05/31.88 '#C') @
% 243.05/31.88 ((('#B') @ (
% 243.05/31.88 (('#B') @ (&))) @
% 243.05/31.88 irel)))))) @
% 243.05/31.88 irel)))))))) @
% 243.05/31.88 irel))))))))),
% 243.05/31.88 inference('lams2combs', [status(thm)], [zip_derived_cl2])).
% 243.05/31.88 thf(zip_derived_cl189, plain,
% 243.05/31.88 (![X2 : $i]:
% 243.05/31.88 (((!!) @ ((('#B') @ (!!) @
% 243.05/31.88 ((('#C') @ ((('#B') @ ('#S') @
% 243.05/31.88 ((('#B') @ ((('#B') @ (=>))) @
% 243.05/31.88 ((('#S') @ ((('#B') @ ('#C') @
% 243.05/31.88 ((('#B') @ ((('#B') @ (&))) @
% 243.05/31.88 irel)))) @
% 243.05/31.88 (irel @ X2))))))) @
% 243.05/31.88 (irel @ X2)))))))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])).
% 243.05/31.88 thf(zip_derived_cl190, plain,
% 243.05/31.88 (![X2 : $i, X4 : $i]:
% 243.05/31.88 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 243.05/31.88 ((('#C') @ ((('#B') @ (&) @ (irel @ X4))) @
% 243.05/31.88 (irel @ X2 @ X4))))) @
% 243.05/31.88 (irel @ X2)))))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl189])).
% 243.05/31.88 thf(zip_derived_cl191, plain,
% 243.05/31.88 (![X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (((((irel @ X4 @ X6) & (irel @ X2 @ X4))) => (irel @ X2 @ X6)))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl190])).
% 243.05/31.88 thf(zip_derived_cl192, plain,
% 243.05/31.88 (![X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (((irel @ X4 @ X6) & (irel @ X2 @ X4))) | (irel @ X2 @ X6))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])).
% 243.05/31.88 thf(zip_derived_cl193, plain,
% 243.05/31.88 (![X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X4 @ X6) | ~ (irel @ X2 @ X4) | (irel @ X2 @ X6))),
% 243.05/31.88 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl192])).
% 243.05/31.88 thf(zip_derived_cl126, plain, ( (irel @ '#sk2' @ '#sk3')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])).
% 243.05/31.88 thf(zip_derived_cl440, plain,
% 243.05/31.88 (![X0 : $i]: ( (irel @ '#sk2' @ X0) | ~ (irel @ '#sk3' @ X0))),
% 243.05/31.88 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl126])).
% 243.05/31.88 thf(zip_derived_cl193, plain,
% 243.05/31.88 (![X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X4 @ X6) | ~ (irel @ X2 @ X4) | (irel @ X2 @ X6))),
% 243.05/31.88 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl192])).
% 243.05/31.88 thf(zip_derived_cl142, plain,
% 243.05/31.88 (~ (mor @ (mbox_s4 @ (iand @ (iatom @ b1) @ (iatom @ a2))) @
% 243.05/31.88 (mbox_s4 @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4)))) @
% 243.05/31.88 '#sk5')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl140])).
% 243.05/31.88 thf(zip_derived_cl146, plain,
% 243.05/31.88 (~ (((mbox_s4 @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))) @
% 243.05/31.88 '#sk5') | (mbox_s4 @ (iand @ (iatom @ b1) @ (iatom @ a2)) @ '#sk5')))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl142, '2'])).
% 243.05/31.88 thf(zip_derived_cl148, plain,
% 243.05/31.88 (~ (mbox_s4 @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))) @
% 243.05/31.88 '#sk5')),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl146])).
% 243.05/31.88 thf(zip_derived_cl152, plain,
% 243.05/31.88 (~ (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ '#sk5' @ Y0) => (ior @
% 243.05/31.88 (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4)) @ Y0))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl148, '3'])).
% 243.05/31.88 thf(zip_derived_cl154, plain,
% 243.05/31.88 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ '#sk5'))) @
% 243.05/31.88 (ior @ (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4)))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl152])).
% 243.05/31.88 thf(zip_derived_cl155, plain,
% 243.05/31.88 (~ (((irel @ '#sk5' @ '#sk7') => (ior @
% 243.05/31.88 (iand @ (iatom @ b2) @ (iatom @ a3)) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4)) @ '#sk7')))),
% 243.05/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl154])).
% 243.05/31.88 thf(zip_derived_cl158, plain,
% 243.05/31.88 (~ (((irel @ '#sk5' @ '#sk7') => (mor @
% 243.05/31.88 (mbox_s4 @ (iand @ (iatom @ b2) @ (iatom @ a3))) @
% 243.05/31.88 (mbox_s4 @ (iand @ (iatom @ b3) @ (iatom @ a4))) @ '#sk7')))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl155, '1'])).
% 243.05/31.88 thf(zip_derived_cl159, plain, ( (irel @ '#sk5' @ '#sk7')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 243.05/31.88 thf(zip_derived_cl434, plain,
% 243.05/31.88 (![X0 : $i]: ( (irel @ X0 @ '#sk7') | ~ (irel @ X0 @ '#sk5'))),
% 243.05/31.88 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl159])).
% 243.05/31.88 thf(zip_derived_cl193, plain,
% 243.05/31.88 (![X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X4 @ X6) | ~ (irel @ X2 @ X4) | (irel @ X2 @ X6))),
% 243.05/31.88 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl192])).
% 243.05/31.88 thf(zip_derived_cl149, plain,
% 243.05/31.88 (~ (mbox_s4 @ (iand @ (iatom @ b1) @ (iatom @ a2)) @ '#sk5')),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl146])).
% 243.05/31.88 thf(zip_derived_cl153, plain,
% 243.05/31.88 (~ (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ '#sk5' @ Y0) => (iand @ (iatom @ b1) @
% 243.05/31.88 (iatom @ a2) @ Y0))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl149, '3'])).
% 243.05/31.88 thf(zip_derived_cl156, plain,
% 243.05/31.88 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ '#sk5'))) @
% 243.05/31.88 (iand @ (iatom @ b1) @ (iatom @ a2))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl153])).
% 243.05/31.88 thf(zip_derived_cl157, plain,
% 243.05/31.88 (~ (((irel @ '#sk5' @ '#sk8') => (iand @ (iatom @ b1) @ (iatom @ a2) @
% 243.05/31.88 '#sk8')))),
% 243.05/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl156])).
% 243.05/31.88 thf(iand, axiom,(( iand @ (X0)@ (X1)@ (X2)) = ((mand @ X0 @ X1 @ X2)))).
% 243.05/31.88 thf('11', plain,
% 243.05/31.88 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 243.05/31.88 ( ( iand @ X0 @ X1 @ X2 ) = ( mand @ X0 @ X1 @ X2 ) )),
% 243.05/31.88 define([status(thm)])).
% 243.05/31.88 thf(zip_derived_cl161, plain,
% 243.05/31.88 (~ (((irel @ '#sk5' @ '#sk8') => (mand @ (iatom @ b1) @ (iatom @ a2) @
% 243.05/31.88 '#sk8')))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl157, '11'])).
% 243.05/31.88 thf(zip_derived_cl162, plain, ( (irel @ '#sk5' @ '#sk8')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl161])).
% 243.05/31.88 thf(zip_derived_cl435, plain,
% 243.05/31.88 (![X0 : $i]: ( (irel @ X0 @ '#sk8') | ~ (irel @ X0 @ '#sk5'))),
% 243.05/31.88 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl162])).
% 243.05/31.88 thf(axiom3, axiom,
% 243.05/31.88 (ivalid @
% 243.05/31.88 ( iimplies @
% 243.05/31.88 ( iatom @ b1 ) @
% 243.05/31.88 ( ior @ ( ior @ ( iatom @ b2 ) @ ( iatom @ a2 ) ) @ ( iatom @ b2 ) ) ))).
% 243.05/31.88 thf(zip_derived_cl6, plain,
% 243.05/31.88 ( (ivalid @
% 243.05/31.88 (iimplies @ (iatom @ b1) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ (iatom @ b2))))),
% 243.05/31.88 inference('cnf', [status(esa)], [axiom3])).
% 243.05/31.88 thf(zip_derived_cl194, plain,
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (iimplies @ (iatom @ b1) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ (iatom @ b2)) @
% 243.05/31.88 Y0))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl6, '4'])).
% 243.05/31.88 thf(zip_derived_cl195, plain,
% 243.05/31.88 ( (((!!) @ (iimplies @ (iatom @ b1) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ (iatom @ b2)))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl194])).
% 243.05/31.88 thf(zip_derived_cl196, plain,
% 243.05/31.88 (![X2 : $i]:
% 243.05/31.88 (iimplies @ (iatom @ b1) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ (iatom @ b2)) @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl195])).
% 243.05/31.88 thf(zip_derived_cl197, plain,
% 243.05/31.88 (![X2 : $i]:
% 243.05/31.88 (mor @ (mnot @ (mbox_s4 @ (iatom @ b1))) @
% 243.05/31.88 (mbox_s4 @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ (iatom @ b2))) @
% 243.05/31.88 X2)),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl196, '5', '6'])).
% 243.05/31.88 thf(zip_derived_cl198, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (((mbox_s4 @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ (iatom @ b2)) @ X0) |
% 243.05/31.88 (mnot @ (mbox_s4 @ (iatom @ b1)) @ X0)))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl197, '7'])).
% 243.05/31.88 thf(zip_derived_cl199, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (mbox_s4 @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ (iatom @ b2)) @ X0)
% 243.05/31.88 | (mnot @ (mbox_s4 @ (iatom @ b1)) @ X0))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl198])).
% 243.05/31.88 thf(zip_derived_cl200, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ X0 @ Y0) => (ior @
% 243.05/31.88 (ior @ (iatom @ b2) @ (iatom @ a2)) @ (iatom @ b2) @
% 243.05/31.88 Y0))))))
% 243.05/31.88 | (mnot @ (mbox_s4 @ (iatom @ b1)) @ X0))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl199, '8'])).
% 243.05/31.88 thf(zip_derived_cl201, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ (iatom @ b2))))))
% 243.05/31.88 | (mnot @ (mbox_s4 @ (iatom @ b1)) @ X0))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl200])).
% 243.05/31.88 thf(zip_derived_cl202, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (mbox_s4 @ (iatom @ b1) @ X0)
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @
% 243.05/31.88 (iatom @ b2)))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl201, '9'])).
% 243.05/31.88 thf(zip_derived_cl203, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (((!!) @ (^[Y0 : $i]: (((irel @ X0 @ Y0) => (iatom @ b1 @ Y0))))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @
% 243.05/31.88 (iatom @ b2)))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl202, '3'])).
% 243.05/31.88 thf(zip_derived_cl204, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @
% 243.05/31.88 (iatom @ b2)))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl203])).
% 243.05/31.88 thf(zip_derived_cl205, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (((irel @ X0 @ ('#sk11' @ X0)) => (iatom @ b1 @ ('#sk11' @ X0))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @
% 243.05/31.88 (iatom @ b2)))))))),
% 243.05/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl204])).
% 243.05/31.88 thf(zip_derived_cl206, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (((irel @ X0 @ ('#sk11' @ X0)) => (b1 @ ('#sk11' @ X0))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @
% 243.05/31.88 (iatom @ b2)))))))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl205, '10'])).
% 243.05/31.88 thf(zip_derived_cl208, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (b1 @ ('#sk11' @ X0))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @
% 243.05/31.88 (iatom @ b2)))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 243.05/31.88 thf(zip_derived_cl210, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @
% 243.05/31.88 (iatom @ b2) @ X2)))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl208])).
% 243.05/31.88 thf(zip_derived_cl213, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (mor @
% 243.05/31.88 (mbox_s4 @ (ior @ (iatom @ b2) @ (iatom @ a2))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b2)) @ X2)))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X0)))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl210, '1'])).
% 243.05/31.88 thf(zip_derived_cl214, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X2)
% 243.05/31.88 | (mor @ (mbox_s4 @ (ior @ (iatom @ b2) @ (iatom @ a2))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b2)) @ X2)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl213])).
% 243.05/31.88 thf(zip_derived_cl216, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ b2) @ X1) | (mbox_s4 @
% 243.05/31.88 (ior @ (iatom @ b2) @ (iatom @ a2)) @ X1)))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl214, '7'])).
% 243.05/31.88 thf(zip_derived_cl218, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ b2) @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ X1)
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl216])).
% 243.05/31.88 thf(zip_derived_cl220, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X1 @ Y0) => (iatom @ b2 @ Y0))))))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl218, '8'])).
% 243.05/31.88 thf(zip_derived_cl223, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b2)))))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ X1))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl220])).
% 243.05/31.88 thf(zip_derived_cl224, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ X0 @ Y0) => (ior @ (iatom @ b2) @
% 243.05/31.88 (iatom @ a2) @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl223, '8'])).
% 243.05/31.88 thf(zip_derived_cl227, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (iatom @ b2) @ (iatom @ a2))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl224])).
% 243.05/31.88 thf(zip_derived_cl228, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (ior @ (iatom @ b2) @ (iatom @ a2) @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl227])).
% 243.05/31.88 thf(zip_derived_cl231, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (mor @ (mbox_s4 @ (iatom @ b2)) @
% 243.05/31.88 (mbox_s4 @ (iatom @ a2)) @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl228, '1'])).
% 243.05/31.88 thf(zip_derived_cl232, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X3)
% 243.05/31.88 | (mor @ (mbox_s4 @ (iatom @ b2)) @ (mbox_s4 @ (iatom @ a2)) @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl231])).
% 243.05/31.88 thf(zip_derived_cl234, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ a2) @ X2) | (mbox_s4 @ (iatom @ b2) @ X2)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl232, '7'])).
% 243.05/31.88 thf(zip_derived_cl236, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ a2) @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b2) @ X2)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2))))))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl234])).
% 243.05/31.88 thf(zip_derived_cl238, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (iatom @ a2 @ Y0))))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b2) @ X2))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl236, '8'])).
% 243.05/31.88 thf(zip_derived_cl241, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X2))) @ (iatom @ a2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b2) @ X2))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl238])).
% 243.05/31.88 thf(zip_derived_cl242, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X0 @ Y0) => (iatom @ b2 @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl241, '8'])).
% 243.05/31.88 thf(zip_derived_cl245, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl242])).
% 243.05/31.88 thf(zip_derived_cl246, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X4) => (iatom @ b2 @ X4)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b2)))))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl245])).
% 243.05/31.88 thf(zip_derived_cl249, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X4) => (b2 @ X4)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b2)))))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl246, '10'])).
% 243.05/31.88 thf(zip_derived_cl250, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X4)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl249])).
% 243.05/31.88 thf(zip_derived_cl252, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X6) => (iatom @ b2 @ X6)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2)))))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl250])).
% 243.05/31.88 thf(zip_derived_cl255, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X6) => (b2 @ X6)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2)))))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl252, '10'])).
% 243.05/31.88 thf(zip_derived_cl256, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X6)
% 243.05/31.88 | (b2 @ X6)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])).
% 243.05/31.88 thf(zip_derived_cl258, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X8) => (iatom @ a2 @ X8)))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b2 @ X6)
% 243.05/31.88 | ~ (irel @ X1 @ X6))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl256])).
% 243.05/31.88 thf(zip_derived_cl261, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X8) => (a2 @ X8)))
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b2 @ X6)
% 243.05/31.88 | ~ (irel @ X1 @ X6))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl258, '10'])).
% 243.05/31.88 thf(zip_derived_cl262, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X8)
% 243.05/31.88 | (a2 @ X8)
% 243.05/31.88 | ~ (irel @ X1 @ X6)
% 243.05/31.88 | (b2 @ X6)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2)))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl261])).
% 243.05/31.88 thf(zip_derived_cl1098, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (b1 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X1)
% 243.05/31.88 | (b2 @ X0)
% 243.05/31.88 | (b2 @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (a2 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X3))),
% 243.05/31.88 inference('eq_fact', [status(thm)], [zip_derived_cl262])).
% 243.05/31.88 thf(zip_derived_cl1110, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X3)
% 243.05/31.88 | (a2 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b2 @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X1)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2)))),
% 243.05/31.88 inference('simplify', [status(thm)], [zip_derived_cl1098])).
% 243.05/31.88 thf(zip_derived_cl14, plain, (![X2 : $i]: (irel @ X2 @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])).
% 243.05/31.88 thf(zip_derived_cl1117, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X3)
% 243.05/31.88 | (a2 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b2 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b1 @ ('#sk11' @ X2)))),
% 243.05/31.88 inference('demod', [status(thm)], [zip_derived_cl1110, zip_derived_cl14])).
% 243.05/31.88 thf(zip_derived_cl14, plain, (![X2 : $i]: (irel @ X2 @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])).
% 243.05/31.88 thf(axiom2, axiom,
% 243.05/31.88 (ivalid @
% 243.05/31.88 ( iimplies @
% 243.05/31.88 ( iatom @ b2 ) @
% 243.05/31.88 ( ior @ ( ior @ ( iatom @ b3 ) @ ( iatom @ a3 ) ) @ ( iatom @ b3 ) ) ))).
% 243.05/31.88 thf(zip_derived_cl5, plain,
% 243.05/31.88 ( (ivalid @
% 243.05/31.88 (iimplies @ (iatom @ b2) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ (iatom @ b3))))),
% 243.05/31.88 inference('cnf', [status(esa)], [axiom2])).
% 243.05/31.88 thf(zip_derived_cl43, plain,
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (iimplies @ (iatom @ b2) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ (iatom @ b3)) @
% 243.05/31.88 Y0))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl5, '4'])).
% 243.05/31.88 thf(zip_derived_cl44, plain,
% 243.05/31.88 ( (((!!) @ (iimplies @ (iatom @ b2) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ (iatom @ b3)))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl43])).
% 243.05/31.88 thf(zip_derived_cl45, plain,
% 243.05/31.88 (![X2 : $i]:
% 243.05/31.88 (iimplies @ (iatom @ b2) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ (iatom @ b3)) @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl44])).
% 243.05/31.88 thf(zip_derived_cl46, plain,
% 243.05/31.88 (![X2 : $i]:
% 243.05/31.88 (mor @ (mnot @ (mbox_s4 @ (iatom @ b2))) @
% 243.05/31.88 (mbox_s4 @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ (iatom @ b3))) @
% 243.05/31.88 X2)),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl45, '5', '6'])).
% 243.05/31.88 thf(zip_derived_cl47, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (((mbox_s4 @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ (iatom @ b3)) @ X0) |
% 243.05/31.88 (mnot @ (mbox_s4 @ (iatom @ b2)) @ X0)))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl46, '7'])).
% 243.05/31.88 thf(zip_derived_cl48, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (mbox_s4 @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ (iatom @ b3)) @ X0)
% 243.05/31.88 | (mnot @ (mbox_s4 @ (iatom @ b2)) @ X0))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl47])).
% 243.05/31.88 thf(zip_derived_cl49, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ X0 @ Y0) => (ior @
% 243.05/31.88 (ior @ (iatom @ b3) @ (iatom @ a3)) @ (iatom @ b3) @
% 243.05/31.88 Y0))))))
% 243.05/31.88 | (mnot @ (mbox_s4 @ (iatom @ b2)) @ X0))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl48, '8'])).
% 243.05/31.88 thf(zip_derived_cl50, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ (iatom @ b3))))))
% 243.05/31.88 | (mnot @ (mbox_s4 @ (iatom @ b2)) @ X0))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl49])).
% 243.05/31.88 thf(zip_derived_cl51, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (mbox_s4 @ (iatom @ b2) @ X0)
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @
% 243.05/31.88 (iatom @ b3)))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl50, '9'])).
% 243.05/31.88 thf(zip_derived_cl52, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (((!!) @ (^[Y0 : $i]: (((irel @ X0 @ Y0) => (iatom @ b2 @ Y0))))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @
% 243.05/31.88 (iatom @ b3)))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl51, '3'])).
% 243.05/31.88 thf(zip_derived_cl53, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @
% 243.05/31.88 (iatom @ b3)))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl52])).
% 243.05/31.88 thf(zip_derived_cl54, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (((irel @ X0 @ ('#sk1' @ X0)) => (iatom @ b2 @ ('#sk1' @ X0))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @
% 243.05/31.88 (iatom @ b3)))))))),
% 243.05/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl53])).
% 243.05/31.88 thf(zip_derived_cl55, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (((irel @ X0 @ ('#sk1' @ X0)) => (b2 @ ('#sk1' @ X0))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @
% 243.05/31.88 (iatom @ b3)))))))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl54, '10'])).
% 243.05/31.88 thf(zip_derived_cl57, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (~ (b2 @ ('#sk1' @ X0))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @
% 243.05/31.88 (iatom @ b3)))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])).
% 243.05/31.88 thf(zip_derived_cl59, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @
% 243.05/31.88 (iatom @ b3) @ X2)))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])).
% 243.05/31.88 thf(zip_derived_cl62, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (mor @
% 243.05/31.88 (mbox_s4 @ (ior @ (iatom @ b3) @ (iatom @ a3))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b3)) @ X2)))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X0)))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl59, '1'])).
% 243.05/31.88 thf(zip_derived_cl63, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X2)
% 243.05/31.88 | (mor @ (mbox_s4 @ (ior @ (iatom @ b3) @ (iatom @ a3))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b3)) @ X2)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])).
% 243.05/31.88 thf(zip_derived_cl65, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ b3) @ X1) | (mbox_s4 @
% 243.05/31.88 (ior @ (iatom @ b3) @ (iatom @ a3)) @ X1)))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl63, '7'])).
% 243.05/31.88 thf(zip_derived_cl67, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ b3) @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ X1)
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl65])).
% 243.05/31.88 thf(zip_derived_cl69, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X1 @ Y0) => (iatom @ b3 @ Y0))))))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl67, '8'])).
% 243.05/31.88 thf(zip_derived_cl72, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b3)))))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ X1))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl69])).
% 243.05/31.88 thf(zip_derived_cl73, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ X0 @ Y0) => (ior @ (iatom @ b3) @
% 243.05/31.88 (iatom @ a3) @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl72, '8'])).
% 243.05/31.88 thf(zip_derived_cl76, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (iatom @ b3) @ (iatom @ a3))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl73])).
% 243.05/31.88 thf(zip_derived_cl77, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (ior @ (iatom @ b3) @ (iatom @ a3) @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3)))))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl76])).
% 243.05/31.88 thf(zip_derived_cl80, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (mor @ (mbox_s4 @ (iatom @ b3)) @
% 243.05/31.88 (mbox_s4 @ (iatom @ a3)) @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3)))))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl77, '1'])).
% 243.05/31.88 thf(zip_derived_cl81, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X3)
% 243.05/31.88 | (mor @ (mbox_s4 @ (iatom @ b3)) @ (mbox_s4 @ (iatom @ a3)) @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])).
% 243.05/31.88 thf(zip_derived_cl83, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ a3) @ X2) | (mbox_s4 @ (iatom @ b3) @ X2)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3)))))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl81, '7'])).
% 243.05/31.88 thf(zip_derived_cl85, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ a3) @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b3) @ X2)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3))))))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl83])).
% 243.05/31.88 thf(zip_derived_cl87, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (iatom @ a3 @ Y0))))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3)))))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b3) @ X2))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl85, '8'])).
% 243.05/31.88 thf(zip_derived_cl90, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X2))) @ (iatom @ a3)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3)))))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b3) @ X2))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl87])).
% 243.05/31.88 thf(zip_derived_cl91, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X0 @ Y0) => (iatom @ b3 @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b3)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl90, '8'])).
% 243.05/31.88 thf(zip_derived_cl94, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3)))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b3)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl91])).
% 243.05/31.88 thf(zip_derived_cl95, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X4) => (iatom @ b3 @ X4)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b3)))))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])).
% 243.05/31.88 thf(zip_derived_cl98, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X4) => (b3 @ X4)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b3)))))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl95, '10'])).
% 243.05/31.88 thf(zip_derived_cl99, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X4)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b3)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl98])).
% 243.05/31.88 thf(zip_derived_cl101, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X6) => (iatom @ b3 @ X6)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3)))))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl99])).
% 243.05/31.88 thf(zip_derived_cl104, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X6) => (b3 @ X6)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3)))))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl101, '10'])).
% 243.05/31.88 thf(zip_derived_cl105, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X6)
% 243.05/31.88 | (b3 @ X6)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl104])).
% 243.05/31.88 thf(zip_derived_cl107, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X8) => (iatom @ a3 @ X8)))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b3 @ X6)
% 243.05/31.88 | ~ (irel @ X1 @ X6))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl105])).
% 243.05/31.88 thf(zip_derived_cl110, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X8) => (a3 @ X8)))
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b3 @ X6)
% 243.05/31.88 | ~ (irel @ X1 @ X6))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl107, '10'])).
% 243.05/31.88 thf(zip_derived_cl111, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X8)
% 243.05/31.88 | (a3 @ X8)
% 243.05/31.88 | ~ (irel @ X1 @ X6)
% 243.05/31.88 | (b3 @ X6)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2)))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])).
% 243.05/31.88 thf(zip_derived_cl774, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (b2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X1)
% 243.05/31.88 | (b3 @ X0)
% 243.05/31.88 | (b3 @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (a3 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X3))),
% 243.05/31.88 inference('eq_fact', [status(thm)], [zip_derived_cl111])).
% 243.05/31.88 thf(zip_derived_cl786, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X3)
% 243.05/31.88 | (a3 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b3 @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X1)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2)))),
% 243.05/31.88 inference('simplify', [status(thm)], [zip_derived_cl774])).
% 243.05/31.88 thf(zip_derived_cl14, plain, (![X2 : $i]: (irel @ X2 @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])).
% 243.05/31.88 thf(zip_derived_cl793, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X3)
% 243.05/31.88 | (a3 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b3 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (b2 @ ('#sk1' @ X2)))),
% 243.05/31.88 inference('demod', [status(thm)], [zip_derived_cl786, zip_derived_cl14])).
% 243.05/31.88 thf(zip_derived_cl159, plain, ( (irel @ '#sk5' @ '#sk7')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 243.05/31.88 thf(zip_derived_cl160, plain,
% 243.05/31.88 (~ (mor @ (mbox_s4 @ (iand @ (iatom @ b2) @ (iatom @ a3))) @
% 243.05/31.88 (mbox_s4 @ (iand @ (iatom @ b3) @ (iatom @ a4))) @ '#sk7')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 243.05/31.88 thf(zip_derived_cl164, plain,
% 243.05/31.88 (~ (((mbox_s4 @ (iand @ (iatom @ b3) @ (iatom @ a4)) @ '#sk7') |
% 243.05/31.88 (mbox_s4 @ (iand @ (iatom @ b2) @ (iatom @ a3)) @ '#sk7')))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl160, '2'])).
% 243.05/31.88 thf(zip_derived_cl167, plain,
% 243.05/31.88 (~ (mbox_s4 @ (iand @ (iatom @ b2) @ (iatom @ a3)) @ '#sk7')),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl164])).
% 243.05/31.88 thf(zip_derived_cl171, plain,
% 243.05/31.88 (~ (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ '#sk7' @ Y0) => (iand @ (iatom @ b2) @
% 243.05/31.88 (iatom @ a3) @ Y0))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl167, '3'])).
% 243.05/31.88 thf(zip_derived_cl174, plain,
% 243.05/31.88 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ '#sk7'))) @
% 243.05/31.88 (iand @ (iatom @ b2) @ (iatom @ a3))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl171])).
% 243.05/31.88 thf(zip_derived_cl175, plain,
% 243.05/31.88 (~ (((irel @ '#sk7' @ '#sk10') => (iand @ (iatom @ b2) @ (iatom @ a3) @
% 243.05/31.88 '#sk10')))),
% 243.05/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl174])).
% 243.05/31.88 thf(zip_derived_cl179, plain,
% 243.05/31.88 (~ (((irel @ '#sk7' @ '#sk10') => (mand @ (iatom @ b2) @ (iatom @ a3) @
% 243.05/31.88 '#sk10')))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl175, '11'])).
% 243.05/31.88 thf(zip_derived_cl181, plain,
% 243.05/31.88 (~ (mand @ (iatom @ b2) @ (iatom @ a3) @ '#sk10')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])).
% 243.05/31.88 thf(mand, axiom, ~ (mand @ X0 @ X1 @ X2) =>
% 243.05/31.88 ((((X0 @ X2) & (X1 @ X2))) != ($true))).
% 243.05/31.88 thf('12', plain,
% 243.05/31.88 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 243.05/31.88 ( ( ~( mand @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X0 @ X2 ) & ( X1 @ X2 ) ) ) )),
% 243.05/31.88 inference('rw.lit', [status(esa)], [mand])).
% 243.05/31.88 thf(zip_derived_cl183, plain,
% 243.05/31.88 (~ (((iatom @ b2 @ '#sk10') & (iatom @ a3 @ '#sk10')))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl181, '12'])).
% 243.05/31.88 thf(zip_derived_cl187, plain, (~ (((b2 @ '#sk10') & (a3 @ '#sk10')))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl183, '10', '10'])).
% 243.05/31.88 thf(zip_derived_cl188, plain, ((~ (b2 @ '#sk10') | ~ (a3 @ '#sk10'))),
% 243.05/31.88 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl187])).
% 243.05/31.88 thf(zip_derived_cl163, plain,
% 243.05/31.88 (~ (mand @ (iatom @ b1) @ (iatom @ a2) @ '#sk8')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl161])).
% 243.05/31.88 thf(zip_derived_cl165, plain,
% 243.05/31.88 (~ (((iatom @ b1 @ '#sk8') & (iatom @ a2 @ '#sk8')))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl163, '12'])).
% 243.05/31.88 thf(zip_derived_cl168, plain, (~ (((b1 @ '#sk8') & (a2 @ '#sk8')))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl165, '10', '10'])).
% 243.05/31.88 thf(zip_derived_cl169, plain, ((~ (b1 @ '#sk8') | ~ (a2 @ '#sk8'))),
% 243.05/31.88 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl168])).
% 243.05/31.88 thf(zip_derived_cl133, plain,
% 243.05/31.88 (~ (mbox_s4 @ (iand @ (iatom @ b) @ (iatom @ a1)) @ '#sk3')),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl131])).
% 243.05/31.88 thf(zip_derived_cl135, plain,
% 243.05/31.88 (~ (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ '#sk3' @ Y0) => (iand @ (iatom @ b) @
% 243.05/31.88 (iatom @ a1) @ Y0))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl133, '3'])).
% 243.05/31.88 thf(zip_derived_cl138, plain,
% 243.05/31.88 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ '#sk3'))) @
% 243.05/31.88 (iand @ (iatom @ b) @ (iatom @ a1))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl135])).
% 243.05/31.88 thf(zip_derived_cl139, plain,
% 243.05/31.88 (~ (((irel @ '#sk3' @ '#sk6') => (iand @ (iatom @ b) @ (iatom @ a1) @
% 243.05/31.88 '#sk6')))),
% 243.05/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl138])).
% 243.05/31.88 thf(zip_derived_cl143, plain,
% 243.05/31.88 (~ (((irel @ '#sk3' @ '#sk6') => (mand @ (iatom @ b) @ (iatom @ a1) @
% 243.05/31.88 '#sk6')))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl139, '11'])).
% 243.05/31.88 thf(zip_derived_cl144, plain, ( (irel @ '#sk3' @ '#sk6')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl143])).
% 243.05/31.88 thf(zip_derived_cl180, plain, ( (irel @ '#sk7' @ '#sk10')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])).
% 243.05/31.88 thf(zip_derived_cl166, plain,
% 243.05/31.88 (~ (mbox_s4 @ (iand @ (iatom @ b3) @ (iatom @ a4)) @ '#sk7')),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl164])).
% 243.05/31.88 thf(zip_derived_cl170, plain,
% 243.05/31.88 (~ (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ '#sk7' @ Y0) => (iand @ (iatom @ b3) @
% 243.05/31.88 (iatom @ a4) @ Y0))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl166, '3'])).
% 243.05/31.88 thf(zip_derived_cl172, plain,
% 243.05/31.88 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ '#sk7'))) @
% 243.05/31.88 (iand @ (iatom @ b3) @ (iatom @ a4))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl170])).
% 243.05/31.88 thf(zip_derived_cl173, plain,
% 243.05/31.88 (~ (((irel @ '#sk7' @ '#sk9') => (iand @ (iatom @ b3) @ (iatom @ a4) @
% 243.05/31.88 '#sk9')))),
% 243.05/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl172])).
% 243.05/31.88 thf(zip_derived_cl176, plain,
% 243.05/31.88 (~ (((irel @ '#sk7' @ '#sk9') => (mand @ (iatom @ b3) @ (iatom @ a4) @
% 243.05/31.88 '#sk9')))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl173, '11'])).
% 243.05/31.88 thf(zip_derived_cl177, plain, ( (irel @ '#sk7' @ '#sk9')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl176])).
% 243.05/31.88 thf(zip_derived_cl193, plain,
% 243.05/31.88 (![X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X4 @ X6) | ~ (irel @ X2 @ X4) | (irel @ X2 @ X6))),
% 243.05/31.88 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl192])).
% 243.05/31.88 thf(zip_derived_cl141, plain, ( (irel @ '#sk3' @ '#sk5')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl140])).
% 243.05/31.88 thf(zip_derived_cl442, plain,
% 243.05/31.88 (![X0 : $i]: ( (irel @ '#sk3' @ X0) | ~ (irel @ '#sk5' @ X0))),
% 243.05/31.88 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl141])).
% 243.05/31.88 thf(zip_derived_cl162, plain, ( (irel @ '#sk5' @ '#sk8')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl161])).
% 243.05/31.88 thf(zip_derived_cl178, plain,
% 243.05/31.88 (~ (mand @ (iatom @ b3) @ (iatom @ a4) @ '#sk9')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl176])).
% 243.05/31.88 thf(zip_derived_cl182, plain,
% 243.05/31.88 (~ (((iatom @ b3 @ '#sk9') & (iatom @ a4 @ '#sk9')))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl178, '12'])).
% 243.05/31.88 thf(zip_derived_cl184, plain, (~ (((b3 @ '#sk9') & (a4 @ '#sk9')))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl182, '10', '10'])).
% 243.05/31.88 thf(axiom1, axiom, (ivalid @ ( iatom @ a4 ))).
% 243.05/31.88 thf(zip_derived_cl4, plain, ( (ivalid @ (iatom @ a4))),
% 243.05/31.88 inference('cnf', [status(esa)], [axiom1])).
% 243.05/31.88 thf(zip_derived_cl10, plain, ( (((!!) @ (^[Y0 : $i]: (iatom @ a4 @ Y0))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl4, '4'])).
% 243.05/31.88 thf(zip_derived_cl11, plain, ( (((!!) @ (iatom @ a4)))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl10])).
% 243.05/31.88 thf(zip_derived_cl12, plain, (![X2 : $i]: (iatom @ a4 @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])).
% 243.05/31.88 thf(zip_derived_cl13, plain, (![X2 : $i]: (a4 @ X2)),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl12, '10'])).
% 243.05/31.88 thf(zip_derived_cl185, plain, (~ (((b3 @ '#sk9') & ($true)))),
% 243.05/31.88 inference('demod', [status(thm)], [zip_derived_cl184, zip_derived_cl13])).
% 243.05/31.88 thf(zip_derived_cl186, plain, (~ (b3 @ '#sk9')),
% 243.05/31.88 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl185])).
% 243.05/31.88 thf(zip_derived_cl145, plain,
% 243.05/31.88 (~ (mand @ (iatom @ b) @ (iatom @ a1) @ '#sk6')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl143])).
% 243.05/31.88 thf(zip_derived_cl147, plain,
% 243.05/31.88 (~ (((iatom @ b @ '#sk6') & (iatom @ a1 @ '#sk6')))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl145, '12'])).
% 243.05/31.88 thf(zip_derived_cl150, plain, (~ (((b @ '#sk6') & (a1 @ '#sk6')))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl147, '10', '10'])).
% 243.05/31.88 thf(zip_derived_cl151, plain, ((~ (b @ '#sk6') | ~ (a1 @ '#sk6'))),
% 243.05/31.88 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl150])).
% 243.05/31.88 thf(zip_derived_cl276, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (irel @ X0 @ ('#sk12' @ X0))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @
% 243.05/31.88 (iatom @ b1)))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl275])).
% 243.05/31.88 thf(zip_derived_cl278, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @
% 243.05/31.88 (iatom @ b1) @ X2)))
% 243.05/31.88 | (irel @ X0 @ ('#sk12' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl276])).
% 243.05/31.88 thf(zip_derived_cl280, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (mor @
% 243.05/31.88 (mbox_s4 @ (ior @ (iatom @ b1) @ (iatom @ a1))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b1)) @ X2)))
% 243.05/31.88 | (irel @ X0 @ ('#sk12' @ X0)))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl278, '1'])).
% 243.05/31.88 thf(zip_derived_cl281, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X2)
% 243.05/31.88 | (mor @ (mbox_s4 @ (ior @ (iatom @ b1) @ (iatom @ a1))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b1)) @ X2)
% 243.05/31.88 | (irel @ X0 @ ('#sk12' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
% 243.05/31.88 thf(zip_derived_cl284, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ b1) @ X1) | (mbox_s4 @
% 243.05/31.88 (ior @ (iatom @ b1) @ (iatom @ a1)) @ X1)))
% 243.05/31.88 | (irel @ X0 @ ('#sk12' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl281, '7'])).
% 243.05/31.88 thf(zip_derived_cl286, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ b1) @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ X1)
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (irel @ X0 @ ('#sk12' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl284])).
% 243.05/31.88 thf(zip_derived_cl288, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X1 @ Y0) => (iatom @ b1 @ Y0))))))
% 243.05/31.88 | (irel @ X0 @ ('#sk12' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl286, '8'])).
% 243.05/31.88 thf(zip_derived_cl290, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b1)))))
% 243.05/31.88 | (irel @ X0 @ ('#sk12' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ X1))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl288])).
% 243.05/31.88 thf(zip_derived_cl291, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ X0 @ Y0) => (ior @ (iatom @ b1) @
% 243.05/31.88 (iatom @ a1) @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (irel @ X1 @ ('#sk12' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl290, '8'])).
% 243.05/31.88 thf(zip_derived_cl294, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (iatom @ b1) @ (iatom @ a1))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (irel @ X1 @ ('#sk12' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl291])).
% 243.05/31.88 thf(zip_derived_cl295, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (ior @ (iatom @ b1) @ (iatom @ a1) @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk12' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl294])).
% 243.05/31.88 thf(zip_derived_cl298, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (mor @ (mbox_s4 @ (iatom @ b1)) @
% 243.05/31.88 (mbox_s4 @ (iatom @ a1)) @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk12' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl295, '1'])).
% 243.05/31.88 thf(zip_derived_cl299, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X3)
% 243.05/31.88 | (mor @ (mbox_s4 @ (iatom @ b1)) @ (mbox_s4 @ (iatom @ a1)) @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (irel @ X1 @ ('#sk12' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl298])).
% 243.05/31.88 thf(zip_derived_cl302, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ a1) @ X2) | (mbox_s4 @ (iatom @ b1) @ X2)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk12' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl299, '7'])).
% 243.05/31.88 thf(zip_derived_cl304, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ a1) @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b1) @ X2)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (irel @ X1 @ ('#sk12' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1))))))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl302])).
% 243.05/31.88 thf(zip_derived_cl306, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (iatom @ a1 @ Y0))))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk12' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b1) @ X2))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl304, '8'])).
% 243.05/31.88 thf(zip_derived_cl308, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X2))) @ (iatom @ a1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk12' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b1) @ X2))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl306])).
% 243.05/31.88 thf(zip_derived_cl309, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X0 @ Y0) => (iatom @ b1 @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl308, '8'])).
% 243.05/31.88 thf(zip_derived_cl312, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b1)))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl309])).
% 243.05/31.88 thf(zip_derived_cl313, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X4) => (iatom @ b1 @ X4)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b1)))))
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl312])).
% 243.05/31.88 thf(zip_derived_cl316, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X4) => (b1 @ X4)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b1)))))
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl313, '10'])).
% 243.05/31.88 thf(zip_derived_cl317, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X4)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b1)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl316])).
% 243.05/31.88 thf(zip_derived_cl320, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X6) => (iatom @ b1 @ X6)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1)))))
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl317])).
% 243.05/31.88 thf(zip_derived_cl322, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X6) => (b1 @ X6)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1)))))
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl320, '10'])).
% 243.05/31.88 thf(zip_derived_cl323, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X6)
% 243.05/31.88 | (b1 @ X6)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a1))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl322])).
% 243.05/31.88 thf(zip_derived_cl326, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X8) => (iatom @ a1 @ X8)))
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b1 @ X6)
% 243.05/31.88 | ~ (irel @ X1 @ X6))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl323])).
% 243.05/31.88 thf(zip_derived_cl328, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X8) => (a1 @ X8)))
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b1 @ X6)
% 243.05/31.88 | ~ (irel @ X1 @ X6))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl326, '10'])).
% 243.05/31.88 thf(zip_derived_cl329, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X8)
% 243.05/31.88 | (a1 @ X8)
% 243.05/31.88 | ~ (irel @ X1 @ X6)
% 243.05/31.88 | (b1 @ X6)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b1 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2)))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl328])).
% 243.05/31.88 thf(zip_derived_cl1248, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 ( (irel @ X2 @ ('#sk12' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X1)
% 243.05/31.88 | (b1 @ X0)
% 243.05/31.88 | (b1 @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (a1 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X3))),
% 243.05/31.88 inference('eq_fact', [status(thm)], [zip_derived_cl329])).
% 243.05/31.88 thf(zip_derived_cl1260, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X3)
% 243.05/31.88 | (a1 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b1 @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X1)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2)))),
% 243.05/31.88 inference('simplify', [status(thm)], [zip_derived_cl1248])).
% 243.05/31.88 thf(zip_derived_cl14, plain, (![X2 : $i]: (irel @ X2 @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])).
% 243.05/31.88 thf(zip_derived_cl1264, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X3)
% 243.05/31.88 | (a1 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk12' @ X2)))),
% 243.05/31.88 inference('demod', [status(thm)], [zip_derived_cl1260, zip_derived_cl14])).
% 243.05/31.88 thf(zip_derived_cl193, plain,
% 243.05/31.88 (![X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X4 @ X6) | ~ (irel @ X2 @ X4) | (irel @ X2 @ X6))),
% 243.05/31.88 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl192])).
% 243.05/31.88 thf(zip_derived_cl159, plain, ( (irel @ '#sk5' @ '#sk7')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 243.05/31.88 thf(zip_derived_cl444, plain,
% 243.05/31.88 (![X0 : $i]: ( (irel @ '#sk5' @ X0) | ~ (irel @ '#sk7' @ X0))),
% 243.05/31.88 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl159])).
% 243.05/31.88 thf(zip_derived_cl56, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (irel @ X0 @ ('#sk1' @ X0))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @
% 243.05/31.88 (iatom @ b3)))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])).
% 243.05/31.88 thf(zip_derived_cl58, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (ior @ (ior @ (iatom @ b3) @ (iatom @ a3)) @
% 243.05/31.88 (iatom @ b3) @ X2)))
% 243.05/31.88 | (irel @ X0 @ ('#sk1' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl56])).
% 243.05/31.88 thf(zip_derived_cl60, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (mor @
% 243.05/31.88 (mbox_s4 @ (ior @ (iatom @ b3) @ (iatom @ a3))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b3)) @ X2)))
% 243.05/31.88 | (irel @ X0 @ ('#sk1' @ X0)))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl58, '1'])).
% 243.05/31.88 thf(zip_derived_cl61, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X2)
% 243.05/31.88 | (mor @ (mbox_s4 @ (ior @ (iatom @ b3) @ (iatom @ a3))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b3)) @ X2)
% 243.05/31.88 | (irel @ X0 @ ('#sk1' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl60])).
% 243.05/31.88 thf(zip_derived_cl64, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ b3) @ X1) | (mbox_s4 @
% 243.05/31.88 (ior @ (iatom @ b3) @ (iatom @ a3)) @ X1)))
% 243.05/31.88 | (irel @ X0 @ ('#sk1' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl61, '7'])).
% 243.05/31.88 thf(zip_derived_cl66, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ b3) @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ X1)
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (irel @ X0 @ ('#sk1' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])).
% 243.05/31.88 thf(zip_derived_cl68, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X1 @ Y0) => (iatom @ b3 @ Y0))))))
% 243.05/31.88 | (irel @ X0 @ ('#sk1' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl66, '8'])).
% 243.05/31.88 thf(zip_derived_cl70, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b3)))))
% 243.05/31.88 | (irel @ X0 @ ('#sk1' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b3) @ (iatom @ a3)) @ X1))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl68])).
% 243.05/31.88 thf(zip_derived_cl71, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ X0 @ Y0) => (ior @ (iatom @ b3) @
% 243.05/31.88 (iatom @ a3) @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (irel @ X1 @ ('#sk1' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl70, '8'])).
% 243.05/31.88 thf(zip_derived_cl74, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (iatom @ b3) @ (iatom @ a3))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (irel @ X1 @ ('#sk1' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl71])).
% 243.05/31.88 thf(zip_derived_cl75, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (ior @ (iatom @ b3) @ (iatom @ a3) @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk1' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl74])).
% 243.05/31.88 thf(zip_derived_cl78, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (mor @ (mbox_s4 @ (iatom @ b3)) @
% 243.05/31.88 (mbox_s4 @ (iatom @ a3)) @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk1' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl75, '1'])).
% 243.05/31.88 thf(zip_derived_cl79, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X3)
% 243.05/31.88 | (mor @ (mbox_s4 @ (iatom @ b3)) @ (mbox_s4 @ (iatom @ a3)) @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (irel @ X1 @ ('#sk1' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])).
% 243.05/31.88 thf(zip_derived_cl82, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ a3) @ X2) | (mbox_s4 @ (iatom @ b3) @ X2)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk1' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl79, '7'])).
% 243.05/31.88 thf(zip_derived_cl84, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ a3) @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b3) @ X2)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (irel @ X1 @ ('#sk1' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3))))))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl82])).
% 243.05/31.88 thf(zip_derived_cl86, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (iatom @ a3 @ Y0))))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk1' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b3) @ X2))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl84, '8'])).
% 243.05/31.88 thf(zip_derived_cl88, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X2))) @ (iatom @ a3)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk1' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b3) @ X2))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl86])).
% 243.05/31.88 thf(zip_derived_cl89, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X0 @ Y0) => (iatom @ b3 @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b3)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl88, '8'])).
% 243.05/31.88 thf(zip_derived_cl92, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b3)))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b3)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl89])).
% 243.05/31.88 thf(zip_derived_cl93, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X4) => (iatom @ b3 @ X4)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b3)))))
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl92])).
% 243.05/31.88 thf(zip_derived_cl96, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X4) => (b3 @ X4)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b3)))))
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl93, '10'])).
% 243.05/31.88 thf(zip_derived_cl97, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X4)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b3)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])).
% 243.05/31.88 thf(zip_derived_cl100, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X6) => (iatom @ b3 @ X6)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3)))))
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl97])).
% 243.05/31.88 thf(zip_derived_cl102, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X6) => (b3 @ X6)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3)))))
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl100, '10'])).
% 243.05/31.88 thf(zip_derived_cl103, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X6)
% 243.05/31.88 | (b3 @ X6)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a3))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])).
% 243.05/31.88 thf(zip_derived_cl106, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X8) => (iatom @ a3 @ X8)))
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b3 @ X6)
% 243.05/31.88 | ~ (irel @ X1 @ X6))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl103])).
% 243.05/31.88 thf(zip_derived_cl108, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X8) => (a3 @ X8)))
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b3 @ X6)
% 243.05/31.88 | ~ (irel @ X1 @ X6))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl106, '10'])).
% 243.05/31.88 thf(zip_derived_cl109, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X8)
% 243.05/31.88 | (a3 @ X8)
% 243.05/31.88 | ~ (irel @ X1 @ X6)
% 243.05/31.88 | (b3 @ X6)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b3 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2)))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])).
% 243.05/31.88 thf(zip_derived_cl608, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 ( (irel @ X2 @ ('#sk1' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X1)
% 243.05/31.88 | (b3 @ X0)
% 243.05/31.88 | (b3 @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (a3 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X3))),
% 243.05/31.88 inference('eq_fact', [status(thm)], [zip_derived_cl109])).
% 243.05/31.88 thf(zip_derived_cl620, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X3)
% 243.05/31.88 | (a3 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b3 @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X1)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2)))),
% 243.05/31.88 inference('simplify', [status(thm)], [zip_derived_cl608])).
% 243.05/31.88 thf(zip_derived_cl14, plain, (![X2 : $i]: (irel @ X2 @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])).
% 243.05/31.88 thf(zip_derived_cl624, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X3)
% 243.05/31.88 | (a3 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b3 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk1' @ X2)))),
% 243.05/31.88 inference('demod', [status(thm)], [zip_derived_cl620, zip_derived_cl14])).
% 243.05/31.88 thf(zip_derived_cl126, plain, ( (irel @ '#sk2' @ '#sk3')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])).
% 243.05/31.88 thf(zip_derived_cl118, plain, (~ (mbox_s4 @ (iatom @ a) @ '#sk2')),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl116])).
% 243.05/31.88 thf(zip_derived_cl120, plain,
% 243.05/31.88 (~ (((!!) @ (^[Y0 : $i]: (((irel @ '#sk2' @ Y0) => (iatom @ a @ Y0))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl118, '3'])).
% 243.05/31.88 thf(zip_derived_cl123, plain,
% 243.05/31.88 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ '#sk2'))) @ (iatom @ a)))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl120])).
% 243.05/31.88 thf(zip_derived_cl124, plain,
% 243.05/31.88 (~ (((irel @ '#sk2' @ '#sk4') => (iatom @ a @ '#sk4')))),
% 243.05/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl123])).
% 243.05/31.88 thf(zip_derived_cl128, plain,
% 243.05/31.88 (~ (((irel @ '#sk2' @ '#sk4') => (a @ '#sk4')))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl124, '10'])).
% 243.05/31.88 thf(zip_derived_cl129, plain, ( (irel @ '#sk2' @ '#sk4')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl128])).
% 243.05/31.88 thf(zip_derived_cl193, plain,
% 243.05/31.88 (![X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X4 @ X6) | ~ (irel @ X2 @ X4) | (irel @ X2 @ X6))),
% 243.05/31.88 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl192])).
% 243.05/31.88 thf(zip_derived_cl141, plain, ( (irel @ '#sk3' @ '#sk5')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl140])).
% 243.05/31.88 thf(zip_derived_cl432, plain,
% 243.05/31.88 (![X0 : $i]: ( (irel @ X0 @ '#sk5') | ~ (irel @ X0 @ '#sk3'))),
% 243.05/31.88 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl141])).
% 243.05/31.88 thf(zip_derived_cl207, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (irel @ X0 @ ('#sk11' @ X0))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @
% 243.05/31.88 (iatom @ b2)))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 243.05/31.88 thf(zip_derived_cl209, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (ior @ (ior @ (iatom @ b2) @ (iatom @ a2)) @
% 243.05/31.88 (iatom @ b2) @ X2)))
% 243.05/31.88 | (irel @ X0 @ ('#sk11' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl207])).
% 243.05/31.88 thf(zip_derived_cl211, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (mor @
% 243.05/31.88 (mbox_s4 @ (ior @ (iatom @ b2) @ (iatom @ a2))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b2)) @ X2)))
% 243.05/31.88 | (irel @ X0 @ ('#sk11' @ X0)))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl209, '1'])).
% 243.05/31.88 thf(zip_derived_cl212, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X2)
% 243.05/31.88 | (mor @ (mbox_s4 @ (ior @ (iatom @ b2) @ (iatom @ a2))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b2)) @ X2)
% 243.05/31.88 | (irel @ X0 @ ('#sk11' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])).
% 243.05/31.88 thf(zip_derived_cl215, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ b2) @ X1) | (mbox_s4 @
% 243.05/31.88 (ior @ (iatom @ b2) @ (iatom @ a2)) @ X1)))
% 243.05/31.88 | (irel @ X0 @ ('#sk11' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl212, '7'])).
% 243.05/31.88 thf(zip_derived_cl217, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ b2) @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ X1)
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (irel @ X0 @ ('#sk11' @ X0)))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl215])).
% 243.05/31.88 thf(zip_derived_cl219, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X1 @ Y0) => (iatom @ b2 @ Y0))))))
% 243.05/31.88 | (irel @ X0 @ ('#sk11' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl217, '8'])).
% 243.05/31.88 thf(zip_derived_cl221, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b2)))))
% 243.05/31.88 | (irel @ X0 @ ('#sk11' @ X0))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b2) @ (iatom @ a2)) @ X1))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl219])).
% 243.05/31.88 thf(zip_derived_cl222, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ X0 @ Y0) => (ior @ (iatom @ b2) @
% 243.05/31.88 (iatom @ a2) @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (irel @ X1 @ ('#sk11' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl221, '8'])).
% 243.05/31.88 thf(zip_derived_cl225, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (iatom @ b2) @ (iatom @ a2))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (irel @ X1 @ ('#sk11' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl222])).
% 243.05/31.88 thf(zip_derived_cl226, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (ior @ (iatom @ b2) @ (iatom @ a2) @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk11' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl225])).
% 243.05/31.88 thf(zip_derived_cl229, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (mor @ (mbox_s4 @ (iatom @ b2)) @
% 243.05/31.88 (mbox_s4 @ (iatom @ a2)) @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk11' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl226, '1'])).
% 243.05/31.88 thf(zip_derived_cl230, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X3)
% 243.05/31.88 | (mor @ (mbox_s4 @ (iatom @ b2)) @ (mbox_s4 @ (iatom @ a2)) @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (irel @ X1 @ ('#sk11' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl229])).
% 243.05/31.88 thf(zip_derived_cl233, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ a2) @ X2) | (mbox_s4 @ (iatom @ b2) @ X2)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk11' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl230, '7'])).
% 243.05/31.88 thf(zip_derived_cl235, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ a2) @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b2) @ X2)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (irel @ X1 @ ('#sk11' @ X1))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2))))))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl233])).
% 243.05/31.88 thf(zip_derived_cl237, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (iatom @ a2 @ Y0))))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk11' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b2) @ X2))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl235, '8'])).
% 243.05/31.88 thf(zip_derived_cl239, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X2))) @ (iatom @ a2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | (irel @ X1 @ ('#sk11' @ X1))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X0 @ X2)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b2) @ X2))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl237])).
% 243.05/31.88 thf(zip_derived_cl240, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X0 @ Y0) => (iatom @ b2 @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl239, '8'])).
% 243.05/31.88 thf(zip_derived_cl243, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b2)))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl240])).
% 243.05/31.88 thf(zip_derived_cl244, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X4) => (iatom @ b2 @ X4)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b2)))))
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl243])).
% 243.05/31.88 thf(zip_derived_cl247, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X4) => (b2 @ X4)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b2)))))
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl244, '10'])).
% 243.05/31.88 thf(zip_derived_cl248, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X4)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b2)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl247])).
% 243.05/31.88 thf(zip_derived_cl251, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X6) => (iatom @ b2 @ X6)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2)))))
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl248])).
% 243.05/31.88 thf(zip_derived_cl253, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X6) => (b2 @ X6)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2)))))
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl251, '10'])).
% 243.05/31.88 thf(zip_derived_cl254, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X6)
% 243.05/31.88 | (b2 @ X6)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a2))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl253])).
% 243.05/31.88 thf(zip_derived_cl257, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X8) => (iatom @ a2 @ X8)))
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b2 @ X6)
% 243.05/31.88 | ~ (irel @ X1 @ X6))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl254])).
% 243.05/31.88 thf(zip_derived_cl259, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X8) => (a2 @ X8)))
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b2 @ X6)
% 243.05/31.88 | ~ (irel @ X1 @ X6))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl257, '10'])).
% 243.05/31.88 thf(zip_derived_cl260, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X8)
% 243.05/31.88 | (a2 @ X8)
% 243.05/31.88 | ~ (irel @ X1 @ X6)
% 243.05/31.88 | (b2 @ X6)
% 243.05/31.88 | ~ (irel @ X0 @ X4)
% 243.05/31.88 | (b2 @ X4)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2)))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl259])).
% 243.05/31.88 thf(zip_derived_cl895, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 ( (irel @ X2 @ ('#sk11' @ X2))
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | ~ (irel @ X1 @ X1)
% 243.05/31.88 | (b2 @ X0)
% 243.05/31.88 | (b2 @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (a2 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X3))),
% 243.05/31.88 inference('eq_fact', [status(thm)], [zip_derived_cl260])).
% 243.05/31.88 thf(zip_derived_cl907, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X3)
% 243.05/31.88 | (a2 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b2 @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X1)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2)))),
% 243.05/31.88 inference('simplify', [status(thm)], [zip_derived_cl895])).
% 243.05/31.88 thf(zip_derived_cl14, plain, (![X2 : $i]: (irel @ X2 @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])).
% 243.05/31.88 thf(zip_derived_cl911, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X3)
% 243.05/31.88 | (a2 @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b2 @ X0)
% 243.05/31.88 | ~ (irel @ X2 @ X1)
% 243.05/31.88 | (irel @ X2 @ ('#sk11' @ X2)))),
% 243.05/31.88 inference('demod', [status(thm)], [zip_derived_cl907, zip_derived_cl14])).
% 243.05/31.88 thf(zip_derived_cl130, plain, (~ (a @ '#sk4')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl128])).
% 243.05/31.88 thf(zip_derived_cl193, plain,
% 243.05/31.88 (![X2 : $i, X4 : $i, X6 : $i]:
% 243.05/31.88 (~ (irel @ X4 @ X6) | ~ (irel @ X2 @ X4) | (irel @ X2 @ X6))),
% 243.05/31.88 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl192])).
% 243.05/31.88 thf(zip_derived_cl144, plain, ( (irel @ '#sk3' @ '#sk6')),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl143])).
% 243.05/31.88 thf(zip_derived_cl433, plain,
% 243.05/31.88 (![X0 : $i]: ( (irel @ X0 @ '#sk6') | ~ (irel @ X0 @ '#sk3'))),
% 243.05/31.88 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl144])).
% 243.05/31.88 thf(axiom5, axiom,
% 243.05/31.88 (ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ))).
% 243.05/31.88 thf(zip_derived_cl8, plain,
% 243.05/31.88 ( (ivalid @ (ior @ (ior @ (iatom @ b) @ (iatom @ a)) @ (iatom @ b)))),
% 243.05/31.88 inference('cnf', [status(esa)], [axiom5])).
% 243.05/31.88 thf(zip_derived_cl15, plain,
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (ior @ (ior @ (iatom @ b) @ (iatom @ a)) @ (iatom @ b) @ Y0))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl8, '4'])).
% 243.05/31.88 thf(zip_derived_cl16, plain,
% 243.05/31.88 ( (((!!) @ (ior @ (ior @ (iatom @ b) @ (iatom @ a)) @ (iatom @ b))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl15])).
% 243.05/31.88 thf(zip_derived_cl17, plain,
% 243.05/31.88 (![X2 : $i]:
% 243.05/31.88 (ior @ (ior @ (iatom @ b) @ (iatom @ a)) @ (iatom @ b) @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])).
% 243.05/31.88 thf(zip_derived_cl18, plain,
% 243.05/31.88 (![X2 : $i]:
% 243.05/31.88 (mor @ (mbox_s4 @ (ior @ (iatom @ b) @ (iatom @ a))) @
% 243.05/31.88 (mbox_s4 @ (iatom @ b)) @ X2)),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl17, '1'])).
% 243.05/31.88 thf(zip_derived_cl19, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 (((mbox_s4 @ (iatom @ b) @ X0) | (mbox_s4 @
% 243.05/31.88 (ior @ (iatom @ b) @ (iatom @ a)) @ X0)))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl18, '7'])).
% 243.05/31.88 thf(zip_derived_cl20, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ b) @ X0)
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b) @ (iatom @ a)) @ X0))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])).
% 243.05/31.88 thf(zip_derived_cl21, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X0 @ Y0) => (iatom @ b @ Y0))))))
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b) @ (iatom @ a)) @ X0))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl20, '8'])).
% 243.05/31.88 thf(zip_derived_cl22, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b)))))
% 243.05/31.88 | (mbox_s4 @ (ior @ (iatom @ b) @ (iatom @ a)) @ X0))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl21])).
% 243.05/31.88 thf(zip_derived_cl23, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]:
% 243.05/31.88 (((irel @ X0 @ Y0) => (ior @ (iatom @ b) @
% 243.05/31.88 (iatom @ a) @ Y0))))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl22, '8'])).
% 243.05/31.88 thf(zip_derived_cl24, plain,
% 243.05/31.88 (![X0 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @
% 243.05/31.88 (ior @ (iatom @ b) @ (iatom @ a))))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl23])).
% 243.05/31.88 thf(zip_derived_cl25, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (ior @ (iatom @ b) @ (iatom @ a) @ X2)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b))))))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl24])).
% 243.05/31.88 thf(zip_derived_cl26, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X2) => (mor @ (mbox_s4 @ (iatom @ b)) @
% 243.05/31.88 (mbox_s4 @ (iatom @ a)) @ X2)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b))))))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl25, '1'])).
% 243.05/31.88 thf(zip_derived_cl27, plain,
% 243.05/31.88 (![X0 : $i, X2 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X2)
% 243.05/31.88 | (mor @ (mbox_s4 @ (iatom @ b)) @ (mbox_s4 @ (iatom @ a)) @ X2)
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])).
% 243.05/31.88 thf(zip_derived_cl28, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((mbox_s4 @ (iatom @ a) @ X1) | (mbox_s4 @ (iatom @ b) @ X1)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b)))))
% 243.05/31.88 | ~ (irel @ X0 @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl27, '7'])).
% 243.05/31.88 thf(zip_derived_cl29, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (mbox_s4 @ (iatom @ a) @ X1)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b) @ X1)
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b))))))),
% 243.05/31.88 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl28])).
% 243.05/31.88 thf(zip_derived_cl30, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X1 @ Y0) => (iatom @ a @ Y0))))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b)))))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b) @ X1))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl29, '8'])).
% 243.05/31.88 thf(zip_derived_cl31, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ a)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b)))))
% 243.05/31.88 | ~ (irel @ X0 @ X1)
% 243.05/31.88 | (mbox_s4 @ (iatom @ b) @ X1))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl30])).
% 243.05/31.88 thf(zip_derived_cl32, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ (^[Y0 : $i]: (((irel @ X0 @ Y0) => (iatom @ b @ Y0))))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a))))))),
% 243.05/31.88 inference('rw_clause', [status(thm)], [zip_derived_cl31, '8'])).
% 243.05/31.88 thf(zip_derived_cl33, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i]:
% 243.05/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ b)))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a))))))),
% 243.05/31.88 inference('comb-normalize', [status(thm)], [zip_derived_cl32])).
% 243.05/31.88 thf(zip_derived_cl34, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (iatom @ b @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b)))))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])).
% 243.05/31.88 thf(zip_derived_cl35, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X3) => (b @ X3)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b)))))
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl34, '10'])).
% 243.05/31.88 thf(zip_derived_cl36, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X3)
% 243.05/31.88 | (b @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X1))) @ (iatom @ b)))))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])).
% 243.05/31.88 thf(zip_derived_cl37, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i, X5 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X5) => (iatom @ b @ X5)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a)))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b @ X3)
% 243.05/31.88 | ~ (irel @ X0 @ X3))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl36])).
% 243.05/31.88 thf(zip_derived_cl38, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i, X5 : $i]:
% 243.05/31.88 ( (((irel @ X1 @ X5) => (b @ X5)))
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a)))))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b @ X3)
% 243.05/31.88 | ~ (irel @ X0 @ X3))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl37, '10'])).
% 243.05/31.88 thf(zip_derived_cl39, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i, X5 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X5)
% 243.05/31.88 | (b @ X5)
% 243.05/31.88 | ~ (irel @ X0 @ X3)
% 243.05/31.88 | (b @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (irel @ X0))) @ (iatom @ a))))))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])).
% 243.05/31.88 thf(zip_derived_cl40, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i, X5 : $i, X7 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X7) => (iatom @ a @ X7)))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b @ X3)
% 243.05/31.88 | ~ (irel @ X0 @ X3)
% 243.05/31.88 | (b @ X5)
% 243.05/31.88 | ~ (irel @ X1 @ X5))),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl39])).
% 243.05/31.88 thf(zip_derived_cl41, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i, X5 : $i, X7 : $i]:
% 243.05/31.88 ( (((irel @ X0 @ X7) => (a @ X7)))
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b @ X3)
% 243.05/31.88 | ~ (irel @ X0 @ X3)
% 243.05/31.88 | (b @ X5)
% 243.05/31.88 | ~ (irel @ X1 @ X5))),
% 243.05/31.88 inference('rw', [status(thm)], [zip_derived_cl40, '10'])).
% 243.05/31.88 thf(zip_derived_cl42, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X3 : $i, X5 : $i, X7 : $i]:
% 243.05/31.88 (~ (irel @ X0 @ X7)
% 243.05/31.88 | (a @ X7)
% 243.05/31.88 | ~ (irel @ X1 @ X5)
% 243.05/31.88 | (b @ X5)
% 243.05/31.88 | ~ (irel @ X0 @ X3)
% 243.05/31.88 | (b @ X3)
% 243.05/31.88 | ~ (irel @ X1 @ X0))),
% 243.05/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])).
% 243.05/31.88 thf(zip_derived_cl387, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X1)
% 243.05/31.88 | (b @ X0)
% 243.05/31.88 | (b @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (a @ X2)
% 243.05/31.88 | ~ (irel @ X1 @ X2))),
% 243.05/31.88 inference('eq_fact', [status(thm)], [zip_derived_cl42])).
% 243.05/31.88 thf(zip_derived_cl393, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X2)
% 243.05/31.88 | (a @ X2)
% 243.05/31.88 | ~ (irel @ X1 @ X0)
% 243.05/31.88 | (b @ X0)
% 243.05/31.88 | ~ (irel @ X1 @ X1))),
% 243.05/31.88 inference('simplify', [status(thm)], [zip_derived_cl387])).
% 243.05/31.88 thf(zip_derived_cl14, plain, (![X2 : $i]: (irel @ X2 @ X2)),
% 243.05/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])).
% 243.05/31.88 thf(zip_derived_cl397, plain,
% 243.05/31.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 243.05/31.88 (~ (irel @ X1 @ X2) | (a @ X2) | ~ (irel @ X1 @ X0) | (b @ X0))),
% 243.05/31.88 inference('demod', [status(thm)], [zip_derived_cl393, zip_derived_cl14])).
% 243.05/31.88 thf(zip_derived_cl26699, plain, ($false),
% 243.05/31.88 inference('eprover', [status(thm)],
% 243.05/31.88 [zip_derived_cl141, zip_derived_cl1503, zip_derived_cl440,
% 243.05/31.88 zip_derived_cl434, zip_derived_cl435, zip_derived_cl1117,
% 243.05/31.88 zip_derived_cl14, zip_derived_cl793, zip_derived_cl159,
% 243.05/31.88 zip_derived_cl188, zip_derived_cl169, zip_derived_cl144,
% 243.05/31.88 zip_derived_cl180, zip_derived_cl177, zip_derived_cl442,
% 243.05/31.88 zip_derived_cl162, zip_derived_cl186, zip_derived_cl151,
% 243.05/31.88 zip_derived_cl1264, zip_derived_cl444, zip_derived_cl624,
% 243.05/31.88 zip_derived_cl126, zip_derived_cl129, zip_derived_cl432,
% 243.05/31.88 zip_derived_cl911, zip_derived_cl130, zip_derived_cl433,
% 243.05/31.88 zip_derived_cl397])).
% 243.05/31.88
% 243.05/31.88 % SZS output end Refutation
% 243.05/31.88
% 243.05/31.88
% 243.05/31.88 % Terminating...
% 243.05/31.97 % Runner terminated.
% 243.05/31.99 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------